Construction of a hypercomplex system from an Urbanik algebra

1987 ◽  
Vol 38 (6) ◽  
pp. 679-682
Author(s):  
I. D. Ol'shanetskii
Keyword(s):  
Hypercomplex System

DIFFERENTIAL EQUATIONS IN A HYPERCOMPLEX SYSTEM

2020 ◽  
Vol 69 (1) ◽  
pp. 7-11
Author(s):  
A.K. Abirov ◽  
◽  
N.K. Shazhdekeeva ◽  
T.N. Akhmurzina ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Inhomogeneous System ◽  
Homogeneous Solutions ◽  
First Order ◽  
Zero Divisors ◽  
Hypercomplex System ◽  
Independent Variable ◽  
The Right

The article considers the problem of solving an inhomogeneous first-order differential equation with a variable with a constant coefficient in a hypercomplex system. The structure of the solution in different cases of the right-hand side of the differential equation is determined. The structure of solving the equation in the case of the appearance of zero divisors is shown. It turns out that when the component of a hypercomplex function is a polynomial of an independent variable, the differential equation turns into an inhomogeneous system of real variables from n equations and its solution is determined by certain methods of the theory of differential equations. Thus, obtaining analytically homogeneous solutions of inhomogeneous differential equations in a hypercomplex system leads to an increase in the efficiency of modeling processes in various fields of science and technology.

scholarly journals Lévy Khinchin Formula on Commutative Hypercomplex System

2008 ◽  
Vol 48 (4) ◽  
pp. 559-575 ◽  
Author(s):  
Ahmed Moustfa Zabel ◽  
Buthinah Abdullateef Bin Dehaish
Keyword(s):  
Hypercomplex System

Nuclear function spaces on the base of a hypercomplex system

1983 ◽  
Vol 35 (1) ◽  
pp. 8-15 ◽  
Author(s):  
Yu. M. Berezanskii ◽  
A. A. Kalyuzhnyi
Keyword(s):  
Function Spaces ◽  
Nuclear Function ◽  
Hypercomplex System

scholarly journals Hypercomplex systems and non-Gaussian stochastic solutions of χ-Wick-type (3+1)-dimensional modified Benjamin-Bona-Mahony equation

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 209-223
Author(s):  
Mohammed Zakarya
Keyword(s):  
White Noise ◽  
Wick Product ◽  
Hermite Transform ◽  
Wave Solutions ◽  
Hypercomplex System ◽  
Non Gaussian ◽  
Type 3

In this paper, we seek non-Gaussian stochastic solutions of ?-Wick-type stochastic (3+1)-dimensional modified Benjamin-Bona-Mahony equations. Using the generalized modified tanh-coth method, the connection between hypercomplex system and transforming white noise theory, ?-Wick product and ?-Hermite transform, we generate a new set of exact travelling non-Gaussian wave solutions for the (3+1)-dimensional modified Benjamin-Bona-Mahony equations. This set contains solutions with non-Gaussian parameters of exponential, hyperbolic, and trigonometric types.

scholarly journals Exponentially Convex Functions on Hypercomplex Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Buthinah A. Bin Dehaish
Keyword(s):  
Convex Functions ◽  
Natural Generalization ◽  
Hypercomplex System ◽  
Exponentially Convex Functions ◽  
Definition Of ◽  
Structure Measure

A hypercomplex system (h.c.s.)L1(Q,m)is, roughly speaking, a space which is defined by a structure measure(c(A,B,r),(A,B∈ℬ(Q))), such space has been studied by Berezanskii and Krein. Our main result is to define the exponentially convex functions (e.c.f.) on (h.c.s.), and we will study their properties. The definition of such functions is a natural generalization of that defined on semigroup.

scholarly journals Hypercomplex systems and non-Gaussian stochastic solutions of χ-Wick-type (3+1)-dimensional modified Benjamin-Bona-Mahony equation

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 209-223
Author(s):  
Mohammed Zakarya
Keyword(s):  
White Noise ◽  
Wick Product ◽  
Hermite Transform ◽  
Wave Solutions ◽  
Hypercomplex System ◽  
Non Gaussian ◽  
Type 3

In this paper, we seek non-Gaussian stochastic solutions of ?-Wick-type stochastic (3+1)-dimensional modified Benjamin-Bona-Mahony equations. Using the generalized modified tanh-coth method, the connection between hypercomplex system and transforming white noise theory, ?-Wick product and ?-Hermite transform, we generate a new set of exact travelling non-Gaussian wave solutions for the (3+1)-dimensional modified Benjamin-Bona-Mahony equations. This set contains solutions with non-Gaussian parameters of exponential, hyperbolic, and trigonometric types.

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