A New Heuristic Approach for the Large-Scale Generalized Assignment Problem

This paper presents a heuristic approach to solve the Generalized Assignment Problem (GAP) which is NP-hard. It is worth mentioning that many researches used to develop algorithms for identifying the redundant constraints and variables in linear programming model. Some of the algorithms are presented using intercept matrix of the constraints to identify redundant constraints and variables prior to the start of the solution process. Here a new heuristic approach based on the dominance property of the intercept matrix to find optimal or near optimal solution of the GAP is proposed. In this heuristic, redundant variables of the GAP are identified by applying the dominance property of the intercept matrix repeatedly. This heuristic approach is tested for 90 benchmark problems of sizes upto 4000, taken from OR-library and the results are compared with optimum solutions. Computational complexity is proved to be O(mn2) of solving GAP using this approach. The performance of our heuristic is compared with the best state-ofthe- art heuristic algorithms with respect to both the quality of the solutions. The encouraging results especially for relatively large size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems.

Estimation of Bayesian Sample Size for Binomial Proportions Using Areas P-tolerance with Lowest Posterior Loss

This paper uses p-tolerance with the lowest posterior loss, quadratic loss function, average length criteria, average coverage criteria, and worst outcome criterion for computing of sample size to estimate proportion in Binomial probability function with Beta prior distribution. The proposed methodology is examined, and its effectiveness is shown.

Iterative Solutions to Some Linear Matrix Equations

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Delay-Dependent H∞ Performance Analysis for Markovian Jump Systems with Time-Varying Delays

This paper considers ­H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotical stability in mean square and a prescribed ­H∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed main results. All these results are expected to be of use in the study of stochastic systems with time-varying delays.

Some Geodesics in Open Surfaces Classified by Clairaut's Relation

In this paper, we studied some properties of geodesic on some open surfaces: Hyperboloid, Paraboloid and Funnel Surface. Geodesic equation in the v-Clairaut parameterization was calculated and reduced to definite integral. Some geodesics on some open surfaces as mention above were classified by Clairaut's relation.

Zeros of Bargmann Analytic Representation in the Complex Plane

The paper contains an investigation of zeros Of Bargmann analytic representation. A brief introduction to Harmonic oscillator formalism is given. The Bargmann analytic representation has been studied. The zeros of Bargmann analytic function are considered. The Q or Husimi functions are introduced. The The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros μn are discussed. Various examples have been given.

A New Application of Stochastic Transformation

In cryptography, confusion and diffusion are very important to get confidentiality and privacy of message in block ciphers and stream ciphers. There are two types of network to provide confusion and diffusion properties of message in block ciphers. They are Substitution- Permutation network (S-P network), and Feistel network. NLFS (Non-Linear feedback stream cipher) is a fast and secure stream cipher for software application. NLFS have two modes basic mode that is synchronous mode and self synchronous mode. Real random numbers are non-deterministic. R-box (random box) based on the dynamic properties and it performs the stochastic transformation of data that can be used effectively meet the challenges of information is protected from international destructive impacts. In this paper, a new implementation of stochastic transformation will be proposed.

Stabilization of the Bernoulli-Euler Plate Equation: Numerical Analysis

The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

On Frenet-Serret Invariants of Non-Null Curves in Lorentzian Space L5

The aim of this paper is to determine Frenet-Serret invariants of non-null curves in Lorentzian 5-space. First, we define a vector product of four vectors, by this way, we present a method to calculate Frenet-Serret invariants of the non-null curves. Additionally, an algebraic example of presented method is illustrated.

A Bootstrap's Reliability Measure on Tests of Hypotheses

Bootstrapping has gained popularity in different tests of hypotheses as an alternative in using asymptotic distribution if one is not sure of the distribution of the test statistic under a null hypothesis. This method, in general, has two variants – the parametric and the nonparametric approaches. However, issues on reliability of this method always arise in many applications. This paper addresses the issue on reliability by establishing a reliability measure in terms of quantiles with respect to asymptotic distribution, when this is approximately correct. The test of hypotheses used is Ftest. The simulated results show that using nonparametric bootstrapping in F-test gives better reliability than parametric bootstrapping with relatively higher degrees of freedom.

The Gerber-Shiu Functions of a Risk Model with Two Classes of Claims and Random Income

In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.

Stochastic Comparisons of Heterogeneous Samples with Homogeneous Exponential Samples

In the present communication, stochastic comparison of a series (parallel) system having heterogeneous components with random lifetimes and series (parallel) system having homogeneous exponential components with random lifetimes has been studied. Further, conditions under which such a comparison is possible has been established.

Multi-labeled Data Expressed by a Set of Labels

Collected data must be organized to be utilized efficiently, and hierarchical classification of data is efficient approach to organize data. When data is classified to multiple categories or annotated with a set of labels, users request multi-labeled data by giving a set of labels. There are several interpretations of the data expressed by a set of labels. This paper discusses which data is expressed by a set of labels by introducing orders for sets of labels and shows that there are four types of orders, which are characterized by whether the labels of expressed data includes every label of the given set of labels within the range of the set. Desirable properties of the orders, data is also expressed by the higher set of labels and different sets of labels express different data, are discussed for the orders.

Dynamical Behaviors in a Discrete Predator-prey Model with a Prey Refuge

By incorporating a prey refuge, this paper proposes new discrete Leslie–Gower predator–prey systems with and without Allee effect. The existence of fixed points are established and the stability of fixed points are discussed by analyzing the modulus of characteristic roots.

Unsteady Laminar Boundary Layer Forced Flow in the Region of the Stagnation Point on a Stretching Flat Sheet

This paper analyses the unsteady, two-dimensional stagnation point flow of an incompressible viscous fluid over a flat sheet when the flow is started impulsively from rest and at the same time, the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. The partial differential equations governing the laminar boundary layer forced convection flow are non-dimensionalised using semi-similar transformations and then solved numerically using an implicit finitedifference scheme known as the Keller-box method. Results pertaining to the flow and heat transfer characteristics are computed for all dimensionless time, uniformly valid in the whole spatial region without any numerical difficulties. Analytical solutions are also obtained for both small and large times, respectively representing the initial unsteady and final steady state flow and heat transfer. Numerical results indicate that the velocity ratio parameter is found to have a significant effect on skin friction and heat transfer rate at the surface. Furthermore, it is exposed that there is a smooth transition from the initial unsteady state flow (small time solution) to the final steady state (large time solution).

Local Error Control in the RK5GL3 Method

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.