Search results for: hyper singular integral equation

Authors: Ahmet Tekcan, Arzu Özkoç, Hatice Alkan

Abstract:

In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp.

Keywords: Diophantine equation, Pell equation, quadratic form.

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Authors: Nicole Pearcy, Jonathan J. Crofts, Nadia Chuzhanova

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In this paper, we employ a directed hypergraph model to investigate the extent to which environmental variability influences the set of available biochemical reactions within a living cell. Such an approach avoids the limitations of the usual complex network formalism by allowing for the multilateral relationships (i.e. connections involving more than two nodes) that naturally occur within many biological processes. More specifically, we extend the concept of network reciprocity to complex hyper-networks, thus enabling us to characterise a network in terms of the existence of mutual hyper-connections, which may be considered a proxy for metabolic network complexity. To demonstrate these ideas, we study 115 metabolic hyper-networks of bacteria, each of which can be classified into one of 6 increasingly varied habitats. In particular, we found that reciprocity increases significantly with increased environmental variability, supporting the view that organism adaptability leads to increased complexities in the resultant biochemical networks.

Keywords: Complexity, hypergraphs, reciprocity, metabolism.

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Authors: Farid Saeidi, Serkan Dag

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In this study, fracture analysis of a fibrous composite laminate with variable fiber spacing is carried out using Jk-integral method. The laminate is assumed to be under thermal loading. Jk-integral is formulated by using the constitutive relations of plane orthotropic thermoelasticity. Developed domain independent form of the Jk-integral is then integrated into the general purpose finite element analysis software ANSYS. Numerical results are generated so as to assess the influence of variable fiber spacing on mode I and II stress intensity factors, energy release rate, and T-stress. For verification, some of the results are compared to those obtained using displacement correlation technique (DCT).

Keywords: Jk-integral, variable fiber spacing, thermoelasticity, t-stress, finite element method, fibrous composite.

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Authors: B. Rezaei, G. R. Boroun, M. Abdolmaleki

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The bound state energy of three quark systems is studied in the framework of a non- relativistic spin independent phenomenological model. The hyper- spherical coordinates are considered for the solution this system. According to Jacobi coordinate, we determined the bound state energy for (uud) and (ddu) quark systems, as quarks are flavorless mass, and it is restrict that choice potential at low and high range in nucleon bag for a bound state.

Keywords: Adiabatic expansion, grand angular momentum, binding energy, perturbation, baryons.

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Authors: Soroosh Rezazadeh, Mehran Yazdi

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In this paper, a robust digital image watermarking scheme for copyright protection applications using the singular value decomposition (SVD) is proposed. In this scheme, an entropy masking model has been applied on the host image for the texture segmentation. Moreover, the local luminance and textures of the host image are considered for watermark embedding procedure to increase the robustness of the watermarking scheme. In contrast to all existing SVD-based watermarking systems that have been designed to embed visual watermarks, our system uses a pseudo-random sequence as a watermark. We have tested the performance of our method using a wide variety of image processing attacks on different test images. A comparison is made between the results of our proposed algorithm with those of a wavelet-based method to demonstrate the superior performance of our algorithm.

Keywords: Watermarking, copyright protection, singular value decomposition, entropy masking, texture segmentation.

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Authors: Chiharu Okuma, Naoki Yamamoto, Jun Murakami

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As a method of expanding a higher-order tensor data to tensor products of vectors we have proposed the Third-order Orthogonal Tensor Product Expansion (3OTPE) that did similar expansion as Higher-Order Singular Value Decomposition (HOSVD). In this paper we provide a computation algorithm to improve our previous method, in which SVD is applied to the matrix that constituted by the contraction of original tensor data and one of the expansion vector obtained. The residual of the improved method is smaller than the previous method, truncating the expanding tensor products to the same number of terms. Moreover, the residual is smaller than HOSVD when applying to color image data. It is able to be confirmed that the computing time of improved method is the same as the previous method and considerably better than HOSVD.

Keywords: Singular value decomposition (SVD), higher-orderSVD (HOSVD), outer product expansion, power method.

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Authors: Anouar Ben Khalifa, Sami Gazzah, Najoua Essoukri BenAmara

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The Choquet integral is a tool for the information fusion that is very effective in the case where fuzzy measures associated with it are well chosen. In this paper, we propose a new approach for calculating fuzzy measures associated with the Choquet integral in a context of data fusion in multimodal biometrics. The proposed approach is based on genetic algorithms. It has been validated in two databases: the first base is relative to synthetic scores and the second one is biometrically relating to the face, fingerprint and palmprint. The results achieved attest the robustness of the proposed approach.

Keywords: Multimodal biometrics, data fusion, Choquet integral, fuzzy measures, genetic algorithm.

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Authors: Tapas Kumar Sinha, Joseph Mathew

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Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).

Keywords: KdV equation, Asymptotic Degeneracy, Solitons, Inverse Scattering

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Authors: Liang Zhang, Hai-Tao Zhang, W ei-Yong Ying, Ding-Ye Fang

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Dehydration of methanol to dimethyl ether (DME) over a commercial Al2O3 catalyst was studied in an isothermal integral fixed bed reactor. The experiments were performed on the temperature interval 513-613 K, liquid hourly space velocity (LHSV) of 0.9-2.1h-1, pressures between 0.1 and 1.0 MPa. The effect of different operation conditions on the dehydration of methanol was investigated in a laboratory scale experiment. A new intrinsic kinetics equation based on the mechanism of Langmuir-Hinshelwood dissociation adsorption was developed for the dehydration reaction by fitting the expressions to the experimental data. An activation energy of 67.21 kJ/mol was obtained for the catalyst with the best performance. Statistic test showed that this new intrinsic kinetics equation was acceptable.

Keywords: catalyst, dimethyl ether, intrinsic kinetics, methanol

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Authors: Longqiao Zhou, Zixin Liu, Shu Lü

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This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

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Authors: Said Laachir, Aziz Laaribi

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The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

Keywords: Helmholtz equation, Nikiforov-Uvarov method, exact solutions, eigenfunctions.

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Authors: Osman Bizim

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In this work we study elliptic divisibility sequences over finite fields. MorganWard in [11, 12] gave arithmetic theory of elliptic divisibility sequences. We study elliptic divisibility sequences, equivalence of these sequences and singular elliptic divisibility sequences over finite fields Fp, p > 3 is a prime.

Keywords: Elliptic divisibility sequences, equivalent sequences, singular sequences.

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Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

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An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation.

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Authors: Artion Kashuri, Rozana Liko

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In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite–Hadamard’s inequalities, k–Riemann–Liouville fractional integral, H¨older’s inequality, Special means.

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Authors: Tohru Kawabe

Abstract:

In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: Sliding Mode Control, Model Predictive Control, Integral Action, Electric Vehicle, Slip suppression.

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Authors: Hidetoshi Konno, Akio Suzuki

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The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.

Keywords: Transient population dynamics, Phase singularity, Birth-death process, Non-stationary Master equation, nonlinear Langevin equation, generalized Logistic equation.

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Authors: Aouachria Mekki

Abstract:

We consider a spin-1/2 particle interacting with a time-dependent magnetic field using path integral formalism. The propagator is first of all written in the standard form replacing the spin by two fermionic oscillators via the Schwinger model. The propagator is then exactly determined, thanks to a simple transformation, and the transition probability is deduced.

Keywords: Path integral, formalism, Propagator.

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Authors: Shai Sarussi

Abstract:

Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: Algebras over integral domains, Alexandroff topology, valuation domains, integral domains.

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Authors: N. Ebrahimi, J. Rashidinia

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In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

Keywords: Convergence analysis, Cubic B-spline, Newton- Cotes formula, System of Fredholm and Volterra integral equations.

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Authors: Nisha Goyal, R.K. Gupta

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This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.

Keywords: Sawada-Kotera-Kadomtsev-Petviashivili equation, Bogoyavlensky-Konoplechenko equation,

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Authors: Rekik Rima, Aouachria Mekki

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We study the movement of a two-level atom in interaction with time dependent nonuniform magnetic filed using the path integral formalism. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions. Then it is determined exactly using perturbation methods. Thus the Rabi formula of the system are deduced.

Keywords: Path integral, Formalism, Propagator, Transition probability.

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Authors: Renata Mekovec, Dijana Peras, Ruben Picek

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The advent of the Internet, mobile devices and social media is revolutionizing the experience of retail customers by linking multiple sources through various channels. Omnichannel retailing is a retailing that combines multiple channels to allow customers to seamlessly leverage all the distribution information online and offline while shopping. Therefore, today data are an asset more critical than ever for all organizations. Nonetheless, because of its heterogeneity through platforms, developers are currently facing difficulties in dealing with personal data. Considering the possibilities of omnichannel communication, this paper presents channel categorization that could enhance the customer experience of omnichannel center called hyper center. The purpose of this paper is fundamentally to describe the connection between the omnichannel hyper center and the customer, with particular attention to privacy protection. The first phase was finding the most appropriate channels of communication for hyper center. Consequently, a selection of widely used communication channels has been identified and analyzed with regard to the effect requirements for optimizing user experience. The evaluation criteria are divided into 3 groups: general, user profile and channel options. For each criterion the weight of importance for omnichannel communication was defined. The most important thing was to consider how the hyper center can make user identification while respecting the privacy protection requirements. The study carried out also shows what customer experience across digital networks would look like, based on an omnichannel approach owing to privacy protection principles.

Keywords: Personal data, privacy protection, omnichannel communication, retail.

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Authors: Khalifa AlShaqsi

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The author introduced the integral operator , by using this operator a new subclasses of analytic functions are introduced. For these classes, several Fekete-Szeg¨ type coefficient inequalities are obtained.

Keywords: Integral operator, Fekete-Szeg¨ inequalities, Analytic functions.

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Authors: Lv Yuhua

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In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.

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Authors: Anjali Verma, Ram Jiwari, Jitender Kumar

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This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

Keywords: Shallow water wave equation, Exact solutions, (G'/G) expansion method.

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Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

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The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.

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Authors: Samson Davoyan, Tatevik Sahakyan

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The purpose of this report is to suggest a new methodology for the assessment of the comparative efficiency of the reforms made in different countries by an integral index. We have highlighted the reforms made in post-crisis period in 21 former socialist countries. The integral index describes the social-economic development level. The integral index contains of six indexes: The Global Competitiveness Index, Doing Business, The Corruption Perception, The Index of Economic Freedom, The Human Development, and The Democracy Index, which are reported by different international organizations. With the help of our methodology we first summarized the above-mentioned 6 indexes and attained 1 general index, besides, our new method enables us to assess the comparative efficiency of the reforms made in different countries by analyzing them. The purpose is to reveal the opportunities and threats of socialeconomic reforms in different directions.

Keywords: Assessment, comparative, effectiveness, reforms

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Authors: Shatirah Akib, Teuku K. Syamsura, S.M. Shirazi, Moatasem M. Fayyadh, Budhi Primasari

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The purpose of this paper is to summarize the following protection of scouring countermeasures by using Bentonite-Enhanced Sand (BES) mixtures. The concept of underground improvement is being used in this study to reduce the void of the sand. The sand bentonite mixture was used to bond the ground soil conditions surrounding the pile of integral bridge. The right composition of sand bentonite mixture was proposed based on previous findings. The swelling effect of bentonite also was investigated to ensure there is no adverse impact to the structure of the integral bridge. ScourScour, another name for severe erosion, occurs when the erosive capacity of water resulting from natural and manmade events exceeds the ability of earth materials to resist its effects. According to AASHTO LRFD Specifications (Section C3.7.5), scour is the most common reason for the collapse of highway bridges in the United States

Keywords: bentonite, integral bridge, possible protection, scouring

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Authors: Irina Eglite, Andrei A. Kolyshkin

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Method of multiple scales is used in the paper in order to derive an amplitude evolution equation for the most unstable mode from two-dimensional shallow water equations under the rigid-lid assumption. It is assumed that shallow mixing layer is slightly curved in the longitudinal direction and contains small particles. Dynamic interaction between carrier fluid and particles is neglected. It is shown that the evolution equation is the complex Ginzburg-Landau equation. Explicit formulas for the computation of the coefficients of the equation are obtained.

Keywords: Shallow water equations, mixing layer, weakly nonlinear analysis, Ginzburg-Landau equation

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