scholarly journals On the Perron-Frobenius Theory of Mv-matrices and equivalent properties to eventually exponentially nonnegative matrices

2019 ◽  
Vol 35 ◽  
pp. 424-440
Author(s):  
Thaniporn Chaysri ◽  
Dimitrios Noutsos
Keyword(s):  
Necessary Conditions ◽  
Nonnegative Matrix ◽  
Nonnegative Matrices ◽  
Numerical Examples ◽  
Generalized Eigenvectors ◽  
Sufficient And Necessary Conditions ◽  
Left And Right ◽  
Equivalent Properties

Mv−matrix is a matrix of the form A = sI −B, where 0 ≤ ρ(B) ≤ s and B is an eventually nonnegative matrix. In this paper, Mv−matrices concerning the Perron-Frobenius theory are studied. Specifically, sufficient and necessary conditions for an Mv−matrix to have positive left and right eigenvectors corresponding to its eigenvalue with smallest real part without considering or not if index0B ≤ 1 are stated and proven. Moreover, analogous conditions for eventually nonnegative matrices or Mv−matrices to have all the non Perron eigenvectors or generalized eigenvectors not being nonnegative are studied. Then, equivalent properties of eventually exponentially nonnegative matrices and Mv−matrices are presented.  Various numerical examples are given to support our theoretical findings.

A JOINT EOQ MODEL FOR SUPPLIER AND RETAILER WITH DETERIORATING ITEMS

2004 ◽  
Vol 21 (02) ◽  
pp. 163-178 ◽  
Author(s):  
CHINHO LIN ◽  
YIHSU LIN
Keyword(s):  
Necessary Conditions ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Solution Procedure ◽  
Sensitivity Analyses ◽  
Mutual Cooperation ◽  
Total Cost ◽  
Numerical Examples ◽  
Eoq Model ◽  
Sufficient And Necessary Conditions

The paper studies the joint inventory model between supplier and retailer relying on mutual cooperation. Unlike other studies, the deteriorated rate and partial back-ordering are consistent with assumptions for dealing with more general cases. Since it is difficult to solve this problem directly, we derived the sufficient and necessary conditions in the planning horizon, and proposed a procedure to find the optimal solution. Numerical examples and sensitivity analyses are also provided to illustrate the solution procedure. The results reveal that the extensions of the model provide a wider and reasonable situation in practice, and that they also reduce the total cost.

scholarly journals ON NONNEGATIVE MATRICES WITH A FULLY CYCLIC PERIPHERAL SPECTRUM

1990 ◽  
Vol 21 (1) ◽  
pp. 65-70
Author(s):  
Bit-Shun Tam
Keyword(s):  
Spectral Radius ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Nonnegative Matrix ◽  
Nonnegative Matrices ◽  
Complex Matrix ◽  
Peripheral Spectrum ◽  
Rho A ◽  
Square Complex

Let $A$ be a square complex matrix. We denote by $\rho(A)$ the spectral radius of $A$. The set of eigenvalues of $A$ with modulus $\rho(A)$ is called the peripheral spectrum of $A$. The latter set is said to to be fully cyclic if whenever $\rho(A)\alpha x =Ax$, $x\neq 0$, $|a|= 1$, then $|x|(sgn \ x)^k$ is an eigenvector of $A$ corresponding to $\rho(A)\alpha^k$ for all integers $k$. In this paper we give some necessary conditions and a set of sufficient conditions for a nonnegative matrix to have a fully cyclic peripheral spectrum. Our conditions are given in terms of the reduced graph of a nonnegative matrix.

scholarly journals Controllability of Multiagent Systems with a Directed Tree

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Wang ◽  
Xiao Han
Keyword(s):  
Multiagent Systems ◽  
Multiagent System ◽  
Necessary Conditions ◽  
New Method ◽  
Information Communication ◽  
Controllability Problem ◽  
Directed Tree ◽  
Numerical Examples ◽  
Sufficient And Necessary Conditions ◽  
Theoretical Results

This paper addresses the controllability problem of multiagent systems with a directed tree based on the classic agreement protocol, in which the information communication topologies being a directed tree and containing a directed tree are both investigated. Different from the literatures, a new method, the star transform, is proposed to study the controllability of multiagent systems with directed topology. Some sufficient and necessary conditions are given for the controllability of such multiagent system. Numerical examples and simulations are proposed to illustrate the theoretical results.

C∗-algebras defined by amalgamated duplication of C∗-algebras

2019 ◽  
pp. 2150019
Author(s):  
Ali Ebadian ◽  
Ali Jabbari
Keyword(s):  
Banach Algebra ◽  
Necessary Conditions ◽  
Approximate Identity ◽  
C Algebras ◽  
Sufficient And Necessary Conditions ◽  
Amalgamated Duplication ◽  
Left And Right

Let [Formula: see text] and [Formula: see text] be two [Formula: see text]-algebras such that [Formula: see text] is a Banach [Formula: see text]-bimodule with the left and right compatible action of [Formula: see text] on [Formula: see text]. We define [Formula: see text] as a [Formula: see text]-algebra, where it is a strongly splitting [Formula: see text]-algebra extension of [Formula: see text] by [Formula: see text]. Normal, self-adjoint, unitary, invertible and projection elements of [Formula: see text] are characterized; sufficient and necessary conditions for existing unit and bounded approximate identity of [Formula: see text] as a Banach algebra and as a [Formula: see text]-algebra are given. We characterize ∗-automorphisms on [Formula: see text] and give some results related to ∗-homomorphisms, ∗-representations and completely bounded maps on this [Formula: see text]-algebra. Also, we have constructed a new Hilbert [Formula: see text]-module [Formula: see text] over [Formula: see text], where [Formula: see text] is a Hilbert [Formula: see text]-module over [Formula: see text] and [Formula: see text] is a Hilbert [Formula: see text]-module over [Formula: see text].

scholarly journals Controllability of Second-Order Multiagent Systems with Multiple Leaders and General Dynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Bo Liu ◽  
Hongke Feng ◽  
Li Wang ◽  
Rong Li ◽  
Junyan Yu ◽  
...  
Keyword(s):  
Multiagent Systems ◽  
Multiagent System ◽  
Necessary Conditions ◽  
Second Order ◽  
The Other ◽  
Numerical Examples ◽  
General Dynamics ◽  
Sufficient And Necessary Conditions ◽  
Multiple Leaders ◽  
Theoretical Results

This paper proposes a new second-order discrete-time multiagent model and addresses the controllability of second-order multiagent system with multiple leaders and general dynamics. The leaders play an important role in governing the other member agents to achieve any desired configuration. Some sufficient and necessary conditions are given for the controllability of the second-order multiagent system. Moreover, the speed controllability of the second-order multiagent system with general dynamics is discussed. Particularly, it is shown that the controllability of the whole system relies on the number of leaders and the connectivity between the leaders and the members. Numerical examples illustrate the theoretical results.

scholarly journals Strict-Sense Nonblocking Conditions for the log2⁡N-1 Multirate Switching Fabric for the Discrete Bandwidth Model

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Remigiusz Rajewski
Keyword(s):  
Necessary Conditions ◽  
Strict Sense ◽  
Optical Elements ◽  
Numerical Examples ◽  
Switching Fabric ◽  
Sufficient And Necessary Conditions ◽  
Switching Fabrics

The article discusses the strict-sense nonblocking conditions derived for the log2⁡N-1 multirate switching fabric for the discrete bandwidth model at the connection level. Architecture of the log2⁡N-1 switching fabric was described in previous study; however, conditions for the multirate discrete bandwidth model as well as comparison with different structures have not been published before. Both sufficient and necessary conditions were introduced and proved in this study. A few numerical examples which help to understand an idea of the multirate bandwidth model for the log2⁡N-1 switching fabrics were delivered as well. Additionally a comparison of achieved results to the banyan switching structures and a comparison of the costs of all mentioned in this study structures expressed as the number of optical elements were done.

scholarly journals Controllability of conformable differential systems

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Xiaowen Wang ◽  
JinRong Wang ◽  
Michal Fečkan
Keyword(s):  
Fixed Point ◽  
Necessary Conditions ◽  
Complete Controllability ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Differential Systems ◽  
Numerical Examples ◽  
Controllability Of Systems ◽  
Sufficient And Necessary Conditions ◽  
Theoretical Results ◽  
Controllability Result

This paper deals with complete controllability of systems governed by linear and semilinear conformable differential equations. By establishing conformable Gram criterion and rank criterion, we give sufficient and necessary conditions to examine that a linear conformable system is null completely controllable. Further, we apply Krasnoselskii’s fixed point theorem to derive a completely controllability result for a semilinear conformable system. Finally, three numerical examples are given to illustrate our theoretical results.  

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

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