Abstract:
The mathematical model for hit phenomena in entertainments is presented as a nonlinear, dynamical and non-equilibrium phenomena. The purchase intention for each person is introduced and direct and indirect communications are expressed as two-body and three-body interaction in our model. The mathematical model is expressed as coupled nonlinear differential equations. The important factor in the model is the decay time of rumor for the hit. The calculated results agree very well with revenues of recent 25 movies.

Abstract:
In the industrially advanced countries, that are different from our ex and present countries, to learning phenomena has been dedicated a significant attention for the last 60 years. One of more basic reasons is multiple purposes of results. Until now, there have been applied various approaches, methods and procedures for empirical data approximation, and in this articles some possibilities of artificial neural network application are researched.

Abstract:
The present article describes the natal rites and customs of the Azerbaijan and Bulgarian nations. Special attention is paid to the resemblances in the practicing and understanding of the traditions. Despite the fact that the two nations live in regions remote from each other, they have common beliefs and strive to provide prosperity for the home, family and children.

Abstract:
In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane) inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate). On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells) by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.

Abstract:
We propose to search for scalar dark matter via its effects on the electromagnetic fine-structure constant and particle masses. Scalar dark matter that forms an oscillating classical field produces `slow' linear-in-time drifts and oscillating variations of the fundamental constants, while scalar dark matter that forms topological defects produces transient-in-time variations of the constants of Nature. These variations can be sought for with atomic clock, laser interferometer and pulsar timing measurements. Atomic spectroscopy and Big Bang nucleosynthesis measurements already give improved bounds on the quadratic interaction parameters of scalar dark matter with the photon, electron, and light quarks by up to 15 orders of magnitude, while Big Bang nucleosynthesis measurements provide the first such constraints on the interaction parameters of scalar dark matter with the massive vector bosons.

Abstract:
Two fundamental concerns must be addressed when attempting to isolate low-level waste in a disposal facility on land. The first concern is isolating the waste from water, or hydrologic isolation. The second is preventing movement of the radionuclides out of the disposal facility, or radionuclide migration. Particularly, we have investigated the latter modified scenario. To assess the safety for disposal of radioactive waste-concrete composition, the leakage of 60Co from a waste composite into a surrounding fluid has been studied. Leakage tests were carried out by original method, developed in Vinca Institute. Transport phenomena involved in the leaching of a radioactive material from a cement composite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a first-order equation, and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Abstract:
We present an overview of recent developments in the detection of light bosonic dark matter, including axion, pseudoscalar axion-like and scalar dark matter, which form either a coherently oscillating classical field or topological defects (solitons). We emphasise new high-precision laboratory and astrophysical measurements, in which the sought effects are linear in the underlying interaction strength between dark matter and ordinary matter, in contrast to traditional detection schemes for dark matter, where the effects are quadratic or higher order in the underlying interaction parameters and are extremely small. New terrestrial experiments include measurements with atomic clocks, spectroscopy, atomic and solid-state magnetometry, torsion pendula, ultracold neutrons, and laser interferometry. New astrophysical observations include pulsar timing, cosmic radiation lensing, Big Bang nucleosynthesis and cosmic microwave background measurements. We also discuss various recently proposed mechanisms for the induction of slow `drifts', oscillating variations and transient-in-time variations of the fundamental constants of Nature by dark matter, which offer a more natural means of producing a cosmological evolution of the fundamental constants compared with traditional dark energy-type theories, which invoke a (nearly) massless underlying field. Thus, measurements of variation of the fundamental constants gives us a new tool in dark matter searches.

Abstract:
In this work, an artificial neural network (ANN) model is developed and used to predict the presence of ducting phenomena for a specific time, taking into account ground values of atmospheric pressure, relative humidity and temperature. A feed forward backpropagation ANN is implemented, which is trained, validated and tested using atmospheric radiosonde data from the Helliniko airport, for the period from 1991 to 2004. The network's quality and generality is assessed using the Area Under the Receiver Operating Characteristics (ROC) Curves (AUC), which resulted to a mean value of about 0.86 to 0.90, depending on the observation time. In order to validate the ANN results and to evaluate any further improvement options of the proposed method, the problem was additionally treated using Least Squares Support Vector Machine (LS-SVM) classifiers, trained and tested with identical data sets for direct performance comparison with the ANN. Furthermore, time series prediction and the effect of surface wind to the presence of tropospheric ducts appearance are discussed. The results show that the ANN model presented here performs efficiently and gives successful tropospheric ducts predictions.

Abstract:
We introduce a set of mathematical constants which is involved naturally in the theory of multiple Gamma functions. Then we present general asymptotic inequalities for these constants whose special cases are seen to contain all results very recently given in Chen 2011. 1. Introduction and Preliminaries The double Gamma function and the multiple Gamma functions were defined and studied systematically by Barnes [1–4] in about 1900. Before their investigation by Barnes, these functions had been introduced in a different form by, for example, H？lder [5], Alexeiewsky [6] and Kinkelin [7]. In about the middle of the 1980s, these functions were revived in the study of the determinants of the Laplacians on the -dimensional unit sphere (see [8–13]). Since then the multiple Gamma functions have attracted many authors' concern and have been used in various ways. It is seen that a set of constants given in (1.11) involves naturally in the theory of the multiple Gamma functions (see [14–20] and references therein). For example, for sufficiently large real and , we have the Stirling formula for the -function (see [1]; see also [21, page 26, equation (7)]): where is the Glaisher-Kinkelin constant (see [7, 22–24]) given in (1.16) below. The Glaisher-Kinkelin constant , the constants and below introduced by Choi and Srivastava have been used, among other things, in the closed-form evaluation of certain series involving zeta functions and in calculation of some integrals of multiple Gamma functions. So trying to give asymptotic formulas for these constants , , and are significant. Very recently Chen [25] presented nice asymptotic inequalities for these constants , , and by mainly using the Euler-Maclaurin summation formulas. Here, we aim at presenting asymptotic inequalities for a set of the mathematical constants ？？ given in (1.11) some of whose special cases are seen to yield all results in [25]. For this purpose, we begin by summarizing some differential and integral formulas of the function in (1.2). Lemma 1.1. Differentiating the function times, we obtain where is a polynomial of degree in satisfying the following recurrence relation: In fact, by mathematical induction on , we can give an explicit expression for as follows: Setting in (1.3) and (1.5), respectively, we get where are the harmonic numbers defined by Differentiating in (1.6) times, we obtain Integrating the function in (1.2) from to , we get For each , define a sequence by where are Bernoulli numbers given in (1.12), are given in (1.5), and denotes (as usual) the greatest integer ≦ . Define a set of

Abstract:
We generalize techniques of Addison to a vastly larger context. We obtain integral representations in terms of the first periodic Bernoulli polynomial for a number of important special functions including the Lerch zeta, polylogarithm, Dirichlet $L$- and Clausen functions. These results then enable a variety of Addison-type series representations of functions. Moreover, we obtain integral and Addison-type series for a variety of mathematical constants.