A variational approach to distribution function theory

1990 ◽  
Vol 61 (1-2) ◽  
pp. 143-160 ◽  
Author(s):  
Antoine G. Schlijper ◽  
Ryoichi Kikuchi
Keyword(s):  
Distribution Function ◽  
Variational Approach ◽  
Function Theory

scholarly journals On One Application of Infinite Systems of Functional Equations in Function Theory

2019 ◽  
Vol 74 (1) ◽  
pp. 117-144 ◽  
Author(s):  
Symon Serbenyuk
Keyword(s):  
Distribution Function ◽  
Unique Solution ◽  
Local Structure ◽  
Functional Equations ◽  
Function Theory ◽  
Shift Operator ◽  
Random Variable ◽  
System Of Functional Equations ◽  
Infinite Systems

Abstract The paper presents the investigation of applications of infinite systems of functional equations for modeling functions with complicated local structure that are defined in terms of the nega-˜Q-representation. The infinite systems of functional equations f\left( {{{\hat \varphi }^k}(x)} \right) = \tilde \beta {i_{k + 1}},k + 1 + \tilde p{i_{k + 1}},k + 1f\left( {{{\hat \varphi }^{k + 1}}(x)} \right), where x = \Delta _{{i_1}(x){i_2}(x) \ldots {i_n}(x) \ldots }^{ - \tilde Q} , and φ ̑ is the shift operator of the Q̃-expansion, are investigated. It is proved that the system has a unique solution in the class of determined and bounded on [0, 1] functions. Its analytical presentation is founded. The continuity of the solution is studied. Conditions of its monotonicity and nonmonotonicity, differential, and integral properties are studied. Conditions under which the solution of the system of functional equations is a distribution function of the random variable \eta = \Delta _{{\xi _1}\,\xi 2 \ldots {\xi _n} \ldots }^{\tilde Q} with independent Q̃-symbols are founded.

Distribution function theory for inhomogeneous fluids

1991 ◽  
Vol 95 (10) ◽  
pp. 7603-7611 ◽  
Author(s):  
A. G. Schlijper ◽  
C. K. Harris
Keyword(s):  
Distribution Function ◽  
Function Theory ◽  
Inhomogeneous Fluids

On the Statistical Distribution Function Theory of Traffic Flow

1962 ◽  
Vol 10 (2) ◽  
pp. 180-196 ◽  
Author(s):  
Robert L. Anderson ◽  
Robert Herman ◽  
I. Prigogine
Keyword(s):  
Distribution Function ◽  
Traffic Flow ◽  
Function Theory ◽  
Statistical Distribution ◽  
Statistical Distribution Function

Distribution Function Theory of Nematic Liquid Crystals

1971 ◽  
Vol 55 (9) ◽  
pp. 4512-4519 ◽  
Author(s):  
Alejandro Wulf
Keyword(s):  
Distribution Function ◽  
Liquid Crystals ◽  
Function Theory ◽  
Nematic Liquid Crystals
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