General Solution and Observability of Singular Differential Systems with Delay

Differential Systems ◽

Exact Observability ◽

We study singular differential systems with delay. A general description for the solutions of singular differential systems with delay is given and a necessary and sufficient condition for exact observability of singular differential systems with delay is derived.

A necessary and sufficient condition of positive solutions for nonlinear singular differential systems with four-point boundary conditions

Applied Mathematics and Computation ◽

10.1016/j.amc.2009.10.044 ◽

2010 ◽

Vol 215 (10) ◽

pp. 3501-3508 ◽

Cited By ~ 8

Author(s):

Xinguang Zhang ◽

Lishan Liu

Keyword(s):

Boundary Conditions ◽

Positive Solutions ◽

Sufficient Condition ◽

Point Boundary ◽

Differential Systems ◽

A New Expression of the Hermitian Solutions to a System of Matrix Equations with Applications

Algebra Colloquium ◽

10.1142/s1005386716000195 ◽

2016 ◽

Vol 23 (01) ◽

pp. 167-180 ◽

Author(s):

Guangjing Song ◽

Shaowen Yu ◽

Ming Chen

Keyword(s):

General Solution ◽

Sufficient Condition ◽

Matrix Equations ◽

System Of Matrix Equations ◽

Hermitian Solution ◽

In this paper, a new necessary and sufficient condition for the existence of a Hermitian solution as well as a new expression of the general Hermitian solution to the system of matrix equations A1X=C1 and A3XB3=C3 are derived. The max-min ranks and inertias of these Hermitian solutions with some interesting applications are shown. In particular, the max-min ranks and inertias of the Hermitian part of the general solution to this system are presented.

Resonance and Nonresonance Periodic Value Problems of First-Order Differential Systems

Discrete Dynamics in Nature and Society ◽

10.1155/2010/863193 ◽

2010 ◽

Vol 2010 ◽

pp. 1-11 ◽

Author(s):

Fengqin Zhang ◽

Jurang Yan

Keyword(s):

Nontrivial Solution ◽

Existence And Uniqueness ◽

Sufficient Conditions ◽

Sufficient Condition ◽

Uniqueness Of Solutions ◽

Differential Systems ◽

First Order ◽

Resonance and nonresonance periodic value problems of first-order differential systems are studied. Several new existence and uniqueness of solutions for the above problems are obtained. To establish such results sufficient conditions of limit forms are given. A necessary and sufficient condition for existence of nontrivial solution is also proved.

Parametrized solutions $X$ of the system $AXA = AY A$ and $A^k Y AX = XAY A^k$

Electronic Journal of Linear Algebra ◽

10.13001/1081-3810.4051 ◽

2019 ◽

Vol 35 ◽

pp. 503-510 ◽

Cited By ~ 2

Author(s):

David Ferreyra ◽

Marina Lattanzi ◽

Fabián Levis ◽

Néstor Thome

Keyword(s):

General Solution ◽

Matrix Equation ◽

Equation System ◽

Drazin Inverse ◽

Sufficient Condition ◽

Complex Matrices ◽

The Matrix ◽

Necessary And Sufficient ◽

Parametrized Solutions

Let A and E be n × n given complex matrices. This paper provides a necessary and sufficient condition for the solvability to the matrix equation system given by AXA = AEA and AkEAX = XAEAk, for k being the index of A. In addition, its general solution is derived in terms of a G-Drazin inverse of A. As consequences, new representations are obtained for the set of all G-Drazin inverses; some interesting applications are also derived to show the importance of the obtained formulas.

A necessary and sufficient condition of existence of positive solutions for nonlinear singular differential systems

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.04.031 ◽

2007 ◽

Vol 327 (1) ◽

pp. 400-414 ◽

Cited By ~ 5

Author(s):

Xinguang Zhang ◽

Lishan Liu

Keyword(s):

Positive Solutions ◽

Sufficient Condition ◽

Differential Systems ◽

Existence Of Positive Solutions ◽

A Note on Solutions of Linear Systems

ISRN Algebra ◽

10.1155/2013/142124 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Author(s):

Branko Malešević ◽

Ivana Jovović ◽

Milica Makragić ◽

Biljana Radičić

Keyword(s):

Linear System ◽

General Solution ◽

Linear Systems ◽

Sufficient Condition ◽

Matrix Equations ◽

Different Types ◽

Free Parameters ◽

We will consider Rohde's general form of {1}-inverse of a matrix A. The necessary and sufficient condition for consistency of a linear system Ax=c will be represented. We will also be concerned with the minimal number of free parameters in Penrose's formula x=A(1)c+(I-A(1)A)y for obtaining the general solution of the linear system. These results will be applied for finding the general solution of various homogenous and nonhomogenous linear systems as well as for different types of matrix equations.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

A Necessary and Sufficient Condition of Supply and Threshold Voltages in CMOS Circuits for Minimum Energy Point Operation

10.1587/transfun.e100.a.2764 ◽

2017 ◽

Vol E100.A (12) ◽

pp. 2764-2775 ◽

Author(s):

Jun SHIOMI ◽

Tohru ISHIHARA ◽

Hidetoshi ONODERA

Keyword(s):

Minimum Energy ◽

Cmos Circuits ◽

Sufficient Condition ◽

Energy Point ◽

Threshold Voltages ◽

Necessary And Sufficient ◽

Minimum Energy Point

A Necessary and Sufficient Condition for a Local Commutative Algebra to be a Moduli Algebra: Weighted Homogeneous Case

Complex Analytic Singularities ◽

10.2969/aspm/00810687 ◽

2018 ◽

Author(s):

Stephen S.-T. Yau

Keyword(s):

Commutative Algebra ◽

Sufficient Condition ◽

Homogeneous Case ◽

Moduli Algebra ◽

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

Accounting Horizons ◽

10.2308/acch.2003.17.3.257 ◽

2003 ◽

Vol 17 (3) ◽

pp. 257-266 ◽

Cited By ~ 31

Author(s):

Mark H. Taylor ◽

F. Todd DeZoort ◽

Edward Munn ◽

Martha Wetterhall Thomas

Keyword(s):

Public Interest ◽

Auditor Independence ◽

Public Confidence ◽

Sufficient Condition ◽

Accounting Profession ◽

The Public ◽

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

10.1093/oso/9780198813972.003.0002 ◽

2018 ◽

Author(s):

Thomas Sinclair

Keyword(s):

Detailed Analysis ◽

Political Authority ◽

The State ◽

Sufficient Condition ◽

State Institutions ◽

State Of Nature ◽

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.