# International Journal of Applied Mathematics and Informatics

**E-**ISSN: 2074-1278

Volume 7, 2013

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**Issue 1, Volume 7, 2013 **

Title of the Paper: **Coping with Incomplete Information in Real Time Scheduling Verification**

Authors: **Maurizio Talamo, Andrea Callia D’Iddio, Christian H. Schunck, Franco Arcieri**

Pages: **1-13**

Abstract: The scheduling of processes is of strategic importance in many areas of software engineering. Verifying the correctness of scheduling is critical to ensure data integrity, process efficiency and system security. Therefore a scheduling must often be verified quickly or even in “real time”. In this case it may be inefficient or too resource consuming to gather all the data about individual jobs. However, missing information may prevent the unique identification of each job in the scheduling. In this paper we define a framework in which we model this information loss and we define methods and algorithms to check the correctness of a scheduling with regard to the order in which the jobs are executed in the presence of such ambiguities. Given a set of jobs and a specification, which is defined as a set of dependencies between the jobs, the task is to check if the order in which the jobs are scheduled satisfies the dependencies. We use partial order structures to mathematically model dependencies in the specification and in the order of execution of the scheduled jobs. If some jobs become indistinguishable due to information loss it is not possible to determine all the precedences between jobs and the notion of dominance is lost. Here we use abstraction mechanisms at the combinatorial level to obtain new notions of dominance that enable the comparison of “ap-proximated” partial orders. Based on these results, methods and algo-rithms are developed which can be used to test actual schedulings with regard to their specifications.

Title of the Paper: **Solution of Linear Equations and Inequalities in Idempotent Vector Spaces**

Authors: **Nikolai Krivulin**

Pages: **14-23**

Abstract: Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The approach reduces the solution of the equation to that of a tropical optimization problem. Based on the approach, existence and uniqueness conditions are established for the solution, and a general solution to linear equations and inequalities are given.

Title of the Paper: **PDEM Estimator for Digital Elevation Model: Utilities**

Authors: **Jose Francisco Zelasco, Patrick Julien, Gaspar Porta, Kevin Ennis, Judith Donayo**

Pages: **24-31**

Abstract: The measurement of the precision of a DSM model in relation to another model of the same physical surface is done primarily by estimating the expectation of the squares of differences between pairs of points (called homologous points) which correspond to the same feature of the physical surface. But frequently there aren’t homologous points. In these cases, the procedure that is generally used has been to square the vertical distances between the models at selected points in a preferred (relative to a ‘natural’ horizontal plane) direction. This procedure only addresses the vertical component of the error, thus giving a biased estimate when the surface is not horizontal. In this paper we describe the Perpendicular Distance Evaluation Method (PDEM). The PDEM allows the estimation of planimetric errors in the x,y plane, not obtainable by other methods, and estimates for the vertical component which are superior to those obtained from the vertical distances method because they are not affected by the bias introduced by slanted surfaces. The planimetric estimates improve if the surface is relatively irregular. The PDEM provides estimates for the three dimensional error components when applied to a DSM (general case). This is the case of Dem obtained by IFSAR technology that has also a problem of correlation. When planimetric isometry is acceptable, a considerable simplification of the method is possible. For this last case we present the utilities allowing better understand the method and apply it appropriately. The PDEM is a useful tool for evaluating digital three dimensional surface model precision.

**Issue 2, Volume 7, 2013**

Title of the Paper: **Collaboration Algorithms between Intermediaries for Supporting Flexible Supply Chain Management**

Authors: **Mohd Izzuddin Mohd Tamrin, Tengku Mohd Tengku Sembok, Mira Kartiwi**

Pages: **33-43**

Abstract: The supply chain group consists of members from various locations in the network working together to deliver services to the client. Integration challenges remain as main issue for the group to create more flexible processes and allow modification to be made to the current and global pre-planned processes for the entire supply chain members in the group. The authors introduce Integrative Information Management Architecture (IIMA) running on collaboration algorithms which create semi automated intermediary processes to support management team address integration challenges. The collaboration algorithms are design to go through five main phases in order to continuously monitor and detect any deviations from the processes currently running at the vacinity of the members. The functionalities of existing systems across the members in the group are wrapped and introduce in the IIMA as services. This is to facilitate process restructuring by addding or dropping the required services into the global execution schedule. The authors had develop the prototype of the IIMA and evaluate it with three other related systems in a simulated environment. These systems simulated to support customization processes with common supply chain problems at the beginning and ending stages of that processes. The results demonstrate that the IIMA has the most stable performance in supporting the shared processes when stoke by the problems at both stages of the processes.

Title of the Paper: **Augmented Integrals for Optimal Control Problems**

Authors: **Javier F. Rosenblueth**

Pages: **44-54**

Abstract: By adding penalty functions to constrained minimum problems in finite dimensional spaces, one deals with unconstrained augmented problems for which the derivation of necessary optimality conditions can be obtained. Also, this technique yields in a natural way a method of multipliers for finding numerical solutions. In this paper we show how certain classes of optimal control problems with equality and inequality constraints can be treated in a similar way. A new notion of augmentability in optimal control is introduced and, without the usual assumption of normality, we derive first and second order necessary conditions for optimality.

Title of the Paper: **Cones of Critical Directions in Optimal Control**

Authors: **Javier F. Rosenblueth, Gerardo Sanchez Licea**

Pages: **55-67**

Abstract: In this paper we study a fundamental aspect of the theory of second order necessary conditions for certain classes of optimal control problems involving equality and/or inequality constraints in the control. It is well-known that, under certain normality assumptions, a certain quadratic form is nonnegative on a cone of critical directions (or differentially admissible variations). The purpose of this paper is to characterize normality in terms of some regularity assumptions and to illustrate through several examples the fact that, by assuming those types of regularity, the result may fail to hold on the former and larger sets of critical directions.

**Issue 3, Volume 7, 2013**

Title of the Paper: **Fuzzy Model for an Early Estimation of Software Development Effort**

Authors: **S. Elyassami, A. Idri**

Pages: **69-77**

Abstract: Estimating the cost of software is one of the most challenging tasks in project management. Accurate cost estimates of software projects and avoiding the overestimates and the underestimates are critical to reach the project’s success. Considerable research attention is now directed at gaining a better software cost estimating models. In this paper, we investigate the use of Fuzzy C5 decision tree for software cost estimation; it is designed by integrating the principles of C5 decision tree and the fuzzy set-theoretic concepts. The fuzzy logic is used to provide a formal description of concepts representing data by linguistic values and fuzzy variables in order to handle imprecision and uncertainties in software cost estimation. We have utilized the two statistics that are often used to measure the accuracy of predictive models: the mean magnitude relative error, MMRE, and the number of predictions within 25% of the actuals, pred(25). An empirical validation of our model is reported using the International Software Benchmarking Standards Group data repository. Empirical results approve the deductions gotten in previous studies: incorporate fuzzy logic and decision tree in cost estimation models improve greatly the accuracy of produced estimates. The results are compared with those produced by the fuzzy version of ID3 decision tree.

Title of the Paper: **Hermite Functions with Discontinuous Coefficients for the Solution of Fractal Diffusion Retrospective Problems**

Authors: **E. Mogileva, O. Yaremko**

Pages: **78-86**

Abstract: In this article we study the retrospective inverse problem. The retrospective inverse problem consists of in the reconstruction of a priori unknown initial condition of the dynamic system from its known final condition. Existence and uniqueness of the solution is proved.

Title of the Paper: **Effect of Perpendicular Magnetic Field on Chaos in a Cavity Heated from Below**

Authors: **Rajendra Prasad, A. K. Singh**

Pages: **87-96**

Abstract: This paper presents chaotic behavior due to a magnetic field applied perpendicular on a cavity heated from below using the theory of dynamical system. The solution to the non-linear problem is obtained by using a truncated Galerkin method to obtain a set of ordinary differential equation for the time evolution of the Galerkin amplitudes. The system of differential equations is solved by using the fourth-order Runge Kutta method. Below a certain critical value of the scaled Rayleigh number the unique motionless conduction solution is obtained. At slightly super-critical values of scaled Rayleigh number a pitchfork bifurcation occurs, leading to two different steady solutions. For highly supercritical scaled Rayleigh numbers transition to chaotic solutions occurs via a Hopf bifurcation. The chaotic behaviour can be obtained faster for decreasing Hartmann number as well as incrasing scaled Rayleigh number . Also variation in Nusselt number inreases with increasing scaled Rayleigh number and decreasing Hartmann number.

Title of the Paper: **A Stepping Stone Perspective to Detection of Network Threats**

Authors: **Mohd Nizam Omar, Angela Amphawan, Roshidi Din**

Pages: **97-106**

Abstract: Current computing trends such as cloud computing, file sharing and social networking promote collaboration and allow greater mobility for users. Nevertheless, these computing trends increase the vulnerability of networks to security threats and challenge network resources. An ingenious technique employed by attackers for retaining anonymity is by exploiting intermediary host computers or stepping stones to instigate attacks on other computers. This paper explores novel application of the stepping stone detection concept in addressing network threats such as spams, backdoors, proxy server intrusions and denial of service attacks. Preliminary stepping stone detection models for each security threat will be constructed and the potential detection process is delineated. These preliminary concepts and models may prove useful for further optimization of network security in conjunction with other conventional detection techniques.

Title of the Paper: **Compares of Some Algorithms by Using First and Second Derivative Multistep Methods**

Authors: **G. Mehdiyeva, M. Imanova, V. Ibrahimov**

Pages: **107-114**

Abstract: As is known, determination the solution of many problems of natural science can be reduced to determination of the solution of first and second orders ordinary differential equations. Typically solutions for ODEs second order are reduced to solving a system differential equations of first order. Here, has been analyzed known numerical methods for chronological manner, determined their advantages and disadvantages. To construct more accurate methods with extended stability region suggested the method constructed at the junction of second derivative multistep methods and hybrid methods. Proved advantage of the proposed method and constructed one-step method with the order of accuracy to which can be considered as a sense generalization of the trapezoid method. Constructed algorithm for using proposed methods.

**Issue 4, Volume 7, 2013**

Title of the Paper: **The Spectral Decomposition of Near-Toeplitz Tridiagonal Matrices**

Authors: **Nuo Shen, Zhaolin Jiang, Juan Li**

Pages: **115-122**

Abstract: Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomial, which is due to the zeros of Chebyshev polynomial of the first kind, and the eigenvectors are obtained by solving symmetric tridiagonal linear systems in terms of Chebyshev polynomial of the third kind or the fourth kind. By constructing the inverse of the transformation matrices, we give the spectral decomposition of this kind of tridiagonal matrices. Furthermore, the inverse (if the matrix is invertible), powers and a square root are also determined.

Title of the Paper: **Comparing Bayesian Methods for Estimating Parameters of Noisy Sinusoids**

Authors: **Dursun Üstündağ, Mehmet Cevri**

Pages: **123-134**

Abstract: This paper deals with parameter estimation of sinusoids within a Bayesian framework, where inferences about parameters require an evaluation of complicated high dimensional integrals or a solution of multi-dimensional optimization. Unfortunately, it is not possible in general to derive analytical Bayesian inferences. Therefore, the purpose of this paper is to study some of existing stochastic procedures, based on different sampling schemes and to compare their performances with respect to Cramér-Rao lower bound (CRLB), defined to be a limit on the best possible performance achievable for a method given a dataset. Furthermore, all simulations support their effectiveness and demonstrate their performances in terms of CRLB for different lengths of data sampling and signal-to noise ratio (SNR) conditions.

Title of the Paper: **Techniques to Create Multitime Extensions of Single-Time ODEs and PDEs**

Authors: **Laura G. Matei, Monica Pırvan, Lavinia L. Petrescu**

Pages: **135-142**

Abstract: The present paper describes some methods to extend classical single-time ODEs and PDEs, creating some multitime versions of these equations. Our approach is justified by examples of possible applications in different fields of science. The first section of paper motivates the interest in this subject. Three original ways to pass from the single-time formulation to several evolution variables are proposed: using some geometrical objects that extend some classical single-time PDEs and then finding families of multitime exact soliton solutions for the obtained multitime geometrical prolongations; creating new versions with more evolution variables for significant ODEs and PDEs, by accepting that the variable ”time” may be a function of certain parameters; introducing a multitime (tα) instead the singletime variable t and a directional derivative instead the partial derivative with respect to t, in first order ODEs. All these methods are applied to some classical modeling equations from physics, biology, economy, ecology. Our original techniques may be useful in modeling, in order to obtain efficient representations of some phenomena including more temporal scales evolving from slow to faster.

Title of the Paper: **Multi Objective Fuzzy Linear Programming Technique for Weighted Additive Model for Supplier Selection in Supply Chain Management**

Authors: **Kavitha C., Vijayalakshmi C.**

Pages: **143-152**

Abstract: Supplier selection and allocating orders to supplier is a complex multi objective problem which includes both quantitative and qualitative factors. In order to achieve an efficient solution in the quantitative factors, a Multi Objective Fuzzy Linear Programming [MOFLP] model with fuzziness in objective, resources, technological coefficient and resources for the proposed weighted additive model and it is compared with zimmermann method to help the management to allocate the optimum order quantities, in which the three objectives are to optimize purchasing cost, quality, and service and satisfy constraints like supplier’s capacity, supply chain demand etc are considered. The model has been applied to supplier selection of a high technology company named Multi-Flex Lami-Print Ltd which manufactures Flexible Packaging materials. In fuzzy supplier selection problem four different cases are considered to incorporate the uncertainty by zimmermann and weighted additive method. The result shows that the model is effective and applicable to industries.

Title of the Paper: **Dynamic Airport Ground Crew Scheduling Using a Heuristic Scheduling Algorithm**

Authors: **B. Rodič, A. Baggia**

Pages: **153-163**

Abstract: We describe the development of a heuristic scheduling algorithm developed for the purpose of workforce scheduling and shift construction at the Ljubljana JožePučnik Airport. The goal of the project was to develop a solution that would generate workforce shifts and allow rapid rescheduling and thus shorten the airport response time and improve the adaptability in conditions of dynamic flight schedules. Airport ground crew scheduling problem proved to be complex as there were conflicting demands in assigning personnel and equipment to tasks connected with aircraft arrivals and departures. We have attempted to use workforce algorithms described in literature to construct the solution, but due to specific requirements of the airport we have constructed heuristic algorithms that perform task schedule optimization, personnel and equipment requirements optimization and shift planning for airport ground crews and that may be also applicable to other airports of similar size and traffic.