Advanced Mathematics

It is well known that a dynamical system is a concept in mathematics where a fixed rule describes how a point in a geometrical space depends on time. A mathematical models is a precise representation of a system's dynamics used to answer questions via analysis and simulation. Mathematica models allow us to reason about a system and make predictions about who a system will behave. Contact geometry is the odd-dimensional analogue of symplectic geometry. It is close to symplectic geometry and like the latter it originated in questions of classical and analytical mechanics. If contact geometry is considered as a symplectic geometry, it has broad applications in mathematical physics, geometrical optics, classical mechanics, analytical mechanics, mechanical systems, thermodynamics, geometric quantization and applied mathematics such as control theory. It is well known fact that one way of solving problems in classical mechanics occur with the help of the Hamilton equations. Hamiltonian method is particularly important because of its utility in formulating quantum mechanics. In this study, Hamilton equations as representive the object motion were found on a contact 5-manifolds. Also, implicit solutions of the differential equations found in this study are solved by Maple computation program.

The aim of this presentation is to connect Extenics with new fields of research, i.e. fuzzy logic and neutrosophic logic. We show herein: - How Extenics is connected to the 3-Valued Neutrosophic Logic, - How Extenics is connected to the 4-Valued Neutrosophic Logic, - How Extenics is connected to the n-Valued Neutrosophic Logic, when contradictions occurs.

The purpose of this subject to know the quality of clinker which produce from the rotary kiln according to amount oxygen rate in the exhausted cases measured by or sat device in smoke chamber .the expert in quality control can be recognize the good clinker and bad clinker according to the condition of kilne to maintain the flame temperature in suitalele range that inverts relation with excess oxygen to protect the material temperature in in the burning zone . if the temperature of materials increased or decreased or decreased will be cause upset the kiln and the material feed become deeay so that the economy cost is rising .

In this paper, we present a counter-example for the stability of reciprocal type functional equation controlled by product of different powers in singular case.

In this paper, a class of -valent - uniformly starlike analytic functions associated with a convolution is introduced and certain properties of functions belonging to this class such as a necessary and sufficient coefficient inequality, growth and distortion properties, neighborhood properties are obtained. With the help of coefficient inequality, extreme points for functions belonging to this class are derived.

Using the initial value problem approach, the evolution of linearized perturbations in a stratified shear flow with rotation is studied. Here the resulting equation in time posed by using Fourier transformation and Square transformation is solved for the Fourier amplitudes for bounded couette flow with a point source of the field of transverse velocity and density as the initial distributions. Perturbation solutions are obtained and the velocity and density plots are drawn to find the effect of density variation and rotation

The aim of this paper is to give decomposition of a weaker form of continuity, namely fuzzy -continuity, by providing the concepts of fuzzy -closed set, fuzzy - set, fuzzy -continuity and fuzzy -continuity.

The purpose of this paper is to establish a common random fixed point theorem for five random multivalued operators satisfying a rational inequality using the concept of weak compatibility, semi compatibility and commutativity of random multivalued operators in polish space.

In the literature, some extensions and generalizations of Enestrom-Kakeya theorem are available. In this paper we refine results by defining the zero –free regions of polynomials.

In this paper, the North east corner [ NEM ] procedure is successfully coded and tested via many randomly generated problem instances . Based on the results we can conclude that the correctness of the newly coded NEM is promising as compared with the previously coded one. We select very big problem of Transportation problem using Object oriented programming in Java and develop a NEM in Java Flowchart, Algorithm, program. In this paper submitted in screen short.