Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise

We study the sharp interface limit of the two dimensional stochastic Cahn-Hilliard equation driven by two types of singular noise: a space-time white noise and a space-time singular divergence-type noise. We show that with appropriate scaling of the noise the solutions of the stochastic problems converge to the solutions of the determinisitic Mullins-Sekerka/Hele-Shaw problem.

COMPARATIVE ANALYSIS OF BIO-INSPIRED OPTIMIZATION ALGORITHMS IN NEURAL NETWORK BASED DATA MINING CLASSIFICATION

It always helps to determine optimal solutions for stochastic problems thereby maintaining good balance between its key elements. Nature inspired algorithms are meta-heuristics that mimic the natural activities for solving optimization issues in the era of computation. In the past decades, several research works have been presented for optimization especially in the field of data mining. This paper addresses the implementation of bio-inspired optimization techniques for machine learning based data mining classification by four different optimization algorithms. The stochastic problems are overcome by training the neural network model with techniques such as barnacles mating , black widow optimization, cuckoo algorithm and elephant herd optimization. The experiments are performed on five different datasets, and the outcomes are compared with existing methods with respect to runtime, mean square error and classification rate. From the experimental analysis, the proposed bio-inspired optimization algorithms are found to be effective for classification with neural network training.

COMPARATIVE ANALYSIS OF BIO-INSPIRED OPTIMIZATION ALGORITHMS IN NEURAL NETWORK BASED DATA MINING CLASSIFICATION

It always helps to determine optimal solutions for stochastic problems thereby maintaining good balance between its key elements. Nature inspired algorithms are meta-heuristics that mimic the natural activities for solving optimization issues in the era of computation. In the past decades, several research works have been presented for optimization especially in the field of data mining. This paper addresses the implementation of bio-inspired optimization techniques for machine learning based data mining classification by four different optimization algorithms. The stochastic problems are overcome by training the neural network model with techniques such as barnacles mating , black widow optimization, cuckoo algorithm and elephant herd optimization. The experiments are performed on five different datasets, and the outcomes are compared with existing methods with respect to runtime, mean square error and classification rate. From the experimental analysis, the proposed bio-inspired optimization algorithms are found to be effective for classification with neural network training.

The Extension of the Physical and Stochastic Problems to Space-Time-Fractional Differential Equations

The fractional calculus gains wide applications nowadays in all fields. The implementation of the fractional differential operators on the partial differential equations make it more reality. The space-time-fractional differential equations mathematically model physical, biological, medical, etc., and their solutions explain the real life problems more than the classical partial differential equations. Some new published papers on this field made many treatments and approximations to the fractional differential operators making them loose their physical and mathematical meanings. In this paper, I answer the question: why do we need the fractional operators?. I give brief notes on some important fractional differential operators and their Grünwald-Letnikov schemes. I implement the Caputo time fractional operator and the Riesz-Feller operator on some physical and stochastic problems. I give some numerical results to some physical models to show the efficiency of the Grünwald-Letnikov scheme and its shifted formulae. MSC 2010: Primary 26A33, Secondary 45K05, 60J60, 44A10, 42A38, 60G50, 65N06, 47G30,80-99

STOCHASTIC PROBLEMS AND APPLIED ORIENTATION IN MATHEMATICS TEACHING

The article deals with some aspects of the study of the discipline “Probability theory and mathematical statistics” by the students of economic specialties through the solution of practical exercises. The main aim of learning the course is to form the skills to apply the knowledge gained to the tasks in economics. The concept of teaching probability theory and mathematical statistics is a process in which stochastic concepts and ideas serve as a mathematical apparatus for solving specific problems. Nowadays it is traditional to acquaint students with certain sections of applied mathematics, including probability theory and mathematical statistics, as purely abstract theories. However, as the best we consider another approach, according to which “a more adequate solution will be to acquaint the students with the methods of mathematical models construction”. In solving the problems of an applied nature, students get an idea of the necessity and universality of mathematics and its methods. The value of stochastic problems is determined predominantly not by the apparatus used in the process of their solution, but by the ability to demonstrate the process of usage of mathematics in solution of non-mathematical problems. It is shown how, with the help of applied tasks, to familiarize students with real examples of application of stochastic ideas and methods, as well as to make it possible to organize specific activities necessary in the process of application of mathematics. The student, researching a mathematical problem, formulates different questions and problems, then “transforms” them into the notions of mathematics, in order to solve them by mathematical methods, and then adapt the solution to the real problem, which was set at the beginning of the learning activity. This process is a process of constructing a mathematical (probabilistic) model of a real situation, which can be considered a mathematical activity in a broad sense. Among the traditional stochastic problems there are many typically mathematical (intramodel) tasks of such a kind, which were formulated by means of non-mathematical terms. It is necessary to note that the real problems of an applied nature are rare in mathematics because the stage of formalization (construction of a mathematical model of a non-mathematical situation) requires to have a deep knowledge and mathematical culture. This fact generated the problem of selection of tasks of applied nature that can be used in teaching. The paper presents a number of examples where students are shown how, with the help of some modification, a number of traditional problems of probability theory (formulated in the language of nonmathematical terms) can be developed into the tasks of applied nature. Expanding the range of such tasks during the study of mathematics would have a positive effect on students’ attitudes to this discipline and would increase their motivation to learn. Besides, the role of stochastic issues in mathematics and general education would become more multifaceted. For the university teachers of mathematics working with the students of economic specialties the most important thing is the formation of students’ mathematical skills to use the mathematical apparatus in their future professional activities.