Given a T-indistinguishability operator E defined between some fuzzy subsets of a universe of discourse X, this paper studies three ways to generate an indistinguishability operator on X compatible with E inspired by the tools used in approximate reasoning and on the duality principle. Of special interest are the cases when the fuzzy subsets determine a partition and a hard-partition of the uni...

We prove some results about the first Steklov eigenvalue d1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera’s principle of duality [9] may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problem...

For a 4-dimensional 3-parametric toy Hamiltonian H(a, b, c) we construct the domain D of couplings in which the eigenvalues En remain real (i.e., in principle, observable). A relationship is found between the reflection symmetry of the spectrum (i.e., its Dunne’s and Shifman’s self-duality Ej = −EN+1−j at N = 4) and a geometric symmetry of the physical domain D. Simultaneously, both remain unbr...

The no trade principle asserts that risk-neutral agents are not prepared to trade if and only if a common prior exists. The purpose of this article is to provide general versions of this duality principle. We argue from a strategic viewpoint that completely regularity is the most general and natural topological assumption that we should make on the state space. We consider two cases. In the fir...

Heisenberg’s uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. More recently, entropic uncertainty relations have emerged as the central ingredient in the...

Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted Msolutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. Several comparison theorems for MF-FSVIEs and MF...

We construct periodic families of Poincaré spaces. This gives a partial solution to a question posed by Hodgson in the proceedings of the 1982 Northwestern homotopy theory conference. In producing these families, we formulate a recognition principle for Poincaré duality in the case of finite complexes having one top cell that splits of after a single suspension. We also explain how a Z-equivari...

A cross-layer network optimization problem is considered. It involves network and transport layers, treating both routing and flows as decision variables. Due to the nonconvexity of the capacity constraints, when using Lagrangian relaxation method a duality gap causes numerical instability. It is shown that the rescue preserving separability of the problem may be the application of the augmente...

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. With the help of the quantum to classical principle we give presentations of the quantum cohomology algebras. These algebras are semi-simple for adjoint non coadjoint varieties and some properties of th...

A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem are introduced for a constrained setvalued optimization problem, respectively. Then, corresponding weak duality, strong duality and converse duality the...