Approximating harmonic functions onRn with one function of a single complex variable

2005 ◽  
Vol 21 (5) ◽  
pp. 905-917 ◽  
Author(s):  
R. J. Whitley ◽  
T. V. Hromadka
Keyword(s):  
Complex Variable ◽  
Harmonic Functions ◽  
Single Complex

Non-Linear A-Proper Mappings of the Analytic Type

1973 ◽  
Vol 25 (3) ◽  
pp. 468-474 ◽  
Author(s):  
A. J. B. Potter
Keyword(s):  
Banach Space ◽  
Open Subset ◽  
Complex Variable ◽  
Complex Banach Space ◽  
Non Linear ◽  
Single Complex

Let Y be a complex Banach space, U an open subset of Y, f a mapping of U into Y. Then f is said to be complex analytic if for each pair of elements x and y of Y with x in U, the function f(x + ξy) of the single complex variable ξ is analytic in ξ on some neighbourhood of the origin.

Entire Mean Periodic Functions

1975 ◽  
Vol 27 (4) ◽  
pp. 805-818 ◽  
Author(s):  
P. G. Laird
Keyword(s):  
Entire Function ◽  
Complex Variable ◽  
Entire Functions ◽  
Complex Numbers ◽  
Periodic Functions ◽  
Exponential Polynomials ◽  
Single Complex ◽  
Compact Subsets

Let H denote the set of all entire functions of a single complex variable equipped with the topology of convergence uniform on all compact subsets of C, the set of complex numbers. Then an entire function f is mean periodic if the subspace spanned by f and its complex translates is not dense in H. It was shown by Schwartz [13, p. 922] in 1947, to whom this definition is due, that any such function is the limit in H of a certain sequence of exponential polynomials.

scholarly journals Solutions for systems of complex Fermat type partial differential-difference equations with two complex variables

2021 ◽  
Vol 6 (11) ◽  
pp. 11796-11814
Author(s):  
Hong Li ◽  
◽  
Keyu Zhang ◽  
Hongyan Xu ◽  
◽  
...  
Keyword(s):  
Finite Order ◽  
Difference Equations ◽  
Complex Variable ◽  
Nevanlinna Theory ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Systems Of Equations ◽  
Entire Solutions ◽  
Partial Differential ◽  
Single Complex

<abstract><p>By making use of the Nevanlinna theory and difference Nevanlinna theory of several complex variables, we investigate some properties of the transcendental entire solutions for several systems of partial differential difference equations of Fermat type, and obtain some results about the existence and the forms of transcendental entire solutions of the above systems, which improve and generalize the previous results given by Cao, Gao, Liu <sup>[<xref ref-type="bibr" rid="b5">5</xref>,<xref ref-type="bibr" rid="b24">24</xref>,<xref ref-type="bibr" rid="b39">39</xref>]</sup>. Some examples are given show that there exist some significant differences in the forms of transcendental entire solutions with finite order of the systems of equations with between several complex variables and a single complex variable.</p></abstract>

TO THE QUESTION OF THE SYSTEMATIC NATURE OF ELECTRONIC EDUCATIONAL MATERIALS FOR HIGHER EDUCATION

2019 ◽  
pp. 54-62
Author(s):  
K. R. Ovchinnikova
Keyword(s):  
Learning Process ◽  
Information Technologies ◽  
Electronic Materials ◽  
Subject Area ◽  
Design Activity ◽  
Learning Technology ◽  
Educational Materials ◽  
Scientific Publications ◽  
Structured Information ◽  
Single Complex

The relevance of the issue under consideration in the article is connected with the confusion in scientific publications of the concepts of “electronic educational materials” and “electronic educational resources”. The article discusses the concept of “electronic educational materials” from the perspective of general systems theory. And their system character is proved. This allows them to be represented as a single complex of structured information of a specific subject area and didactic materials. These didactic materials support the learning process at all stages of its didactic cycle in accordance with the chosen learning technology based on the didactic capabilities of information technologies. It is concluded that the system of high school electronic materials allows to expand the boundaries of the design activity of the teacher, provide management of the student’s thinking activity, to implement a competence approach to the learning process at university

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