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Multiplier
Multiplier may refer to: Mathematics * Multiplier (coefficient), the number of multiples being computed in multiplication, also known as a coefficient in algebra * Lagrange multiplier, a scalar variable used in mathematics to solve an optimisation problem for a given constraint * Multiplier (Fourier analysis), an operator that multiplies the Fourier coefficients of a function by a specified function (known as the symbol) * Multiplier of orbit, a formula for computing a value of a variable based on its own previous value or values; see Periodic points of complex quadratic mappings * Characteristic multiplier, an eigenvalue of a monodromy matrix * Multiplier algebra, a construction on C*-Algebras and similar structures Electrical engineering * Binary multiplier, a digital circuit to perform rapid multiplication of two numbers in binary representation * Analog multiplier, a device that multiplies two analog signals * Frequency multiplier, a device that generates a signal at an i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplier (Fourier Analysis)
In Fourier analysis, a multiplier operator is a type of linear operator, or transformation of functions. These operators act on a function by altering its Fourier transform. Specifically they multiply the Fourier transform of a function by a specified function known as the multiplier or symbol. Occasionally, the term ''multiplier operator'' itself is shortened simply to ''multiplier''. In simple terms, the multiplier reshapes the frequencies involved in any function. This class of operators turns out to be broad: general theory shows that a translation-invariant operator on a group which obeys some (very mild) regularity conditions can be expressed as a multiplier operator, and conversely. Many familiar operators, such as translations and differentiation, are multiplier operators, although there are many more complicated examples such as the Hilbert transform. In signal processing, a multiplier operator is called a "filter", and the multiplier is the filter's frequency response ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fiscal Multiplier
In economics, the fiscal multiplier (not to be confused with the money multiplier) is the ratio of change in national income arising from a change in government spending. More generally, the exogenous spending multiplier is the ratio of change in national income arising from any autonomous change in spending (including private investment spending, consumer spending, government spending, or spending by foreigners on the country's exports). When this multiplier exceeds one, the enhanced effect on national income may be called the multiplier effect. The mechanism that can give rise to a multiplier effect is that an initial incremental amount of spending can lead to increased income and hence increased consumption spending, increasing income further and hence further increasing consumption, etc., resulting in an overall increase in national income greater than the initial incremental amount of spending. In other words, an initial change in aggregate demand may cause a change in ag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voltage Multiplier
280px, Villard cascade voltage multiplier. A voltage multiplier is an electrical circuit that converts AC electrical power from a lower voltage to a higher DC voltage, typically using a network of capacitors and diodes. Voltage multipliers can be used to generate a few volts for electronic appliances, to millions of volts for purposes such as high-energy physics experiments and lightning safety testing. The most common type of voltage multiplier is the half-wave series multiplier, also called the Villard cascade (but actually invented by Heinrich Greinacher). Operation Assuming that the peak voltage of the AC source is +Us, and that the C values are sufficiently high to allow, when charged, that a current flows with no significant change in voltage, then the (simplified) working of the cascade is as follows: # negative peak (−Us): The C1 capacitor is charged through diode D1 to Us V ( potential difference between left and right plate of the capacitor is Us) # positive p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Multiplier
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange. The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a reformulation of the original problem, known as the Lagrangian function. The method can be summarized as follows: in order to find the maximum or minimum of a function f(x) subjected to the equality constraint g(x) = 0, form the Lagrangian function :\mathcal(x, \lambda) = f(x) + \lambda g(x) and find the stationary points of \mathcal considered as a function of x and the Lagrange ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Money Multiplier
In monetary economics, a money multiplier is one of various closely related ratios of commercial bank money to central bank money (also called the monetary base) under a fractional-reserve banking system. It relates to the ''maximum'' amount of commercial bank money that can be created, given a certain amount of central bank money. In a fractional-reserve banking system that has legal reserve requirements, the total amount of loans that commercial banks are allowed to extend (the commercial bank money that they can legally create) is equal to a multiple of the amount of reserves. This multiple is the reciprocal of the reserve ratio minus one, and it is an economic multiplier. The actual ratio of money to central bank money, also called the money multiplier, is lower because some funds are held by the non-bank public as currency. Also, banks may hold excess reserves, being reserves above the reserve requirement set by the central bank. Although the money multiplier concept is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplier (economics)
In macroeconomics, a multiplier is a factor of proportionality that measures how much an endogenous variable changes in response to a change in some exogenous variable. For example, suppose variable ''x'' changes by ''k'' units, which causes another variable ''y'' to change by ''M'' × ''k'' units. Then the multiplier is ''M''. Common uses Two multipliers are commonly discussed in introductory macroeconomics. Commercial banks create money, especially under the fractional-reserve banking system used throughout the world. In this system, money is created whenever a bank gives out a new loan. This is because the loan, when drawn on and spent, mostly finishes up as a deposit back in the banking system and is counted as part of money supply. After putting aside a part of these deposits as mandated bank reserves, the balance is available for the making of further loans by the bank. This process continues multiple times, and is called the multiplier effect. The multiplier m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analog Multiplier
In electronics, an analog multiplier is a device that takes two analog signals and produces an output which is their product. Such circuits can be used to implement related functions such as ''squares'' (apply same signal to both inputs), and ''square roots''. An electronic analog multiplier can be called by several names, depending on the function it is used to serve (see analog multiplier applications). Voltage-controlled amplifier versus analog multiplier If one input of an analog multiplier is held at a steady-state voltage, a signal at the second input will be scaled in proportion to the level on the fixed input. In this case, the analog multiplier may be considered to be a voltage controlled amplifier. Obvious applications would be for electronic volume control and automatic gain control (AGC). Although analog multipliers are often used for such applications, voltage-controlled amplifiers are not necessarily true analog multipliers. For example, an integrated circuit des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Multiplier
In electronics, a frequency multiplier is an electronic circuit that generates an output signal and that output frequency is a harmonic (multiple) of its input frequency. Frequency multipliers consist of a nonlinear circuit that distorts the input signal and consequently generates harmonics of the input signal. A subsequent bandpass filter selects the desired harmonic frequency and removes the unwanted fundamental and other harmonics from the output. Frequency multipliers are often used in frequency synthesizers and communications circuits. It can be more economical to develop a lower frequency signal with lower power and less expensive devices, and then use a frequency multiplier chain to generate an output frequency in the microwave or millimeter wave range. Some modulation schemes, such as frequency modulation, survive the nonlinear distortion without ill effect (but schemes such as amplitude modulation do not). Frequency multiplication is also used in nonlinear optics. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CPU Multiplier
In computing, the clock multiplier (or CPU multiplier or bus/core ratio) sets the ratio of an internal CPU clock rate to the externally supplied clock. A CPU with a 10x multiplier will thus see 10 internal cycles (produced by PLL-based frequency multiplier circuitry) for every external clock cycle. For example, a system with an external clock of 100 MHz and a 36x clock multiplier will have an internal CPU clock of 3.6 GHz. The external address and data buses of the CPU (often collectively termed front side bus (FSB) in PC contexts) also use the external clock as a fundamental timing base; however, they could also employ a (small) multiple of this base frequency (typically two or four) to transfer data faster. The internal frequency of microprocessors is usually based on FSB frequency. To calculate internal frequency the CPU multiplies bus frequency by a number called the clock multiplier. For calculation, the CPU uses actual bus frequency, and not effective bus frequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Multiplier
A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic techniques can be used to implement a digital multiplier. Most techniques involve computing the set of ''partial products,'' which are then summed together using binary adders. This process is similar to long multiplication, except that it uses a base-2 ( binary) numeral system. History Between 1947 and 1949 Arthur Alec Robinson worked for English Electric Ltd, as a student apprentice, and then as a development engineer. Crucially during this period he studied for a PhD degree at the University of Manchester, where he worked on the design of the hardware multiplier for the early Mark 1 computer. However, until the late 1970s, most minicomputers did not have a multiply instruction, and so programmers used a "multiply routine" which repeatedly shifts and accumulates partial results, often written using loop unwinding. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplier (coefficient)
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a ''product''. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''. Both numbers can be referred to as ''factors''. :a\times b = \underbrace_ For example, 4 multiplied by 3, often written as 3 \times 4 and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: :3 \times 4 = 4 + 4 + 4 = 12 Here, 3 (the ''multiplier'') and 4 (the ''multiplicand'') are the ''factors'', and 12 is the ''product''. One of the main properties of multiplication is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Force Multiplier
In military science, force multiplication or a force multiplier is a factor or a combination of factors that gives personnel or weapons (or other hardware) the ability to accomplish greater feats than without it. The expected size increase required to have the same effectiveness without that advantage is the ''multiplication factor''. For example, if a technology like GPS enables a force to accomplish the same results as a force five times as large without GPS, then the multiplier is five. Such estimates are used to justify the investment for force multipliers. History Notable historical examples of force multiplication include: * Fortifications: e.g. the Theodosian Wall of Constantinople * Reliance on air force by the Coalition in the Gulf War and the 2003 invasion of Iraq Doctrinal changes In the First World War, the Germans experimented with what were called "storm tactics", where a small group of highly trained soldiers ( stormtroopers) would open a salient through whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
