Adopting Zakowski’s upper approximation operator C and lower approximation operator C, this paper investigates granularity-wise separations in covering approximation spaces. Some characterizations of granularity-wise separations are obtained by means of Pawlak rough sets and some relations among granularitywise separations are established, which makes it possible to research covering approximat...

Morphological covariance, one of the most frequently employed texture analysis tools offered by mathematical morphology, makes use of the sum of pixel values, i.e. “volume” of its input. In this paper, we investigate the potential of alternative measures to volume, and extend the work of Wilkinson (ICPR’02) in order to obtain a new covariance operator, more sensitive to spatial details, namely ...

In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as " why mathematicians are/should be interested in algebraic quantum field theory " would be equally fitting. Besides a presentation of the framework and the main results of local quantum physics these notes may s...

This paper addresses some mathematical problems arising from the infrared (IR) catastrophe in quantum field theory. IR catastrophe is formulated and studied in operator theory, characterized by the Carleman operator. Non-existence of ground state under IR catastrophe is also investigated with the help of the characterization. The theory presented in this paper is applied to the Hamiltonian of t...

The aim of this text is the study of the fine spectra for a class of Cesàro generalized operators, Rhaly operators, when those are defined on the spaces lp, p > 1. 2000 Mathematical Subject Classification: 65F15 The averaging operators A are determined by relations inf x∈X f(x) ≤ A(f) ≤ sup x∈X f(x) , ∀ f ∈ F = {f | f : X → R}, where ∅ 6= X ⊂ R. A(f) is the mean of f for the operator A. For a =...

During the past several years, deadly COVID-19 pandemic has dramatically affected world; death toll exceeds 4.8 million across world according to current statistics. Mathematical modeling is one of critical tools being used fight against this infectious disease. It been observed that transmission follows a fading memory process. We have fractional order differential operator identify kind disea...

Computer aided circuit analysis is a complex procedure, which may be roughly divided into three steps. The first stage is device modelling, where quantitative properties of the participating electronic devices are determined. In the second step, the circuit’s topology in conjunction with the device equations is being exploited, in order to formulate a linearized nonsingular equation set. Eventu...

The paper describes a class of mathematical problems at an intersection of operator theory and combinatorics, and discusses their application in complex system analysis. The main object of study is duality gap bounds in quadratic programming which deals with problems of maximizing quadratic functionals subject to quadratic constraints. Such optimization is known to be universal, in the sense th...

It is shown that in elliptic cohomology as recently formulated in the mathematical literature the supercharge of the supersymmetric nonlinear sigma model plays a role similar to the role of the Dirac operator in X-theory. This leads to several insights concerning both elliptic cohomology and string theory. Some of the relevant calculations have been done previously by Schellekens and Warner in ...

This paper introduces the notion of an {Ft, 0 ≤ t ≤ T}-consistent dynamic operator with a floor, by suitably formulating four axioms. It is shown that an {Ft, 0 ≤ t ≤ T}consistent dynamic operator {Es,t, 0 ≤ s ≤ t ≤ T} with a continuous upper-bounded floor S is necessarily represented by the solution of a backward stochastic differential equation (BSDE) reflected upwards on the floor, if it is ...