Painting chapter
QMRTokyo Tower (東京タワー Tōkyō tawā?) is a communications and observation tower located in the Shiba-koen district of Minato, Tokyo, Japan. At 332.9 metres (1,092 ft), it is the second-tallest structure in Japan. The structure is an Eiffel Tower-inspired lattice tower that is painted white and international orange to comply with air safety regulations.
Built in 1958, the tower's main sources of revenue are tourism and antenna leasing. Over 150 million people have visited the tower since its opening. FootTown, a four-story building located directly under the tower, houses museums, restaurants and shops. Departing from there, guests can visit two observation decks. The two-story Main Observatory is located at 150 metres (490 ft), while the smaller Special Observatory reaches a height of 249.6 metres (819 ft).
The tower acts as a support structure for an antenna. Originally intended for television broadcasting, radio antennas were installed in 1961, but the tower is now used to broadcast signals for Japanese media outlets such as NHK, TBS and Fuji TV. Japan's planned digital television transition by July 2011 was problematic, however; Tokyo Tower's height, 332.9 m (1,092 ft) was not high enough to adequately support complete terrestrial digital broadcasting to the area. A taller digital broadcasting tower, known as Tokyo Skytree, was completed on February 29, 2012.
Music chapter
QMRWhile calculations of days, months and years are based on fixed hours equal to 1/24 of a day, the beginning of each halachic day is based on the local time of sunset. The end of the Shabbat and other Jewish holidays is based on nightfall (Tzeth haKochabim) which occurs some amount of time, typically 42 to 72 minutes, after sunset. According to Maimonides, nightfall occurs when three medium-sized stars become visible after sunset. By the 17th century this had become three second-magnitude stars. The modern definition is when the center of the sun is 7° below the geometric (airless) horizon, somewhat later than civil twilight at 6°. The beginning of the daytime portion of each day is determined both by dawn and sunrise. Most halachic times are based on some combination of these four times and vary from day to day throughout the year and also vary significantly depending on location. The daytime hours are often divided into Sha`oth Zemaniyoth or "Halachic hours" by taking the time between sunrise and sunset or between dawn and nightfall and dividing it into 12 equal hours. The nighttime hours are similarly divided into 12 equal portions, albeit a different amount of time than the "hours" of the daytime. The earliest and latest times for Jewish services, the latest time to eat Chametz on the day before Passover and many other rules are based on Sha`oth Zemaniyoth. For convenience, the modern day using Sha`oth Zemaniyoth is often discussed as if sunset were at 6:00pm, sunrise at 6:00am and each hour were equal to a fixed hour. For example, halachic noon may be after 1:00pm in some areas during daylight saving time. Within the Mishnah, however, the numbering of the hours starts with the "first" hour after the start of the day.[7]
QMRIn algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself.[1][2] That is, the matrix M is idempotent if and only if MM = M. For this product MM to be defined, M must necessarily be a square matrix. Viewed this way, idempotent matrices are idempotent elements of matrix rings.
QMRThe Gram determinant or Gramian is the determinant of the Gram matrix:
G(x_{1},\dots ,x_{n})={\begin{vmatrix}\langle x_{1},x_{1}\rangle &\langle x_{1},x_{2}\rangle &\dots &\langle x_{1},x_{n}\rangle \\\langle x_{2},x_{1}\rangle &\langle x_{2},x_{2}\rangle &\dots &\langle x_{2},x_{n}\rangle \\\vdots &\vdots &\ddots &\vdots \\\langle x_{n},x_{1}\rangle &\langle x_{n},x_{2}\rangle &\dots &\langle x_{n},x_{n}\rangle \end{vmatrix}}.
Geometrically, the Gram determinant is the square of the volume of the parallelotope formed by the vectors. In particular, the vectors are linearly independent if and only if the Gram determinant is nonzero (if and only if the Gram matrix is nonsingular).
The Gram determinant can also be expressed in terms of the exterior product of vectors by
G(x_{1},\dots ,x_{n})=\|x_{1}\wedge \cdots \wedge x_{n}\|^{2}.
If R is a binary relation between the finite indexed sets X and Y (so R ⊆ X×Y), then R can be represented by the adjacency matrix M whose row and column indices index the elements of X and Y, respectively, such that the entries of M are defined by:
M_{i,j}={\begin{cases}1&(x_{i},y_{j})\in R\\0&(x_{i},y_{j})\not \in R\end{cases}}
In order to designate the row and column numbers of the matrix, the sets X and Y are indexed with positive integers: i ranges from 1 to the cardinality (size) of X and j ranges from 1 to the cardinality of Y. See the entry on indexed sets for more detail.
Example[edit]
The binary relation R on the set {1, 2, 3, 4} is defined so that aRb holds if and only if a divides b evenly, with no remainder. For example, 2R4 holds because 2 divides 4 without leaving a remainder, but 3R4 does not hold because when 3 divides 4 there is a remainder of 1. The following set is the set of pairs for which the relation R holds.
{(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 4), (3, 3), (4, 4)}.
The corresponding representation as a Boolean matrix is:
{\begin{pmatrix}1&1&1&1\\0&1&0&1\\0&0&1&0\\0&0&0&1\end{pmatrix}}.
QMRIn computer architecture, 64-bit computing is the use of processors that have datapath widths, integer size, and memory address widths of 64 bits (eight octets). Also, 64-bit CPU and ALU architectures are those that are based on registers, address buses, or data buses of that size. From the software perspective, 64-bit computing means the use of code with 64-bit virtual memory addresses.
I said that 64 is four quadrant models
wiki sanskrit prosody
3 × 3 matrices[edit]
The volume of this parallelepiped is the absolute value of the determinant of the matrix formed by the rows constructed from the vectors r1, r2, and r3.
The determinant of a 3 × 3 matrix is defined by
\begin{align}\begin{vmatrix}a&b&c\\d&e&f\\g&h&i\end{vmatrix} & = a\begin{vmatrix}e&f\\h&i\end{vmatrix}-b\begin{vmatrix}d&f\\g&i\end{vmatrix}+c\begin{vmatrix}d&e\\g&h\end{vmatrix} \\
& = a(ei-fh)-b(di-fg)+c(dh-eg) \\
& = aei+bfg+cdh-ceg-bdi-afh.
\end{align}
Sarrus' rule: The determinant of the three columns on the left is the sum of the products along the solid diagonals minus the sum of the products along the dashed diagonals
The rule of Sarrus is a mnemonic for the 3 × 3 matrix determinant: the sum of the products of three diagonal north-west to south-east lines of matrix elements, minus the sum of the products of three diagonal south-west to north-east lines of elements, when the copies of the first two columns of the matrix are written beside it as in the illustration. This scheme for calculating the determinant of a 3 × 3 matrix does not carry over into higher dimensions.
Properties 1, 7 and 9 — which all follow from the Leibniz formula — completely characterize the determinant; in other words the determinant is the unique function from n × n matrices to scalars that is n-linear alternating in the columns, and takes the value 1 for the identity matrix (this characterization holds even if scalars are taken in any given commutative ring). To see this it suffices to expand the determinant by multi-linearity in the columns into a (huge) linear combination of determinants of matrices in which each column is a standard basis vector. These determinants are either 0 (by property 8) or else ±1 (by properties 1 and 11 below), so the linear combination gives the expression above in terms of the Levi-Civita symbol. While less technical in appearance, this characterization cannot entirely replace the Leibniz formula in defining the determinant, since without it the existence of an appropriate function is not clear. For matrices over non-commutative rings, properties 7 and 8 are incompatible for n ≥ 2,[3] so there is no good definition of the determinant in this setting.
Property 2 above implies that properties for columns have their counterparts in terms of rows:
Viewing an n × n matrix as being composed of n rows, the determinant is an n-linear function.
This n-linear function is an alternating form: whenever two rows of a matrix are identical, its determinant is 0.
Interchanging any pair of columns or rows of a matrix multiplies its determinant by −1. This follows from properties 7 and 9 (it is a general property of multilinear alternating maps). More generally, any permutation of the rows or columns multiplies the determinant by the sign of the permutation. By permutation, it is meant viewing each row as a vector Ri (equivalently each column as Ci) and reordering the rows (or columns) by interchange of Rj and Rk (or Cj and Ck), where j,k are two indices chosen from 1 to n for an n × n square matrix.
Adding a scalar multiple of one column to another column does not change the value of the determinant. This is a consequence of properties 7 and 8: by property 7 the determinant changes by a multiple of the determinant of a matrix with two equal columns, which determinant is 0 by property 8. Similarly, adding a scalar multiple of one row to another row leaves the determinant unchanged.
roperty 5 says that the determinant on n × n matrices is homogeneous of degree n. These properties can be used to facilitate the computation of determinants by simplifying the matrix to the point where the determinant can be determined immediately. Specifically, for matrices with coefficients in a field, properties 11 and 12 can be used to transform any matrix into a triangular matrix, whose determinant is given by property 6; this is essentially the method of Gaussian elimination.
For example, the determinant of
A = \begin{bmatrix}-2&2&-3\\
-1& 1& 3\\
2 &0 &-1\end{bmatrix}
QMRIn linear algebra, a circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element to the right relative to the preceding row vector. In numerical analysis, circulant matrices are important because they are diagonalized by a discrete Fourier transform, and hence linear equations that contain them may be quickly solved using a fast Fourier transform.[1] They can be interpreted analytically as the integral kernel of a convolution operator on the cyclic group \mathbb{Z}/n\mathbb{Z} and hence frequently appear in formal descriptions of spatially invariant linear operations. In cryptography, a circulant matrix is used in the MixColumns step of the Advanced Encryption Standard.
An n\times n circulant matrix \ C takes the form
C=
\begin{bmatrix}
c_0 & c_{n-1} & \dots & c_{2} & c_{1} \\
c_{1} & c_0 & c_{n-1} & & c_{2} \\
\vdots & c_{1}& c_0 & \ddots & \vdots \\
c_{n-2} & & \ddots & \ddots & c_{n-1} \\
c_{n-1} & c_{n-2} & \dots & c_{1} & c_0 \\
\end{bmatrix}.
A circulant matrix is fully specified by one vector, \ c, which appears as the first column of \ C. The remaining columns of \ C are each cyclic permutations of the vector \ c with offset equal to the column index. The last row of \ C is the vector \ c in reverse order, and the remaining rows are each cyclic permutations of the last row. Note that different sources define the circulant matrix in different ways, for example with the coefficients corresponding to the first row rather than the first column of the matrix, or with a different direction of shift.
The polynomial f(x) = c_0 + c_1 x + \dots + c_{n-1} x^{n-1} is called the associated polynomial of matrix C .
QMRIn linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant. For instance, the following matrix is a Toeplitz matrix:
\begin{bmatrix}
a & b & c & d & e \\
f & a & b & c & d \\
g & f & a & b & c \\
h & g & f & a & b \\
i & h & g & f & a
\end{bmatrix}.
Any n×n matrix A of the form
A =
\begin{bmatrix}
a_{0} & a_{-1} & a_{-2} & \ldots & \ldots &a_{-(n-1)} \\
a_{1} & a_0 & a_{-1} & \ddots & & \vdots \\
a_{2} & a_{1} & \ddots & \ddots & \ddots& \vdots \\
\vdots & \ddots & \ddots & \ddots & a_{-1} & a_{-2}\\
\vdots & & \ddots & a_{1} & a_{0}& a_{-1} \\
a_{n-1} & \ldots & \ldots & a_{2} & a_{1} & a_{0}
\end{bmatrix}
is a Toeplitz matrix. If the i,j element of A is denoted Ai,j, then we have
A_{i,j} = A_{i+1,j+1} = a_{i-j}.\
Discrete convolution[edit]
The convolution operation can be constructed as a matrix multiplication, where one of the inputs is converted into a Toeplitz matrix. For example, the convolution of h and x can be formulated as:
y = h \ast x =
\begin{bmatrix}
h_1 & 0 & \ldots & 0 & 0 \\
h_2 & h_1 & \ldots & \vdots & \vdots \\
h_3 & h_2 & \ldots & 0 & 0 \\
\vdots & h_3 & \ldots & h_1 & 0 \\
h_{m-1} & \vdots & \ldots & h_2 & h_1 \\
h_m & h_{m-1} & \vdots & \vdots & h_2 \\
0 & h_m & \ldots & h_{m-2} & \vdots \\
0 & 0 & \ldots & h_{m-1} & h_{m-2} \\
\vdots & \vdots & \vdots & h_m & h_{m-1} \\
0 & 0 & 0 & \ldots & h_m
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3 \\
\vdots \\
x_n
\end{bmatrix}
y^T =
\begin{bmatrix}
h_1 & h_2 & h_3 & \ldots & h_{m-1} & h_m
\end{bmatrix}
\begin{bmatrix}
x_1 & x_2 & x_3 & \ldots & x_n & 0 & 0 & 0& \ldots & 0 \\
0 & x_1 & x_2 & x_3 & \ldots & x_n & 0 & 0 & \ldots & 0 \\
0 & 0 & x_1 & x_2 & x_3 & \ldots & x_n & 0 & \ldots & 0 \\
\vdots & \vdots & \vdots & \vdots & \vdots & \ldots & \vdots & \vdots & \ldots & 0 \\
0 & \ldots & 0 & 0 & x_1 & \ldots & x_{n-2} & x_{n-1} & x_n & \vdots \\
0 & \ldots & 0 & 0 & 0 & x_1 & \ldots & x_{n-2} & x_{n-1} & x_n
\end{bmatrix}.
This approach can be extended to compute autocorrelation, cross-correlation, moving average etc.
Infinite Toeplitz Matrix[edit]
Main article: Toeplitz operator
A bi-infinite Toeplitz matrix (i.e. entries indexed by \mathbb Z\times\mathbb Z) A induces a linear operator on \ell^2.
A=\begin{bmatrix}
\ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\
\ldots & a_0 & a_{-1} & a_{-2} & a_{-3} & \ldots \\
\ldots & a_1 & a_0 & a_{-1} & a_{-2} & \ldots \\
\ldots & a_2 & a_1 & a_0 & a_{-1} & \ldots \\
\ldots & a_3 & a_2 & a_1 & a_0 & \ldots \\
\ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\
\end{bmatrix}.
The induced operator is bounded if and only if the coefficients of the Toeplitz matrix A is the Fourier coefficients of some essentially bounded function f.
In such cases, f is called the symbol of the Toeplitz matrix A, and the spectral norm of the Toeplitz matrix A coincides with the L^{\infty} norm of its symbol. The proof is easy to establish and can be found as Theorem 1.1 in the google book link: [10]
QMRIn linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.:
{\begin{bmatrix}a&b&c&d&e\\b&c&d&e&f\\c&d&e&f&g\\d&e&f&g&h\\e&f&g&h&i\\\end{bmatrix}}.
Any n×n matrix A of the form
A={\begin{bmatrix}a_{0}&a_{1}&a_{2}&\ldots &\ldots &a_{n-1}\\a_{1}&a_{2}&&&&\vdots \\a_{2}&&&&&\vdots \\\vdots &&&&&a_{2n-4}\\\vdots &&&&a_{2n-4}&a_{2n-3}\\a_{n-1}&\ldots &\ldots &a_{2n-4}&a_{2n-3}&a_{2n-2}\end{bmatrix}}
is a Hankel matrix. If the i,j element of A is denoted Ai,j, then we have
A_{i,j}=A_{i+1,j-1}=a_{i+j-2}.\
The Hankel matrix is closely related to the Toeplitz matrix (a Hankel matrix is an upside-down Toeplitz matrix). For a special case of this matrix see Hilbert matrix.
A Hankel operator on a Hilbert space is one whose matrix with respect to an orthonormal basis is a (possibly infinite) Hankel matrix (A_{i,j})_{i,j\geq 1}, where A_{i,j} depends only on i+j.
The determinant of a Hankel matrix is called a catalecticant.
QMRIn mathematics, a Cauchy matrix, named after Augustin Louis Cauchy, is an m×n matrix with elements aij in the form
a_{ij}={\frac {1}{x_{i}-y_{j}}};\quad x_{i}-y_{j}\neq 0,\quad 1\leq i\leq m,\quad 1\leq j\leq n
where x_{i} and y_{j} are elements of a field {\mathcal {F}}, and (x_{i}) and (y_{j}) are injective sequences (they do not contain repeated elements; elements are distinct).
The Hilbert matrix is a special case of the Cauchy matrix, where
x_{i}-y_{j}=i+j-1.\;
Every submatrix of a Cauchy matrix is itself a Cauchy matrix.
QMRA submatrix of a matrix is obtained by deleting any collection of rows and/or columns.[16][17][18] For example, from the following 3-by-4 matrix, we can construct a 2-by-3 submatrix by removing row 3 and column 2:
\mathbf{A}=\begin{bmatrix}
1 & \color{red}{2} & 3 & 4 \\
5 & \color{red}{6} & 7 & 8 \\
\color{red}{9} & \color{red}{10} & \color{red}{11} & \color{red}{12}
\end{bmatrix} \rightarrow \begin{bmatrix}
1 & 3 & 4 \\
5 & 7 & 8
\end{bmatrix}.
The minors and cofactors of a matrix are found by computing the determinant of certain submatrices.[18][19]
A principal submatrix is a square submatrix obtained by removing certain rows and columns. The definition varies from author to author. According to some authors, a principal submatrix is a submatrix in which the set of row indices that remain is the same as the set of column indices that remain.[20][21] Other authors define a principal submatrix to be one in which the first k rows and columns, for some number k, are the ones that remain;[22] this type of submatrix has also been called a leading principal submatrix.[23]
QMRIn linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row, i.e., an m × n matrix
V={\begin{bmatrix}1&\alpha _{1}&\alpha _{1}^{2}&\dots &\alpha _{1}^{n-1}\\1&\alpha _{2}&\alpha _{2}^{2}&\dots &\alpha _{2}^{n-1}\\1&\alpha _{3}&\alpha _{3}^{2}&\dots &\alpha _{3}^{n-1}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&\alpha _{m}&\alpha _{m}^{2}&\dots &\alpha _{m}^{n-1}\end{bmatrix}}
or
V_{i,j}=\alpha _{i}^{j-1}\,
for all indices i and j.[1] (Some authors use the transpose of the above matrix.)
The determinant of a square Vandermonde matrix (where m = n) can be expressed as:
\det(V)=\prod _{1\leq i<j\leq n}(\alpha _{j}-\alpha _{i}).
This is called the Vandermonde determinant or Vandermonde polynomial. If all the numbers \alpha _{i} are distinct, then it is non-zero.
The Vandermonde determinant is sometimes called the discriminant, although many sources, including this article, refer to the discriminant as the square of this determinant. Note that the Vandermonde determinant is alternating in the entries, meaning that permuting the \alpha _{i} by an odd permutation changes the sign, while permuting them by an even permutation does not change the value of the determinant. It thus depends on the order, while its square (the discriminant) does not depend on the order.
When two or more αi are equal, the corresponding polynomial interpolation problem (see below) is underdetermined. In that case one may use a generalization called confluent Vandermonde matrices, which makes the matrix non-singular while retaining most properties. If αi = αi + 1 = ... = αi+k and αi ≠ αi − 1, then the (i + k)th row is given by
V_{i+k,j}={\begin{cases}0,&{\text{if }}j\leq k;\\{\frac {(j-1)!}{(j-k-1)!}}\alpha _{i}^{j-k-1},&{\text{if }}j>k.\end{cases}}
The above formula for confluent Vandermonde matrices can be readily derived by letting two parameters \alpha _{i} and \alpha _{j} go arbitrarily close to each other. The difference vector between the rows corresponding to \alpha _{i} and \alpha _{j} scaled to a constant yields the above equation (for k = 1). Similarly, the cases k > 1 are obtained by higher order differences. Consequently, the confluent rows are derivatives of the original Vandermonde row.
QMRIn linear algebra, the Frobenius companion matrix of the monic polynomial
p(t)=c_{0}+c_{1}t+\cdots +c_{n-1}t^{n-1}+t^{n}~,
is the square matrix defined as
C(p)={\begin{bmatrix}0&0&\dots &0&-c_{0}\\1&0&\dots &0&-c_{1}\\0&1&\dots &0&-c_{2}\\\vdots &\vdots &\ddots &\vdots &\vdots \\0&0&\dots &1&-c_{n-1}\end{bmatrix}}.
With this convention, and on the basis v1, ... , vn, one has
Cv_{i}=C^{i}v_{1}=v_{i+1}
(for i < n), and v1 generates V as a K[C]-module: C cycles basis vectors.
Some authors use the transpose of this matrix, which (dually) cycles coordinates, and is more convenient for some purposes, like linear recurrence relations.
Given a linear recursive sequence with characteristic polynomial
p(t)=c_{0}+c_{1}t+\cdots +c_{n-1}t^{n-1}+t^{n}\,
the (transpose) companion matrix
C^{T}(p)={\begin{bmatrix}0&1&0&\cdots &0\\0&0&1&\cdots &0\\\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\cdots &1\\-c_{0}&-c_{1}&-c_{2}&\cdots &-c_{n-1}\end{bmatrix}}
generates the sequence, in the sense that
C^{T}{\begin{bmatrix}a_{k}\\a_{k+1}\\\vdots \\a_{k+n-1}\end{bmatrix}}={\begin{bmatrix}a_{k+1}\\a_{k+2}\\\vdots \\a_{k+n}\end{bmatrix}}.
increments the series by 1.
The vector (1,t,t2, ..., tn-1) is an eigenvector of this matrix for eigenvalue t, when t is a root of the characteristic polynomial p(t).
For c0 = −1, and all other ci=0, i.e., p(t) = tn−1, this matrix reduces to Sylvester's cyclic shift matrix, or circulant matrix.
QMRIn mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. Here, a few classes of such matrices are summarized.
Construction[edit]
Let Ejk be the matrix with 1 in the jk-th entry and 0 elsewhere. Consider the space of d×d complex matrices, ℂd×d, for a fixed d.
Define the following matrices,
For k < j , fk,jd = Ekj + Ejk .
For k > j , fk,jd = − i (Ejk − Ekj) .
Let h1d = Id , the identity matrix.
For 1 < k < d , hkd =hkd−1⊕ 0 .
For k = d , ~~~h_{d}^{d}={\sqrt {\tfrac {2}{d(d-1)}}}\left(h_{1}^{d-1}\oplus (1-d)\right)~.
The collection of matrices defined above without the identity matrix are called the generalized Gell-Mann matrices, in dimension d.[1] The symbol ⊕ (utilized in the Cartan subalgebra above) means matrix direct sum.
The generalized Gell-Mann matrices are Hermitian and traceless by construction, just like the Pauli matrices. One can also check that they are orthogonal in the Hilbert–Schmidt inner product on ℂd×d. By dimension count, one sees that they span the vector space of d × d complex matrices, {\mathfrak {gl}}(d,ℂ). They then provide a Lie-algebra-generator basis acting on the fundamental representation of {\mathfrak {su}}(d ).
In dimensions d=2 and 3, the above construction recovers the Pauli and Gell-Mann matrices, respectively.
A non-Hermitian generalization of Pauli matrices[edit]
The Pauli matrices \sigma _{1} and \sigma _{3} satisfy the following:
\sigma _{1}^{2}=\sigma _{3}^{2}=I,\;\sigma _{1}\sigma _{3}=-\sigma _{3}\sigma _{1}=e^{\pi i}\sigma _{3}\sigma _{1}.
The so-called Walsh–Hadamard conjugation matrix is
W={\tfrac {1}{\sqrt {2}}}{\begin{bmatrix}1&1\\1&-1\end{bmatrix}}.
Like the Pauli matrices, W is both Hermitian and unitary. \sigma _{1},\;\sigma _{3} and W satisfy the relation
\;\sigma _{1}=W\sigma _{3}W^{*}.
The goal now is to extend the above to higher dimensions, d, a problem solved by J. J. Sylvester (1882).
Construction: The clock and shift matrices[edit]
Fix the dimension d as before. Let ω = exp(2πi/d), a root of unity. Since ωd = 1 and ω ≠ 1, the sum of all roots annuls:
1+\omega +\cdots +\omega ^{d-1}=0.
Integer indices may then be cyclically identified mod d.
Now define, with Sylvester, the shift matrix[2]
\Sigma _{1}={\begin{bmatrix}0&0&0&\cdots &0&1\\1&0&0&\cdots &0&0\\0&1&0&\cdots &0&0\\0&0&1&\cdots &0&0\\\vdots &\vdots &\vdots &\ddots &\vdots &\vdots \\0&0&0&\cdots &1&0\\\end{bmatrix}}
and the clock matrix,
\Sigma _{3}={\begin{bmatrix}1&0&0&\cdots &0\\0&\omega &0&\cdots &0\\0&0&\omega ^{2}&\cdots &0\\\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\cdots &\omega ^{d-1}\end{bmatrix}}.
These matrices generalize σ1 and σ3, respectively.
Note that the unitarity and tracelessness of the two Pauli matrices is preserved, but not Hermiticity in dimensions higher than two. Since Pauli matrices describe Quaternions, Sylvester dubbed the higher-dimensional analogs "nonions", "sedenions", etc.
These two matrices are also the cornerstone of quantum mechanical dynamics in finite-dimensional vector spaces[3][4][5] as formulated by Hermann Weyl, and find routine applications in numerous areas of mathematical physics.[6] The clock matrix amounts to the exponential of position in a "clock" of d hours, and the shift matrix is just the translation operator in that cyclic vector space, so the exponential of the momentum. They are (finite-dimensional) representations of the corresponding elements of the Heisenberg group on a d-dimensional Hilbert space.
The following relations echo those of the Pauli matrices:
\Sigma _{1}^{d}=\Sigma _{3}^{d}=I
and the braiding relation,
\;\Sigma _{3}\Sigma _{1}=\omega \Sigma _{1}\Sigma _{3}=e^{2\pi i/d}\Sigma _{1}\Sigma _{3},
the Weyl formulation of the CCR, or
\;\Sigma _{3}\Sigma _{1}\Sigma _{3}^{d-1}\Sigma _{1}^{d-1}=\omega ~.
On the other hand, to generalize the Walsh–Hadamard matrix W, note
W={\tfrac {1}{\sqrt {2}}}{\begin{bmatrix}1&1\\1&\omega ^{2-1}\end{bmatrix}}={\tfrac {1}{\sqrt {2}}}{\begin{bmatrix}1&1\\1&\omega ^{d-1}\end{bmatrix}}.
Define, again with Sylvester, the following analog matrix,[7] still denoted by W in a slight abuse of notation,
W={\frac {1}{\sqrt {d}}}{\begin{bmatrix}1&1&1&\cdots &1\\1&\omega ^{d-1}&\omega ^{2(d-1)}&\cdots &\omega ^{(d-1)^{2}}\\1&\omega ^{d-2}&\omega ^{2(d-2)}&\cdots &\omega ^{(d-1)(d-2)}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&\omega &\omega ^{2}&\cdots &\omega ^{d-1}\end{bmatrix}}~.
It is evident that W is no longer Hermitian, but is still unitary. Direct calculation yields
\;\Sigma _{1}=W\Sigma _{3}W^{*}~,
which is the desired analog result. Thus, W , a Vandermonde matrix, arrays the eigenvectors of Σ1, which has the same eigenvalues as Σ3.
When d = 2k, W * is precisely the matrix of the discrete Fourier transform, converting position coordinates to momentum coordinates and vice versa.
The family of d2 unitary (but non-Hermitian) independent matrices
(\Sigma _{1})^{k}(\Sigma _{3})^{j}=\sum _{m=0}^{d-1}|m+k\rangle \omega ^{jm}\langle m|,
provides Sylvester's well-known basis for {\mathfrak {gl}}(d,ℂ), known as "nonions" {\mathfrak {gl}}(3,ℂ), "sedenions" {\mathfrak {gl}}(4,ℂ), etc...[8]
This basis can be systematically connected to the above Hermitian basis.[9] (For instance, the powers of Σ3, the Cartan subalgebra, map to linear combinations of the hkds.) It can further be used to identify {\mathfrak {gl}}(d,ℂ) , as d → ∞, with the algebra of Poisson brackets.
Dirac matrices are four by four matrices fundamental to physics. The quadrant model is a four by four matrix
QMRCORDIC (for COordinate Rotation DIgital Computer),[1][2][3] also known as the digit-by-digit method and Volder's algorithm, is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. It is commonly used when no hardware multiplier is available (e.g. in simple microcontrollers and FPGAs), as the only operations it requires are addition, subtraction, bitshift and table lookup.
It is done within a unit square quadrant
QMR In mathematics, a symplectic matrix is a 2n×2n matrix M with real entries that satisfies the condition
M^{\text{T}}\Omega M=\Omega \,,
(1)
where MT denotes the transpose of M and Ω is a fixed 2n×2n nonsingular, skew-symmetric matrix. This definition can be extended to 2n×2n matrices with entries in other fields, e.g. the complex numbers.
Typically Ω is chosen to be the block matrix
\Omega ={\begin{bmatrix}0&I_{n}\\-I_{n}&0\\\end{bmatrix}}
where In is the n×n identity matrix. The matrix Ω has determinant +1 and has an inverse given by Ω−1 = ΩT = −Ω.
Every symplectic matrix has unit determinant, and the 2n×2n symplectic matrices with real entries form a subgroup of the special linear group SL(2n, R) under matrix multiplication, specifically a connected noncompact real Lie group of real dimension n(2n + 1), the symplectic group Sp(2n, R). The symplectic group can be defined as the set of linear transformations that preserve the symplectic form of a real symplectic vector space.
An example of a group of symplectic matrices is the group of three symplectic 2x2-matrices consisting in the identity matrix, the upper triagonal matrix and the lower triangular matrix, each with entries 0 and 1.
Every symplectic matrix is invertible with the inverse matrix given by
M^{-1}=\Omega ^{-1}M^{\text{T}}\Omega .
Furthermore, the product of two symplectic matrices is, again, a symplectic matrix. This gives the set of all symplectic matrices the structure of a group. There exists a natural manifold structure on this group which makes it into a (real or complex) Lie group called the symplectic group.
It follows easily from the definition that the determinant of any symplectic matrix is ±1. Actually, it turns out that the determinant is always +1. One way to see this is through the use of the Pfaffian and the identity
{\mbox{Pf}}(M^{\text{T}}\Omega M)=\det(M){\mbox{Pf}}(\Omega ).
Since M^{\text{T}}\Omega M=\Omega and {\mbox{Pf}}(\Omega )\neq 0 we have that det(M) = 1.
Suppose Ω is given in the standard form and let M be a 2n×2n block matrix given by
M={\begin{pmatrix}A&B\\C&D\end{pmatrix}}
where A, B, C, D are n×n matrices. The condition for M to be symplectic is equivalent to the conditions
A^{\text{T}}D-C^{\text{T}}B=I
A^{\text{T}}C=C^{\text{T}}A
D^{\text{T}}B=B^{\text{T}}D.
When n = 1 these conditions reduce to the single condition det(M) = 1. Thus a 2×2 matrix is symplectic iff it has unit determinant.
With Ω in standard form, the inverse of M is given by
M^{-1}=\Omega ^{-1}M^{\text{T}}\Omega ={\begin{pmatrix}D^{\text{T}}&-B^{\text{T}}\\-C^{\text{T}}&A^{\text{T}}\end{pmatrix}}.
The group has dimension n(2n + 1). This can be seen by noting that the group condition implies that
\Omega M^{\text{T}}\Omega M=-I
this gives equations of the form
-\delta _{ij}=\sum _{k=1}^{n}m_{k,i+n}m_{n+k,j}-m_{n+k,i+n}m_{n,j}-m_{k,i}m_{n+k,j}+m_{k,i}m_{k,j}
where m_{ij} is the i,j-th element of M. The sum is antisymmetric with respect to indices i,j, and since the left hand side is zero when i differs from j, this leaves n(2n-1) independent equations.
Symplectic transformations[edit]
In the abstract formulation of linear algebra, matrices are replaced with linear transformations of finite-dimensional vector spaces. The abstract analog of a symplectic matrix is a symplectic transformation of a symplectic vector space. Briefly, a symplectic vector space is a 2n-dimensional vector space V equipped with a nondegenerate, skew-symmetric bilinear form ω called the symplectic form.
A symplectic transformation is then a linear transformation L : V → V which preserves ω, i.e.
\omega (Lu,Lv)=\omega (u,v).
Fixing a basis for V, ω can be written as a matrix Ω and L as a matrix M. The condition that L be a symplectic transformation is precisely the condition that M be a symplectic matrix:
M^{\text{T}}\Omega M=\Omega .
Under a change of basis, represented by a matrix A, we have
\Omega \mapsto A^{\text{T}}\Omega A
M\mapsto A^{-1}MA.
One can always bring Ω to either the standard form given in the introduction or the block diagonal form described below by a suitable choice of A.
QMRThe Four Freshmen is an American male vocal band quartet that blends open-harmonic jazz arrangements with the big band vocal group sounds of The Modernaires (Glenn Miller), The Pied Pipers (Tommy Dorsey), and The Mel-Tones (Artie Shaw), founded in the barbershop tradition. The Four Freshmen is considered a vocal band because the singers accompany themselves on guitar, horns, bass, and drums, among other instrumental configurations.
The last original member retired in 1993,[1] but the group still tours internationally and has recorded jazz harmonies since its late 1940s founding in the halls of the Jordan School of Music at Butler University (Indianapolis).[2]
QMRWestern music inherited the concept of metre from poetry (Scholes 1977; Latham 2002b) where it denotes: the number of lines in a verse; the number of syllables in each line; and the arrangement of those syllables as long or short, accented or unaccented (Scholes 1977; Latham 2002b). The first coherent system of rhythmic notation in modern Western music was based upon rhythmic modes derived from the basic types of metrical unit in the quantitative meter of classical ancient Greek and Latin poetry (Hoppin 1978, 221).
Later music for dances such as the pavane and galliard consisted of musical phrases to accompany a fixed sequence of basic steps with a defined tempo and time signature. The English word "measure", originally an exact or just amount of time, came to denote either a poetic rhythm, a bar of music, or else an entire melodic verse or dance (Merriam-Webster 2015) involving sequences of notes, words and/or movements that may last four, eight or sixteen bars
QMRTraditional and popular songs may draw heavily upon a limited range of meters, leading to interchangeability of melodies. Early hymnals commonly did not include musical notation but simply texts that could be sung to any tune known by the singers that had a matching meter. For example, The Blind Boys of Alabama rendered the hymn Amazing Grace to the setting of The Animals' version of the folk song The House of the Rising Sun. This is possible because the texts share a popular basic four-line (quatrain) verse-form called ballad meter or, in hymnals, common meter, the four lines having a syllable-count of 8:6:8:6 (Hymns Ancient and Modern Revised), the rhyme-scheme usually following suit: ABAB. There is generally a pause in the melody in a cadence at the end of the shorter lines so that the underlying musical meter is 8:8:8:8 beats, the cadences dividing this musically into two symmetrical "normal" phrases of four measures each (MacPherson 1930, 14).
In some regional music, for example Balkan music (like Bulgarian music, and the Macedonian 3+2+2+3+2 meter), a wealth of irregular or compound meters are used. Other terms for this are "additive meter" (London 2001, §I.8) and "imperfect time" (Read 1964, 147[not in citation given]).
QMRIn music of the common practice period (about 1600–1900), there are four different families of time signature in common use:
Simple duple—two or four beats to a bar, each divided by two, the top number being "2" or "4" (2/4, 2/8, 2/2 … 4/4, 4/8, 4/2 …). When there are four beats to a bar, it is alternatively referred to as "quadruple" time.
Simple triple (About this sound 3/4 (help·info))—three beats to a bar, each divided by two, the top number being "3" (3/4, 3/8, 3/2 …)
Compound duple—two beats to a bar, each divided by three, the top number being "6" (6/8, 6/16, 6/4 …)
Compound triple—three beats to a bar, each divided by three, the top number being "9" (9/8, 9/16, 9/4)
QMRRhythm is marked by the regulated succession of opposite elements, the dynamics of the strong and weak beat, the played beat and the inaudible but implied rest beat, the long and short note. As well as perceiving rhythm we must be able to anticipate it. This depends upon repetition of a pattern that is short enough to memorize.
The alternation of the strong and weak beat is fundamental to the ancient language of poetry, dance and music. The common poetic term "foot" refers, as in dance, to the lifting and tapping of the foot in time. In a similar way musicians speak of an upbeat and a downbeat and of the "on" and "off" beat. These contrasts naturally facilitate a dual hierarchy of rhythm and depend upon repeating patterns of duration, accent and rest forming a "pulse-group" that corresponds to the poetic foot. Normally such pulse-groups are defined by taking the most accented beat as the first and counting the pulses until the next accent (MacPherson 1930, 5; Scholes 1977b). A rhythm that accents another beat and de-emphasises the down beat as established or assumed from the melody or from a preceding rhythm is called syncopated rhythm.
Normally, even the most complex of meters may be broken down into a chain of duple and triple pulses (MacPherson 1930, 5; Scholes 1977b) either by addition or division. According to Pierre Boulez, beat structures beyond four, in western music, are "simply not natural" (Slatkin n.d., at 5:05).
QMR6:4[edit]
The primary cycle of four beats
File:Polyrhythm6c4.theora.ogv
Polyrhythm 6:4
A great deal of African music is built upon a cycle of four main beats. This basic musical period has a bipartite structure; it is made up of two cells, consisting of two beats each. Ladzekpo states: "The first most useful measure scheme consists of four main beats with each main beat measuring off three equal pulsations [12
8] as its distinctive feature … The next most useful measure scheme consists of four main beats with each main beat flavored by measuring off four equal pulsations [4
4]." (b: "Main Beat Schemes")[5] The four-beat cycle is a shorter period than what is normally heard in European music. This accounts for the stereotype of African music as "repetitive." (Kubik, p. 41)[2] A cycle of only two main beats, as in the case of 3:2, does not constitute a complete primary cycle. (Kubik, Vol. 2, p. 63)[2] Within the primary cycle there are two cells of 3:2, or, a single cycle of six-against-four (6:4). The six cross-beats are represented below as quarter-notes for visual emphasis.
QMRIf every other cross-beat is sounded, the three-against-four (3:4) cross-rhythm is generated. The "slow" cycle of three beats is more metrically destabilizing and dynamic than the six beats. The Afro-Cuban rhythm abakuá (Havana-style) is based on the 3:4 cross-rhythm.[9] The three-beat cycle is represented as half-notes in the following example for visual emphasis.
Three-against-four cross-rhythm. About this sound Play (help·info)
“ In contrast to the four main beat scheme, the rhythmic motion of the three beat scheme is slower. A simultaneous interaction of these two beat schemes with contrasting rhythmic motions produces the next most useful cross rhythmic texture in the development of sub-Saharan dance-drumming. The composite texture of the three-against-four cross rhythm produces a motif covering a length of the musical period. The motif begins with the component beat schemes coinciding and continues with the beat schemes in alternate motions thus showing a progression from a "static" beginning to a "dynamic" continuation
QMR1.5:4 (or 3:8)[edit]
File:Polyrhythm-1.5 with 4 o 4 simultaneously.ogv
Polyrhythm 4:1.5
Even more metrically destabilizing and dynamic than 3:4, is the one and a half beat-against-four (1.5:4) cross-rhythm. Another way to think of it is as three "very slow" cross-beats spanning two main beat cycles (of four beats each), or three beats over two periods (measures), a type of macro "hemiola." In terms of the beat scheme comprising the complete 24-pulse cross-rhythm, the ratio is 3:8. The three cross-beats are shown as whole notes below for visual emphasis.
QMR4:3[edit]
When duple pulses (4
4) are grouped in sets of three, the four-against-three (4:3) cross-rhythm is generated. The four cross-beats cycle every three main beats. In terms of cross-rhythm only, this is the same as having duple cross-beats in a triple beat scheme, such as 3
4 or 6
4. The pulses on the top line are grouped in threes for visual emphasis.
4:3 cross-rhythm in modular form.
However, this 4:3 is within a duple beat scheme, with duple (quadruple) subdivisions of the beats. Since the musical period is a cycle of four main beats, the 4:3 cross-rhythm significantly contradicts the period by cycling every three main beats. The complete cross-beat cycle is shown below in relation to the key pattern known in Afro-Cuban music as clave. (Rumba, p. xxxi)[11] The subdivisions are grouped (beamed) in sets of four to reflect the proper metric structure. The complete cross-beat cycle is three claves in length. Within the context of the complete cross-rhythm, there is a macro 4:3—four 4:3 modules-against-three claves. Continuous duple-pulse cross-beats are often sounded by the quinto, the lead drum in the Cuban genres rumba and conga. (Rumba, pps. 69–86)[11][b][c]
In sub-Saharan rhythm the four main beats are typically divided into three or four pulses, creating a 12-pulse (12
8), or 16-pulse (4
4) cycle. (Ladzekpo, b: "Main Beat Scheme")[5] Every triple-pulse pattern has its duple-pulse correlative; the two pulse structures are two sides of the same coin. Cross-beats are generated by grouping pulses contrary to their given structure, for example: groups of two or four in 12
8 or groups of three or six in 4
4. (Rumba, p. 180)[11] The duple-pulse correlative of the three cross-beats of the hemiola, is a figure known in Afro-Cuban music as tresillo. Tresillo is a Spanish word meaning ‘triplet’—three equal notes within the same time span normally occupied by two notes. As used in Cuban popular music, tresillo refers to the most basic duple-pulse rhythmic cell.[13] The pulse names of tresillo and the three cross-beats of the hemiola are identical: one, one-ah, two-and.
QMREarly ethnomusicological analysis often perceived African music as polymetric. Pioneers such as A.M. Jones and Anthony King identified the prevailing rhythmic emphasis as metrical accents (main beats), instead of the contrametrical accents (cross-beats) they in fact are. Some of their music examples are polymetric, with multiple and conflicting main beat cycles, each requiring its own separate time signature. King shows two Yoruba dundun pressure drum ("talking drum") phrases in relation to the five-stroke standard pattern, or "clave," played on the kagano dundun (top line).[18] The standard pattern is written in a polymetric 7
8 + 5
8 time signature. One dundun phrase is based on a grouping of three pulses written in 3
8, and the other, a grouping of four pulses written in 4
8. Complicating the transcription further, one polymetric measure is offset from the other two.
QMRthe most common Hindustani tala, Teental, is a regularly-divisible cycle of four measures of four beats each.
QMR Tintal (or teental, trital; Hindi: तीन ताल) is one of the most famous talas of Hindustani music. It is also the most common tal in North India. The structure of tintal is so symmetrical that it presents a very simple rhythmic structure against which a performance can be laid.[1]
Contents [hide]
1 Arrangement
2 Uses
3 Theka
4 References
Arrangement[edit]
Tintal has sixteen (16) beats[2] in four equal divisions (vibhag). The period between every two beats is equal. The first beat out of 16 beats is called sam and the 9th beat is called khali ('empty'). To count the Teental, the audience claps on the first beat, claps on the 5th beat, then waves on the 9th beat and lastly again claps on the 13th beat; these three claps (Hindi tin 'three' + tāl 'clap') give the rhythm its name.
16 is the squares of the quadrant model. Four is the number of quadrants in the quadrant model and the number of squares per quadrant
QMRThere are a variety of used by the Coptic Christians.
Old Coptic crosses often incorporate a circle which may vary in size depending on the representation. For the Coptic Church, the circle represents the eternal and everlasting love of God, as shown through Christ's crucifixion, Christ's halo and resurrection.[1]
Contents [hide]
1 History and use
2 Influence
3 Modern form
4 Gallery
5 See also
6 References
7 External links
History and use[edit]
The Coptic cross is widely used in the Coptic church and the Ethiopian and Eritrean churches. Many Copts have the cross tattooed on the inside of their right arm.[2] The Coptic cross in its modern and ancient forms is considered a sign of faith and pride to the Copts [3] The Ethiopians Christians wear it as a symbol of faith.[4]
In 1984, a Coptic Cross was given as a gift by the Coptic Orthodox Church and mounted on the top of the All Africa Conference of Churches building, since the Coptic Church is considered to be the mother church in Africa.[5]
One of the forms of the Coptic cross, which is referred to as the Ethiopian Coptic cross[6] was worn by Stevie Ray Vaughan.[7] Keith Richards [8] also wears an Ethiopian Coptic Cross.
Visual arts[edit]
Jacques Laudy illustrated a comic book version of the tale for the weekly Franco-Belgian comics magazine Tintin from 1946 to 1947 (including several covers).
Music and performing arts[edit]
Franz Joseph Glæser, a Czech/Danish composer, wrote a work called Die vier Haimonskinder (1809).
Les quatre fils Aymon (1844) is an opera by Michael William Balfe, written for the Opéra-Comique (also popular in German-speaking countries for many years as Die Vier Haimonskinder).
During the German occupation of Belgium during World War II, the story of Les Quatre Fils Aymon was made into a play that was banned by the German authorities, because of the sympathy it displayed for resisting authority; the play was performed underground and became quite popular.[11]
La Légende des fils Aymon, a stage work by Frédéric Kiesel, was created in 1967 in Habay-la-Neuve.
Les Quatre Fils Aymon is a ballet by Maurice Béjart and Janine Charrat from 1961.
Dance chapter
QMRThere are four steps to the dance move the shuffle
On the dance move the whip there is four counts of freestyles between each whip
In order to teach the arm wave the dance instructor breaks it down into four parts. The shoulder the elbow the wrist and the hand
QMR. The YMCA dance has four letters to it. YMC.A." is a song by the American disco group Village People. It was released in 1978 as the only single from their third studio album Cruisin' (1978). The song reached number two on the US charts in early 1979 and reached number one in the UK around the same time, becoming the group's biggest hit. It is one of fewer than forty singles to have sold 10 million (or more) physical copies worldwide. A medley with "Hot Cop" reached number 2 on Billboard's Dance Music/Club Play Singles chart.[1]
The song remains popular and is played at many sporting events in the U.S. and Europe, with crowds using the dance in which the arms are used to spell out the four letters of the song's title as an opportunity to stretch. Moreover, the song also remains particularly popular due to its status as a disco classic and gay anthem, even among listeners who are otherwise uninvolved in disco or gay culture. "Y.M.C.A." appeared as Space Shuttle Wakeup call on mission STS-106, on day 11.[2]
In 2009, "Y.M.C.A." was entered into the Guinness World Book of Records when over 44,000 people danced to the song with Village People singing live at the 2008 Sun Bowl game in El Paso, Texas.[3] "Y.M.C.A." is number 7 on VH1's list of The 100 Greatest Dance Songs of the 20th Century.[4]
YMCA is also the name of a group dance with cheerleader Y-M-C-A choreography invented to fit the song. One of the phases involves moving arms to form the letters Y-M-C-A as they are sung in the chorus:
Y —arms outstretched and raised upwards
M —made by bending the elbows from the 'Y' pose so the fingertips meet over the chest[13]
C —arms extended to the left
A —hands held together above head
The dance originated on Dick Clark's American Bandstand. During the January 6, 1979 episode, which featured the Village People as guests throughout the hour, the dance was performed by audience members while the group performed "YMCA." Clark then said to Willis that he would like to show him something. Clark again played the song with the audience doing the YMCA hand gestures. Willis immediately picked up on the dance and mimicked the hand movements back at the audience as other Village People members stared at him with puzzled looks. Clark then turned to Willis and said, "Victor, think you can work this dance into your routine?" Willis responded, "I think we're gonna have to."[14] In a 2008 retrospective article for Spin, Randy Jones has opined that the dance may have originated as a misunderstanding: The group's original choreographed dance had the group clapping above their heads during the chorus and he believes that the audience, believing them to be making the letter "Y", began following suit.[15]
Following the fifth inning of New York Yankees baseball games at Yankee Stadium, the grounds crew traditionally grooms the infield while leading the crowd in the dance.[16] In July 2008, Village People performed "Y.M.C.A." with the Yankees grounds crew at the last MLB All-Star Game held at the old Yankee Stadium. Similarly at the Sapporo Dome, during Hokkaido Nippon-Ham Fighters baseball games, "Y.M.C.A." is enthusiastically enjoyed by the crowd and ground staff during the fifth inning stretch.[citation needed]
The hokey pokey required putting a limb in out in and shaking it about. The fourth is always different
According to this dance teacher there are four things to remember when doing the lean. They are rock switch burst resist
The dance teacher says that three knee spins is difficult. Four gets inconsistent although he can do more than four. Four is always different. Three is always bad. Five is ultra transcendent.
This dance teacher says that there is four steps to the gravity spin dance move. He says the third step is difficult. The third step is always bad and the most action. The third square is a bad square. He says the fourth step is kind of magical and makes you aerodynamic although he does not know how. The fourth square is always transcendent.
QMRIn weaving, the woof (sometimes weft) is the term for the thread or yarn which is drawn through the warp yarns to create cloth. Warp is the lengthwise or longitudinal thread in a roll, while weft is the transverse thread. A single thread of the weft, crossing the warp, is called a pick. Terms do vary (for instance, in North America, the weft is sometimes referred to as the fill or the filling yarn).[1][2]
The weft is a thread or yarn usually made of spun fibre. The original fibres used were wool, flax or cotton. Today, man-made fibres are often used in weaving. Because the weft does not have to be stretched on a loom in the way that the warp is, it can generally be less strong.
The weft is threaded through the warp using a "shuttle", air jets or "rapier grippers." Hand looms were the original weaver's tool, with the shuttle being threaded through alternately raised warps by hand. Inventions during the 18th century spurred the Industrial Revolution, with the "picking stick"[3] and the "flying shuttle" (John Kay, 1733) speeding up production of cloth. The power loom patented by Edmund Cartwright in 1785 allowed sixty picks per minute.[3]
A useful way of remembering which is warp and which is weft is: 'one of them goes from weft to wight'.
Warp and weft are orthogonal quadrants
In weaving cloth, the warp is the set of lengthwise yarns that are held in tension on a frame or loom. The yarn that is inserted over-and-under the warp threads is called the weft, woof, or filler. Each individual warp thread in a fabric is called a warp end or end.[1][2] Warp means "that which is thrown across" (Old English wearp, from weorpan, to throw, cf. German werfen, Dutch werpen).
Very simple looms use a spiral warp, in which a single, very long yarn is wound around a pair of sticks or beams in a spiral pattern to make up the warp.[3]
Because the warp is held under high tension during the entire process of weaving and warp yarn must be strong, yarn for warp ends is usually spun and plied fibre. Traditional fibres for warping are wool, linen, alpaca, and silk. With the improvements in spinning technology during the Industrial Revolution, it became possible to make cotton yarn of sufficient strength to be used as the warp in mechanized weaving. Later, artificial or man-made fibres such as nylon or rayon were employed.
While most people are familiar with weft-faced weavings, it is possible to create warp-faced weavings using densely arranged warp threads. In warp-faced weavings, the design for the textile is in the warp, and so all colors must be decided upon and placed during the first part of the weaving process and cannot be changed. Warp-faced weavings are defined by length-wise stripes and vertical designs due to the limitations of color placement. Many South American cultures, including the ancient Incas and Aymaras used a type of warp-faced weaving called backstrap weaving, which uses the weight of the weaver's body to control the tension of the loom. [4]
QMRTablet Weaving (often card weaving in the United States) is a weaving technique where tablets or cards are used to create the shed through which the weft is passed. As the materials and tools are relatively cheap and easy to obtain, tablet weaving is popular with hobbyist weavers. Currently most tablet weavers produce narrow work such as belts, straps, or garment trims.
The popular tablet shape is a quincunx cross with four holes and a fifth in the center
QMRBasketweave or Panama weave[1] is a simple type of textile weave.
In basketweave, groups of warp and weft threads are interlaced so that they form a simple criss-cross pattern. Each group of weft threads crosses an equal number of warp threads by going over one group, then under the next, and so on. The next group of weft threads goes under the warp threads that its neighbor went over, and vice versa.
Basketweave can be identified by its checkered appearance, made of two or more threads in each group.
Monkscloth is an example of a basketweave fabric.
The term Panama weave may also refer to a lightweight or midweight woollen fabric made using this weave. It is soft and loose, with a fine, grainy surface, used for men's and women's suits and dresses. The name of the fabric may also relate to the straw weave used in a Panama hat.[2]
QMRBasketweave or Panama weave[1] is a simple type of textile weave.
In basketweave, groups of warp and weft threads are interlaced so that they form a simple criss-cross pattern. Each group of weft threads crosses an equal number of warp threads by going over one group, then under the next, and so on. The next group of weft threads goes under the warp threads that its neighbor went over, and vice versa.
Basketweave can be identified by its checkered appearance, made of two or more threads in each group.
Monkscloth is an example of a basketweave fabric.
The term Panama weave may also refer to a lightweight or midweight woollen fabric made using this weave. It is soft and loose, with a fine, grainy surface, used for men's and women's suits and dresses. The name of the fabric may also relate to the straw weave used in a Panama hat.[2]
Basketweave looks like quadrants
A Panama hat (toquilla straw hat) is a traditional brimmed straw hat of Ecuadorian origin. Traditionally, hats were made from the plaited leaves of the Carludovica palmata plant, known locally as the toquilla palm or jipijapa palm,[1] although it is a palm-like plant rather than a true palm.
Panama hats are light-colored, lightweight, and breathable, and often worn as accessories to summer-weight suits, such as those made of linen or silk. Beginning around the turn of the 20th century, panamas began to be associated with the seaside and tropical locales.[citation needed]
The art of weaving the traditional Ecuadorian toquilla hat was added to the UNESCO Intangible Cultural Heritage Lists on 6 December 2012.[2] Panama hat is an Intangible Cultural Heritage, a term used to define practices, traditions, knowledge and skills communities pass down from generation to generation as part of their cultural heritage.[3]
The hat is created with basketweaving, and therefore its texture reflects quadrants
QMRCross-stitch is a popular form of counted-thread embroidery in which X-shaped stitches in a tiled, raster-like pattern are used to form a picture. Cross-stitch is often executed on easily countable evenweave fabric called aida cloth. The stitcher counts the threads in each direction so that the stitches are of uniform size and appearance. This form of cross-stitch is also called counted cross-stitch in order to distinguish it from other forms of cross-stitch. Sometimes cross-stitch is done on designs printed on the fabric (stamped cross-stitch); the stitcher simply stitches over the printed pattern.
Fabrics used in cross-stitch include aida, linen and mixed-content fabrics called 'evenweave'. All cross stitch fabrics are technically "evenweave," it refers to the fact that the fabric is woven to make sure that there are the same number of threads in an inch both left to right and top to bottom (vertically and horizontally). Fabrics are categorized by threads per inch (referred to as 'count'), which can range from 11 to 40 count. Aida fabric has a lower count because it is made with two threads grouped together for ease of stitching. Cross stitch projects are worked from a gridded pattern and can be used on any count fabric, the count of the fabric determines the size of the finished stitching.
Cross-stitch is the oldest form of embroidery and can be found all over the world.[1] Many folk museums show examples of clothing decorated with cross-stitch, especially from continental Europe, Asia, and Eastern and Central Europe.[2]
The cross stitch sampler is called that because it was generally stitched by a young girl to learn how to stitch and to record alphabet and other patterns to be used in her household sewing. These samples of her stitching could be referred back to over the years. Often, motifs and initials were stitched on household items to identify their owner, or simply to decorate the otherwise-plain cloth. In the United States, the earliest known cross-stitch sampler is currently housed at Pilgrim Hall in Plymouth, Massachusetts.[3] The sampler was created by Loara Standish, daughter of Captain Myles Standish and pioneer of the Leviathan stitch, circa 1653.
Traditionally, cross-stitch was used to embellish items like household linens, tablecloths, dishcloths, and doilies (only a small portion of which would actually be embroidered, such as a border). Although there are many cross-stitchers who still employ it in this fashion, it is now increasingly popular to work the pattern on pieces of fabric and hang them on the wall for decoration. Cross stitch is also often used to make greeting cards, pillowtops, or as inserts for box tops, coasters and trivets.
Multicoloured, shaded, painting-like patterns as we know them today are a fairly modern development, deriving from similar shaded patterns of Berlin wool work of the mid-nineteenth century. Besides designs created expressly for cross stitch, there are software programs that convert a photograph or a fine art image into a chart suitable for stitching. One stunning example of this is in the cross stitched reproduction of the Sistine Chapel charted and stitched by Joanna Lopianowski-Roberts.[4][5]
It is no coincidence cross stitch is the oldest and most fundamental form of embroidery. The cross/quadrant is the Form of Being
There are many cross-stitching "guilds" and groups across the United States and Europe which offer classes, collaborate on large projects, stitch for charity, and provide other ways for local cross-stitchers to get to know one another. Individually owned local needlework shops (LNS) often have stitching nights at their shops, or host weekend stitching retreats.
Cross stitch from Surif. Top half of picture is the reverse side.
Today cotton floss is the most common embroidery thread. It is a thread made of mercerized cotton, composed of six strands that are only loosely twisted together and easily separable. While there are other manufacturers, the two most-commonly used (and oldest) brands are DMC and Anchor [1], both of which have been manufacturing embroidery floss since the 1800s.[6][7]
Other materials used are pearl (or perle) cotton, Danish flower thread, silk and Rayon. Different wool threads, metallic threads or other novelty threads are also used, sometimes for the whole work, but often for accents and embellishments. Hand-dyed cross stitch floss is created just as the name implies - it is dyed by hand. Because of this, there are variations in the amount of color throughout the thread. Some variations can be subtle, while some can be a huge contrast. Some also have more than one color per thread, which in the right project, creates amazing results.
Cross stitch is widely used in traditional Palestinian dressmaking.
Other stitches are also often used in cross-stitch, among them ¼, ½, and ¾ stitches and backstitches.
Cross-stitch is often used together with other stitches. A cross stitch can come in a variety of prostational forms. It is sometimes used in crewel embroidery, especially in its more modern derivatives. It is also often used in needlepoint.
A specialized historical form of embroidery using cross-stitch is Assisi embroidery.
There are many stitches which are related to cross-stitch and were used in similar ways in earlier times. The best known are Italian cross-stitch, Celtic Cross Stitch, Irish Cross Stitch, long-armed cross-stitch, Ukrainian cross-stitch and Montenegrin stitch. Italian cross-stitch and Montenegrin stitch are reversible, meaning the work looks the same on both sides. These styles have a slightly different look than ordinary cross-stitch. These more difficult stitches are rarely used in mainstream embroidery, but they are still used to recreate historical pieces of embroidery or by the creative and adventurous stitcher.
The double cross-stitch, also known as a Leviathan stitch or Smyrna cross stitch, combines a cross-stitch with an upright cross-stitch.
Berlin wool work and similar petit point stitchery resembles the heavily shaded, opulent styles of cross-stitch, and sometimes also used charted patterns on paper.
Cross-stitch is often combined with other popular forms of embroidery, such as Hardanger embroidery or blackwork embroidery. Cross-stitch may also be combined with other work, such as canvaswork or drawn thread work. Beadwork and other embellishments such as paillettes, charms, small buttons and speciality threads of various kinds may also be used.
Recent trends in the UK[edit]
Cross-stitch has become increasingly popular with the younger generation of the United Kingdom in recent years.[8] The Great Recession has also seen renewal of interest in home crafts. Retailers such as John Lewis experienced a 17% rise in sales of haberdashery products between 2009 and 2010.[9] Hobbycraft, a chain of stores selling craft supplies, also enjoyed an 11% increase in sales over the past year.[10] The chain is said[by whom?] to have benefited from the "make do and mend" mentality of the credit crisis, which has driven people to make their own cards and gifts.
Knitting and cross stitching have become more popular hobbies for a younger market, in contrast to its traditional reputation as a hobby for retirees.[11] Sewing and craft groups such as Stitch and Bitch London have resurrected the idea of the traditional craft club.[12] At Clothes Show Live 2010 there was a new area called "Sknitch" promoting modern sewing, knitting and embroidery.[13]
In a departure from the traditional designs associated with cross stitch, there is a current trend for more postmodern or tongue-in-cheek designs featuring retro images or contemporary sayings.[14] It is linked to a concept known as 'subversive cross stitch', which involves more risque designs, often fusing the traditional sampler style with sayings designed to shock or be incongruous with the old-fashioned image of cross stitch.
Stitching designs on other materials can be accomplished by using a Waste Canvas. This waste canvas is a temporary gridded canvas similar to regular canvas used for embroidery that is held together by a water-soluble glue, which is removed after completion of stitch design.
QMROrganza is a thin, plain weave, sheer fabric traditionally made from silk. Many modern organzas are woven with synthetic filament fibers such as polyester or nylon. Silk organza is woven by a number of mills along the Yangtze River and in the province of Zhejiang in China. A coarser silk organza is woven in the Bangalore area of India. Deluxe silk organzas are woven in France and Italy.[1]
Organza is used for bridalwear and eveningwear. In the interiors market it is used for effects in bedrooms and between rooms. Double-width organzas in viscose and acetate are used as sheer curtains.
Plain weave is composed of a quadrant pattern
QMRAlso unearthed in Complex A were three rectangular mosaics (also known as "Pavements") each roughly 4.5 by 6 metres (15 by 20 feet) and each consisting of up to 485 blocks of serpentine. These blocks were arranged horizontally to form what has been variously interpreted as an ornate Olmec bar-and-four-dots motif, the Olmec Dragon,[11] a very abstract jaguar mask,[12] a cosmogram,[13] or a symbolic map of La Venta and environs.[14] Not intended for display, soon after completion these pavements were covered over with colored clay and then many feet of earth.
QMRFlavors and varieties[edit]
Wheat Chex Cereal
Corn Chex Cereal
Rice Chex Cereal
Honey Nut Chex Cereal
Chocolate Chex Cereal
Vanilla Chex Cereal
Chex Morning Party Mix
Cinnamon Chex Cereal
Discontinued[edit]
Apple Cinnamon Chex
Oat Chex Cereal
Bran Chex
Double Chex Cereal
Wheat & Raisin Chex
Graham Chex
Honey Graham Chex
Frosted Mini-Chex Cereal
Strawberry Chex Cereal
Sugar Chex Cereal
Multi-Bran Chex Cereal[1]
Raisin Bran Chex Cereal [2]
Space Patrol[edit]
From 1950 to 1955, Chex served as the primary sponsor of the popular TV and radio show Space Patrol, which ran for over 1,000 television episodes and 129 radio episodes. These episodes included many advertisements, promotional offers and prizes related to Chex cereal, specifically Wheat Chex and Rice Chex.
Chex Mix[edit]
This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2014)
See also: Chex Mix
Chex Mix
Chex is also known as the basis for a baked snack called Chex Mix, in which various kinds of Chex are mixed with other grains and nuts and baked crackers/chips, then often re-baked with butter and various other spices (Worcestershire sauce in the original mix) to add flavor. Both commercial and homemade varieties exist and the dish comprises a common holiday snack and pastime in the United States. Chex Mix recipes were regularly featured on Chex cereal boxes, and later, commercially prepared Chex Mix snacks began to be sold in supermarkets. Chex can also be used to make a chocolate snack called Chex Muddy Buddies, also known as Puppy Chow.
Video games[edit]
Chex was featured in a series of first person shooter computer games (Chex Quest, Chex Quest 2 and Chex Quest 3) where the player takes on the role of a Chex Warrior clad in Chex Armor. The games use a modified version of DOOM's IWAD (graphics, sounds, levels, etc.) and executable.
QMRShreddies
From Wikipedia, the free encyclopedia
Shreddies cereal pieces
A former Shreddies box in the United Kingdom
Shreddies is a breakfast cereal produced from shredded wheat, made from lattices of wholegrain wheat.
It is made up of quadrant grids
Manufacture[edit]
In the United Kingdom, the cereal was first produced by Nabisco's former UK division but is now made by Cereal Partners under the Nestlé brand at Welwyn Garden City. The factory opened in 1926. It began making Shreddies in 1953. The site was briefly owned by Rank Hovis McDougall in 1988, who sold it to Cereal Partners in 1990. Nestlé's site at Staverton started making Shreddies in 1998, and is where all production was moved to in 2007.
In Canada, production began in 1939 at Lewis Avenue, Niagara Falls, Ontario. Shreddies were produced under the Nabisco name until the brand in Canada was purchased in 1993 by Post Cereals whose parent company in 1995 became Kraft General Foods which sold Post to Ralcorp in 2008 and is now Post Foods Canada Corp., a unit of Post Holdings, which was spun off from Ralcorp in 2012.
The cereal is marketed with the whole grain symbol, as part of a marketing campaign emphasising the healthiness of the cereal. Wheat for Shreddies is sourced from over 500 different farms within the UK.[1]
Sugared, chocolate and honey-flavoured versions of the cereal are available in the UK as Frosted Shreddies, Coco Shreddies and Honey Shreddies, and an orange-flavoured version of the Coco Shreddies has also become available recently. The former advertising slogan in the UK was: Keeps hunger locked up until lunch. The advertising slogan for the Frosted and Coco Shreddies was: Too tasty for geeks.
QMRPuppy chow, also typically known as muddy buddies, monkey munch, or reindeer food, is the name for a homemade snack made in the United States.[1] The recipe's name and ingredients can differ depending on the version, but most recipes will typically include cereal, melted chocolate, peanut butter, and powdered sugar. Cereals used in the recipes are usually Chex or Crispix.
The snack's name is based upon its look and consistency, which can resemble the Dog Chow brand of dog food in its appearance. Many tend to make the snack during special events such as holidays and gaming events, although it is also a popular snack to make for children.[2][3]
General Mills has made their own version of the snack, which they began selling under the name of Muddy Buddies in 2010.[4][5]
QMREtymology and terminology[edit]
Soldiers from a Highland Regiment circa 1744. The private (on the left) is wearing a belted plaid.
The English word "tartan" is most likely derived from the French tartarin meaning "Tartar cloth".[4] It has also been suggested that "tartan" may be derived from modern Scottish Gaelic tarsainn,[5] meaning "across". Today "tartan" usually refers to coloured patterns, though originally a tartan did not have to be made up of any pattern at all. As late as the 1830s tartan was sometimes described as "plain coloured ... without pattern".[6] Patterned cloth from the Gaelic speaking Scottish Highlands was called breacan, meaning many colours. Over time the meanings of tartan and breacan were combined to describe certain type of pattern on a certain type of cloth. The pattern of a tartan is called a sett. The sett is made up of a series of woven threads which cross at right angles.[6]
Today tartan is generally used to describe the pattern, not limited to textiles.[6] In America the term plaid is commonly used to describe tartan.[7] The word plaid, derived from the Scottish Gaelic plaide, meaning "blanket",[8] was first used of any rectangular garment, sometimes made up of tartan, particularly that which preceded the modern kilt (see: belted plaid). In time, plaid was used to describe blankets themselves.[7]
Variant flag of Monaco
Mardi gras (Pierrot and Harlequin) by Paul Cézanne
Both represent Harlequin print
Five types mutations fourth fifth different
QMRAssociation football is the country's most popular and most televised franchised sport. Its important venues in Mexico City include the Azteca Stadium, home to the Mexico national football team and giants América, which can seat 105,000 fans, making it the biggest stadium in Latin America. The Olympic Stadium in Ciudad Universitaria is home to the football club giants Universidad Nacional, with a seating capacity of over 63,000. The Estadio Azul, which seats 35,000 fans, is near the World Trade Center Mexico City in the Nochebuena neighborhood, and is home to the giants Cruz Azul. The three teams are based in Mexico City and play in the First Division; they are also part, with Guadalajara-based giants Club Deportivo Guadalajara, of Mexico's traditional "Big Four" (though recent years have tended to erode the teams' leading status at least in standings). The country hosted the FIFA World Cup in 1970 and 1986, and Azteca Stadium is the first stadium in World Cup history to host the final twice.
Literature chapter
QMR a choriamb, a four syllable metric foot with a stressed syllable followed by two unstressed syllables and closing with a stressed syllable. The choriamb is derived from some ancient Greek and Latin poetry
QMRIn Greek and Latin poetry, a choriamb /ˈkɔriˌæmb/ is a metron (prosodic foot) consisting of four syllables in the pattern long-short-short-long (— ‿ ‿ —), that is, a trochee alternating with an iamb. Choriambs are one of the two basic metra[1] that do not occur in spoken verse, as distinguished from true lyric or sung verse.[2] The choriamb is sometimes regarded as the "nucleus" of Aeolic verse, because the pattern long-short-short-long pattern occurs, but to label this a "choriamb" is potentially misleading.[3]
In the prosody of English and other modern European languages, "choriamb" is sometimes used to describe four-syllable sequence of the pattern stressed-unstressed-unstressed-stressed (again, a trochee followed by an iamb): for example, "over the hill", "under the bridge", and "what a mistake!".
English prosody[edit]
In English, the choriamb is often found in the first four syllables of iambic pentameter verses, as here in Keats' To Autumn:
Who hath not seen thee oft amid thy store?
Sometimes whoever seeks abroad may find
Thee sitting careless on a granary floor,
Thy hair soft-lifted by the winnowing wind;
Or on a half-reap'd furrow sound asleep,
Drows'd with the fume of poppies, while thy hook
Spares the next swath and all its twined flowers:
And sometimes like a gleaner thou dost keep
Steady thy laden head across a brook;
Or by a cider-press, with patient look,
Thou watchest the last oozings hours by hours.
QMRIncas regarded space and time as a single concept, referred to as pacha (Quechua: pacha, Aymara: pacha).[3][4] The peoples of the Andes maintain a similar understanding.[5]
The idea of a unified spacetime is stated by Edgar Allan Poe in his essay on cosmology titled Eureka (1848) that "Space and duration are one". In 1895, in his novel The Time Machine, H. G. Wells wrote, "There is no difference between time and any of the three dimensions of space except that our consciousness moves along it", and that "any real body must have extension in four directions: it must have Length, Breadth, Thickness, and Duration".
Marcel Proust, in his novel Swann's Way (published 1913), describes the village church of his childhood's Combray as "a building which occupied, so to speak, four dimensions of space—the name of the fourth being Time".
QMRThe geometry of spacetime in special relativity is described by the Minkowski metric on R4. This spacetime is called Minkowski space. The Minkowski metric is usually denoted by \eta and can be written as a four-by-four matrix:
\eta_{ab} \, = \operatorname{diag}(1, -1, -1, -1)
where the Landau–Lifshitz time-like convention is being used. A basic assumption of relativity is that coordinate transformations must leave spacetime intervals invariant. Intervals are invariant under Lorentz transformations. This invariance property leads to the use of four-vectors (and other tensors) in describing physics.
Strictly speaking, one can also consider events in Newtonian physics as a single spacetime. This is Galilean–Newtonian relativity, and the coordinate systems are related by Galilean transformations. However, since these preserve spatial and temporal distances independently, such a spacetime can be decomposed into spatial coordinates plus temporal coordinates, which is not possible in the general case.
A four by four matrix is the quadrant model
Main article: Sonnet
Shakespeare
Among the most common forms of poetry through the ages is the sonnet, which by the 13th century was a poem of fourteen lines following a set rhyme scheme and logical structure. By the 14th century, the form further crystallized under the pen of Petrarch, whose sonnets were later translated in the 16th century by Sir Thomas Wyatt, who is credited with introducing the sonnet form into English literature.[99] A sonnet's first four lines typically introduce the topic, the second elaborates and the third posits a problem - the couplet usually, but not always, includes a twist, or an afterthought. A sonnet usually follows an a-b-a-b-c-d-c-d-e-f-e-f-gg rhyme pattern. The sonnet's conventions have changed over its history, and so there are several different sonnet forms. Traditionally, in sonnets English poets use iambic pentameter, the Spenserian and Shakespearean sonnets being especially notable.[100] In the Romance languages, the hendecasyllable and Alexandrine are the most widely used meters, though the Petrarchan sonnet has been used in Italy since the 14th century.[101]
Sonnets are particularly associated with love poetry, and often use a poetic diction heavily based on vivid imagery, but the twists and turns associated with the move from octave to sestet and to final couplet make them a useful and dynamic form for many subjects.[102] Shakespeare's sonnets are among the most famous in English poetry, with 20 being included in the Oxford Book of English Verse.[103]
QMR Classical Chinese poetics identifies four tones: the level tone, rising tone, departing tone, and entering tone.[41]
QMRThe following table shows the four main tones of Standard Chinese, together with the neutral (or fifth) tone.
Tone number 1 2 3 4 5
Description high rising low (dipping) falling neutral
Pinyin diacritic ā á ǎ à a
Tone letter ˥ (55) ˧˥ (35) ˨˩, ˩, ˩˧, ˨˩˦
(21, 11, 13, 214) ˥˩ (51) -
IPA diacritic /á/ /ǎ/ [a᷄] /à/[27] [à̤, a̤᷆, a̤᷅, a̤᷉] /â/ -
Tone name yīn píng yáng píng shǎng qù qīng shēng
The four main tones of Standard Mandarin, pronounced with the syllable ma.
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The Chinese names of the main four tones are respectively 阴平 [陰平] yīn píng ("dark level"), 阳平 [陽平] yáng píng ("light level"), 上 shǎng[28][29] ("rising"), and 去 qù ("departing"). As descriptions, they apply rather to the predecessor Middle Chinese tones than to the modern tones; see below. The modern Standard Chinese tones are produced as follows:
First tone, or high-level tone, is a steady high sound, produced as if it were being sung instead of spoken. (In a few syllables the quality of the vowel is changed when it carries first tone; see the vowel table, above.)
Second tone, or rising tone, or more specifically high-rising, is a sound that rises from middle to high pitch (like in the English "What?!"). In a three-syllable expression, if the first syllable has first or second tone and the final syllable is not weak, then a second tone on the middle syllable may change to first tone.[30]
Third tone, low or dipping tone, descends from mid-low to low; between other tones it may simply be low. This tone is often demonstrated as having a rise in pitch after the low fall; however, when a third-tone syllable is not said in isolation, this rise is normally heard only if it appears at the end of a sentence or before a pause, and then usually only on stressed monosyllables.[31] The third tone without the rise is sometimes called half third tone. Third tone syllables that include the rise are significantly longer than other syllables. For further variation in syllables carrying this tone, see Third tone sandhi, below. Unlike the other tones, third tone is pronounced with breathiness or murmur.[32]
Fourth tone, falling tone, or high-falling, features a sharp fall from high to low (as is heard in curt commands in English, such as "Stop!"). When followed by another fourth-tone syllable, the fall may be only from high to mid-level.[33]
For the neutral tone or fifth tone, see the following section.
Most romanization systems, including pinyin, represent the tones as diacritics on the vowels (as does zhuyin), although some, like Wade–Giles, use superscript numbers at the end of each syllable. The tone marks and numbers are rarely used outside of language textbooks: in particular, they are usually absent in public signs, company logos, and so forth. Gwoyeu Romatzyh is a rare example of a system where tones are represented using normal letters of the alphabet (although without a one-to-one correspondence).
The first square is always inspring. The second is rising. The second square is still good. The third square is dipping. The third square is destruction. The fourth square is falling. The fourth square is death. The fifth is neutral. the fifth is always ultra transcendent.
QMRPitch-accented languages may have a more complex accentual system than stress-accented languages. In some cases, they have more than a binary distinction but are less complex than fully tonal languages such as Chinese or Yoruba, which assign a separate tone to each syllable. For example, in Japanese short nouns (1-4 moras) may have a drop in pitch after any one mora but more frequently on none at all so in disyllabic words followed by a particle, there are three-way minimal contrasts such as kaꜜki wa "oyster" vs. kakiꜜ wa "fence" vs. kaki wa "persimmon". Ancient Greek words had high pitch on one of the last four vocalic morae in a word, and since a vowel may have one or two morae, a syllable can be accented in one of four ways (high pitch, rising pitch, falling pitch, none). Also, the mapping between phonemic and phonetic tone may be more involved than the simple one-to-one mapping between stress and dynamic intensity in stress-accented languages.
QMRNeoštokavian idiom used for the basis of standard Bosnian, Croatian and Serbian distinguishes four types of pitch accents: short falling ⟨◌̏⟩, short rising ⟨◌̀⟩, long falling ⟨◌̑⟩ and long rising ⟨◌́⟩. The accent is said to be relatively free as it can be manifested in any syllable but the last one. The long accents are realized by pitch change within the long vowel; the short ones are realized by the pitch difference from the subsequent syllable.[13] Accent alternations are very frequent in inflectional paradigms, both by quality and placement in the word (the so-called "mobile paradigms", which were present in the PIE itself but in Proto-Balto-Slavic have become much more widespread). Different inflected forms of the same lexeme can exhibit all four accents: lònac 'pot' (nominative sg.), lónca (genitive sg.), lȏnci (nominative pl.), lȍnācā (genitive pl.).
QMRFirstly, while the primary indication of accent is pitch (tone), there is only one or a few tonic syllables or morae in a word, or at least in simple words, the position of which determines the tonal pattern of the whole word.[nb 4] Pitch accent may also be restricted in distribution, being found for example only on one of the last two syllables. This is unlike the situation in typical tone languages, where the tone of each syllable is independent of the other syllables in the word. For example, comparing two-syllable words like [aba] in a pitch-accented language and in a tonal language, both of which make only a binary distinction, the tonal language has four possible patterns:
Tone:
low-low [àbà],
high-high [ábá],
high-low [ábà],
low-high [àbá].
The pitch-accent language, on the other hand, has only three possibilities:
Pitch accent:
accented on the first syllable, [ába],
accented on the second syllable, [abá], or
no accent [aba].
The combination *[ábá] does not occur.
With longer words, the distinction becomes more apparent: eight distinct tonal trisyllables [ábábá, ábábà, ábàbá, àbábá, ábàbà, àbábà, àbàbá, àbàbà], vs. four distinct pitch-accented trisyllables [ábaba, abába, ababá, ababa].
QMRStandard Seoul Korean uses pitch only for prosodic purposes. However, several dialects outside Seoul retain a Middle Korean pitch accent system. In the dialect of North Gyeongsang, in southeastern South Korea, any one syllable may have pitch accent in the form of a high tone, as may the initial two syllables. For example, in trisyllabic words, there are four possible tone patterns:[16]
Examples
Hangul IPA English
며느리 mjé.nə.ɾi daughter-in-law
어머니 ə.mə.ni mother
원어민 wə.nə.mín native speaker
오라비 ó.ɾá.bi elder brother
QMRIn poetry, a tetrameter is a line of four metrical feet. The particular foot can vary, as follows:
Anapestic tetrameter:
"And the sheen of their spears was like stars on the sea" (Lord Byron, "The Destruction of Sennacherib")
"Twas the night before Christmas when all through the house" ("A Visit from St. Nicholas")
Iambic tetrameter:
"Because I could not stop for Death" (Emily Dickinson, eponymous lyric)
Trochaic tetrameter:
"Peter, Peter, pumpkin-eater" (English nursery rhyme)
Dactylic tetrameter:
Picture your self in a boat on a river with [...] (The Beatles, "Lucy in the Sky with Diamonds")
Spondaic tetrameter:
Long sounds move slow
Pyrrhic tetrameter (with spondees ["white breast" and "dim sea"]):
And the white breast of the dim sea
Amphibracic tetrameter:
And, speaking of birds, there's the Russian Palooski, / Whose headski is redski and belly is blueski. (Dr. Seuss)
QMRThe number of metrical feet in a line are described using Greek terminology: tetrameter for four feet and hexameter for six feet, for example.[45] Thus, "iambic pentameter" is a meter comprising five feet per line, in which the predominant kind of foot is the "iamb". This metric system originated in ancient Greek poetry, and was used by poets such as Pindar and Sappho, and by the great tragedians of Athens. Similarly, "dactylic hexameter", comprises six feet per line, of which the dominant kind of foot is the "dactyl". Dactylic hexameter was the traditional meter of Greek epic poetry, the earliest extant examples of which are the works of Homer and Hesiod.[46] Iambic pentameter and dactylic hexameter were later used by a number of poets, including William Shakespeare and Henry Wadsworth Longfellow, respectively.[47] The most common metrical feet in English are:[48]
There are acrostics in the Bible that portray crosses
QMRLamentations consists of five distinct poems, corresponding to its five chapters. The first four are written as acrostics – chapters 1, 2, and 4 each have 22 verses, corresponding to the 22 letters of the Hebrew alphabet, the first lines beginning with the first letter of the alphabet, the second with the second letter, and so on. Chapter 3 has 66 verses, so that each letter begins three lines, and the fifth poem is not acrostic but still has 22 lines.
The purpose of this is to reflect the quadrant model image. Each chapter reflects a square of the quadrant model
QMRAnother book, the 13th-century Kabbalistic text Sefer HaTemunah, holds that a single letter of unknown pronunciation, held by some to be the four-pronged shin on one side of the teffilin box, is missing from the current alphabet. The world's flaws, the book teaches, are related to the absence of this letter, the eventual revelation of which will repair the universe.[19] Another example of messianic significance attached to the letters is the teaching of Rabbi Eliezer that the five letters of the alphabet with final forms hold the "secret of redemption". The reason the four pronged shin is so important is because it is the quadrant four. Most shins have three prongs but the box that Jews put on their forehead in the morning to pray with has four. The fourth is different. That is because it is reflecting the quadrant four.
QMRThe Arabic letters generally (as six of the primary letters can have only two variants) have four forms, according to their place in the word. The same goes with the Mandaic ones, except for three of the 22 letters, which have only one form.
QMRThe Arabic alphabet is always cursive and letters vary in shape depending on their position within a word. Letters can exhibit up to four distinct forms corresponding to an initial, medial (middle), final, or isolated position (IMFI). While some letters show considerable variations, others remain almost identical across all four positions. Generally, letters in the same word are linked together on both sides by short horizontal lines, but six letters (و ز ر ذ د ا) can only be linked to their preceding letter. For example, أرارات (Ararat) has only isolated forms because each letter cannot be connected to its following one. In addition, some letter combinations are written as ligatures (special shapes), notably lām-alif.[3]
QMR Arabic letters have dots, the most four
QMRThe Persian alphabet (الفبای فارسی alefbā-ye fārsi) or Perso-Arabic script is a writing system based on the Arabic script and used for the Persian language. It has four letters more than Arabic: پ [p], چ [t͡ʃ], ژ [ʒ], and گ [ɡ].
QMRThe first ten letters of the alphabet, a–j, use the upper four dot positions: ⠁⠃⠉⠙⠑⠋⠛⠓⠊⠚ (black dots in the table below). These stand for the ten digits 1–9 and 0 in a system parallel to Hebrew gematria and Greek isopsephy. (Though the dots are assigned in no obvious order, the cells with the fewest dots are assigned to the first three letters (and lowest digits), abc = 123 (⠁⠃⠉), and to the three vowels in this part of the alphabet, aei (⠁⠑⠊), whereas the even digits, 4, 6, 8, 0 (⠙⠋⠓⠚), are corners/right angles.)
These dots reflect the quadrant four
QMRQWERTY is the most common modern-day keyboard layout for Latin script. The name comes from reading the first six keys appearing on the top left letter row of the keyboard (Q, W, E, R, T, and Y) from left to right. The QWERTY design is based on a layout created for the Sholes and Glidden typewriter and sold to Remington in 1873. It November 1868 he changed the arrangement of the latter half of the alphabet, O to Z, right-to-left.[9] In April 1870 he arrived at a four-row, upper case keyboard approaching the modern QWERTY standard, moving six vowel letters, A, E, I, O, U, and Y, to the upper row as followsOn Linux systems, the Swedish keyboard may also give access to additional characters as follows:
first row: AltGr ¶¡@£$€¥{[]}\± and AltGr+⇧ Shift ¾¹²³¼¢⅝÷«»°¿¬
second row: AltGr @ł€®þ←↓→œþ"~ and AltGr+⇧ Shift ΩŁ¢®Þ¥↑ıŒÞ°ˇ
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Several of these characters function as dead keys.
QWERTY, the keyboard is based off of four rows
QMREuphony is used for effects which are pleasant, rhythmical and harmonious.[1][2][3] An example of euphony is the poem Some Sweet Day.
Some day Love shall claim his own
Some day Right ascend his throne,
Some day hidden Truth be known;
Some day—some sweet day.
— Lewis J. Bates, the poem Some Sweet Day
The famous poem has four lines
QMR The Waiste Land by TS Elliot is written in mostly four line stanzas
QMRPeredur son of Efrawg is one of the three Welsh Romances associated with the Mabinogion. It tells a story roughly analogous to Chrétien de Troyes' unfinished romance Perceval, the Story of the Grail, but it contains many striking differences from that work, most notably the absence of the French poem's central object, the grail.
Contents [hide]
1 Manuscripts
2 Synopsis
3 Sources and analogues
4 References
5 Further reading
6 External links
Manuscripts[edit]
Versions of the text survive in four manuscripts from the 14th century: (1) the mid-14th century White Book of Rhydderch or Aberystwyth, NLW, MS Peniarth 4; (2) MS Peniarth 7, which dates from the beginning of the century, or earlier, and lacks the beginning of the text; (3) MS Peniarth 14, a fragment from the 2nd quarter of the 14th century, and (4) the Red Book of Hergest, from the end of the same century.[1] The texts found in the White Book of Rhydderch and Red Book of Hergest represent the longest version. They are generally in close agreement and most of their differences are concentrated in the first part of the text, before the love-story of Angharad.[2] MS Peniarth 7, the earliest manuscript, concludes with Peredur's 14-year sojourn with the Empress of Constantinople.[3] This has been taken to indicate that the adventures in the Fortress of Marvels, which follow this episode in the longest version, represent a later addition to the text.[4]
QMRFour Adventures of Reinette and Mirabelle (French: Quatre aventures de Reinette et Mirabelle) is a 1987 French film directed by Éric Rohmer, starring Joëlle Miquel, Jessica Forde and Philippe Laudenbach.
Synopsis[edit]
The film consists of four episodes in the relationship of two young women: Reinette, a country girl, and Mirabelle, a Parisian. The first episode is entitled The Blue Hour and recounts their meeting. The second centers on a café and a difficult waiter. In the third, the girls discuss their differing views on society's margins: beggars, thieves and swindlers. In the fourth episode, Reinette and Mirabelle succeed in selling one of Reinette's paintings to an art dealer while Reinette pretends to be mute and Mirabelle, acting as if she does not know Reinette, does all the talking.
QMRThe Little Iliad (Greek: Ἰλιὰς μικρά, Ilias mikra; Latin: Ilias parva) is a lost epic of ancient Greek literature. It was one of the Epic Cycle, that is, the "Trojan" cycle, which told the entire history of the Trojan War in epic verse. The story of the Little Iliad comes chronologically after that of the Aethiopis, and is followed by that of the Iliou persis ("Sack of Troy"). The Little Iliad was variously attributed by ancient writers to Lesches of Pyrrha, Cinaethon of Sparta, Diodorus of Erythrae, Thestorides of Phocaea, or Homer himself (see Cyclic poets). The poem comprised four books of verse in dactylic hexameter, the heroic meter.
QMRThe Telemachy (from Greek Τηλεμάχεια) is a term traditionally applied to the first four books of Homer's epic poem the Odyssey. They are named so because – just as the Odyssey tells the story of Odysseus – they tell the story of Odysseus' son Telemachus as he journeys from home for the first time in search of news about his missing father.QMRTelemachus (/təˈlɛməkəs/ tə-lem-ə-kəs; Greek: Τηλέμαχος, Tēlemakhos, literally "far-fighter") is a figure in Greek mythology, the son of Odysseus and Penelope, and a central character in Homer's Odyssey. The first four books of the Odyssey focus on Telemachus' journeys in search of news about his father, who has yet to return home from the Trojan War, and are traditionally given the title the Telemachy.[1]QMRTelemachus (/təˈlɛməkəs/ tə-lem-ə-kəs; Greek: Τηλέμαχος, Tēlemakhos, literally "far-fighter") is a figure in Greek mythology, the son of Odysseus and Penelope, and a central character in Homer's Odyssey. The first four books of the Odyssey focus on Telemachus' journeys in search of news about his father, who has yet to return home from the Trojan War, and are traditionally given the title the Telemachy.[1]
Contents [hide]
1 Etymology
2 Odyssey
3 Telegony
4 Later classical authors
5 Other appearances
6 Notes
7 External links
Etymology[edit]
Telemachus' name in Greek means "far from battle", perhaps reflecting his absence from the Trojan War. Homer also calls Telemachus by the patronymic epithet "Odysseus' son".
In the Odyssey by Homer, under the instructions of Athena, Telemachus spends the first four books trying to gain knowledge of his father, Odysseus, who left for Troy when Telemachus was still an infant. At the outset of Telemachus' journey, Odysseus has been absent from his home at Ithaca for twenty years due to the Trojan War and the intervention of Poseidon. During his absence, Odysseus' house has been occupied by hordes of suitors seeking the hand of Penelope.[3] Telemachus first visits Nestor and is well received by the old man who regales him with stories of his father's glory. Telemachus then departs with Nestor's son Peisistratus,[4] who accompanies him to the halls of Menelaus and his wife Helen. Whilst there, Telemachus is again treated as an honored guest as Menelaus and Helen tell complementary, yet contradictory stories of his father's exploits at Troy.[5]
The Odyssey returns focus to Telemachus upon his father's return to Ithaca in Book XV. He visits Eumaeus, the swineherd, who happens to be hosting a disguised Odysseus. After Odysseus reveals himself to Telemachus due to Athena's advice, the two men plan the downfall of the suitors. Telemachus then returns to the palace to keep an eye on the suitors and to await his father as the beggar.[6]
When Penelope challenges the suitors to string Odysseus' bow and shoot an arrow through the handle-holes of twelve axeheads, Telemachus is the first to attempt the task. He would have completed the task, nearly stringing the bow on his fourth attempt; however, Odysseus subtly stops him before he can finish his attempt. Following the failure of the suitors at this task, Odysseus reveals himself, and he and Telemachus bring swift and bloody death to the suitors.
QMR culture has gone through four main stages, which Spengler symbolizes by the seasons of the year. It had its "spring" inmedieval times, and the features of
such a cultural spring are a warrior aristocracy, a priesthood, a peasantry bound to the soil, a limited urban development, anonymous and impersonal art, mainly in the
service of the priests and the fighters (churches and castles), and intense spiritual
development
"autumn" took place in the eighteenth century, when it began to exhaust its inner
possibilities, of music in Mozart and Beethoven, of literature in Goethe, of
philosophy in Kant. Then itmoved into its "winter" phase, which Spengler calls a
"civilization" as distinct from a culture. Here its accomplishments in the arts and
philosophy are either a further exhaustion of possibilities or an inorganic repetition of what has been done. Its distinctive energies are now technological.
QMRPerceval, the story of the Grail (French: Perceval, le Conte du Graal) is the unfinished fifth romance of Chrétien de Troyes. Probably written between 1135 and 1190, it is dedicated to Chrétien's patron Philip, Count of Flanders.[1] It is said by some scholars that during the time Chrétien was writing Perceval, there was a political crisis taking place between the aristocracy, which included his patron, Philip of Flanders, and the monarchy, which may have influenced Chrétien’s work.[2]
Chrétien claimed to be working from a source given to him by Philip. The poem relates the adventures and growing pains of the young knight Perceval but the story breaks off, there follows an adventure of Gawain of similar length that also remains incomplete: there are some 9,000 lines in total, whereas Chrétien's other romances seldom exceed 7,000 lines.
Later authors added 54,000 more lines in what are known collectively as the Four Continuations.[3] Perceval is the earliest recorded account of what was to become the Quest for the Holy Grail[4] but describes only a golden grail (a serving dish) in the central scene and does not call it "holy" but treats a lance, appearing at the same time, as equally significant.
QMRThe four troubadours Bernart d'Auriac, Pere Salvatge, Roger Bernard III of Foix, and Peter III of Aragon composed a cycle of four sirventes in the summer of 1285 concerning the Aragonese Crusade.
QMRThe Mythological Cycle is a conventional division within Irish mythology, concerning a set of tales about the godlike peoples said to have arrived in five migratory invasions into Ireland and principally recounding the doings of the Tuatha Dé Danann.[1] It is one of the four major cycles of early Irish literary tradition, the others being the Ulster Cycle, the Fenian Cycle and the Cycles of the Kings.
QMRCeithri cathracha i r-robadar Tuatha De Danand ("[The four jewels of the Tuatha Dé Danann|The Four Jewels of the Tuatha Dé Danann
QMRThe Tuatha Dé Danann brought four magical treasures with them to Ireland, one apiece from their Four Cities:
The Dagda's Cauldron
The Spear of Lugh
The Stone of Fal
The Sword of Light of Nuada
QMRThe Tuatha Dé Danann were descended from Nemed, leader of a previous wave of inhabitants of Ireland. They came from four cities to the north of Ireland–Falias, Gorias, Murias and Finias–where they acquired their magical skills and attributes. According to Lebor Gabála Érenn, they came to Ireland "in dark clouds" and "landed on the mountains of [the] Conmaicne Rein in Connachta; and they brought a darkness over the sun for three days and three nights". According to a later version of the story, they arrived in ships on the coast of the Conmaicne Mara's territory (modern Connemara). They immediately burnt the ships "so that they should not think of retreating to them; and the smoke and the mist that came from the vessels filled the neighboring land and air. Therefore it was conceived that they had arrived in clouds of mist".
QMRThe Fenian Cycle (/ˈfiːniən/) or the Fiannaíocht (Irish: an Fhiannaíocht[1] ), also referred to as the Ossianic Cycle /ˌɒʃiˈænɪk/ after its narrator Oisín, is a body of prose and verse centring on the exploits of the mythical hero Fionn mac Cumhaill and his warriors the Fianna. It is one of the four major cycles of Irish mythology along with the Mythological Cycle, the Ulster Cycle, and the Historical Cycle. Put in chronological order, the Fenian cycle is the third cycle, between the Ulster and Historical cycles. The cycle also contains stories about other famous Fianna members, including Diarmuid, Caílte, Oisín's son Oscar, and Fionn's enemy, Goll mac Morna.
QMR DH Lawrence
The Rainbow (1915) was suppressed after an investigation into its alleged obscenity in 1915. Later, they were accused of spying and signalling to German submarines off the coast of Cornwall where they lived at Zennor. During this period he finished writing Women in Love in which he explored the destructive features of contemporary civilization through the evolving relationships of four major characters as they reflect upon the value of the arts, politics, economics, sexual experience, friendship and marriage. The novel is a bleak, bitter vision of humanity and proved impossible to publish in wartime conditions. Not published until 1920, it is now widely recognised as an English novel of great dramatic force and intellectual subtlety.
QMRThe Four Sons of Aymon (French: [Les] Quatre fils Aymon, Dutch: De Vier Heemskinderen, German: Die Vier Haimonskinder), sometimes also referred to as Renaud de Montauban (after its main character) is a medieval tale spun around the four sons of Duke Aymon: the knight Renaud de Montauban (also spelled Renaut, Renault, Italian: Rinaldo di Montalbano, Dutch: Reinout van Montalbaen), his brothers Guichard, Allard and Richardet, their magical horse Bayard (Italian: Bayardo), their adventures and revolt against the emperor Charlemagne. The story had a European success and echoes of the story are still found today in certain folklore traditions.
The four brothers—usually represented all together seated on their horse Bayard—have inspired many sculptures:
The oldest extant statue is found on a tomb in Portugal (dated to the first half of the 12th century).
A bronze statue (Ros Beyaert) depicting the four sons of Aymon (Reinout, Adelaert, Ritsaert and Writsaert) on their horse Beyaert (Bayard), was erected on the central approach avenue to the Exposition universelle et internationale (1913) held in Ghent (Belgium).[12] This statue was created by Aloïs de Beule and Domien Ingels.
One of the most famous representations was created by Olivier Strebelle for the Expo 58. Situated by the Meuse in the city of Namur, the horse appears to want to carry its riders across the river with a leap.
Another statue showing the four brothers standing beside their horse can be found at Bogny-sur-Meuse, created by Albert Poncin.
Dendermonde is home to several statues representing the brothers.
The statue Vier Heemskinderen (1976) by Gerard Adriaan Overeem was placed in the "Torenstraat" of Nijkerk
In Köln, since 1969, a bronze sculpture by Heinz Klein-Arendt depicts them.
QMRChastúshka, Russian: часту́шка, pronounced [tɕɐsˈtuʂkə], derives from "часто" - "frequently", or from "части́ть" - old word, that means "to do something with high frequency" and probably refers to high beat frequency (tempo) of chastushki.
Chastushka is a traditional type of short Russian or Ukrainian folk humorous song with high beat frequency, that consists of one four-lined couplet, full of humor, satire or irony. Usually many chastushki are sung one after another. Chastushka makes use of a simple rhyming scheme to convey humorous or ironic content. The singing and recitation of such rhymes were an important part of peasant popular culture both before and after the Bolshevik Revolution of 1917.
A chastushka (plural: chastushki) is a simple rhyming poem which would be characterized derisively in English as doggerel. The name originates from the Russian word "часто" ("chasto") - "frequently", or from части́ть ("chastit"), meaning "to do something with high frequency" and probably refers to high beat frequency of chastushkas.
The basic form is a simple four-line verse making use of an ABAB, ABCB, or AABB rhyme scheme.
Usually humorous, satirical, or ironic in nature, chastushki are often put to music as well, usually with balalaika or accordion accompaniment. The rigid, short structure (and, to a lesser degree, the type of humor used) parallels the poetic genre of limericks in British culture.
QMRNahuatl poetry is preserved in principally two sources: the Cantares Mexicanos and the Romances de los señores de Nueva España, both collections of Aztec songs written down in the 16th and 17th centuries. Some songs may have been preserved through oral tradition from pre-conquest times until the time of their writing, for example the songs attributed to the poet-king of Texcoco, Nezahualcoyotl. Karttunen & Lockhart (1980) identify more than four distinct styles of songs, e.g. the icnocuicatl ("sad song"), the xopancuicatl ("song of spring"), melahuaccuicatl ("plain song") and yaocuicatl ("song of war"), each with distinct stylistic traits. Aztec poetry makes rich use of metaphoric imagery and themes and are lamentation of the brevity of human existence, the celebration of valiant warriors who die in battle, and the appreciation of the beauty of life.
cinema chapter
QMRNaked and Afraid is an American reality series that airs on the Discovery Channel. The fourth season premiered on April 19, 2015.[1][2] Each episode chronicles the lives of two survivalists who meet for the first time and are given the task of surviving a stay in the wilderness naked for 21 days.[3][4] After they meet in the assigned locale, the partners must find and/or produce these four items, water, food, shelter, and clothing within the environment.
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