The current paper discusses the global existence and asymptotic behavior of solutions of the following new nonlocal problem$$ u_{tt}-M\left(\displaystyle \int_{\Omega}|\nabla u|^{2}\, dx\right)\triangle u + \delta u_{t}= |u|^{\rho-2}u \log|u|, \quad \text{in}\ \Omega \times ]0, \infty[,  $$where\begin{equation*}M(s)=\left\{\begin{array}{ll}{a-bs, }&{\text{for}\ s \in [0, \frac{a}{b}[, }\\{0, }&{\text{for}\ s \in [\frac{a}{b}, +\infty[. }\end{array}\right. \end{equation*}If the initial data are appropriately small, we derive existence of global strong solutions and the  exponential decay of the energy.

The problem of personal identity among others may stem from the following question—what does be the person that you are, from one day to the next, necessarily consist of? The diachronic problem of personal identity raises question on the necessary and sufficient conditions for the identity of the person over time. The synchronic problem is grounded in the question of what features or traits characterize a given person at one time. To answer these questions, John Locke discarded the soul and the body as necessary and sufficient substances for personal identity over time. He accepted consciousness as the only criterion for personal identity; the only thing capable of remaining the same and preserving personal identity through change. Though Locke’s argument is somewhat clear and coherent but what remains vague and incoherent is embedded in the question—what exactly is consciousness? How and why should it be the basis or criterion for the determination of personal identity? Using the method of critical analysis, I argue that Locke’s choice of consciousness as the determinant of personal identity, though quite novel, is incoherent and vague. Secondly, Locke had already presumed and anticipated clearly though fallaciously the very thing he wishes to substantiate. I therefore conclude that Locke’s argument is just another way of trying to escape but inadvertently prolonging the difficulty of apparently articulating a distinction between the psychological approach and physiological approach to the problem of personal identity. However, in my submission, I propose the concept of the “other” as alternative approach— a sort of an extrinsic-intrinsic approach to the problem of personal identity.

The Fermat-Weber location problem is to find a point in Rn that minimizes the sum of the weighted Euclidean distances from m given points in Rn. In this paper we consider the Fermat-Weber problem of one new facilitiy with respect ton unknown customers in order to minimizing the sum of transportation costs between this facility and the customers. We assumed that each customer is located in a nonempty convex closed bounded subset of Rn.

In this paper, we investigate the Single-Source Capacitated Multi-Facility Weber problem. The aim is to locate several new facilities among existing customers and simultaneously allocate customers to facilities, so that capacity constraints are met and each customer will provide all its demand from just one facility, and as a result, the total cost of transporting between new facilities and existing customers gets minimum. A Genetic Algorithm is proposed for solving the problem, in which a local search method is embedded. The proposed Genetic Algorithm is tested on existing data sets to evaluate its robustness over available methods in the literature.

In this paper, simultaneous control of Source terms is considered in a vibrational string problem. In the considered problem, the terms to be controlled are the force and the initial velocity functions. We state the generalized (weak) solution about the considered problem. The existence and uniqueness of the solution for optimal control problem is investigated. The Frechet derivative of the functional and the Lipschitz continuity of the gradient are investigated. Minimizing sequence is obtained by the method of the projection of the gradient.

Background: The need for a rapid, noninvasive method for unwanted hair removal has led to the development of various light Sources for this purpose. Objective: To evaluate the efficacy of Intense Pulsed Light Source (IPLS) on unwanted hairs. Patients & Methods: In this open, uncontrolled clinical trial, 77 different anatomical areas in 34 referred patients to "Novin Didegan Clinic" in Tehran in 1380-1381, were treated by IPLS at fluencies ranging from 22 to 34 j/cm2 after their demographic data and the number of hairs were recorded. The 3 to 7 treatment sessions were accomplished 4 to 6 weeks apart. All of the patients were followed 6 months after the last therapy. The quantitative data were  analyzed by paired t test. Results: Six months after the last therapy, more than 50% reduction in number of hairs was noted in 80% of the treated areas; with mean reduction of 72±23 percent. Side effects were mild and reversible and occurred in ten patients. Conclusion: The IPLS appears to provide an effective and safe method for long term excess hair removal in various skin types.      

Inverse time-dependent heat Source problems have an important role in many branches of science and technology. The aim of this paper is to solve these classes of problems using a variational iteration method (VIM). The method applied does not require discretization of the region, as in the case of classical methods based on the finite difference method, the boundary element method or the other methods. Applying this method, we obtain a stable approximation to an unknown Source term in an inverse heat equation from over-specified data that the Source term is only time-dependent. Some numerical examples using this approach are presented and discussed.