The positivity of the difference operator with periodic conditions and its application

2016 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Fatih Sabahattin Tetikoglu
Keyword(s):  
Difference Operator ◽  
The Difference

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 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.

scholarly journals Boundary-Value Problems for Differential-Difference Equations with Incommeasurable Shifts of Arguments Reducible to Nonlocal Problems

2019 ◽  
Vol 65 (4) ◽  
pp. 613-622
Author(s):  
E. P. Ivanova
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Original Problem ◽  
Difference Operator ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Nonlocal Problems ◽  
Higher Order Terms ◽  
The Difference

We consider boundary-value problems for differential-difference equations containing incommeasurable shifts of arguments in higher-order terms. We prove that in the case of finite orbits of boundary points generated by the set of shifts of the difference operator, the original problem is reduced to the boundary-value problem for differential equation with nonlocal boundary conditions.

An Oscillation Result for Singular Neutral Equations

1994 ◽  
Vol 37 (1) ◽  
pp. 54-65
Author(s):  
István Gyori ◽  
Janos Turi
Keyword(s):  
Large Class ◽  
Difference Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Neutral Equations ◽  
Oscillation Result ◽  
The Difference ◽  
Necessary And Sufficient

AbstractIn this paper, extending the results in [ 1 ], we establish a necessary and sufficient condition for oscillation in a large class of singular (i.e., the difference operator is nonatomic) neutral equations.

A SET OF NEW PARANORMED DIFFERENCE SEQUENCE SPACES AND THEIR MATRIX TRANSFORMATIONS

2013 ◽  
Vol 06 (03) ◽  
pp. 1350040 ◽  
Author(s):  
P. Baliarsingh
Keyword(s):  
Difference Operator ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Structures ◽  
The Matrix ◽  
The Difference ◽  
Positive Integers ◽  
Difference Sequence Spaces

In this paper, by using a new difference operator Δj, the author likes to introduce new classes of paranormed difference sequence spaces X(Δj, u, v; p) for X ∈ {ℓ∞, c, c0} and investigates their topological structures, where (un) and (vn) are two sequences satisfying certain conditions. The difference operator Δjis defined by Δj(xj) = jxj- (j + 1)xj+1for all j ∈ ℕ, the set of positive integers. Also, we determine the α-, β- and γ-duals of these classes. Furthermore, the matrix transformations from these classes to the sequence spaces ℓ∞(q), c0(q) and c(q) have been characterized.

scholarly journals The factorization of the difference operator

2001 ◽  
Vol 42 (3-5) ◽  
pp. 729-733 ◽  
Author(s):  
K. Janglajew ◽  
K. Valeev
Keyword(s):  
Difference Operator ◽  
The Difference
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