Fourier sentence example
The third line gives the range of the regular diurnal inequality, the next four lines the amplitudes of the first four Fourier waves into which the regular diurnal inequality has been analysed.
Under the general heading "Analysis" occur the subheadings "Foundations of Analysis," with the topics theory of functions of real variables, series and other infinite processes, principles and elements of the differential and of the integral calculus, definite integrals, and calculus of variations; "Theory of Functions of Complex Variables," with the topics functions of one variable and of several variables; "Algebraic Functions and their Integrals," with the topics algebraic functions of one and of several variables, elliptic functions and single theta functions, Abelian integrals; "Other Special Functions," with the topics Euler's, Legendre's, Bessel's and automorphic functions; "Differential Equations," with the topics existence theorems, methods of solution, general theory; "Differential Forms and Differential Invariants," with the topics differential forms, including Pfaffians, transformation of differential forms, including tangential (or contact) transformations, differential invariants; "Analytical Methods connected with Physical Subjects," with the topics harmonic analysis, Fourier's series, the differential equations of applied mathematics, Dirichlet's problem; "Difference Equations and Functional Equations," with the topics recurring series, solution of equations of finite differences and functional equations.
For the subjects of this heading see the articles DIFFERENTIAL EQUATIONS; FOURIER'S SERIES; CONTINUED FRACTIONS; FUNCTION; FUNCTION OF REAL VARIABLES; FUNCTION COMPLEX; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; MAXIMA AND MINIMA; SERIES; SPHERICAL HARMONICS; TRIGONOMETRY; VARIATIONS, CALCULUS OF.
It is scarcely necessary to remark that in all such cases the calculation applies in the first instance to homogeneous light, and that, in accordance with Fourier's theorem, each homogeneous component of a mixture may be treated separately.
A full discussion would call for the formal application of Fourier's theorem, but some conclusions of importance are almost obvious.Advertisement
Fourier was one of the savants who accompanied Bonaparte to Egypt in 1798; and during this expedition he was called to discharge important political duties in addition to his scientific ones.
On the return of Napoleon from Elba, in 1815, Fourier published a royalist proclamation, and left Grenoble as Napoleon entered it.
In 1826 Fourier became a member of the French Academy, and in 1827 succeeded Laplace as president of the council of the Ecole Polytechnique.
As a politician Fourier achieved uncommon success, but his fame chiefly rests on his strikingly original contributions to science and mathematics.
After his death Navier completed and published Fourier's unfinished work, Analyse des equations indeterminees (1831), which contains much original matter.Advertisement
In addition to the works above mentioned, Fourier wrote many memoirs on scientific subjects, and eloges of distinguished men of science.
His works have been collected and edited by Gaston Darboux with the title Ouvres de Fourier (Paris, 1889-1890).
For a list of Fourier's publications see the Catalogue of Scientific Papers of the Royal Society of London.
Reference may also be made to Arago, "Joseph Fourier," in the Smithsonian Report (1871).
Example 3.-Analysing in this way the rotation of a rectangle filled with liquid into the two components of shear, the stream function 1//1 is to be made to satisfy the conditions v 2 /1 =0, 111+IRx 2 = IRa 2, or /11 =o when x= = a, +b1+IRx 2 = I Ra2, y ' 1 = IR(a 2 -x 2), when y = b Expanded in a Fourier series, 2 232 2 cos(2n+ I)Z?rx/a a -x 7r3 a Lim (2n+I) 3 ' (1) so that '?"Advertisement
Fourier's theorem asserts that such a curve may be built up by the superposition, or addition of ordinates, of a series of sine curves of wave-lengths X, IX, 3A, 4A...
Fourier's theorem can also be usefully applied to the disturbance of a source of sound under certain conditions.
Now we may resolve these trains by Fourier's theorem into harmonics of wave-lengths X, 2X, 3A, &c., where X=2AB and the conditions as to the values of y can be shown to require that the harmonics shall all have nodes, coinciding with the nodes of the fundamental curve.
If then we resolve Ahbkc into harmonics by Fourier's theorem, we may follow the motion of the separate harmonics, and their superposition will give the form of the string at any instant.
We see, then, that the conditions for the application of Fourier's theorem are equivalent to saying that all disturbances will travel along the system with the same velocity.Advertisement
In many vibrating systems this does not hold, and then Fourier's theorem is no longer an appropriate resolution.
In March 1842 The Tribune began to give one column daily to a discussion of the doctrines of Charles Fourier, contributed by Albert Brisbane.
Greeley dissented from many of Fourier's propositions, and in later years was careful to explain that the principle of association for the common good of working men and the elevation of labour was the chief feature which attracted him.
This analogy is useful because the application of Fourier's analysis to the optical theory of spectroscopes has been doubted, and it may be urged in answer to the objections raised that the instrument acts in all respects like a mechanical analyser,' the applicability of which has never been called into question.
Graham showed that the diffusion was approximately proportional to the difference in concentration, and on these lines a theory of diffusion was founded on the lines of Fourier's treatment of the conduction of heat.Advertisement
The mathematical theory of conduction of heat was developed early in the 19th century by Fourier and other workers, and was brought to so high a pitch of excellence that little has remained for later writers to add to this department of the subject.
Fourier need not be considered in detail here, as they are in many cases of mathematical rather than physical interest.
To take the simple case of the " wall " or flat plate considered by Fourier for the definition of thermal conductivity, suppose that a quantity of heat Q passes in the time T through an area A of a plate of conductivity k and thickness x, the sides of which are constantly maintained at temperatures B' and 8".
Fourier defined another constant expressing the rate of loss of heat at a bounding surface per degree of difference of temperature between the surface of the body and its surroundings.
With a view to more minute examination, the annual frequency can be expressed in Fourier series, whose terms represent waves, whose periods are 12, 6, 4, 3, &c. months.Advertisement
Ohm's law, as it is called, was based upon an analogy with the flow of heat in a circuit, discussed by Fourier.
C. Fourier's doctrines, as modified by Albert Brisbane (1809-1890), had gained in the minds of Ripley and many of his associates, combined to change the whole plan of the community.
Whatever the deformation of the originally straight boundary of the axial section may be, it can be resolved by Fourier's theorem into deformations of the harmonic type.
Becoming imbued, however, with the phalansterian ideas of Francois Fourier, he resigned his commission in 1831, in order to devote himself to advancing the doctrines of his master.
On the death of Fourier in 1837 he became the acknowledged head of the movement, and took charge of La Phalange, the organ of Fourierism.Advertisement
Fourier, has been of immense and ever increasing value in physical applications of mathematics.
He strongly detested the prurient immorality of the schools of Saint-Simon and Fourier.
The Mecanique celeste, in which Laplace welded into a whole the items of knowledge accumulated by the labours of a century, has been termed the " Almagest of the 18th century " (Fourier).
Fourier for the propagation of heat; and if, in Fourier's solution of any problem of heat-conduction, we change the word "temperature" to "potential" and write "electric current" instead of "flux of heat," we have the solution of a corresponding problem of electric conduction.
The basis of Fourier's work was his clear conception and definition of conductivity.Advertisement
Following a section on normed linear spaces, we will consider periodic approximation using classical Fourier series.
Then = n (f g ). In other words, the discrete Fourier transform maps convolution to pointwise multiplication.
Hamiltonian matrix is then calculated using the discrete Fast Fourier Transform method to compute the kinetic energy part of the operator.
The interaction of chitosan and indomethacin after impregnation was then studied by Fourier transform infrared (FTIR) and Raman spectroscopy, respectively.
This is recorded by a high sample rate oscilloscope and a fast Fourier transform (FFT) analysis is performed on the collected signal.Advertisement
Abstract Fourier decomposition is a well-established technique used in the study of stellar pulsation.
In AutoSignal, the Fourier basis functions are reported as phase bearing sinusoids.
Additional species can be measured with portable Fourier transform infrared spectrometers.
Fourier transform infrared spectroscopy (FTIR) can be used to assess the state of cure of thermoset resins.
The alteration that takes place in the regular diurnal inequality throughout the year is best seen by analysing it into a Fourier series of the type c 1 sin (t+ a l) +c2 sin (2t+ a 2)+c 3 sin (3t+a3)+c4 sin (4t+a 4)+..Advertisement
At Potsdam the data represent the arithmetic means derived from the Fourier analysis for the individual months comprising the season.
Debarred from entering the army on account of his lowness of birth and poverty, he was appointed 1 Several experiments were made to this end in the United States (see Communism) by American followers of Fourier, whose doctrines were introduced there by Albert Brisbane (1809-1890).
Any periodic curve may be resolved into sine or harmonic curves by Fourier's theorem.
When you perform Fourier analysis, you assume that the signal is composed of sine waves of different frequencies.
You may have to play around with the ranges of the slant plane Fourier map depending on the structure.