(Received) Mathematical analysis of Bible passages promises surprising new insights into the meanings of the texts. Relations among God, man and sheep, for example, are clarified with simple algebraic manipulation.

Pawlak’s Rough set theory was originally proposed as a general mathematical tool for dealing with uncertainty in modeling imperfect knowledge. The purpose of this paper is to introduce the concept of multifuzzy rough sets by combining the multi-fuzzy set and rough set models. Some operations such as Complement, Union, Intersection etc. are defined for multi-fuzzy rough sets and De Morgan’s laws...

Strict partial order is a mathematical structure commonly seen in relational data. One obstacle to extracting such type of relations at scale is the lack of large scale labels for building effective data-driven solutions. We develop an active learning framework for mining such relations subject to a strict order. Our approach incorporates relational reasoning not only in finding new unlabeled p...

This paper deals with relations of mathematics and fine art with a focus on geometric structures captured as visual art compositions. It aims to show similarities between mathematical and artistic solutions applied in the creation of a piece of work – artistic masterpiece or mathematical assumption. Some ideas are brought about their common underlying principles and motifs together with the con...

An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are re...

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft congruence relations by using the soft set theory. The notions of soft quotient rings, generalized soft ideals and generalized soft quotient rings, are introduced, and several related properties are investigated. Also, we obtain a...

Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the direct description of the limiting continuum theory. The resulting structure is expected to exhibit strict conformal invariance, and facilitate the mathematical...

This paper discusses a mathematical model together with its computational realization, for the motivic analysis of a piece of music. Relations between the mathematical model (motivic topologies), computational counter-part (OM-Melos), and music analysis are presented in the light of general concepts of computational music analysis, stressing the importance of neutrality and scientific rigour in...

We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical method based on biquaternionic fundamental solutions for solving standard electromagnetic scattering problems, relations between different operators of mathe...

Natural language definitions of mathematical expressions are essential for understanding the mathematical content of scientific papers. A textual description corresponding to a mathematical expression determines the type of symbol or function and the specific name for reference. Our objective is to create an automatic way of extracting definitions of mathematical expressions. We needed to creat...