To answer the generalized Kretschman objection, we propose a criterion to decide if the gauge symmetry of a theory is artificial or substantial. It is based on the dressing field method of gauge symmetry reduction, a new simple tool from mathematical physics. Given this criterion we argue that the notion of spontaneous symmetry breaking is superfluous to the empirical success of the electroweak...

In this paper we use the Triangular and Trapezoidal Fuzzy Numbers as tools for assessing student Mathematical Modelling (MM) skills. Fuzzy Numbers play a fundamental role in fuzzy mathematics analogous to the role played by the ordinary numbers in classical mathematics, On the other hand, MM appears today as a dynamic tool for teaching and learning mathematics, because it connects mathematics w...

abraham ungar is professor in the department of mathematics at north dakota state university. after gaining his b.sc. (1965) and m.sc. (1967) from the hebrew university in pure mathematics and ph.d. (1973) from tel-aviv university in applied mathematics, he held a postdoctoral position at the university of toronto (1974). ungar moved from toronto to pretoria where he held the position of a seni...

1 Department of Mathematics, Eastern University, Chenkalady 30350, Sri Lanka 2 International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa 3 Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathemat...

Motivated by mirror symmetry, we study certain integral repre-sentations of solutions to the Gel′fand-Kapranov-Zelevinsky (GKZ) hypergeo-metric system. Some of these solutions arise as period integrals for Calabi-Yaumanifolds in mirror symmetry. We prove that for a suitable compactificationof the parameter space, there exist certain special boundary points, whichwe called ma...

the control problem and dynamic programming is a powerful tool in economics and management. we review the dynamic programming problem from its beginning up to its present stages. a problem which was involved in physics and mathematics in i 7” century led to a branch of mathematics called calculus of variation which was used in economic, and management at the end of the first quarter of the 20” ...

We discuss within one common context topics of color symmetry, using semigroups for generalization of symmetry, fractals, and some naturally occurring interrelations thereof. This free essay is emotionally inspired by the impressive scientific work of Prof. Douglas Jay Klein and his numerous collaborators, who contributed into diverse fields of chemistry, physics, and mathematics. (doi: 10.5562...

In this paper we study the coupled integrable dispersionless system (CIDS), which arises in the analysis of several problems in applied mathematics and physics. Lie symmetry analysis is performed on CIDS and symmetry reductions and exact solutions with the aid of simplest equation method are obtained. In addition, the conservation laws of the CIDS are also derived using the multiplier (and homo...

We discuss the characterization of relative equilibria of Lagrangian systems with symmetry. Mathematics Subject Classification (2000). 34A05, 34A26, 37J15, 37J15, 70H03.

We prove the symmetry of the diffusion coefficient that appears in the fluctuation-dissipation theorem for asymmetric simple exclusion processes. Mathematics Subject Classification (2000): Primary 60K35; secondary 82C22