Philosophy chapter
QMRFour Forms of Fourier Transform
Depending on whether a signal $x(t)$ is periodic and discrete, its Fourier transform will take one of the four forms:
I. Aperiodic, continuous time signal $x(t)$, continuous, aperiodic spectrum $X(f)$
This is the most general form of Fourier transform:
\begin{displaymath}X(f)=\int_{-\infty}^{\infty} x(t) e^{-j2\pi ft} dt,\;\;\;\;
x(t)=\int_{-\infty}^{\infty} X(f) e^{j2\pi ft} df \end{displaymath}
II. Aperiodic, discrete time signal $x[n]$, continuous, periodic spectrum $X_F(f)$
The discrete time signal can be considered as a sequence of samples of a continuous signal. The time interval between two consecutive samples $x[m]$ and $x[m+1]$ is $t_0=1/F$, where $F$ is the sampling rate, which is also the period of the spectrum in the frequency domain.
The discrete time signal can be written as
\begin{displaymath}x(t)=\sum_{m=-\infty}^{\infty} x[m]\delta(t-mt_0) \end{displaymath}
and its transform is:
\begin{displaymath}X_F(f)=\sum_{m=-\infty}^{\infty} x[m]e^{-j2\pi fmt_0},\;\;\;\...
...^F X_F(f) e^{j2\pi fmt_0} df,
\;\;\;(m=0,\pm 1,\pm 2, \cdots) \end{displaymath}
III. Periodic, continuous time signal $x_T(t)$, discrete, aperiodic spectrum $X[n]$
This is the Fourier series expansion of periodic signals. The time period is $T$, and the interval between two consecutive frequency components is $f_0=1/T$, and its transform is:
\begin{displaymath}X[n]=\frac{1}{T} \int_0^T x_T(t) e^{-j2\pi nf_0t} dt,\;\;\;\;...
...infty} X[n]e^{j2\pi nf_0t},
\;\;\;(n=0, \pm 1, \pm 2, \cdots) \end{displaymath}
The discrete spectrum can also be represented as:
\begin{displaymath}X(f)=\sum_{n=-\infty}^{\infty} X[n]\delta(f-nf_0) \end{displaymath}
IV. Periodic, discrete time signal $x[m]$, discrete, periodic spectrum $X[n]$
\begin{displaymath}X[n]=\frac{1}{T}\sum_{m=0}^{N-1} x[m]e^{-j2\pi nmf_0t_0},\;\;...
..._{n=0}^{N-1} X[n]e^{j2\pi nmf_0t_0},\;\;\;(m,n=0,1,\cdots,N-1) \end{displaymath}
where $N=T/t_0=F/f_0$ is the number of samples in each period in both temporal and frequency domains. Since $t_0f_0=1/FT=1/N$, the above can be rewritten as:
\begin{displaymath}X[n]=\frac{1}{N}\sum_{m=0}^{N-1} x[m] e^{-j2\pi mn/N},\;\;\;\...
..._{m=0}^{N-1} X[n] e^{ j2\pi mn/N},\;\;\;\;(m,n=0,1,\cdots,N-1) \end{displaymath}
The coefficients for forward and inverse transforms can be either $1/N$ and 1, or $1/\sqrt{N}$ for both of them to make the transform pair perfectly symmetric. These scaling factors are not essential in practice.
QMRFour forms of Fourier transform (Table 5.3):
\begin{displaymath}\begin{tabular}{c\vert\vert c\vert c} \hline
& {\bf Signal $x...
...& ($T/t_0=N$) & ($F/f_0=T/t_0=N$) \hline
\par
\end{tabular} \end{displaymath}
The Convolution theorem
\begin{displaymath}\begin{tabular}{c\vert\vert c\vert c} \hline
& Time domain &...
...\sum_{k=0}^{N-1} X_F[k]Y_F[n-k]$ \hline
\par
\end{tabular} \end{displaymath}
Parseval's formula
\begin{displaymath}\begin{tabular}{c\vert\vert c} \hline
I & $\int_{-\infty}^\in...
...sum_{n=0}^{N-1} \vert X_F[n] \vert^2$ \hline
\end{tabular} \end{displaymath}
Data is in four forms table, graph story and equation
QMRIn G.I. Gurdjieff's Fourth Way teaching, also known as The Work, centers or brains refer to separate apparatuses within a being that dictate its specific functions. According to this teaching, there are three main centers: intellectual, emotional, and moving. These centers in the human body are analogous to a three-storey factory, the intellectual center being the top storey, the emotional center being the middle one, and the moving center being the bottom storey. The moving center, or the bottom storey is further divided into three separate functions: sex, instinctive, and motor.
According to the teaching:
Lower centers[edit]
1. Moving or physical center. This brain is located in the spinal column. This brain makes beings capable of physical actions. Some, but not all, Fourth Way schools have further divided this Center into three distinct parts:
Motor: Controls motor functions. The acts of walking, the physical aspects of talking, as well as even functions that are considered "reflexive," are all part of this sub-center.
Instinctive: Controls faculties which are completely involuntary. This does not typically encompass "knee-jerk" reactions, nor what we would typically consider reflexes. A common example of the functioning of this center is the contracting of blood vessels to facilitate the pumping of blood.
Sexual. Controls sexual functions.
2. Emotional or feeling center. This faculty makes beings capable of feeling emotions. This brain is dispersed throughout the human body as nerves which have been labeled as the "nerve nodes" . The biggest concentration of these nerves is in the solar plexus.[2]
3. Intellectual or thinking center. This center is the faculty which makes a being capable of logic and reasoning. It is located in the head.
Higher centers[edit]
While the lower centers are considered separate faculties of one's material body, one can think of these higher centers as being faculties for "higher bodies".
4. Higher Emotional Center: faculty of the astral body. It enables one to have sustained states of self-consciousness, self-awareness, and other deep feelings. It does not replace, nor is it an "upgraded" version of the emotional center, as it is a completely separate center.
5. Higher Intellectual Center: faculty of the mental body. It enables one to have sustained states of objective consciousness and superior intellect. As above, it does not replace, nor is it an "upgraded" version of the intellectual center.
QMRSubtle bodies[edit]
The Fourth Way says that there are four possible bodies of man, composed of increasingly rarefied matter, interpenetrating one another;[3] all people have the first body., while the other three are obtained through the correct type of effort. The bodies are as follows:
The Material Body (Normal Human Physical Body). This body is considered the seat of the lower five centers: intellectual, emotional, physical, instinctual, and sexual. The material body's actions are purely automatic and depend completely on the influences coming from outside factors, and its perception is confined to observation in a "subjective" manner. When the material body dies, then it returns to the earth from which it came, and nothing of it remains.
The Astral Body This body is also sometimes called the Emotional body or the Kesdjan Body. This body, by itself is not subject to the laws of automation; that is to say, the astral body is capable of a degree of free will. Also, the perceptions of the astral body are capable of being of an objective nature in matters regarding one's self. An astral body is considered a prerequisite to maintaining a state of "self-consciousness". The lifespan of the astral body is unknown exactly, but it is far larger than the lifespan of the Material Body because it continues living after the death of the material body. According to the Fourth Way, a man is not born with an astral body and an average man does not have one, while even if someone does, it's in a very immature state, and has no contact with it whatsoever in his daily life.
The Intellectual Body This body, by itself is not subject to the laws of automation; that is to say, the intellectual body is capable of a degree of free will beyond that of the astral body. Also, the perceptions of the intellectual body are capable of being of an objective nature in matters regarding both one's self, and things outside of one's self. An intellectual body is considered a prerequisite to maintaining a state of "objective consciousness" which is the fourth possible state of man. The lifespan of the intellectual is also rather incalculable. According to Gurdjieff, an average man does not have one.
The Causal Body
QMRCrossings is a two-player abstract strategy board game invented by Robert Abbott. The rules were published in Sid Sackson's A Gamut of Games. Crossings was the precursor to Epaminondas, which uses a larger board and expanded rules.
It is played on a quadrant board 8 by 8 which is four quadrant models.
QMRArimaa Listeni/əˈriːmə/ (ə-ree-mə) is a two-player strategy board game that was designed to be playable with a standard chess set and difficult for computers while still being easy to learn and fun to play for humans. Every year since 2004, the Arimaa community has held three tournaments: a World Championship (humans only), a Computer Championship (computers only), and the Arimaa Challenge (human vs. computer). In 2015, the challenge was won decisively by the computer (Sharp by David Wu), with top players agreeing it was no fluke but proof that computers are currently superior to humans.[1] As it was a prerequisite for the prize to be awarded, most of ICGA Journal Issue 38/1 was dedicated to this topic.[2]
Arimaa was invented in 2003 by Omar Syed,[3] an Indian American computer engineer trained in artificial intelligence. Syed was inspired by Garry Kasparov's defeat at the hands of the chess computer Deep Blue to design a new game which could be played with a standard chess set, would be difficult for computers to play well, but would have rules simple enough for his then four-year-old son Aamir to understand.[4] ("Arimaa" is "Aamir" spelled backwards plus an initial "a".)
Arimaa has won several awards including GAMES Magazine 2011 Best Abstract Strategy Game,[5] Creative Child Magazine 2010 Strategy Game of the Year,[6] and the 2010 Parents' Choice Approved Award.[7] It has also been the subject of several research papers. It is another 8 by 8 game
QMRThe coat of arms of the Republic of Croatia (Croatian: Grb Republike Hrvatske) consists of one main shield and five smaller shields which form a crown over the main shield. The main coat of arms is a checkerboard (chequy) that consists of 13 red and 12 silver (white) fields. It's also informally known in Croatian as šahovnica ("chessboard", from šah, "chess"). The five smaller shields represent five different historical regions within Croatia.
Checkerboards are quadrants
QMRCheckerboarding refers to a situation where land ownership is intermingled between two or more owners, resulting in a checkerboard pattern. Checkerboarding is prevalent in the Western United States due to its extensive use in railroad grants for western expansion, although it had its beginnings in the canal land grant era.[1 Checkerboards are quadrants
Golden Checkerboard (1965) is a book by Ed Ainsworth.[nb 1] Its subject matter concerns the mid-20th century economic conditions of the Agua Caliente Band of Cahuilla Indians of Palm Springs, California, and the history of the 99-year lease law which enabled them to commercially develop tribal owned lands. It focuses on Indio Superior Court Judge Hilton McCabe, who is described as "The Little White Father of the Indians of Palm Springs",[1]:2 Intro by U.S. Supreme Court Justice Tom Clark and recalls the steps taken by McCabe to set up conservatorships and leases that would give the tribe investment opportunities and economic self-sufficiency. The title of the book refers to the Agua Caliente Agua Caliente Band of Cahuilla Indians' reservation checkerboard pattern, originating from land grants to the Southern Pacific Railroad as an incentive to build rail lines through the region,[1]:29 when President Ulysses S. Grant signed an Executive Order granting "San Bernardino Base and Meridian, Township 4 South, Range 4 East, Section 14" to the Agua Caliente Indians.[1]:49
QMRThe Air Force checkerboard (Polish: szachownica lotnicza) is a national marking for the aircraft of the Polish Air Force, equivalent to roundels used in other nations' air forces. It consists of four equal squares, of which the upper left and lower right are white, and the other two – red. These are surrounded by a border of inverted (counterchanged) colors 1/5 the thickness of a single square. In 1993 the colors were reversed (i.e. red in the upper left).
Initially, Polish military aircraft used various signs in national colors (red and white), most frequently shields party per bend, pale, or red letter "Z" in a white square. The four-field, red-white checkerboard, was first used as a personal insignia of the Polish fighter pilot Stefan Stec. It was adopted as the Polish national roundel on 1 December 1918.
In 1921 a contrasting red and white border was added, but without specified dimensions. In 1930 the ratio of border to fields was fixed at 1:5. According to current regulations, an additional gray border can be added, 1:6 the size of the field, if the insignia is displayed on a white or red background.
Between the 1960s and 1980s the checkerboard (usually rotated 45 degrees) was also painted on turrets and hulls of Polish Army tanks and APCs. This tradition has since been discontinued.
In 1993 the color order was changed from red-dominant (red in the upper left) to white-dominant, to conform to heraldic rules, though ignoring the 70-year-old tradition. The first white-dominant checkerboard was used in 1940 in France.
It is a quadrant
QMRAtlantic Richfield Company (ARCO) is an American oil company with operations in the United States, Indonesia, the North Sea, and the South China Sea.[1] It has more than 1,300 gas stations in the western part of the United States.[2] ARCO was formed by the merger of East Coast–based Atlantic Refining and California-based Richfield Oil Corporation in 1966. A merger in 1969 brought in Sinclair Oil Corporation.[1] It's symbol is sort of a quadrant
QMRBayerische Motoren Werke AG (About this sound pronunciation (help·info); English: Bavarian Motor Works; BMW) is a German luxury automobile, motorcycle, and engine manufacturing company founded in 1916. Headquartered in Munich, Bavaria, Germany, it also owns and produces Mini cars and serves as the parent company of Rolls-Royce Motor Cars. BMW produces motorcycles under BMW Motorrad, and plug-in electric cars under the BMW i sub-brand. It is one of the best-selling luxury automakers in the world.[4] The company is a component of the Euro Stoxx 50 stock market index.[5. BMW's symbol is a blue and white quadrant
QMrEngine[edit]
Main article: Ford Model T engine
1926 Model T engine
The Model T had a front-mounted 177-cubic-inch (2.9 L) inline four-cylinder engine, producing 20 hp (15 kW), for a top speed of 40–45 mph (64–72 km/h). According to Ford Motor Company, the Model T had fuel economy on the order of 13–21 mpg-US (16–25 mpg-imp; 18–11 L/100 km).[22] The engine was capable of running on gasoline, kerosene, or ethanol,[23][24] although the decreasing cost of gasoline and the later introduction of Prohibition made ethanol an impractical fuel for most users.
Chevrolet's logo is a cross
QMRThe T engine was an inline-four, with all four cylinders cast into one engine block. Such monobloc design was an uncommon practice when T production started in 1908. It lent itself to mass production, showing the Ford company's prescient focus on design for manufacturability. The head, however, was detachable, which not only aided Ford in manufacturing but also made valve jobs (cleaning, grinding, or replacement of the poppet valves) easier. The block and head were both of cast iron.
The engine's bore was 3 3⁄4 inches (95.25 mm) and its stroke was 4 inches (101.6 mm) even, for a total displacement of 177 cu in (2,900 cc). The compression ratio was low by modern standards, but typical for the era, making the engine forgiving of poor fuel quality and minimizing cranking effort at starting.
The valvetrain was a side valve (flathead) design.
The crankshaft had 3 main bearings.
The inline-four engine or straight-four engine is a type of inline internal combustion four-cylinder engine with all four cylinders mounted in a straight line, or plane along the crankcase. The single bank of cylinders may be oriented in either a vertical or an inclined plane with all the pistons driving a common crankshaft. Where it is inclined, it is sometimes called a slant-four. In a specification chart or when an abbreviation is used, an inline-four engine is listed either as I4 or L4 (for longitudinal, to avoid confusion between the digit 1 and the letter I).
The inline-four layout is in perfect primary balance and confers a degree of mechanical simplicity which makes it popular for economy cars.[1] However, despite its simplicity, it suffers from a secondary imbalance which causes minor vibrations in smaller engines. These vibrations become more powerful as engine size and power increase, so the more powerful engines used in larger cars generally are more complex designs with more than four cylinders.
Today almost all manufacturers of four-cylinder engines for automobiles produce the inline-four layout, with Subaru's flat-four engine being a notable exception, and so four-cylinder is synonymous with and a more widely used term than inline-four. The inline-four is the most common engine configuration in modern cars, while the V6 engine is the second most popular.[2] In the late 2000s (decade), with auto manufacturers making efforts to reduce emissions and increase fuel efficiency due to the high price of oil and the economic recession, the proportion of new vehicles sold in the U.S. with four-cylinder engines (largely of the inline-four type) rose from 30 percent to 47 percent between 2005 and 2008, particularly in mid-size vehicles where a decreasing number of buyers have chosen the V6 performance option.[3][4]
A flat-four or horizontally opposed-four is a type of four-cylinder engine, a flat engine with four cylinders arranged horizontally in two banks of two cylinders on each side of a central crankcase.
QMRThe Saturn Corporation is a registered trademark established on January 7, 1985 as a subsidiary of General Motors in response to the success of automobile imports in the United States.[2] The company marketed itself as a "different kind of car company", and operated somewhat independently from its parent company for a time, with its own assembly plant in Spring Hill, Tennessee, unique models, and a separate retailer network.[3]
Following the withdrawal of a bid by Penske Automotive to acquire Saturn in September 2009, General Motors discontinued the Saturn brand and ended its outstanding franchises on October 31, 2010.[1][4] All new production was halted on October 7, 2009.[5]
It's logo is an X or a cross
Subaru's logo is a lot of little crosses
Porsche's logo is a coat of arms with four parts like a quadrant
Cadillacs logo is also sort of a quadrant
Scion's label is sort of a quadrant
Lincolns logo is a quadrant cross
QMRPool checkers, also called "American pool checkers", is a variant of draughts, mainly played in the southeastern United States.
It is played on a quadrant board
No comments:
Post a Comment