in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

chemical hardness () and absolute electronegativity () have important applications in chemistry. inthe conceptual density functional theory (dft), these concepts has been associated with electronicenergy and the relationship with ionization energy (i) and electron affinity (a) of these concepts hasbeen given. in this study, graphical method was used in order to see the relationship with the a...

The atomic norm provides a generalization of the l1-norm to continuous parameter spaces. When applied as a sparse regularizer for line spectral estimation the solution can be obtained by solving a convex optimization problem. This problem is known as atomic norm soft thresholding (AST). It can be cast as a semidefinite program and solved by standard methods. In the semidefinite formulation ther...

Ionocovalency (IC), a quantitative dual nature of the atom, is defined and correlated with quantum-mechanical potential to describe quantitatively the dual properties of the bond. Orbiotal hybrid IC model scale, IC, and IC electronegativity scale, X(IC), are proposed, wherein the ionicity and the covalent radius are determined by spectroscopy. Being composed of the ionic function I and the cova...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

In this paper, the concept of dual models of a propositional linear temporal logic formula is defined: A formula f has dual models if it has two models (namely two ω-sequences of states) such that the assignments to atomic propositions at each position of them are dual. Then for various propositional linear temporal logics, the complexity of the problem deciding whether a formula f has dual mod...