In this work, we are studying about a special oscillator system, which consists of one spring and a magnet-mass. The system is placed in nonlinear magnetic field, produced by two other permanent magnets, which are oriented for attraction, where can appear different types of oscillations. The magnet-body is simultaneously the subject of the linear field of spring and also of the nonlinear magnetic field of permanent magnets which has inverse quadratic dependence on distance. We are studying the ideal case, without friction, where the oscillations are produced with energy conservation, the oscillator system is started by applying the initial impulse and we consider the hypothesis that magnetic field produced by the permanent magnets is conservative and there is no loss of energy in the magnetic interactions. We are going to find the law of motion for the general case of study and a typically numerical application will be done.

In this paper, we investigate the effect of the mean curvature of the boundary ∂Ω on the behavior of the blow-up solutions to the p-Laplacian type quasilinear elliptic equation

div(|∇u|^{p-2}∇u) = u^{m}|∇u|, p > 1,

where the Ω ∈ R^{N} be a bounded smooth domain. Under appropriate conditions on p and m, we find the estimates of the solution u interms of the distance from x to the boundary ∂Ω. To the equation

The determinant of a given square matrix is obtained as the product of pivot elements evaluated via the iterative matrix order condensation. It follows as the by-product that the inverse of this matrix is then evaluated via the iterative matrix order expansion. The fast and straightforward basic iterative procedure involves only simple elementary arithmetical operations without any high mathematical process. Remarkably, the revised optimal iterative process will compute without failing the inverse of any square matrix within minutes, be it real or complex, singular or nonsingular, and amazingly enough even for size as huge as 999x999. The manually extended iteration process is also developed to shorten the iteration process steps.

This paper presents a typewritten characters recognition system using Hidden Markov Model (HMM). Character recognition systems convert images of printed, typewritten or handwritten documents into computer readable texts that can be easily edited or searched. Character recognition for typewritten documents is however difficult due to broken edges, touching characters, shape variance, skewing, and heavy printing resulting from the typewriter impact. Three documents (old memo, old war letter and newly typewritten essay) were used to create three datasets of typewritten characters each consisting of 1995, 702 and 2049 characters respectively. The research result showed that, recognition accuracy values are 94.88%, 91.45% and 97.24% for old memo, old war letter and newly typewritten essay datasets respectively. Hence, HMM is an efficient method that can be employed to recognise typewritten documents.

The present study describes variational finite element method for one dimensional heat transfer model based on time independent sweating responses. The Penne's model with mixed boundary condition is considered for describing comparative temperature profiles of human females luteal and follicular phases of menstrual cycle and temperature profiles of males. Human dermal region under consideration is divided into six parts along with fatty and muscle parts of subcutaneous tissue (ST). Sweat rate of females is lower as compared to males owing to a lower density of sweat glands and different hormone patterns. Sweating is considered as a heat loss within the body. The physical and physiological parameters in each layer that affect the heat regulations in human body are taken as a function of position. The steady state analysis delineates that during the luteal phase females tissue temperature is higher as compared to follicular phase of the menstrual cycle. These temperatures are less as compared to males body temperatures when atmospheric temperature T_{∞ } falls below the body core temperature. But the tissue temperature of females luteal phase is slightly higher as compared to males when T_{∞} exceeds the body core temperature. The result may be useful to study thermal behavior of the biological system.

Hilbert’s Fourth Problem is one of the most important mathematical problems, formulated by Hilbert in 1900. Unfortunately, attempts to solve this problem during 20^{th} century did not lead to the generally recognized solution, and now modern mathematicians believe that the problem has been formulated by Hilbert "very vague" and therefore it can not be solved. The main purpose of this article is to develop a new view on authors’ original solution to this problem and to interpret this problem as MILLENNIUM PROBLEM in Geometry what has an interdisciplinary importance and affects not only on geometry, but also on all theoretical natural sciences. The source of a new approach to solving this problem is a new branch of mathematics, the Mathematics of Harmony, which goes back in its origins to Euclid’s Elements and has interdisciplinary importance for modern science.

An interval-valued fuzzy set denotes a fuzzy set whose membership function is many -valued and form an interval in the member ship scale. The notion of cubic sets as an extension of fuzzy set in which not only a membership degree is given but also a non-membership degree is involved. In this present study, we introduce the concept of cubic fuzzy positive implicative ideals, cubic fuzzy positive implicative extension ideals in BCK-algebras and investigate some of its properties.