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What is the term for A sequence of numbers in which the ratio between two consecutive numbers is a constant?
A geometric series.
What does a constant slope mean?
It means that the rise divided by the run for a curve has the same value. If A and B are any two points on the curve, with coordinates (Xa, Ya) and (Xb, Yb), then (Yb - Ya)/(Xb - Xa) is a constant.
What is a constant ratio of two variables that are related proportionally?
It is the constant of proportionality.
What is 26 divided by two?
26 divided by two is equal to 13
What is 144 divided by two?
144 divided by two equals 72.
Is the Harry Potter series divided in two parts?
No, but the last movie is.
What is the history of fourier series?
It is quite complicated, and starts before Fourier. Trigonometric series arose in problems connected with astronomy in the 1750s, and were tackled by Euler and others. In a different context, they arose in connection with a vibrating string (e.g. a violin string) and solutions of the wave equation.Still in the 1750s, a controversy broke out as to what curves could be represented by trigonometric series and whether every solution to the wave equation could be represented as the sum of a trigonometric series; Daniel Bernoulli claimed that every solution could be so represented and Euler claimed that arbitrary curves could not necessarily be represented. The argument rumbled on for 20 years and dragged in other people, including Laplace. At that time the concepts were not available to settle the problem.Fourier worked on the heat equation (controlling the diffusion of heat in solid bodies, for example the Earth) in the early part of the 19th century, including a major paper in 1811 and a book in 1822. Fourier had a broader notion of function than the 18th-century people, and also had more convincing examples.Fourier's work was criticised at the time, and his insistence that discontinuous functions could be represented by trigonometric series contradicted a theorem in a textbook by the leading mathematician of the time, Cauchy.Nonetheless Fourier was right; Cauchy (and Fourier, and everyone else at that time) was missing the idea of uniform convergence of a series of functions. Fourier's work was widely taken up, and also the outstanding problems (just which functions can be represented by Fourier series?; how different can two functions be if they have the same Fourier series?) were slowly solved.Source: Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972, pages 478-481, 502-514, 671-678,and 964.
Difference between fourier series and z-transform?
Laplace = analogue signal Fourier = digital signal Notes on comparisons between Fourier and Laplace transforms: The Laplace transform of a function is just like the Fourier transform of the same function, except for two things. The term in the exponential of a Laplace transform is a complex number instead of just an imaginary number and the lower limit of integration doesn't need to start at -∞. The exponential factor has the effect of forcing the signals to converge. That is why the Laplace transform can be applied to a broader class of signals than the Fourier transform, including exponentially growing signals. In a Fourier transform, both the signal in time domain and its spectrum in frequency domain are a one-dimensional, complex function. However, the Laplace transform of the 1D signal is a complex function defined over a two-dimensional complex plane, called the s-plane, spanned by two variables, one for the horizontal real axis and one for the vertical imaginary axis. If this 2D function is evaluated along the imaginary axis, the Laplace transform simply becomes the Fourier transform.
What is the term for A sequence of numbers in which the ratio between two consecutive numbers is a constant?
A geometric series.
Cross-power spectrum of two fourier transform images?
It's (I1./I2*)/(|I1./I2*|), where I2* is the complex conjugate of the Fourier transformed Image 2
Some two-way roads are divided into three lanes?
Two-way roads are divided into there lanes throughout the country. This occurs in big cities, because there is constant traffic throughout the day.
Is the figure that is multiplied by the product of the masses of two objects divided by the square of the distance between them to give the gravitational force between the two objects?
The "figure" is the gravitational constant.
Will 'Harry Potter and the Deathly Hallows' be the last movie in the series?
The Deathly Hallows is being divided into two movies. After the Deathly Hallows Part II, the series will be over.
What does a constant slope mean?
It means that the rise divided by the run for a curve has the same value. If A and B are any two points on the curve, with coordinates (Xa, Ya) and (Xb, Yb), then (Yb - Ya)/(Xb - Xa) is a constant.
What is the expression for average acceleration?
Acceleration = Change in velocity divided by the change in time. This formula only works if velocity is constant. If velocity is not constant, find the acceleration for both points in time. Then add the two accelerations and divide by 2.
Difference between fourier transform and first fourier transform?
The question almost certainly intends "fast" instead of "first". The difference between a Fourier Transform and a Fast Fourier Transform is only the amount of effort required to generate the result. Both have the same the result. The original Fourier Transform requires an amount of effort which is proportional to the square of the amount of data being used. So if the amount of data doubles, the amount of effort to calculate the result quadruples. In contrast, the subsequently discovered Fast Fourier Transform requires an amount of effort proportional to the product of the amount of data and the base-two logarithm of the amount of data. Thus, if the amount of data doubles, the amount of effort increases but by less than a quadruple. With each doubling of the data size, the amount of effort increases by a diminishing factor which slowly drops toward but never reaches two.
a container of an ideal gas is at a constant volume what occurs when the volume of the contianer is doubled from 1 liter to 2 liters?
The volume doubles
