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In the present day scenario, in developing countries, solid waste management is declared as a dangerous issue. Population explosion, high standard of living, urbanization, lack of knowledge about management of waste etc. are the main cause of waste generation. An educational institution can play an important role in terms of waste management. It is observed that environmental studies is being introduced in all programs as a subject from lower primary up to higher level with the objectives to make concern everyone about their nature from childhood but it could not fulfill the objectives in deed. In this paper we propose a mathematical model using linear programming to manage the solid waste of an educational institution with minimum cost within the limited facilities there in. [ABSTRACT FROM AUTHOR]

In this paper we consider the group of symmetries of the Sulphur molecule (S8 ) which is a finite point group of order 16 denote by D16 generated by two elements having the presentation {u,v/u² = v8 = (uv)² = 1} and find the complete set of genera (g ≥ 2) of Compact Riemann surfaces on which D16acts as a group of automorphisms as follows: D16, the group of symmetries of the sulphur (S8) molecule of order 16 acts as an automorphism group of a compact Riemann surfaces of genus g ≥ 2 if and only if there are integers λ and μ such that λ ≤1 and μ≥1 and g = λ + 8 μ( ≥ 2), μ ≥ | ≥ |. [ABSTRACT FROM AUTHOR]

A finite group G acts as a group of automorphisms on a compact Riemann surface S of genus g if and only if there exist a Fuchsian group Φ and an epimorphism Φ: Γ→G such that kerΦ = K is a surface group of genus g. And then Φ is named as smooth homomorphism. The objective of this paper is to establish a set of necessary and sufficient conditions for the existence of smooth epimorphism from a Fuchsian group to the finite group of symmetries of Carbon Tetra chloride molecule, whose abstract group representation is a,b|a4= b3=(ab)2?. [ABSTRACT FROM AUTHOR]

Mathematics plays vital role in various fields. Graph theory is a branch in Mathematics and its results have applications in many areas of the computing, social and natural sciences. Here we study about some objects (points) connected by a particular relation among themselves. With the help of graph theory many mathematical models have been formulated to solve real life problems in different fields. Different kinds of optimization can be done with the help of graph theory in Physics, Chemistry, Computer Science, Communication Science, Electrical Engineering etc. Electrical circuits can be studied and simplified by using many well known theorems of Electrical Engineering. But it seems to be laborious to use the existing and traditional methods to find branch currents and loop currents of electrical circuits if it contains many branches. For this kind of difficulties graph theory is useful and powerful technique. Different kinds of optimization can be done with the help of graph theory. In this paper, we have formulated a graph theoretic model to find the currents of an electrical circuits containing finite number of 'n' branches. [ABSTRACT FROM AUTHOR]

The theory of Fuchsian group plays an important role in the study of compact Riemann surfaces Automorphism groups, which was initially studied by A.M. Macbeth. The biholomorphic self transformations of a compact Riemann surface S of genus g (≥2) forms a finite group whose order cannot exceed 84 (g-1). This maximum bound is attained for infinitely many values of g, the least being 3. The groups for which this bound is attained are called Hurwitz groups, and this groups belong to the class of perfect groups which are non soluble. In context to the class of soluble groups, the corresponding bound is 48 (g-1) and this bound is also attained for infinitely many values of g. The problem of finding such bounds for various sub-classes of the finite soluble groups and the number of values of g for which these bounds are attained has been the theme of many research papers during the last few decades. In this paper, a set of necessary and sufficient conditions for the existence of smooth epimorphism from a Fuchsian group to the point group Oh, which belongs to the sub-class of octahedral group considering the symmetries of Sulfur-Hexafloride (S F6) molecule Having the abstract group representation „'<α² =β4=(αβ)²=1> is established to fulfill the objective. [ABSTRACT FROM AUTHOR]

The symmetry present in molecules is a fundamental concept in Chemistry. Group Theory is an extremely powerful tool which, in spite of abstractness provides the systematic treatment of symmetry of molecules that simplifies the process of obtaining a variety of information about molecules. Molecules are classified according to their symmetry properties. In this paper, analyzing all the symmetry operations as well as symmetry elements of Sulphur-hexa--floride (SF6) molecule, the authors determine the point group and its abstract presentation as <α, β / α² = β4 = (αβ)6 = 1> . [ABSTRACT FROM AUTHOR]

Modern human civilization has been plagued with a host of ecological challenges. The rapid pace of global warming, rising sea level leading to loss of habitats and unprecedented flood causing havoc in both rural and city lives and other problems have still found no permanent solutions. In fact, the best ever scientific and technological interventions have failed miserably to mitigate these issues. Traditional and innovative ideas have been proved inadequate to address the issue of flood that has a global presence in varied form or severity. Hence there are many scopes for research and development of mathematical models or interventions to offer solution to this issue of global and local concern. So it is a most appealing branch of study to develop feasible solutions to these problems. In this paper we have considered one of the most burning problems, the flood problem and try to develop the best feasible solution this problem by using Fuzzy Soft Set theory which was introduced by Molodtsov in the year 1999. We have developed a sequence of key factors responsible for the flood problem as follows. {Population explosion, Deforestation, Global Warming, Big dam, Embankment, Blockage, Heavy rainfall} From this sequence we found that population explosion is the main cause for flood problem. Therefore, it is high time to control the population through a worldwide common policy. [ABSTRACT FROM AUTHOR]