NEW RESOLUTION OF FINITE FUZZY RELATION EQUATIONS WITH MAX-MIN COMPOSITION

2008 ◽  
Vol 16 (01) ◽  
pp. 19-33 ◽  
Author(s):  
BIH-SHEUE SHIEH
Keyword(s):  
Fast Algorithm ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fuzzy Relation ◽  
Necessary And Sufficient Conditions ◽  
Fuzzy Relation Equation ◽  
Fuzzy Relation Equations ◽  
Necessary And Sufficient

The work considers the problem of solvability of a fuzzy relation equation with max-min composition. It presents the necessary and sufficient conditions for the existence of solutions, then derives a fast algorithm for finding all minimal solutions. The results are compared with those of previous publications regarding this subject.

scholarly journals Solvability ofNth Order Linear Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
P. Almenar ◽  
L. Jódar
Keyword(s):  
Integral Operator ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Boundary ◽  
Order Linear ◽  
Linear Integral ◽  
Necessary And Sufficient

This paper presents a method that provides necessary and sufficient conditions for the existence of solutions ofnth order linear boundary value problems. The method is based on the recursive application of a linear integral operator to some functions and the comparison of the result with these same functions. The recursive comparison yields sequences of bounds of extremes that converge to the exact values of the extremes of the BVP for which a solution exists.

scholarly journals Calculation of single-layer dielectric coatings for antireflection in a given range of angles of incidence

2021 ◽  
pp. 5-13
Author(s):  
Ilya Shulman ◽  
Yana Sadovnikova ◽  
Alina Kobysh ◽  
Alexander Rogov
Keyword(s):  
Electromagnetic Wave ◽  
Existence Of Solutions ◽  
Plane Electromagnetic Wave ◽  
Sufficient Conditions ◽  
Single Layer ◽  
Necessary And Sufficient Conditions ◽  
Dielectric Coatings ◽  
Dielectric System ◽  
Necessary And Sufficient

In this work, the problem of antireflection a single-layer magneto-dielectric system is formulated when a plane electromagnetic wave passes through it in the range of angles of incidence, and necessary and sufficient conditions for the existence of solutions to this problem are obtained

scholarly journals A Nonlocal Operator Breaking the Keller–Osserman Condition

2017 ◽  
Vol 17 (4) ◽  
pp. 715-725 ◽  
Author(s):  
Raúl Ferreira ◽  
Mayte Pérez-Llanos
Keyword(s):  
Blow Up ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Nonlocal Operator ◽  
Large Solutions ◽  
Necessary And Sufficient ◽  
Semilinear Problem

AbstractThis work is concerned about the existence of solutions to the nonlocal semilinear problem\left\{\begin{aligned} &\displaystyle{-}\int_{{\mathbb{R}}^{N}}J(x-y)(u(y)-u(x% ))\,dy+h(u(x))=f(x),&&\displaystyle x\in\Omega,\\ &\displaystyle u=g,&&\displaystyle x\in{\mathbb{R}}^{N}\setminus\Omega,\end{% aligned}\right.verifying that {\lim_{x\to\partial\Omega,\,x\in\Omega}u(x)=+\infty}, known in the literature as large solutions. We find out that the relation between the diffusion and the absorption term is not enough to ensure such existence, not even assuming that the boundary datum g blows up close to {\partial\Omega}. On the contrary, the role to obtain large solutions is played only by the interior source f, which gives rise to large solutions even without the presence of the absorption. We determine necessary and sufficient conditions on f providing large solutions and compute the blow-up rates of such solutions in terms of h and f. Finally, we also study the uniqueness of large solutions.

scholarly journals Analysis of Multiterm Initial Value Problems with Caputo–Fabrizio Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Mohammed Al-Refai ◽  
Muhammed Syam
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Initial Value ◽  
The Laplace Transform ◽  
Necessary And Sufficient

In this paper, we discuss the solvability of a class of multiterm initial value problems involving the Caputo–Fabrizio fractional derivative via the Laplace transform. We derive necessary and sufficient conditions to guarantee the existence of solutions to the problem. We also obtain the solutions in closed forms. We present two examples to illustrate the validity of the obtained results.

scholarly journals Necessary and Sufficient Conditions for Set-Valued Maps with Set Optimization

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Abdessamad Oussarhan ◽  
Ikram Daidai
Keyword(s):  
Optimality Conditions ◽  
Existence Of Solutions ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Set Optimization ◽  
Contingent Derivative ◽  
Necessary And Sufficient

Optimality conditions are studied for set-valued maps with set optimization. Necessary conditions are given in terms of S-derivative and contingent derivative. Sufficient conditions for the existence of solutions are shown for set-valued maps under generalized quasiconvexity assumptions.

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