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## The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp

Let p ≥ 5 be a prime number and let Fp be a finite field. In this work, we determine the number of rational points on singular curves Ea : y2 = x(x - a)2 over Fp for some specific values of a.

## Ranking DMUs by Ideal PPS in Data Envelopment Analysis

An original DEA model is to evaluate each DMU optimistically, but the interval DEA Model proposed in this paper has been formulated to obtain an efficiency interval consisting of Evaluations from both the optimistic and the pessimistic view points. DMUs are improved so that their lower bounds become so large as to attain the maximum Value one. The points obtained by this method are called ideal points. Ideal PPS is calculated by ideal of efficiency DMUs. The purpose of this paper is to rank DMUs by this ideal PPS. Finally we extend the efficiency interval of a DMU under variable RTS technology.

## Induced Acyclic Path Decomposition in Graphs

A decomposition of a graph G is a collection ψ of graphs H1,H2, . . . , Hr of G such that every edge of G belongs to exactly one Hi. If each Hi is either an induced path in G, then ψ is called an induced acyclic path decomposition of G and if each Hi is a (induced) cycle in G then ψ is called a (induced) cycle decomposition of G. The minimum cardinality of an induced acyclic path decomposition of G is called the induced acyclic path decomposition number of G and is denoted by ¤Çia(G). Similarly the cyclic decomposition number ¤Çc(G) is defined. In this paper we begin an investigation of these parameters.

## Quadrature Formula for Sampled Functions

This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we update quadrature weights accordingly. We supply the theoretical quadrature error formula for this new approach. We show on examples the potential gain of this approach.

## Mathematical Model for the Transmission of P. Falciparum and P. Vivax Malaria along the Thai-Myanmar Border

The most Malaria cases are occur along Thai-Mynmar border. Mathematical model for the transmission of Plasmodium falciparum and Plasmodium vivax malaria in a mixed population of Thais and migrant Burmese living along the Thai-Myanmar Border is studied. The population is separated into two groups, Thai and Burmese. Each population is divided into susceptible, infected, dormant and recovered subclasses. The loss of immunity by individuals in the infected class causes them to move back into the susceptible class. The person who is infected with Plasmodium vivax and is a member of the dormant class can relapse back into the infected class. A standard dynamical method is used to analyze the behaviors of the model. Two stable equilibrium states, a disease-free state and an epidemic state, are found to be possible in each population. A disease-free equilibrium state in the Thai population occurs when there are no infected Burmese entering the community. When infected Burmese enter the Thai community, an epidemic state can occur. It is found that the disease-free state is stable when the threshold number is less than one. The epidemic state is stable when a second threshold number is greater than one. Numerical simulations are used to confirm the results of our model.

## Stability Analysis in a Fractional Order Delayed Predator-Prey Model

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

## Flow and Heat Transfer of a Nanofluid over a Shrinking Sheet

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

## Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

## Cryptography Over Elliptic Curve Of The Ring Fq[e], e4 = 0

Groups where the discrete logarithm problem (DLP) is believed to be intractable have proved to be inestimable building blocks for cryptographic applications. They are at the heart of numerous protocols such as key agreements, public-key cryptosystems, digital signatures, identification schemes, publicly verifiable secret sharings, hash functions and bit commitments. The search for new groups with intractable DLP is therefore of great importance.The goal of this article is to study elliptic curves over the ring Fq[], with Fq a finite field of order q and with the relation n = 0, n ≥ 3. The motivation for this work came from the observation that several practical discrete logarithm-based cryptosystems, such as ElGamal, the Elliptic Curve Cryptosystems . In a first time, we describe these curves defined over a ring. Then, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. In anther article we study their cryptographic properties, an attack of the elliptic discrete logarithm problem, a new cryptosystem over these curves.

## Some (v + 1, b + r + λ + 1, r + λ + 1, k, λ + 1) Balanced Incomplete Block Designs (BIBDs) from Lotto Designs (LDs)

The paper considered the construction of BIBDs using potential Lotto Designs (LDs) earlier derived from qualifying parent BIBDs. The study utilized Li’s condition  pr t−1  ( t−1 2 ) + pr− pr t−1 (t−1) 2  < ( p 2 ) λ, to determine the qualification of a parent BIBD (v, b, r, k, λ) as LD (n, k, p, t) constrained on v ≥ k, v ≥ p, t ≤ min{k, p} and then considered the case k = t since t is the smallest number of tickets that can guarantee a win in a lottery. The (15, 140, 28, 3, 4) and (7, 7, 3, 3, 1) BIBDs were selected as parent BIBDs to illustrate the procedure. These BIBDs yielded three potential LDs each. Each of the LDs was completely generated and their properties studied. The three LDs from the (15, 140, 28, 3, 4) produced (9, 84, 28, 3, 7), (10, 120, 36, 3, 8) and (11, 165, 45, 3, 9) BIBDs while those from the (7, 7, 3, 3, 1) produced the (5, 10, 6, 3, 3), (6, 20, 10, 3, 4) and (7, 35, 15, 3, 5) BIBDs. The produced BIBDs follow the generalization (v + 1, b + r + λ + 1, r +λ+1, k, λ+1) where (v, b, r, k, λ) are the parameters of the (9, 84, 28, 3, 7) and (5, 10, 6, 3, 3) BIBDs. All the BIBDs produced are unreduced designs.

## Statistical Computational of Volatility in Financial Time Series Data

It is well known that during the developments in the economic sector and through the financial crises occur everywhere in the whole world, volatility measurement is the most important concept in financial time series. Therefore in this paper we discuss the volatility for Amman stocks market (Jordan) for certain period of time. Since wavelet transform is one of the most famous filtering methods and grows up very quickly in the last decade, we compare this method with the traditional technique, Fast Fourier transform to decide the best method for analyzing the volatility. The comparison will be done on some of the statistical properties by using Matlab program.

## Mathematical Modeling for Dengue Transmission with the Effect of Season

Mathematical models can be used to describe the transmission of disease. Dengue disease is the most significant mosquito-borne viral disease of human. It now a leading cause of childhood deaths and hospitalizations in many countries. Variations in environmental conditions, especially seasonal climatic parameters, effect to the transmission of dengue viruses the dengue viruses and their principal mosquito vector, Aedes aegypti. A transmission model for dengue disease is discussed in this paper. We assume that the human and vector populations are constant. We showed that the local stability is completely determined by the threshold parameter, 0 B . If 0 B is less than one, the disease free equilibrium state is stable. If 0 B is more than one, a unique endemic equilibrium state exists and is stable. The numerical results are shown for the different values of the transmission probability from vector to human populations.

## Generalized Differential Quadrature Nonlinear Consolidation Analysis of Clay Layer with Time-Varied Drainage Conditions

In this article, the phenomenon of nonlinear consolidation in saturated and homogeneous clay layer is studied. Considering time-varied drainage model, the excess pore water pressure in the layer depth is calculated. The Generalized Differential Quadrature (GDQ) method is used for the modeling and numerical analysis. For the purpose of analysis, first the domain of independent variables (i.e., time and clay layer depth) is discretized by the Chebyshev-Gauss-Lobatto series and then the nonlinear system of equations obtained from the GDQ method is solved by means of the Newton-Raphson approach. The obtained results indicate that the Generalized Differential Quadrature method, in addition to being simple to apply, enjoys a very high accuracy in the calculation of excess pore water pressure.

## Group Similarity Transformation of a Time Dependent Chemical Convective Process

The time dependent progress of a chemical reaction over a flat horizontal plate is here considered. The problem is solved through the group similarity transformation method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation. The problem shows a singularity at the chemical reaction order n=1 and is analytically solved through the perturbation method. The behavior of the process is then numerically investigated for n≠1 and different Schmidt numbers. Graphical results for the velocity and concentration of chemicals based on the analytical and numerical solutions are presented and discussed.

## Statistical Properties and Performance of Ecological Indices Based On Relative Abundances

The Improved Generalized Diversity Index (IGDI) has been proposed as a tool that can be used to identify areas that have high conservation value and measure the ecological condition of an area. IGDI is based on the species relative abundances. This paper is concerned with particular attention is given to comparisons involving the MacArthur model of species abundances. The properties and performance of various species indices were assessed. Both IGDI and species richness increased with sampling area according to a power function. IGDI were also found to be acceptable ecological indicators of conditions and consistently outperformed coefficient of conservatism indices.

## Applications of Entropy Measures in Field of Queuing Theory

In the present communication, we have studied different variations in the entropy measures in the different states of queueing processes. In case of steady state queuing process, it has been shown that as the arrival rate increases, the uncertainty increases whereas in the case of non-steady birth-death process, it is shown that the uncertainty varies differently. In this pattern, it first increases and attains its maximum value and then with the passage of time, it decreases and attains its minimum value.

## Hopf Bifurcation Analysis for a Delayed Predator–prey System with Stage Structure

In this paper, a delayed predator–prey system with stage structure is investigated. Sufficient conditions for the system to have multiple periodic solutions are obtained when the delay is sufficiently large by applying Bendixson-s criterion. Further, some numerical examples are given.

## New Exact Three-Wave Solutions for the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System

New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.

## HIV Modelling - Parallel Implementation Strategies

We report on the development of a model to understand why the range of experience with respect to HIV infection is so diverse, especially with respect to the latency period. To investigate this, an agent-based approach is used to extract highlevel behaviour which cannot be described analytically from the set of interaction rules at the cellular level. A network of independent matrices mimics the chain of lymph nodes. Dealing with massively multi-agent systems requires major computational effort. However, parallelisation methods are a natural consequence and advantage of the multi-agent approach and, using the MPI library, are here implemented, tested and optimized. Our current focus is on the various implementations of the data transfer across the network. Three communications strategies are proposed and tested, showing that the most efficient approach is communication based on the natural lymph-network connectivity.

## Robot Vision Application based on Complex 3D Pose Computation

The paper presents a technique suitable in robot vision applications where it is not possible to establish the object position from one view. Usually, one view pose calculation methods are based on the correspondence of image features established at a training step and exactly the same image features extracted at the execution step, for a different object pose. When such a correspondence is not feasible because of the lack of specific features a new method is proposed. In the first step the method computes from two views the 3D pose of feature points. Subsequently, using a registration algorithm, the set of 3D feature points extracted at the execution phase is aligned with the set of 3D feature points extracted at the training phase. The result is a Euclidean transform which have to be used by robot head for reorientation at execution step.