A NEW KIND OF FUZZY RELATIONAL EQUATIONS

2010 ◽  
Vol 18 (03) ◽  
pp. 333-342 ◽  
Author(s):  
FENG QIN ◽  
PING FANG
Keyword(s):  
Unique Solvability ◽  
Complete Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Solution Set ◽  
Fuzzy Relational Equations ◽  
Necessary And Sufficient

In this paper, a new kind of fuzzy relational equations (FREs for short) A ∘R*x = b is first introduced, and then the problem of solving solution to the FREs is discussed, where A is an m × n matrix, x and b are an n and an m dimensional column vectors, respectively. More specifically, their solvability and unique solvability are investigated, the corresponding necessary and sufficient conditions are presented, the complete solution set is obtained. It is worth noting the method to construct the complete solution set.

On the solvability of the antiperiodic boundary value problem for systems of linear generalized differential equations

2017 ◽  
Vol 24 (2) ◽  
pp. 169-184
Author(s):  
Malkhaz Ashordia
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Spectral Type ◽  
Unique Solvability ◽  
Boundary Value ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Differential ◽  
Necessary And Sufficient

AbstractAn antiperiodic boundary value problem is considered for systems of linear generalized differential equations. A Green-type theorem on the unique solvability of the problem and representation of its solution are established. Effective necessary and sufficient conditions (of spectral type) are given for the unique solvability of the problem as well.

Summability methods which include the Riesz typical means. I

1971 ◽  
Vol 69 (1) ◽  
pp. 99-106 ◽  
Author(s):  
Dennis C. Russell
Keyword(s):  
Complete Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Alternative Form ◽  
Cesàro Summability ◽  
Abel Summability ◽  
Summability Methods ◽  
Cesaro Summability ◽  
Riesz Summability ◽  
Necessary And Sufficient

A number of special results exist for summability methods B which, include Riesz summability (R,λ,k)—for example, when B is generalized Abel summability (A,λ,ρ) [Kuttner(5)], or Riemann summability (,λ,μ) [Russell(14)], or Riemann-Cesàro summability (,λ,p,α) [Rangachari(12)], or generalized Cesàro summability (C,λ,k) [Meir (9); Borwein and Russell (l)]. The question of necessary and sufficient conditions to be satisfied by an arbitrary method B in order that B ⊇ (R,λ,k) has received an answer only for limited values of λ and k—for example, by Lorentz [(6), Theorem 10] for k = 1; the restrictions on λ in this case were removed by Maddox [(8), Theorem 1]. Thus (apart from the well-known case k = 0) the case k = 1 is the only one for which a complete solution exists, though application of a theorem of Russell [(13), Theorem 1A] yields one form of a result for 0 < k ≤ 1. Maddox's results, however, suggest an alternative form capable of generalization to all k ≥ 0, and in this paper we obtain a complete solution for 0 < k ≤ 1 in that form, without restriction on λ. We first recall the following definitions.

scholarly journals On the Directed Oberwolfach Problem with Equal Cycle Lengths

10.37236/2982 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Andrea Burgess ◽  
Mateja Šajna
Keyword(s):  
Complete Solution ◽  
Sufficient Conditions ◽  
Partial Solution ◽  
Necessary And Sufficient Conditions ◽  
Cycle Lengths ◽  
Necessary And Sufficient ◽  
Directed Cycles ◽  
Oberwolfach Problem

We examine the necessary and sufficient conditions for a complete symmetric digraph $K_n^\ast$ to admit a resolvable decomposition into directed cycles of length $m$. We give a complete solution for even $m$, and a partial solution for odd $m$.

On the Existence of Mayer’s Potential

1997 ◽  
Vol 64 (3) ◽  
pp. 606-612 ◽  
Author(s):  
V. M. Cˇovic´ ◽  
M. M. Lukacˇevic´
Keyword(s):  
Dynamical Systems ◽  
Complete Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Nonconservative Systems ◽  
Necessary And Sufficient ◽  
The Given ◽  
Special Case

A complete solution of the well-known Mayer’s problem, which is concerned with the possibility of extending Hamilton’s principle expressed in the form valid for conservative dynamical systems to one special case of nonconservative systems (Appell, 1911), is obtained. Namely, the necessary and sufficient conditions which have to be satisfied by the coefficients of the given nonconservative generalized forces so that the Mayer’s potential (and, as a consequence, the descriptive function of the system) can be constructed, are established. This result is illustrated by an example.

scholarly journals Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Zhe Chen
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Solution Set ◽  
Asymptotic Cone ◽  
Convex Optimization Problem ◽  
Composite Optimization ◽  
Convex Composite Optimization ◽  
Necessary And Sufficient

We characterize the asymptotic cone of the solution set of a convex composite optimization problem. We then apply the obtained results to study the necessary and sufficient conditions for the nonemptiness and compactness of the solution set of the problem. Our results generalize and improve some known results in literature.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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