The development of mathematical insight, the knack for discovering novel solutions to mathematical problems, might be one of the most erudite forms of learning that we can hope to achieve. However, Wagner and his colleague now report that a night of sleep after being exposed to a class of mathematical problems more than doubles the likelihood of discovering just such a novel solution.

The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range of fields of mathematics. We demonstrate applications of this representation in mathematical formula search, and learning.

Simultaneous reactions between solids and gases are very important in the chemical and metallurgical processes. In the modeling, the chemical reaction and diffusion of gases must be considered. Therefore, a set of coupled partial differential equations is found. When the kinetic is a function of solid concentration, there is not any analytical solution for these equations. Therefore, numerical ...

Integral and integro-differential equations are one of the most useful mathematical tools in both pure and applied mathematics. In this article, we present a variational iteration method for solving Fredholm integro-differential equations. This study provides an analytical approximation to determine the behavior of the solution. To show the efficiency of the present method for our proble...

In this paper, we considered solving approaches to flexible job shop problems. Makespan is not a good evaluation criterion with overlapping in operations assumption. Accordingly, in addition to makespan, we used total machine work loading time and critical machine work loading time as evaluation criteria. As overlapping in operations is a practical assumption in chemical, petrochemical, and gla...

This study concentrates on designing a medical waste management system with a hierarchical structure, including a local government and a waste management planner. The upper-level seeks to design and control the waste management facilities by minimizing the environmental risks related to the disposal of medical waste. While the lower-level model is to determine the waste collection plans by only...

The development of new mathematical theory and its application in software systems for the solution of hard optimization problems have a long tradition in mathematical programming. In this tradition we implemented ABACUS, an object-oriented software framework for branch-and-cut-and-price algorithms for the solution of mixed integer and combinatorial optimization problems. This paper discusses s...

In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision ...

This article examines a new approach which solves Linear Programming (LP) problems with stochastic parameters as a generalized model of the fuzzy mathematical model analyzed by Verdegay. An expectation model is provided for solving the problem. A multi-parametric programming is applied to access to a solution with different desired degrees as well as problem constraints. Additionally, we presen...