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An Efficient Analytical Method For Solving Singular Initial Value Problems Of Nonlinear Systems, Iryna Komashynska, Mohammed Al-Smadi, Omar Abu Arqub, Shaher Momani
An Efficient Analytical Method For Solving Singular Initial Value Problems Of Nonlinear Systems, Iryna Komashynska, Mohammed Al-Smadi, Omar Abu Arqub, Shaher Momani
Applied Mathematics & Information Sciences
The aim of the present analysis is to apply a relatively recent method, the residual-power series method (RPSM), in order to obtain efficient analytical numerical solutions for a class of nonlinear systems of initial value problems with finitely many singularities. The solution methodology provided the analytical solutions in terms of a rapidly convergent series with easily computable components. This novel approach possesses main advantage as compared to other exiting methods; it reproduces exact form when the solution is polynomial without linearization or perturbation; it can be applied without any limitation on the nature of the problem, type of classification, and …
Some Statistical Quantities Of A Quantum System In Hypergeometric And Negative Hypergeometric Distributions, Ali Algarni, S. Abdel-Khalek
Some Statistical Quantities Of A Quantum System In Hypergeometric And Negative Hypergeometric Distributions, Ali Algarni, S. Abdel-Khalek
Applied Mathematics & Information Sciences
In this paper we introduce a quantum system of the interaction between a two-level atom and input field initially prepared in hypergeometric and negative hypergeometric distributions. We study the dynamics of nonlocal correlation measured by von Neumann entropy or the field entropy. The statistical properties of the considered field will be discussed through the evolution of Wehrl space entropy. The relationship between Wehrl space entropy and entanglement will be explored. The effects of the field distribution parameters on the evolution of statistical quantities will be examined. It is shown that when the field is closed to the classical state no …
Effect Of Partial Slip On Peristaltic Flow Of A Sisko Fluid With Mild Stenosis Through A Porous Medium, Nabil T. M. El-Dabe, Galal M. Moatimid, Mohamed A. Hassan, Doaa R. Mostapha
Effect Of Partial Slip On Peristaltic Flow Of A Sisko Fluid With Mild Stenosis Through A Porous Medium, Nabil T. M. El-Dabe, Galal M. Moatimid, Mohamed A. Hassan, Doaa R. Mostapha
Applied Mathematics & Information Sciences
This paper investigates the effect of partial slip on peristaltic flow of a Sisko fluid through a porous medium. The flow is streaming through a tapered artery having a mild stenosis. The influences of heat and chemical reactions on blood flow are also taken into account. The governing equations of motion, energy and concentration are simplified by using the long wavelength and low Reynolds number approximations. The analytical solutions of these equations are obtained by considering a perturbation technique for small non- Newtonian Sisko fluid parameter. The pressure rise and friction force are numerically calculated. The numerical calculations with the …
An Interactive Method For Solving Multiple Objective Linear Fractional Programming Problem Based On Linear Optimization Models, Tahere Hossein-Abadi, Ali Payan
An Interactive Method For Solving Multiple Objective Linear Fractional Programming Problem Based On Linear Optimization Models, Tahere Hossein-Abadi, Ali Payan
Applied Mathematics & Information Sciences
This study aims to present an interactive method in order to solve multiple objective linear fractional programming problem (MOLFPP) according to the linear optimization models. Based on the nonlinear nature of the MOLFPP, presenting interactive methods to solve this problem usually involves long, massive, and complex calculation processes. In this paper, the MOLFPP turns into a linear programming problem (LPP) by disregarding some facts (by considering some negligence) through a linearization process. Then, the answer obtained from the new LPP is tested by an LPP in order to determine whether it is efficient or not. Finally, an efficient or dominant …
A Relation Between Hadamard Codes And Some Special Codes Over F2+Uf2, Mustafa ?Zkan, Figen ?Ke
A Relation Between Hadamard Codes And Some Special Codes Over F2+Uf2, Mustafa ?Zkan, Figen ?Ke
Applied Mathematics & Information Sciences
A Hadamard code which is written via a Hadamard matrix is (2n,4n,n) code. In this study some special codes over F2+uF2 = {0, 1, u, 1+u} where u2 = 0 are written and it is shown that images of these codes under a Gray map correspond binary Hadamard codes.
Different Method Estimations Of The Three Parameters Of Exponentiated Gompertz Distribution, Hanaa H. Abu-Zinadah, Anhar S. Al-Oufi
Different Method Estimations Of The Three Parameters Of Exponentiated Gompertz Distribution, Hanaa H. Abu-Zinadah, Anhar S. Al-Oufi
Applied Mathematics & Information Sciences
This article discusses the maximum likelihood, least squares, weighted least squares, and percentiles estimates of three parameters of an exponentiated Gompertz distribution based on complete sample. By using the mean square error through Monte Carlo simulation, this study compares the performances of estimates. Real data set is used as an example of the methods of estimations for the three parameters of exponentiated Gompertz distribution.
Reliable Wavelet Based Approximation Method For Some Nonlinear Differential Equations, Pandy Pirabaharan, R. David Chandrakumar, G. Hariharan
Reliable Wavelet Based Approximation Method For Some Nonlinear Differential Equations, Pandy Pirabaharan, R. David Chandrakumar, G. Hariharan
Applied Mathematics & Information Sciences
In this paper, we have developed a Chebyshev wavelet based approximation method to solve some nonlinear differential equations (NLDEs) arrising in science and engineering. To the best of our knowledge, until now there is no rigorous shifted second kind Chebyshev wavelet (S2KCWM) solution has been addressed for the nonlinear differential equations. With the help of shifted second kind Chebyshev wavelets operational matrices, the linear and nonlinear differential equations are converted into a system of algebraic equations. The convergence of the proposed method is established. Finally, we have given some numerical examples to demonstrate the validity and applicability of the proposed …
Using Clustering Algorithm To Validate The Golf Backswing Action Simulated By Microsoft Kinect Motion-Sensing Photography, Wen-Cheng Wang, Hao-Hsiang Ku, Seng-Su Tsang
Using Clustering Algorithm To Validate The Golf Backswing Action Simulated By Microsoft Kinect Motion-Sensing Photography, Wen-Cheng Wang, Hao-Hsiang Ku, Seng-Su Tsang
Applied Mathematics & Information Sciences
While most golfers concern about the path that golf club travels on swing plane or the angle of the club face when addressing, rather the detrimental part may lie in golfer’s body rotation. This research delineate a measure in capturing golfer’s swing motions in which the Kinect motion tracking by Microsoft is adopted to validate the proposed measure. Subjects were hired to perform golf swings in front of the Kinect skeleton tracking system where subject’s 20 joint positions were recorded. The derived data were analyzed with ANOVA and multivariate clustering. Without clustering, the three investigated factors (gender, age and experience) …
A Comparison On Solutions Of Fifth-Order Boundary- Value Problems, Ali Akgül, Mustafa Inc, Adem Kılıçman
A Comparison On Solutions Of Fifth-Order Boundary- Value Problems, Ali Akgül, Mustafa Inc, Adem Kılıçman
Applied Mathematics & Information Sciences
A fast and accurate numerical scheme for the solution of fifth-order boundary-value problems has been investigated in this work. We apply the reproducing kernel method (RKM) for solving this problem. The analytical results of the equations have been acquired in terms of convergent series with easily computable components. We compare our results with the numerical methods: Bspline method, decomposition method, variational iteration method, Sinc-Galerkin method and homotopy perturbation method. The comparison of the results with exact ones is made to confirm the validity and efficiency.
On Commutator And Power Subgroups Of Some Coxeter Groups, Firat Ates, I. Naci Cangul, Esra K. Cetinalp, A. Sinan Cevik, Eylem Guzel Karpuz
On Commutator And Power Subgroups Of Some Coxeter Groups, Firat Ates, I. Naci Cangul, Esra K. Cetinalp, A. Sinan Cevik, Eylem Guzel Karpuz
Applied Mathematics & Information Sciences
In this paper the commutator subgroups of the affine Weyl group of type e C n−1 (n ≥ 3) and the triangle Coxeter groups are studied. Also it is given all power subgroups of the affine Weyl group of type e A n−1 (n ≥ 3). We should note that, as in our knowledge, although the concept of this study seems in pure mathematics, it is known that affine Weyl groups have a direct relationship between discrete dynamical systems and Painlev´e equations (cf. [16]).
A Fuzzy Eoq Model With Allowable Shortage Under Different Trade Credit Terms, Chandra K. Jaggi, V. S. S. Yadavalli, Anuj Sharma, Sunil Tiwari
A Fuzzy Eoq Model With Allowable Shortage Under Different Trade Credit Terms, Chandra K. Jaggi, V. S. S. Yadavalli, Anuj Sharma, Sunil Tiwari
Applied Mathematics & Information Sciences
The present study formulates a fuzzy economic order quantity model under conditions of permissible delay in payments by considering price-dependent demand and higher interest earn rate on fixed sales revenue. This research paper scrutinizes all the possible cases which may exist inclusive of those that have not been considered by researchers so far. The proposed models allow fully backlog shortages. The proper mathematical models for various cases are developed to determine the optimal order quantity, the time period in which inventory of the positive stock is finished in addition to the total cycle length by maximizing the total fuzzy profit …
Solitary Solutions For Some Nonlinear Evolution Equations Using Bernoulli Method, A. Hussein
Solitary Solutions For Some Nonlinear Evolution Equations Using Bernoulli Method, A. Hussein
Applied Mathematics & Information Sciences
New solitary solutions of some nonlinear partial differential equations are constructed using the generalized Bernoulli method. The main idea of this method is to make use of Bernoulli differential equation which has a simple exponential solution. The ZK-BBM (Zakharov-Kuznetsov-Benjamin–Bona–Mahony), a nonlinear dispersive, and the general Burgers-Fisher equations are solved and numerically investigated. The ZK equation that describes two-dimensional, magnetized, collisionless pair ions plasma is also presented as a problem of physical interest. Comparisons with G’/G-expansion method are given for the sake of assessments of Bernoulli method. Successfully, this method not only gives new solitary solutions of the problems under consideration …
New Perspectives On Nonlinear Multi-Atoms Interacting With A Cavity Field, Y. S. El-Saman, S. Abdel-Khalek, A. Badawi, M. Abdel-Aty
New Perspectives On Nonlinear Multi-Atoms Interacting With A Cavity Field, Y. S. El-Saman, S. Abdel-Khalek, A. Badawi, M. Abdel-Aty
Applied Mathematics & Information Sciences
We investigate the entanglement dynamics of two two-level atoms interacting with a quantized cavity field, considering the level shifts produced by the Stark effect.We perform comparisons of the entanglement evolution of this system when the cavity is filled with a Kerr-like medium. The presence of entanglement sudden death and sudden birth using extended Werner-like states is observed. Entanglement is guaranteed to survive and can be easily adapted to allow for periodic behavior. The similar dynamic relations between both the Kerr-like medium and the Stark-shift models are shown.
Stochastic Analysis Of A System With Cold Standby, General Distribution And Random Change In Units, Mohamed Salah El-Sherbeny
Stochastic Analysis Of A System With Cold Standby, General Distribution And Random Change In Units, Mohamed Salah El-Sherbeny
Applied Mathematics & Information Sciences
This paper discusses the stochastic analysis of a two-unit cold standby system, taking into account that the operative and the standby units are exchanged at random time intervals. Failure, repair and exchanging time are following general distributions. Using semi-Markov process and regenerative point technique in Markov renewal process, we develop the explicit expressions for the mean time to system failure, MTSF and steady-state availability, A(¥) for the system. Some special cases have been studied numerically and graphically to explain the effect of the system parameters on system performance. We also compute the sensitivity and relative sensitivity analysis for the MTSF …
A Residual Power Series Technique For Solving Systems Of Initial Value Problems, Shaher Momani, Omar Abu Arqub, Ma’Mon Abu Hammad, Zaer S. Abo-Hammour
A Residual Power Series Technique For Solving Systems Of Initial Value Problems, Shaher Momani, Omar Abu Arqub, Ma’Mon Abu Hammad, Zaer S. Abo-Hammour
Applied Mathematics & Information Sciences
In this article, a residual power series technique for the power series solution of systems of initial value problems is introduced. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. The proposed technique obtains Taylor expansion of the solution of a system and reproduces the exact solution when the solution is polynomial. Numerical examples are included to demonstrate the efficiency, accuracy, and applicability of the presented technique. The results reveal that the technique is very effective, straightforward, and simple.
New Efficient Method For Coding Color Images, Walaa M. Abd-Elhafiez, Essam O. Abdel-Rahman
New Efficient Method For Coding Color Images, Walaa M. Abd-Elhafiez, Essam O. Abdel-Rahman
Applied Mathematics & Information Sciences
In this paper a novel color image compression technique for efficient storage and delivery of data is proposed. The proposed compression technique started by RGB to YCbCr color transformation process. Secondly, the canny edge detection is used to classify the blocks into edge and non-edge block. Each color component Y, Cb, and Cr compressed by discrete cosine transform (DCT) process, quantizing and coding step by step using adaptive arithmetic coding. Our technique is concerned with the compression ratio, bits per pixel and peak signal to noise ratio, and produc better results than JPEG and more recent published schemes (like, CBDCT-CABS …
Automatic Data Understanding: The Tool For Intelligent Man-Machine Communication, Wladyslaw Homenda, Witold Pedrycz
Automatic Data Understanding: The Tool For Intelligent Man-Machine Communication, Wladyslaw Homenda, Witold Pedrycz
Applied Mathematics & Information Sciences
The paper is focused on man-machine communication, which is perceived in terms of data exchange. Understanding data being exchanged is the fundamental property of intelligent communication. The main objective of this paper is to introduce the paradigm of intelligent data understanding. The paradigm stems from syntactic and semantic characterization of data and is soundly based on the paradigm of granular structuring of data and computation. The paper does not introduce a formal theory of intelligent data understanding. Instead this paradigm as well as notions of granularity, semantics and syntax are cast within the domain of music information. The domain immersion …
Multidimensional Scaling In The Poincaré Disk, Andrej Cvetkovski, Mark Crovella
Multidimensional Scaling In The Poincaré Disk, Andrej Cvetkovski, Mark Crovella
Applied Mathematics & Information Sciences
Multidimensional scaling (MDS) is a class of projective algorithms traditionally used in Euclidean space to produce twoor three-dimensional visualizations of datasets of multidimensional points or point distances. More recently however, several authors have pointed out that for certain datasets, hyperbolic target space may provide a better fit than Euclidean space. In this paper we develop PD-MDS, a metric MDS algorithm designed specifically for the Poincar´e disk (PD) model of the hyperbolic plane. Emphasizing the importance of proceeding from first principles in spite of the availability of various black box optimizers, our construction is based on an elementary hyperbolic line search …
On The Solvability Of A Nonlinear Optimization Problem For Thermal Processes Described By Fredholm Integro-Differential Equations With External And Boundary Controls, Akylbek Kerimbekov, Elmira Abdyldaeva, Raihan Nametkulova, Aisha Kadirimbetova
On The Solvability Of A Nonlinear Optimization Problem For Thermal Processes Described By Fredholm Integro-Differential Equations With External And Boundary Controls, Akylbek Kerimbekov, Elmira Abdyldaeva, Raihan Nametkulova, Aisha Kadirimbetova
Applied Mathematics & Information Sciences
In the present paper we studied the problem of nonlinear optimal control of the thermal processes described by Fredholm integro-differential equations when the control parameters are nonlinearly included into the equation as well as into the boundary condition. The concept of weak generalized solution of the boundary value problem is introduced and the algorithm for its construction is indicated. It is established that optimal control is defined as the solution of the system of nonlinear integral equations which contain unknown functions under and out of the integral and satisfy the additional condition in the form of the system of inequalities. …
An Effective Network Security Log Mining Algorithm Based On Fuzzy Clustering, Peng Wang, Xikun Ma, Jingjie Yu
An Effective Network Security Log Mining Algorithm Based On Fuzzy Clustering, Peng Wang, Xikun Ma, Jingjie Yu
Applied Mathematics & Information Sciences
In this paper, we concentrate on the network security log mining problem, and proposed a novel fuzzy clustering algorithm to solve it. The architecture of network security log mining system is discussed at first, and three main modules are included in this system, such as data pre-processing, pattern mining and pattern analyzing. The main work of network security log mining is to find the frequent attack sequences from log files, several properties related to network security are considered in this paper, that is, start time of attacking, attacking type, end time of attacking, source IP of attackers, route path of …
Structural Parameter Identification Of Wind-Excited High-Rise Buildings With Limited Output Measurements, Ying Lei, Qiaona Wang, Lijun Liu
Structural Parameter Identification Of Wind-Excited High-Rise Buildings With Limited Output Measurements, Ying Lei, Qiaona Wang, Lijun Liu
Applied Mathematics & Information Sciences
In this paper, an algorithm is proposed for the identification of structural parameters of tall buildings under unknown wind loading with limited measurements of acceleration response outputs. Dynamic wind loading on tall buildings at typical levels is estimated based on the fluctuating properties of wind. A tall building is decomposed into small size substructures based on its finite element formulation. Interconnection effects between adjacent substructures are considered as ‘additional unknown inputs’ to substructures. For each substructure, the identification algorithm is based on sequential application of extended Kalman estimator for the extended state vector of the substructure and least-squares estimation of …
On The Application Of Multicomplex Algebras In Numerical Integration, S. Shirinkam, A. Alaeddini, H. R. Millwater
On The Application Of Multicomplex Algebras In Numerical Integration, S. Shirinkam, A. Alaeddini, H. R. Millwater
Applied Mathematics & Information Sciences
In this paper, we propose a methodology to numerically integrate functions using multicomplex algebras and their corresponding matrix representations. The methodology employs multicomplex Taylor series expansion (MCTSE) to adaptively approximate and integrate a function using sufficiently small number of points. We investigate this methodology by presenting three different algorithms for various approximation strategies.We also use numerical studies to demonstrate the performance of the proposed methodology.
Alternative Method Of Measuring Concentration, Zygmunt Jacek Zawistowski, Wiesław Szczesny, Bolesław Borkowski, Ryszard Kozera, Yochanan Shachmurove
Alternative Method Of Measuring Concentration, Zygmunt Jacek Zawistowski, Wiesław Szczesny, Bolesław Borkowski, Ryszard Kozera, Yochanan Shachmurove
Applied Mathematics & Information Sciences
The most popular measure of concentration, Gini coefficient G, does not show uniformly all the changes taking place in a flow of goods between objects. This work presents alternative index of concentration IC that when used together with Gini index mitigate that inconvenience. Studies have shown that coefficient IC differs considerably from Gini index in sensitivity to flow of ”good”. The coefficient IC is more sensitive because it depends on value of change quadratically while Gini index only linearly. IC depends on coordinates more properly than G as it depends on difference in values of coordinates opposite to G which …
Computerized Classification Systemfor The Identification Of Soil Microorganisms, Michał Kruk, Ryszard Kozera, Stanisław Osowski, Paweł Trzciǹski, Lidia Sas-Paszt, Beata Sumorok
Computerized Classification Systemfor The Identification Of Soil Microorganisms, Michał Kruk, Ryszard Kozera, Stanisław Osowski, Paweł Trzciǹski, Lidia Sas-Paszt, Beata Sumorok
Applied Mathematics & Information Sciences
This paper presents the method of soil microorganisms identification from the microscopic digital images. The proposed approach includes: segmentation of the image, feature generation, selection of the most important features and the final recognition stage applying five different solutions of classifiers. The paper presents and discusses the results concerning the recognition of several most popular soil microorganisms: Bacillus subtilis, Paenibacillus glucanolyticus, Rachnella aquatilis, Scoleobasidium sp., Trichoderma sp., Pseudomonas fluorescens, Bacillus atrophaeus, Azotobacter sp., Streptomyces sp. and other bacterias and fungi. The proposed system enables the recognition of the microorganisms with the accuracy close to 98%.
Exponential Parameterization And Ε-Uniformly Sampled Reduced Data, Ryszard Kozera, Lyle Noakes
Exponential Parameterization And Ε-Uniformly Sampled Reduced Data, Ryszard Kozera, Lyle Noakes
Applied Mathematics & Information Sciences
We study the quality of piecewise-quadratic Lagrange interpolation for nonparametric data based on e -uniform sampling and different forms of exponential parameterization. Surprisingly, it turns out that there is a sharp discontinuity in the quality of interpolation: exponential parameterization performs no better than a blind uniform guess, except for the case of scaled cumulative chord, which matches parametric interpolation.
An Algorithm For Multiplication Of Two Biquaternions, Aleksandr Cariow, Galina Cariowa, Anna Malewicz
An Algorithm For Multiplication Of Two Biquaternions, Aleksandr Cariow, Galina Cariowa, Anna Malewicz
Applied Mathematics & Information Sciences
In this paper we introduce efficient algorithm for the multiplication of biquaternions. The direct multiplication of two biquaternions requires 64 real multiplications and 56 real additions. More effective solutions still do not exist.We show how to compute a product of the Pauli numbers with 24 real multiplications and 64 real additions. During synthesis of the discussed algorithm we use the fact that product of two biquaternions may be represented as vector-matrix product. The matrix that participates in the product calculating has unique structural properties that allow performing its advantageous decomposition. Namely this decomposition leads to significant reducing of the computational …
Functional Body Mesh Representation,, A Simplified Kinematic Model, Its Inference And Applications, Przemysław Skurowski, Magdalena Pawlyta
Functional Body Mesh Representation,, A Simplified Kinematic Model, Its Inference And Applications, Przemysław Skurowski, Magdalena Pawlyta
Applied Mathematics & Information Sciences
The paper describes a simplified representation of a body structure and a GMM based method for inferring from the motion capture data based on a functional relationship between the points. The proposed representation can be efficiently used for marker-wise processing of the data. The parent-child and sibling relationships are inferred on a coherence of movement and constancy of distances. For creating groups representing specific body parts we propose an incremental multicriterial clustering algorithm employing Gaussian mixture models. To infer body parts hierarchy we propose utilizing a consensus method.
Discrete Analogs Of The Comparison Theorem And Two-Sided Estimates Of Solution Of Parabolic Equations, Piotr Matus, Ryszard Kozera, Agnieszka Paradzinska, Denis Schadinskii
Discrete Analogs Of The Comparison Theorem And Two-Sided Estimates Of Solution Of Parabolic Equations, Piotr Matus, Ryszard Kozera, Agnieszka Paradzinska, Denis Schadinskii
Applied Mathematics & Information Sciences
In this paper, we prove the difference analogs of the comparison theorems for solutions of the Cauchy problem for a nonlinear ordinary differential equation (ODE). These theorems are used to analyse blow-up solution of finite-difference schemes (FDS) approximating the Neumann problem for a parabolic equation with a nonlinear source of power form. We also propose the method for obtaining the two-sided estimates of solution. This method is based on implicit and explicit FDS.
Fuzzy Cognitive Map Reconstruction: Dynamics Versus History, Wladyslaw Homenda, Agnieszka Jastrzebska, Witold Pedrycz
Fuzzy Cognitive Map Reconstruction: Dynamics Versus History, Wladyslaw Homenda, Agnieszka Jastrzebska, Witold Pedrycz
Applied Mathematics & Information Sciences
This study is concerned with a fundamental issue of time series representation for modeling and prediction with Fuzzy Cognitive Maps. We introduce two distinct time series representation schemes for Fuzzy Cognitive Map design. The first method is based on the temporal relationships, namely time series amplitude, amplitude change, and change of amplitude change (dynamics perspective). The second scheme is based on three consecutive historical observations: present value, past value and before past value (history perspective, 2nd order relationships). Introduced procedures are experimentally verified and compared on several synthetic and real-world time series of various characteristics. The history-oriented time series representation …
Convergence Orders In Length Estimation With Exponential Parameterization And E -Uniformly Sampled Reduced Data, Ryszard Kozera, Lyle Noakes, Piotr Szmielew
Convergence Orders In Length Estimation With Exponential Parameterization And E -Uniformly Sampled Reduced Data, Ryszard Kozera, Lyle Noakes, Piotr Szmielew
Applied Mathematics & Information Sciences
We investigate the length approximation of the unknown regular curve in arbitrary Euclidean space upon applying a piecewise-quadratic interpolation based on e -uniformly sampled reduced data in combination with the exponential parameterization. As proved in this paper, similarly to the trajectory estimation, there is a discontinuity in the quality of length estimation with exponential parameterization performing no better than a blind uniform guess for the unknown knots, except for the case of cumulative chords. The theoretical asymptotic estimates established here for length approximation are also experimentally confirmed to be nearly sharp.