Georgii Polozii

Georgii Nikolaevich Polozii
Born	(1914-04-23)April 23, 1914 Transbaikal, Russian Empire
Died	November 26, 1968(1968-11-26) (aged 54) Kiev, Kiev Oblast, Ukrainian Soviet Socialist Republic, Soviet Union
Citizenship	Russian Empire → Soviet Union
Education	Saratov University
Known for	theory of functions of a complex variable, approximation theory and numerical analysis
Scientific career
Fields	Mathematician

Georgii Nikolaevich Polozii (23 April 1914 – 26 November 1968) was a Russian mathematician who mostly worked in pure mathematics such as complex analysis, approximation theory and numerical analysis. He also worked on elasticity theory, which is used in applied math and physics.

Education

Georgii Nikolaevich Polozii graduated from Saratov University in 1937 and stayed to teach until he moved to the University of Kiev in 1949.

Works

Polozii mostly worked in the following four areas.

Complex functions

Main article: Complex plane

He produced “original results in the theory of functions of a complex variable”

A complex function is a function whose domain and range are subsets of the complex plane. For any complex function, the values $z$ from the domain and their images $f(z)$ in the range may be separated into real and imaginary parts:

$z=x+iy\quad$ and $\quad f(z)=f(x+iy)=u(x,y)+iv(x,y)$,

where $x,y,u(x,y),v(x,y)$ are all real-valued.

In other words, a complex function $f:\mathbb {C} \to \mathbb {C}$ may be decomposed into

$u:\mathbb {R} ^{2}\to \mathbb {R} \quad$ and $\quad v:\mathbb {R} ^{2}\to \mathbb {R} ,$

i.e., into two real-valued functions ($u$, $v$) of two real variables ($x$, $y$).

The basic concepts of complex analysis are often introduced by extending the elementary real functions (e.g., exponential functions, logarithmic functions, and trigonometric functions) into a complex domain and the corresponding complex range.

Approximation theory

He developed methods to solve boundary value problems which arise in mathematical physics. His work produced the method of summary representation. He “devised a new approximation method for the solution of problems in elasticity and filtration.”

Approximation theory tries to develop simpler functions to mimic or get close to more complex ones and define the errors that can be introduced by these approximations.

Numerical analysis

Main article: Numerical analysis

He “defined the notion of derivative and integral for these functions, developed their calculus, obtained a generalised Cauchy's formula”

Theory of elasticity

Main article: Solid Mechanics

Polozii came up with a new class of (p,q) analytic functions.