Examples of using Several variables in English and their translations into Tagalog
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Perhaps his most important contribution was to the calculus of several variables.
He also extended his transform to several variables and applied it to the solution of partial differential equations.
He contributed important results to the theory of functions of several variables.
The amount of chromic acid mist generated depends on several variables such as part loading, time, current density and concentration.
Of course the cost of obtaining andstarting a franchise depends on several variables.
Hörmander's text, An Introduction to Complex Analysis in Several Variables, has become a classic dealing with the theory of functions of several complex variables. .
The main theme underlying the book is the problem of solving equations of systems of polynomials in several variables.
Played an important role in the development of the theory of the kernel and its generalisations to several variables, notably to pseudo-conformal transformations in space of more than three dimensions.
Whether you opt for woven fabrics, ie simple, non-stretchy cotton fabrics, or jersey, sweat, fleece, Niki or plush, of course,depends on several variables.
Bochner found that the Riemann Localisation Theorem was not valid for Fourier series of several variables(1935-1936), which led him indirectly to consider functions of several complex variables(1937).
Among work undertaken after this was work on the representation of rational functions as sums of squares, integral points on certain elliptic curves, Kummer sums, andon factorising polynomials in several variables.
Blumenthal did the first pioneering work in a programme outlined by Hilbert with the aim of creating a theory of modular functions of several variables that should be just as important in number theory and geometry as the theory of modular functions of one variable was at the beginning of the[20th] century.
Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.
Its contents were: numbers, the function concept with Weierstrass's power series approach, continuity and differentiability, analytic continuation, points of singularity,analytic functions of several variables, in particular Weierstrass's"preparation theorem", and contour integrals.
While he taught at these schools he was working on his habilitation thesis, still being advised by Carathéodory, and he submitted this work on partial andtotal differentiability of functions of several variables and about the transformation of double integrals to Berlin in 1919.
For in the field of real variable Marcinkiewicz had exceptionally strong intuition and technique, and the results he obtained in the theory of conjugate functions,had they been extended to functions of several variables might have given(as we see clearly now) a strong push to the theory of partial differential equations.
(iii) partial differential equations connected with several complex variables;
He worked on the theory of functions of several complex variables.
All advanced calculus books now use his approach to functions of several complex variables.
Poincaré is also considered the originator of the theory of analytic functions of several complex variables.
In this area he worked on differential equations,analytic functions and functions of several complex variables.
He became interested in unsolved problems in the theory of functions of several complex variables while working in Paris.
He has significantly influenced number theory, algebraic geometry,partial differential equations, several complex variables, and the theory of finite groups.
Lefschetz worked on results which provided a deep generalisation of Emile Picard 's theorems in function theory to several complex variables.
In particular he studied automorphic functions in several complex variables, Siegel's modular functions, which have led to a much deeper understanding.
His research was summarised in Several Complex Variables(1948), written with W T Martin, which was the first American book on the subject.
His work is in many areas of mathematics including differential equations, functions of a complex variable, functions of several complex variables, measure theory and differential geometry.
Chandrasekharan in describes Bombieri's contributions to the distribution of primes, to univalent functions andthe local Bieberbach conjecture and to functions of several complex variables.
The publication in 1934 of a monograph by Behnke-Thullen marked a crucial stage in the development of the theory of analytic functins of several complex variables.
Siegel enjoyed teaching, however, even elementary courses, and he published textbooks on the theory of numbers, celestial mechanics, andthe theory of functions of several complex variables.