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आयतन 7, मुद्दा 1 (2018)

शोध आलेख

Simulation of Dimple Characteristics on the Trajectories of a Dimpled Sphere (Golf Ball) in Motion

Wainaina M, Kimathi M and Malonza D

A mathematical model describing the flight motion of a golf ball is developed, and the effects of dimple characteristics are studied. Using the Newton’s second law of motion, the equations governing the motion of the golf ball are developed in three dimensions. In this development the size, depth and number of dimples are taken into account. By varying the dimple size, depth and number, the effects of these characteristics are simulated via a MatLab code in which the Dormand-Prince Runge Kutta method is implemented to solve the model equations. The results of the numerical simulations that show how the golf ball trajectory is influenced by the dimple characteristics such as dimple depth, size and number within the accepted range of the Reynolds number are displayed and discussed.

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Hosoya Polynomial and Topological Indices of the Jahangir Graph J7,m

Nizami AR and Farman T

The Hosoya polynomial of a graph was introduced by H. Hosoya in 1988, and the most interesting application of the Hosoya polynomial is that almost all distance-based graph invariants, which are used to predict physical, chemical and pharmacological properties of organic molecules, can be recovered from the Hosoya polynomial. In this article we not only give the general form of the Hosoya polynomial of the Jahangir graph J7,m, m ≥ 3, but also give the general forms of the topological indices, Wiener, hyper Wiener, Harary, and Tratch Stankevitch-Zefirov.

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Segmentation Model for Noisy and Intensity Inhomogeneity Images via Logarithmic Density Function

Ali S and Dayyan B

This manuscript is devoted to the study of a new image segmentation model for noisy and intensity inhomogeneity images based on logarithmic density function. Local image information is necessary for inhomogeneous images but at the same time, it is defective for noisy images as a consequence local information misguide the motion of active contour. However, the logarithmic function in our new proposed model is capable to capture minute details in images, while ignoring the noise in it which makes it robust in such kinds of images. Comparing with local Chan-Vese Model our new proposed model gives better performance treating noisy and intensity inhomogeneity images. Finally, experiments on some noisy and intensity inhomogeneity images show the robustness of our new proposed model.

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An Algorithm for Solving Indefinite Quadratic Programming Problems

Siddieg AMAEl

In this paper, we give in section (1) compact description of the algorithm for solving general quadratic programming problems (that is, obtaining a local minimum of a quadratic function subject to inequality constraints) is presented. In section (2), we give practical application of the algorithm, we also discuss the computation work and performing by the algorithm and try to achieve efficiency and stability as possible as we can. In section (3), we show how to update the QR-factors of , when the tableau is complementary ,we give updating to the LDLT-Factors of . In section (4) we are not going to describe a fully detailed method of obtaining an initial feasible point, since linear programming literature is full of such techniques.

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Modeling and Periodicity Analysis of Sunspot Time Series 1700-2015

Al-Khayat BYT and Hamdi MS

This paper deals with the modeling of sunspot time series 1700-2015. Different models are fitted from four different classes of mathematical and stochastic models in order to describe this series. A special attention is made for the periodicity analysis of this series through these models as well as their main properties.

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Great Matrix Equations

Jumaboyevich KN, Yuldashevich AQ and Ugli IOB

This paper is devoted to some identities of matrix and determinants. In this article, matrices inequalities are widely used. Matrices are non-optimistic. The matrix's determinants have been proven. In addition to the left module and the right module descriptions in this article. In general, this article is devoted to matrix approximation.

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High Order Mimetic Finite Difference Operators Satisfying a Gauss Divergence Theorem

Corbino J and Castillo JE

High order mimetic finite difference operators that satisfy a discrete extended Gauss Divergence theorem are presented. These operators have the same order of accuracy in the interior as well as the boundary, no free parameters and optimal bandwidth. They are constructed on staggered grids, using weighted inner products with a diagonal norm. We present several examples to demonstrate that mimetic finite difference schemes using these operators produce excellent results.

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Derivations on Trellises

Ebadi D and Sattari MH

In this paper, we introduce the notion of derivations for a trellis and investigate some related properties of this subject. We give some equivalent conditions under which a derivation is isotone for trellises. Also, we study fixed points and define f-derivation on T and Cartesian derivation on T1 × T2.

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Mathematical Modeling of Airflow on Respiratory Narrowing Due to Mumps Using Finite Element Method

Fatahillah A, Dafik and Aisyah S

Mumps can cause narrowing of the airway respiratory when the swelling occurs toward the chest because it can suppress the airways (trachea). This research will be constructed a mathematical model airway on respiratory narrowing due to mumps and solve it by using finite element method. The main problem in this research, how the results of simulation analysis airflow velocity airway on respiratory narrowing due to mumps are influenced by the size of radius of respiratory tract and the initial velocity. After the simulated, will be searched a relative error to be compared with the value of tolerance. Based on the simulation result using MATLAB found that the first simulation influence the size of radius with an initial velocity 0.4 m/s during normal condition (r=0.025 m) velocity in the narrowing airway 0.4010 m/s. If r=0.020 m and r=0.015 m the velocity will be increased being 1.0060 m/s and 3.2199 m/s with relative error value 0.005964. The second simulation an initial velocity and r=0.01631 m and velocity are 0.2 m/s, 0.4 m/s and 0.6 m/s found that the velocity in the narrowing airways increase being 1.0024 m/s, 2.2982 m/s and 4.0929 m/s with relative error value 0.002394.

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A New [ 14 8 3 ]-Linear Code From the Aunu Generated [ 7 4 2 ] -Linear Code and the Known [7 4 3 ] Hamming Code Using the (U|U+V) Construction

Ibrahim AA, Chun PB and Kamoh NM

In this communication, we enumerate the construction of a [ 7 4 2 ]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code. Our construction is due to the Carley table for n=7of the generated points of was permutations of the (132) and (123)-avoiding patterns of the non-associative AUNU schemes. Next, [ 7 4 2 ] linear code so constructed is combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code.

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Degree Diameter Problem on Oxide Network

Akhtar MS

The degree diameter problem is the problem of finding the largest graph (in terms of number of vertices) subject to the constraints on the degree and the diameter of the graph. Beyond the degree constraint there is no restriction on the number of edges (apart from keeping the graph simple) so the resulting graph may be thought of as being embedded in the complete graph. In a generalization of this problem, the graph is considered to be embedded in some connected host graph. This article considers embedding the graph in the oxide network and provides some exact values and some upper and lower bounds for the optimal graphs.

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A Methodology for Calculating Customer Credit Score Based on Customer Lifetime Value Model

Ghassempouri M and Hoseini SMS

Proper customer relationship management is among the facets that contribute to productivity at institutions. It is a requirement for customer relationship managers, especially at financial and credit institutions and at banks, to calculate and determine the customer’s creditworthiness and credit score. The aim of this study is to present a solution for calculating the customers’ value and their credit score without incurring the costs for collecting extra information. The primary source of data for this study is operation system database. Due to differences among operation systems, a comprehensive schema of the database is defined first. Only conventional indices and variables have been used in this schema, so that the presented solution can be generalized and will be applicable to most economic institutions. The calculation of the customer’s creditworthiness is performed with regard to the three variables of the “recency” of contact, the “frequency” of transactions, and the “monetary” amount. The collected data is divided into the two populations of “good” and “bad” customers. Variables from those two populations that possess significant differences are identified using statistical methods. Those variables are used in determining the customer’s credit score. Next, a solution is presented for comparing the efficiency of the models for the identification of the customer’s credit score. We will test and compare two statistical methods, the Logistic Regression model and the Fisher Discriminant Analysis, and two soft computing methods, the Multilayer Perception Network and the Vector Machine for determining the customer’s credit score. Additionally, a solution is offered for setting the number of layers and the number of neurons in the Multilayer Perception Network.

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The Relation between Centre Folding of Graph and its Chromatic Number

Rafat H

Coloring graph is a good branch in graph theory and has a lot of application in our life. So, in this paper we have defined a new type of folding. Also, we have found strong relations between this folding of graph and its chromatic number. Theorems governing the relations to be obtained. Traffic lights problem here was solved.

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On an Intrinsic Stochastic Fitzhugh: Nagumo Model

Elazab NS

The Fitzhugh-Nagumo model for excitable systems with a high excitation parameter solves the question of selfoscillatory and self-adaptivity in these systems. This is not the case in systems with low excitation parameter. An intrinsic stochastic model that accounts for endogenous fluctuations is proposed. This model solves the question of self-oscillatory and self-adaptivity in systems with low excitation parameter.

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The Very Cost Effective Graph Folding of the Join of Two Graphs

El-Kholy EM1

In this paper, we studied the very cost effective graph property for the join graph of two graphs. In general this is may or may not be a very cost effective graph. We obtained the conditions for the join graph of two graphs to be a very cost effective graph. First we proved that the join graph Pn∨Pm of path graphs is very cost effective graph if n+m is an even number and is not if n+m is an odd number. Then we proved that the join graph of any two cycle graphs Cn and Cm where n, m are both odd is very cost effective, and the join graph Pn∨Cn is a very cost effective graph if n is an odd number. Also we proved that the join graph G1∨G2 of two very cost effective graphs G1 and G2 is a very cost effective graph if n(G1) + n(G2) is even. Finally we proved that the graph folding of the join graph of two very cost effective graphs not always very cost effective but this will be the case if the sum of the numbers of the vertices in the image of the graph folding is even.

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