Abstract:
Some seasonal products have limited sales season, and the demand of such products over the sales season is of increasing-steady-decreasing type. Customers are highly sensitive to the prices of the products. In such situation, adjustment of unit selling price is needed to accelerate inventory depletion rate and for determining order quantity for the sales season. In this paper, we focus on the issue by jointly determining optimal unit selling prices and optimal lot size over the sales season. Unlike the conventional inventory models with pricing strategy, which were restricted to prespecified pricing cycle lengths, that is, fixed number of price changes over the time horizon, we allow the number of price changes to be a decision variable. The mathematical model is developed and existence of optimal solution is verified. A solution procedure is developed to determine optimal prices, optimal number of pricing cycles, and optimal lot size. The model is illustrated by a numerical example. Sensitivity analysis of the model is also carried out. 1. Introduction Items like fashion apparel, hi-tech product parts, periodicals, Christmas accessories, and so forth, have limited sales season and become outdated at end of season. Demand of such products is sensitive to time as well as price. Initially after introduction of the product, demand increases up to a point of time then it becomes steady. Finally towards end the of the season, it decreases. Ramp-type time-dependent demand pattern is very close to the demand pattern in such situations. The inventory model with ramp-type demand rate was first proposed by Hill [1]. Since then many researchers and practitioners have given considerable attention to analyze ramp-type demand. Mandal and Pal [2] have extended the inventory model with ramp-type demand for exponentially deteriorating items by allowing shortages. Wu and Ouyang [3] have developed an inventory model by considering two different replenishment policies: shortage followed by inventory and inventory followed by shortage. Wu [4] has further proposed an inventory model for deteriorating items with ramp-type demand, Weibull distribution deteriorating rate, and waiting time-dependent partial backlogging rate. Giri et al. [5] have extended ramp-type demand inventory model with more general Weibull distribution deterioration rate. Manna and Chaudhuri [6] have developed a production inventory model with ramp-type two time periods classified demand pattern where the finite production rate depends on demand. Deng et al. [7] have pointed out the questionable results

Abstract:
The concept of -convex function and its generalizations is studied with differentiability assumption. Generalized differentiable -convexity and generalized differentiable -invexity are used to derive the existence of optimal solution of a general optimization problem. 1. Introduction convex function was introduced by Youness [1] and revised by Yang [2]. Chen [3] introduced Semi- -convex function and studied some of its properties. Syau and Lee [4] defined -quasi-convex function, strictly -quasi-convex function and studied some basic properties. Fulga and Preda [5] introduced the class of -preinvex and -prequasi-invex functions. All the above -convex and generalized -convex functions are defined without differentiability assumptions. Since last few decades, generalized convex functions like quasiconvex, pseudoconvex, invex, -vex, -invex, and so forth, have been used in nonlinear programming to derive the sufficient optimality condition for the existence of local optimal point. Motivated by earlier works on convexity and convexity, we have introduced the concept of differentiable -convex function and its generalizations to derive sufficient optimality condition for the existence of local optimal solution of a nonlinear programming problem. Some preliminary definitions and results regarding -convex function are discussed below, which will be needed in the sequel. Throughout this paper, we consider functions , , and are nonempty subset of . Definition 1.1 (see [1]). is said to be -convex set if for , . Definition 1.2 (see [1]). is said to be -convex on if is an -convex set and for all and , Definition 1.3 (see [3]). Let be an -convex set. is said to be semi- -convex on if for and , Definition 1.4 (see [5]). is said to be -invex with respect to if for and ,？？ . Definition 1.5 (see [6]). Let be an -invex set with respect to . ？Also ？ is said to be -preinvex with respect to on if for and , Definition 1.6 (see [7]). Let be an -invex set with respect to . Also ？ is said to be semi- -invex with respect to at if for all and . Definition 1.7 (see [7]). Let be a nonempty -invex subset of with respect to , . Let and be an open set in ？Also ？ and are differentiable on . Then, is said to be semi- -quasiinvex at if or Lemma 1.8 (see [1]). If a set is -convex, then . Lemma 1.9 (see [5]). If is -invex, then . Lemma 1.10 (see [5]). If is a collection of -invex sets and , for all , then is -invex. 2. -Convexity and Its Generalizations with Differentiability Assumption -convexity and convexity are different from each other in several contests. From the previous results on

Abstract:
The paper deals with Dynamic Voltage Restorer (DVR) that aims at the integration of series active filter with minimum VA handling. The DVR not only regulates the voltage at load end but also acts as series active filter. The scheme of DVR is modeled and simulated with MATLAB/Simulink under feedback and feedforward controller. It is also thoroughly analyzed, both from the point of view of the choice of the components and their ratings. The proposed scheme provides stability under varying gains thus eliminating the problem of tuning of conventional proportional and integral controller and improves the speed of response of the device. The results of simulation for the proposed scheme are presented.

Abstract:
A patient was referred to us with asymptomatic, erythematous, nonitchy, scaly lesions present bilaterally on the dorsa of his feet and toes since the last 2 months. Both the legs had pitting edema as well. There were hyperkeratosis, focal parakeratosis, acanthosis and scattered spongiosis in the epidermis, and proliferation of capillaries with perivascular infiltration of lymphomononuclear cells in the dermis. There was no serological evidence of hepatitis C virus. Laboratory investigations revealed hypoalbuminemia and low-normal serum zinc. On clinicopathological correlation, we made a diagnosis of necrolytic acral erythema (NAE). The lesions responded dramatically to oral zinc sulfate and topical clobetasol propionate within 3 weeks with disappearance of edema and scaling and only a minimal residual erythema. This is the first reported case of NAE from Eastern India. NAE with negative serology for hepatitis C may be viewed as a distinct subset of the condition that had been originally described.

Abstract:
Debate over the status of medicine as an Art or Science continues. The aim of this paper is to discuss the meaning of Art and Science in terms of medicine, and to find out to what extent they have their roots in the field of medical practice. What is analysed is whether medicine is an "art based on science"; or, the "art of medicine" has lost its sheen (what with the rapid advancements of science in course of time, which has made present day medicine more sophisticated). What is also analysed is whether the "science of medicine" is a pure one, or merely applied science; or the element of science in it is full of uncertainty, simply because what is accepted as "scientific" today is discarded by medical practitioners tomorrow in the light of newer evidence. The paper also briefly touches upon how, in the field of present medical education, the introduction of medical humanities or humanistic education has the potential to swing the pendulum of medicine more towards the lost "art of medicine". The paper concludes by saying that the art and science of medicine are complementary. For successful practice, a doctor has to be an artist armed with basic scientific knowledge in medicine.

Abstract:
Information is flowing in assorted network across the globe via copious channels. The commercial, personal as well defense communication is relying on different protocols for secured data transmission to provide the quality of service as well as confidentiality to the client. A significant research work is going on in the stream of cryptography and secured data transmission and a number of data encryption techniques have been devised to secure the network infrastructure and the trust on service. Cryptology refers to the execution as well as the study of hiding information from different eyes. Now days, cryptography is used in almost many disciplines including mathematics, computer science, and engineering. The applications of cryptography include Smart Cards, ATM Cards, computer passwords, defense communications and electronic commerce. This paper emphasizes on the proportional analysis on different cryptography techniques and their relative performance issues. Keywords - Asymmetric Encryption, Cryptography, Comparison of Cryptographic Techniques, Data Communication, Hash Function, Network Architecture, Performance of Cryptography Methods, Symmetric Encryption,

Abstract:
We analyse the spectrum of non-BPS branes in the type I theory on the orbifold $T^4/{\cal I}_4$. We present a detailed analysis of the action of the worldsheet parity $\Omega$ on the different D-brane boundary state sectors of type IIB on $T^4/{\cal I}_4$, using the covariant formulation. Using these results we derive the spectrum of branes in the type I orbifold. We find $\Z_2$- and $\Z$- charged non-BPS branes. A study of the stability of these branes in the type I orbifold is also presented. We find that the type I non-BPS D-particle and D-instanton remain stable in the orbifold. The D-particle carries no charge whereas the non-BPS D-instanton can carry twisted R-R charge.

Abstract:
We propose an analytic perturbative scheme for determining the eigenvalues of the Helmholtz equation, $(\nabla^2 + k^2) \psi = 0$, in three dimensions with an arbitrary boundary where $\psi$ satisfies either the Dirichlet boundary condition ($\psi =0$ on the boundary) or the Neumann boundary condition (the normal gradient of $\psi$, $\frac{\partial \psi}{\partial n}$ is vanishing on the boundary). Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schr{\"o}dinger perturbation theory. The efficiency of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.