scholarly journals Uniqueness Theorems of Difference Operator on Entire Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jie Ding
Keyword(s):  
Difference Operator ◽  
Entire Functions ◽  
Uniqueness Theorems ◽  
The Difference

We investigate the uniqueness questions of the difference operator on entire functions and obtain three uniqueness theorems using the idea of weight sharing.

scholarly journals Uniqueness Theorems on Difference Monomials of Entire Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Gang Wang ◽  
Deng-li Han ◽  
Zhi-Tao Wen
Keyword(s):  
Finite Order ◽  
Entire Functions ◽  
Uniqueness Theorems ◽  
Complex Constant ◽  
Transcendental Entire Functions ◽  
The Difference

The aim of this paper is to discuss the uniqueness of the difference monomialsfnf(z+c). It assumed thatfandgare transcendental entire functions with finite order andEk)(1,fnf(z+c))=Ek)(1,gng(z+c)), wherecis a nonzero complex constant andn,kare integers. It is proved that if one of the following holds (i)n≥6andk=3, (ii)n≥7andk=2, and (iii)n≥10andk=1, thenfg=t1orf=t2gfor some constantst2andt3which satisfyt2n+1=1andt3n+1=1. It is an improvement of the result of Qi, Yang and Liu.

Periodic Points of the Difference Operator

1997 ◽  
Vol 28 (1) ◽  
pp. 20-26
Author(s):  
Chris Bernhardt ◽  
Thomas Yuster
Keyword(s):  
Difference Operator ◽  
Periodic Points ◽  
The Difference

scholarly journals Design of preview controller for a type of discrete-time interconnected systems

2020 ◽  
Vol 53 (3-4) ◽  
pp. 719-729
Author(s):  
Hao Xie ◽  
Fucheng Liao ◽  
Usman ◽  
Jiamei Deng
Keyword(s):  
Discrete Time ◽  
Difference Operator ◽  
Interconnected Systems ◽  
Preview Control ◽  
Interconnected System ◽  
Lyapunov Function Method ◽  
System Equations ◽  
Error System ◽  
The Difference ◽  
Theoretical Results

This article proposes and studies a problem of preview control for a type of discrete-time interconnected systems. First, adopting the technique of decentralized control, isolated subsystems are constructed by splitting the correlations between the systems. Utilizing the difference operator to the system equations and error vectors, error systems are built. Then, the preview controller is designed for the error system of each isolated subsystem. The controllers of error systems of isolated subsystems are aggregated as a controller of the interconnected system. Finally, by employing Lyapunov function method and the properties of non-singular M-matrix, the guarantee conditions for the existence of preview controllers for interconnected systems are given. The numerical simulation shows that the theoretical results are effective.

scholarly journals Dichotomy and positivity of neutral equations with nonautonomous past

2014 ◽  
Vol 8 (2) ◽  
pp. 224-242 ◽  
Author(s):  
Nguyen Huy ◽  
Pham Bang
Keyword(s):  
Exponential Dichotomy ◽  
Difference Operator ◽  
Functional Differential Equations ◽  
Sufficient Condition ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Exponentially Stable ◽  
The Difference ◽  
Functional Differential ◽  
Delay Operator

Consider the linear partial neutral functional differential equations with nonautonomous past of the form (?/?t) F(u(t, ?)) = BFu(t, ?) + ?u(t, ?), t ? 0; (? / ?t) u(t, s) = (? / ?s) u(t, s) + A(s)u(t, s), t ? 0 ? s, where the function u(?, ?) takes values in a Banach space X. Under appropriate conditions on the difference operator F and the delay operator ? we prove that the solution semigroup for this system of equations is hyperbolic (or admits an exponential dichotomy) provided that the backward evolution family U = (U(t, s))t?s?0 generated by A(s) is uniformly exponentially stable and the operator B generates a hyperbolic semigroup (etB)t?0 on X. Furthermore, under the positivity conditions on (etB)t?0, U, F and ? we prove that the above-mentioned solution semigroup is positive and then show a sufficient condition for the exponential stability of this solution semigroup.

Difference Operators in Simulation Data Warehouses

2017 ◽  
Vol 12 (2) ◽  
pp. 347-354 ◽  
Author(s):  
Jing Zhao ◽  
◽  
Yoshiharu Ishikawa ◽  
Yukiko Wakita ◽  
Kento Sugiura
Keyword(s):  
Difference Operator ◽  
Difference Operators ◽  
Observation Data ◽  
Temporal Data ◽  
Data Warehouses ◽  
Simulation Data ◽  
Tsunami Disaster ◽  
Spatio Temporal ◽  
The Difference ◽  
Mass Evacuation

In analyzing observation data and simulation results, there are frequent demands for comparing more than one data on the same subject to detect any differences between them. For example, comparison of observation data for an object in a certain spatial domain at different times or comparison of spatial simulation data with different parameters. Therefore, this paper proposes the difference operator in spatio-temporal data warehouses, which store temporal and spatial observation data and simulation data. The requirements for the difference operator are summarized, and the approaches to implement them are presented. In addition, the proposed approach is applied to the mass evacuation of simulation data in a tsunami disaster, and its effectiveness is verified. Extensions of the difference operator and their applications are also discussed.

scholarly journals Difference Equations and Sharing Values Concerning Entire Functions and Their Difference

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhiqiang Mao ◽  
Huifang Liu
Keyword(s):  
Difference Equations ◽  
Entire Functions ◽  
Value Distribution ◽  
Difference Operators ◽  
Sharing Values ◽  
Difference Analogue ◽  
The Difference ◽  
Brück Conjecture

The value distribution of solutions of certain difference equations is investigated. As its applications, we investigate the difference analogue of the Brück conjecture. We obtain some results on entire functions sharing a finite value with their difference operators. Examples are provided to show that our results are the best possible.

scholarly journals On the fine spectrum of the generalized difference operatorB(r,s)over the sequence spacesc0andc

2005 ◽  
Vol 2005 (18) ◽  
pp. 3005-3013 ◽  
Author(s):  
Bilâl Altay ◽  
Feyzı Başar
Keyword(s):  
Difference Operator ◽  
Sequence Spaces ◽  
Band Matrix ◽  
Fine Spectrum ◽  
Special Cases ◽  
The Difference ◽  
The Right

We determine the fine spectrum of the generalized difference operatorB(r,s)defined by a band matrix over the sequence spacesc0andc, and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operatorΔ, and includes as other special cases the right shift and the Zweier matrices.

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