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In this work, topological spaces are enriched by additional structures in order to give a more realistic representation of real life phenomena and computational processes and at the same time, to provide for utilization of the powerful…

General Topology · Mathematics 2007-05-23 M. Burgin

We consider various definitions of degrees of discrete functions and establish relations between the number of relevant (essential) variables and degrees of two- and three-valued functions. Keywords: relevant variable, sensitivity, degree…

Combinatorics · Mathematics 2025-12-01 V. N. Potapov

A statistic based on increment ratios (IR) and related to zero crossings of increment sequence is defined and studied for measuring the roughness of random paths. The main advantages of this statistic are robustness to smooth additive and…

Statistics Theory · Mathematics 2010-07-26 Jean-Marc Bardet , Donatas Surgailis

In this paper, we introduce the concept of several products of rough finite state machines. We establish their relationships through coverings and investigate some algebraic properties for these products.

Logic · Mathematics 2016-11-26 S. P. Tiwari , Shambhu Sharan

In this paper we assemble some results about the upper-semicontinuity and lower-semicontinuity of the feasible correspondence and the solution correspondence of linear programming problems allowing variability of all parameters of such…

Optimization and Control · Mathematics 2024-12-10 Somdeb Lahiri

A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture…

Pricing of Securities · Quantitative Finance 2017-10-23 Christian Bayer , Peter K. Friz , Paul Gassiat , Joerg Martin , Benjamin Stemper

In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…

Probability · Mathematics 2017-08-31 Jinlu Li , Robert Mendris

In this paper, we give an introduction for rough groups and rough homomorphisms. Then we present some properties related to topological rough subgroups and rough subsets. We construct the product of topological rough groups and give an…

Group Theory · Mathematics 2019-09-06 Nof Alharbi , Alla Altassan , Hassen Aydi , Cenap Ozel

Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and…

Probability · Mathematics 2014-06-17 Lev B. Klebanov , Lenka Slámová

For an $n$-by-$n$ matrix $A$, let $f_A$ be its "field of values generating function" defined as $f_A\colon x\mapsto x^*Ax$. We consider two natural versions of the continuity, which we call strong and weak, of $f_A^{-1}$ (which is of course…

Functional Analysis · Mathematics 2013-07-19 Dan Corey , Charles R. Johnson , Ryan Kirk , Brian Lins , Ilya Spitkovsky

We highlight some facts about continued fractions of real cubic irrationalities. This may be thought as a small section in a textbook on continued fractions.

Number Theory · Mathematics 2023-11-29 Wadim Zudilin

Soft set theory and rough set theory are mathematical tools to deal with uncertainties. In [3], authors combined these concepts and introduced soft rough sets. In this paper, we introduce the concepts of soft rough graphs, vertex and edge…

General Mathematics · Mathematics 2017-07-20 R. Noor , I. Irshad , I. Javaid

In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…

Classical Analysis and ODEs · Mathematics 2015-01-28 Árpád Baricz , Tibor K. Pogány

In this paper, we first study the arithmetic properties of intuitionistic fuzzy number, the monotonicity of intuitionistic fuzzy function and the derivative of intuitionistic fuzzy functions and then we study the fundamental properties on…

General Mathematics · Mathematics 2023-12-18 Efendi , Admi Nazra , Haripamyu , Mahdhivan Syafwan

Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays…

Optimization and Control · Mathematics 2014-03-13 Frank Heyde , Carola Schrage

We extend the definition of weak symmetric continuity to be applicable for functions defined on any nonempty subset of $\R$. Then we investigate basic properties of weakly symmetrically continuous functions and compare them with those of…

Classical Analysis and ODEs · Mathematics 2014-05-29 Prapanpong Pongsriiam , Teraporn Thongsiri

For real factors the notions of the coupling constant and the index are introduced and investigated. The possible values of the index for type II$_1$ real factors are calculated, in a similar way as for the complex case.

Operator Algebras · Mathematics 2009-02-09 S. Albeverio , Sh. A. Ayupov , A. A. Rakhimov , R. A. Dadakhodjaev

We establish some monotonicity results and functional inequalities for modified Lommel functions of the first kind. In particular, we obtain new Tur\'{a}n type inequalities and bounds for ratios of modified Lommel functions of the first…

Classical Analysis and ODEs · Mathematics 2021-10-13 Robert E. Gaunt

We axiomatize and generalize Markov's approach to the continuity problem for Type 1 computable functions, i.e. the problem of finding sufficient conditions on a computable topological space to obtain a theorem of the form "computable…

Logic · Mathematics 2024-12-12 Emmanuel Rauzy

In this article, we present some explicit solutions showing rough dependence upon initial data. We also studies viscous effects. An extension of a theorem of Cauchy to the viscous case is also presented.

Fluid Dynamics · Physics 2015-06-19 Y. Charles Li