Search results for: algebraic decomposition

Authors: S. R. Santhanam

Abstract:

A gifted child is one who gives evidence of creativity, good memory, rapid learning. In mathematics, a teacher often comes across some gifted children and they exhibit the following characteristics: unusual alertness, enjoying solving problems, getting bored on repetitions, self-taught, going beyond what teacher taught, ask probing questions, connecting unconnected concepts, vivid imagination, readiness for research work, perseverance of a topic. There are two main areas of research carried out on them: 1)identifying gifted children, 2) interacting and channelizing them. A lack of appropriate recognition will lead the gifted child demotivated. One of the main findings is if proper attention and nourishment are not given then it leads a gifted child to become depressed, underachieving, fail to reach their full potential and sometimes develop negative attitude towards school and study. After identifying them, a mathematics teacher has to develop them into a fall fledged achiever. The responsibility of the teacher is enormous. The teacher has to be resourceful and patient. But interacting with them one finds a lot of surprises and awesomeness. The elementary algebraic identities like (a+b)(a-b)=a²-b², expansion of like (a+b)²(a-b)² and others are taught to students, of age group 13-15 in India. An average child will be satisfied with a single proof and immediate application of these identities. But a gifted child expects more from the teacher and at one stage after a little training will surpass the teacher also. In this short paper, the author shares his experience regarding teaching algebraic identities to gifted children. The following problem was given to a set of 10 gifted children of the specified age group: If a natural number ‘n’ to expressed as the sum of the two squares, will 2n also be expressed as the sum of two squares? An investigation has been done on what multiples of n satisfying the criterion. The attempts of the gifted children were consolidated and conclusion was drawn. A second problem was given to them as: can two natural numbers be found such that the difference of their square is 3? After a successful solution, more situations were analysed. As a third question, the finding of the sign of an algebraic expression in three variables was analysed. As an example: if a,b,c are real and unequal what will be sign of a²+4b²+9c²-4ab-12bc-6ca? Apart from an expression as a perfect square what other methods can be employed to prove an algebraic expression as positive negative or non negative has been analysed. Expressions like 4x²+2y²+13y²-2xy-4yz-6zx were given, and the children were asked to find the sign of the expression for all real values of x,y and z. In all investigations, only basic algebraic identities were used. As a next probe, a divisibility problem was initiated. When a,b,c are natural numbers such that a+b+c is at least 6, and if a+b+c is divisible by 6 then will 6 divide a³+b³+c³. The gifted children solved it in two different ways.

Keywords: algebraic identities, gifted children, Indian scenario, research

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Authors: Salma Krafessi

Abstract:

The financial markets have a multifaceted, intricate environment, and enormous volumes of data are produced every day. To find investment possibilities, possible fraudulent activity, and market oddities, accurate anomaly identification in this data is essential. Conventional methods for detecting anomalies frequently fail to capture the complex organization of financial data. In order to improve the identification of abnormalities in financial time series data, this study presents Tucker Decomposition as a reliable multi-way analysis approach. We start by gathering closing prices for the S&P 500 index across a number of decades. The information is converted to a three-dimensional tensor format, which contains internal characteristics and temporal sequences in a sliding window structure. The tensor is then broken down using Tucker Decomposition into a core tensor and matching factor matrices, allowing latent patterns and relationships in the data to be captured. A possible sign of abnormalities is the reconstruction error from Tucker's Decomposition. We are able to identify large deviations that indicate unusual behavior by setting a statistical threshold. A thorough examination that contrasts the Tucker-based method with traditional anomaly detection approaches validates our methodology. The outcomes demonstrate the superiority of Tucker's Decomposition in identifying intricate and subtle abnormalities that are otherwise missed. This work opens the door for more research into multi-way data analysis approaches across a range of disciplines and emphasizes the value of tensor-based methods in financial analysis.

Keywords: tucker decomposition, financial markets, financial engineering, artificial intelligence, decomposition models

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Authors: S. Srednyak

Abstract:

We study a class of functional partial differential equations(FPDEs). This class is suggested by Quantum Field Theory. We derive general properties of solutions to such equations. In particular, we demonstrate that they lead to systems of coupled integral equations with singular kernels. We show that solutions to such hierarchies can be sought among functions with regular singularities at a countable set of subvarieties of the physical space. We also develop a formal analogy of basic constructions of differential geometry on functional manifolds, as this is necessary for in depth study of FPDEs. We also consider the case of linear overdetermined systems of functional differential equations and show that it can be completely solved in terms of formal solutions of a functional equation that is a functional analogy of a system of determined algebraic equations. This development leads us to formally define the functional analogy of algebraic geometry, which we call functional algebraic geometry. We study basic properties of functional algebraic varieties. In particular, we investigate the case of a formally discrete set of solutions. We also define and study functional analogy of discriminants. In the case of fully determined systems such that the defining functionals have regular singularities, we demonstrate that formal solutions can be sought in the class of functions with regular singularities. This case provides a practical way to apply our results to physics problems.

Keywords: functional equations, quantum field theory, holomorphic functions, Yang Mills mass gap problem, quantum chaos

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Authors: F. J. Adeyeye, D. Eni, K. M. Okedoye

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In this paper we present a Hybrid of Adomian decomposition method (ADM). This is the substitution of a One-step method of Taylor’s series approximation of orders I and II, into the nonlinear part of Adomian decomposition method resulting in a convergent series scheme. This scheme is applied to solve some Logistic problems represented as Abelian differential equation and the results are compared with the actual solution and Runge-kutta of order IV in order to ascertain the accuracy and efficiency of the scheme. The findings shows that the scheme is efficient enough to solve logistic problems considered in this paper.

Keywords: Adomian decomposition method, nonlinear part, one-step method, Taylor series approximation, hybrid of Adomian polynomial, logistic problem, Malthusian parameter, Verhulst Model

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Authors: Ahmed Machmoum, Malika El Kyal

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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: R. H. Hwang, J. H. Park, K. B. Yi

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Nitrous oxide (N2O) is now distinguished as an environmental pollutant. N2O is one of the representative greenhouse gases and N2O is produced by both natural and anthropogenic sources. So, it is very important to reduce N2O. N2O abatement processes are various processes such as HC-SCR, NH3-SCR and decomposition process. Among them, decomposition process is advantageous because it does not use a reducing agent. N2O decomposition is a reaction in which N2O is decomposed into N2 and O2. There are noble metals, transition metal ion-exchanged zeolites, pure and mixed oxides for N2O decomposition catalyst. Among the various catalysts, cobalt-based catalysts derived from hydrotalcites gathered much attention because spinel catalysts having large surface areas and high thermal stabilities. In this study, the effect of promoter and K addition on the activity was compared and analyzed. Co3O4 catalysts for N2O decomposition were prepared by co- precipitation method. Ce and Zr were added during the preparation of the catalyst as promoter with the molar ratio (Ce or Zr) / Co = 0.05. In addition, 1 wt% K2CO3 was doped to the prepared catalyst with impregnation method to investigate the effect of K on the catalyst performance. Characterizations of catalysts were carried out with SEM, BET, XRD, XPS and H2-TPR. The catalytic activity tests were carried out at a GHSV of 45,000 h-1 and a temperature range of 250 ~ 375 ℃. The Co3O4 catalysts showed a spinel crystal phase, and the addition of the promoter increased the specific surface area and reduced the particle and crystal size. It was exhibited that the doping of K improves the catalytic activity by increasing the concentration of Co2+ in the catalyst which is an active site for catalytic reaction. As a result, the K-doped catalyst showed higher activity than the promoter added. Also, it was found through experiments that Co2+ concentration and reduction temperature greatly affect the reactivity.

Keywords: Co₃O4, K-doped, N₂O decomposition, promoter

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Authors: Ranjit Biswas

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The existing subject Algebra is incomplete to support mathematical computations being done by scientists of all areas: Mathematics, Physics, Statistics, Chemistry, Space Science, Cosmology etc. even starting from the era of great Einstein. A huge hidden gap in the subject ‘Algebra’ is unearthed. All the scientists today, including mathematicians, physicists, chemists, statisticians, cosmologists, space scientists, and economists, even starting from the great Einstein, are lucky that they got results without facing any contradictions or without facing computational errors. Most surprising is that the results of all scientists, including Nobel Prize winners, were proved by them by doing experiments too. But in this paper, it is rigorously justified that they all are lucky. An algebraist can define an infinite number of new algebraic structures. The objective of the work in this paper is not just for the sake of defining a distinct algebraic structure, but to recognize and identify a major gap of the subject ‘Algebra’ lying hidden so far in the existing vast literature of it. The objective of this work is to fix the unearthed gap. Consequently, a different algebraic structure called ‘Region’ has been introduced, and its properties are studied.

Keywords: region, ROR, RORR, region algebra

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Authors: Christian Meinecke, Bernd Scholz-Reiter

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The integrated problem of production and distribution scheduling is relevant in many industrial applications. Thus, many heuristics to solve this integrated problem have been developed in the last decade. Most of these heuristics use a sequential working principal or a single decomposition and integration approach to separate and solve sub-problems. A heuristic using a multi-step decomposition and integration approach is presented in this paper and evaluated in a case study. The result show significant improved results compared with sequential scheduling heuristics.

Keywords: production and outbound distribution, integrated planning, heuristic, decomposition, integration

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Authors: Elham Kiyani

Abstract:

In this paper, we first introduce the concept of Q-efficient solutions in a real linear space not necessarily endowed with a topology, where Q is some nonempty (not necessarily convex) set. We also used the scalarization technique including the Gerstewitz function generated by a nonconvex set to characterize these Q-efficient solutions. The algebraic concepts of interior and closure are useful to study optimization problems without topology. Studying nonconvex vector optimization is valuable since topological interior is equal to algebraic interior for a convex cone. So, we use the algebraic concepts of interior and closure to define Q-weak efficient solutions and Q-Henig proper efficient solutions of set-valued optimization problems, where Q is not a convex cone. Optimization problems with set-valued maps have a wide range of applications, so it is expected that there will be a useful analytical tool in optimization theory for set-valued maps. These kind of optimization problems are closely related to stochastic programming, control theory, and economic theory. The paper focus on nonconvex problems, the results are obtained by assuming generalized non-convexity assumptions on the data of the problem. In convex problems, main mathematical tools are convex separation theorems, alternative theorems, and algebraic counterparts of some usual topological concepts, while in nonconvex problems, we need a nonconvex separation function. Thus, we consider the Gerstewitz function generated by a general set in a real linear space and re-examine its properties in the more general setting. A useful approach for solving a vector problem is to reduce it to a scalar problem. In general, scalarization means the replacement of a vector optimization problem by a suitable scalar problem which tends to be an optimization problem with a real valued objective function. The Gerstewitz function is well known and widely used in optimization as the basis of the scalarization. The essential properties of the Gerstewitz function, which are well known in the topological framework, are studied by using algebraic counterparts rather than the topological concepts of interior and closure. Therefore, properties of the Gerstewitz function, when it takes values just in a real linear space are studied, and we use it to characterize Q-efficient solutions of vector problems whose image space is not endowed with any particular topology. Therefore, we deal with a constrained vector optimization problem in a real linear space without assuming any topology, and also Q-weak efficient and Q-proper efficient solutions in the senses of Henig are defined. Moreover, by means of the Gerstewitz function, we provide some necessary and sufficient optimality conditions for set-valued vector optimization problems.

Keywords: algebraic interior, Gerstewitz function, vector closure, vector optimization

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Authors: Peni Rizki

Abstract:

This article presents decomposition on Aqua logo design 2013 as well as exploration on the meanings denoting marketing resolution. In the analysis, it is described decomposition details on Aqua logo design 2013, a semiotics implementation on marketing enterprise. 2013’s design is different in parts from its first establishment in 1973. Upon that, design elements such as pictures and colors are examined in semiotic theories of sign utilized as directives to the meaning constructed. Each part of the design is analyzed based on its significations that generate denotation and connotation as well as myth. At the end will be concluded the converses of Aqua logo design 2013 in reflection to its initiated marketing creativity; what pictures and colors do in it.

Keywords: design, aqua, semiotics, signification

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Authors: Hyun Kyu Lee, Won Zin Oh, June Hyun Kim, Jin Hee Kim, Sang June Choi, Hak Soo Kim

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The oxidative dissolution of chromium oxide by manganese oxides including permanganate have been widely studied not only for the chemical decontamination of nuclear power plant, but also for the environmental control of the toxic chromate caused by naturally occurring manganese dioxide. However, little attention has been made for the spontaneous reductive decomposition of permanganate in the water, which is a competing reaction with the oxidation of the chromium oxide by permanganate. The objective of this study is to investigate the spontaneous reductive decomposition behavior of permanganate in the water, depending on the variation of acidity, temperature and concentration. Results of the experiments showed that the permanganate reductive decomposition product is manganese dioxide, and this reaction accompanies with the same molar amount of hydrogen ion consumption. Therefore, at the neutral condition (ex. potassium permanganate solution without acidic chemicals), the permanganate do not reduce by itself at any condition of temperature, concentration within the experimental range. From the results, we confirmed that the oxidation reaction for the permanganate reduction is the water oxidation that is accompanying the oxygen evolution. The experimental results on the reductive decomposition behavior of permanganate in the water also showed that the degree and rate of permanganate reduction increases with the temperature, acidity and concentration. The spontaneous decomposition of the permanganates obtained in the studies would become a good reference to select the operational condition, such as temperature, acidity and concentration, for the chemical decontamination of nuclear power plants.

Keywords: permanganate reduction, spontaneous decomposition, water oxidation, acidity, temperature, permanganate concentration, chemical decontamination, nuclear power plant

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Authors: Myungkyu Park, Minkun Kim, Sunghoon Kim, Samgon Ryu

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Recently, research for reactive fabrics which have the characteristics of CWA (Chemical Warfare Agent) decomposition is being performed actively. The performance level of decomposition for CWA decomposition in various environmental condition is one of the critical factors in applicability as protective materials for NBC (Nuclear, Biological, and Chemical) protective clothing. In this study, results of performance test for CWA decomposition by reactive fabric made of electrospinning web and reactive particle are presented. Currently, the MOF (metal organic framework) type of UiO-66-NH₂ is frequently being studied as material for decomposing CWA especially blister agent HD [Bis(2-chloroethyl) sulfide]. When we test decomposition rate with electrospinning web made of PVB (Polyvinyl Butiral) polymer and UiO-66-NH₂ particle, we can get very high protective performance than the case other particles are applied. Furthermore, if the repellant surface fabric is added on reactive material as the component of protective fabric, the performance of layer by layered reactive fabric could be approached to the level of current NBC protective fabric for HD decomposition rate. Reactive fabric we used in this study is manufactured by electrospinning process of polymer which contains the reactive particle of UiO-66-NH₂, and we performed crystalizing process once again on that polymer fiber web in solvent systems as a second step for manufacturing reactive fabric. Three kinds of polymer materials are used in this process, but PVB was most suitable as an electrospinning fiber polymer considering the shape of product. The density of particle on fiber web and HD decomposition rate is enhanced by secondary crystallization compared with the results which are not processed. The amount of HD penetration by 24hr AVLAG (Aerosol Vapor Liquid Assessment Group) swatch test through the reactive fabrics with secondary crystallization and without crystallization is 24 and 146μg/cm² respectively. Even though all of the reactive fiber webs for this test are combined with repellant surface layer at outer side of swatch, the effects of secondary crystallization of particle for the reactive fiber web are remarkable.

Keywords: CWA, Chemical Warfare Agent, gas decomposition, particle growth, protective clothing, reactive fabric, swatch test

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Authors: Elham Kiyani, S. Mansour Vaezpour, Javad Tavakoli

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In this paper, we first introduce a new distance function in a linear space not necessarily endowed with a topology. The algebraic concepts of interior and closure are useful to study optimization problems without topology. So, we define Q-weak efficient solutions generated by the algebraic interior of a set Q, where Q is not necessarily convex. Studying nonconvex vector optimization is valuable since, for a convex cone K in topological spaces, we have int(K)=cor(K), which means that topological interior of a convex cone K is equal to the algebraic interior of K. Moreover, we used the scalarization technique including the distance function generated by the vectorial closure of a set to characterize these Q-weak efficient solutions. Scalarization is a useful approach for solving vector optimization problems. This technique reduces the optimization problem to a scalar problem which tends to be an optimization problem with a real-valued objective function. For instance, Q-weak efficient solutions of vector optimization problems can be characterized and computed as solutions of appropriate scalar optimization problems. In the convex case, linear functionals can be used as objective functionals of the scalar problems. But in the nonconvex case, we should present a suitable objective function. It is the aim of this paper to present a new distance function that be useful to obtain sufficient and necessary conditions for Q-weak efficient solutions of general optimization problems via scalarization.

Keywords: weak efficient, algebraic interior, vector closure, linear space

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Authors: Kuo-Teng Tsai, You-Min Huang

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In this study, the problem of a spiral fin with a period base temperature is analyzed by using the Adomian decomposition method. The Adomian decomposition method is a useful and practice method to solve the nonlinear energy equation which are associated with the heat radiation. The period base temperature is around a mean value. The results including the temperature distribution and the heat flux from the spiral fin base can be calculated directly. The results also discussed the effects of the dimensionless variables for the temperature variations and the total energy transferred from the spiral fin base.

Keywords: spiral fin, period, adomian decomposition method, nonlinear

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Authors: Nileshkumar Vaishnav, Aditya Tatu

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An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.

Keywords: graph signal processing, graph partitioning, inverse filtering on graphs, algebraic signal processing

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Authors: M. M. Qasaymeh, M. A. Khodeir

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Subspace channel estimation methods have been studied widely. It depends on subspace decomposition of the covariance matrix to separate signal subspace from noise subspace. The decomposition normally is done by either Eigenvalue Decomposition (EVD) or Singular Value Decomposition (SVD) of the Auto-Correlation matrix (ACM). However, the subspace decomposition process is computationally expensive. In this paper, the multipath channel estimation problem for a Slow Frequency Hopping (SFH) system using noise space based method is considered. An efficient method to estimate multipath the time delays basically is proposed, by applying MUltiple Signal Classification (MUSIC) algorithm which used the null space extracted by the Rank Revealing LU factorization (RRLU). The RRLU provides accurate information about the rank and the numerical null space which make it a valuable tool in numerical linear algebra. The proposed novel method decreases the computational complexity approximately to the half compared with RRQR methods keeping the same performance. Computer simulations are also included to demonstrate the effectiveness of the proposed scheme.

Keywords: frequency hopping, channel model, time delay estimation, RRLU, RRQR, MUSIC, LS-ESPRIT

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Authors: Wilson Enríquez, Daniel Cardenas

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This article proposes a filter bank format combined with the mathematical tool called polyphase decomposition and the discrete Fourier transform (DFT) with the purpose of improving the performance of the fifth-generation communication systems (5G). We started with a review of the literature and the study of the filter bank theory and its combination with DFT in order to improve the performance of wireless communications since it reduces the computational complexity of these communication systems. With the proposed technique, several experiments were carried out in order to evaluate the structures in 5G systems. Finally, the results are presented in graphical form in terms of bit error rate against the ratio bit energy/noise power spectral density (BER vs. Eb / No).

Keywords: multi-carrier system (5G), filter bank, polyphase decomposition, FIR equalizer

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Authors: Galal Elkobrosy, Amr M. Abdelrazek, Bassuny M. Elsouhily, Mohamed E. Khidr

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Crank shaft length, connecting rod length, crank angle, engine rpm, cylinder bore, mass of piston and compression ratio are the inputs that can control the performance of the slider crank mechanism and then its efficiency. Several combinations of these seven inputs are used and compared. The throughput engine torque predicted by the simulation is analyzed through two different regression models, with and without interaction terms, developed according to multi-linear regression using LU decomposition to solve system of algebraic equations. These models are validated. A regression model in seven inputs including their interaction terms lowered the polynomial degree from 3^rd degree to 1^st degree and suggested valid predictions and stable explanations.

Keywords: design of experiments, regression analysis, SI engine, statistical modeling

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Authors: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: spectral decomposition, linear RHS, homogeneous linear systems, eigenvalues of the Jacobian

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: Siraa Ben Ftima, Mourad Talbi, Tahar Ezzedine

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In this paper, we present a technique of secure watermarking of grayscale and color images. This technique consists in applying the Singular Value Decomposition (SVD) in LWT (Lifting Wavelet Transform) domain in order to insert the watermark image (grayscale) in the host image (grayscale or color image). It also uses signature in the embedding and extraction steps. The technique is applied on a number of grayscale and color images. The performance of this technique is proved by the PSNR (Pick Signal to Noise Ratio), the MSE (Mean Square Error) and the SSIM (structural similarity) computations.

Keywords: lifting wavelet transform (LWT), sub-space vectorial decomposition, secure, image watermarking, watermark

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Authors: Adil Al-Rammahi

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Image or document encryption is needed through e- government data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal basis, and spectral diagonal basis. Product of the two row basis is calculated. Similarly the product of the two column basis is achieved. Finally we transform or save the files of public, row product and column product. In decryption stage, the original image is deduced by mutual method of the three public files.

Keywords: image cryptography, singular values decomposition

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Authors: Shai Sarussi

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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: integral domains, Alexandroff topology, prime spectrum of a ring, valuation domains

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Authors: Olivier Delage, Hassan Bencherif, Alain Bourdier

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Signal decomposition approaches represent an important step in time series analysis, providing useful knowledge and insight into the data and underlying dynamics characteristics while also facilitating tasks such as noise removal and feature extraction. As most of observational time series are nonlinear and nonstationary, resulting of several physical processes interaction at different time scales, experimental time series have fluctuations at all time scales and requires the development of specific signal decomposition techniques. Most commonly used techniques are data driven, enabling to obtain well-behaved signal components without making any prior-assumptions on input data. Among the most popular time series decomposition techniques, most cited in the literature, are the empirical mode decomposition and its variants, the empirical wavelet transform and singular spectrum analysis. With increasing popularity and utility of these methods in wide ranging applications, it is imperative to gain a good understanding and insight into the operation of these algorithms. In this work, we describe all of the techniques mentioned above as well as their ability to denoise signals, to capture trends, to identify components corresponding to the physical processes involved in the evolution of the observed system and deduce the dimensionality of the underlying dynamics. Results obtained with all of these methods on experimental total ozone columns and rainfall time series will be discussed and compared

Keywords: denoising, empirical mode decomposition, singular spectrum analysis, time series, underlying dynamics, wavelet analysis

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Authors: M. Babul Hasan

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Management sciences (MS), big group of companies and industries or government policies (GP) is affiliated with a huge number of decision ingredients and complicated restrictions. Every factor in MS, every product in Industries or decision in GP is not always bankable in practice. After formulating these models there arises large-scale mixed integer programming (MIP) problem. In this paper, we developed decomposition-based pricing procedure to filter the unnecessary decision ingredients from MIP where the variables in huge number will be abated and the complicacy of restrictions will be elementary. A real life numerical example has been illustrated to demonstrate the methods. We develop the computer techniques for these methods by using a mathematical programming language (AMPL).

Keywords: Lagrangian relaxation, decomposition, sub-problem, master-problem, pricing, mixed IP, AMPL

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Authors: Y. Xu, L. Xiong, Z. Xu

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In order to protect data privacy, image with sensitive or private information needs to be encrypted before being outsourced to the cloud. However, this causes difficulties in image retrieval and data management. A secure image retrieval method based on orthogonal decomposition is proposed in the paper. The image is divided into two different components, for which encryption and feature extraction are executed separately. As a result, cloud server can extract features from an encrypted image directly and compare them with the features of the queried images, so that the user can thus obtain the image. Different from other methods, the proposed method has no special requirements to encryption algorithms. Experimental results prove that the proposed method can achieve better security and better retrieval precision.

Keywords: secure image retrieval, secure search, orthogonal decomposition, secure cloud computing

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Authors: Ebrahim Asadi-Gangraj

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Hybrid flow shop scheduling problem (HFS) contains sequencing in a flow shop where, at any stage, there exist one or more related or unrelated parallel machines. This production system is a common manufacturing environment in many real industries, such as the steel manufacturing, ceramic tile manufacturing, and car assembly industries. In this research, a mixed integer linear programming (MILP) model is presented for the hybrid flow shop scheduling problem, in which, the objective consists of minimizing the maximum completion time (makespan). For this purpose, a Benders Decomposition (BD) method is developed to solve the research problem. The proposed approach is tested on some test problems, small to moderate scale. The experimental results show that the Benders decomposition approach can solve the hybrid flow shop scheduling problem in a reasonable time, especially for small and moderate-size test problems.

Keywords: hybrid flow shop, mixed integer linear programming, Benders decomposition, makespan

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Authors: Nur Azlina Mohamed Mokmin, Mona Masood

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Guided by the theory of learning style, this study is based on the development of a multimedia learning application for students with mastery learning style. The learning material was developed by applying a graduated difficulty learning strategy. Algebraic fraction was chosen as the learning topic for this application. The effectiveness of this application in helping students learn is measured by giving a pre- and post-test. The result shows that students who learn using the learning material that matches their preferred learning style performs better than the students with a non-personalized learning material.

Keywords: algebraic fractions, graduated difficulty, mastery learning style, multimedia

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Authors: Mohamed Hassan Abdullahi

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Decomposition is used as a synthesis tool in several physical systems. It can also be used for tearing and restructuring, which is large-scale system analysis. On the other hand, the commutativity of series-connected systems has fascinated the interest of researchers, and its advantages have been emphasized in the literature. The presentation looks into the necessary conditions for decomposing any third-order discrete-time linear time-varying system into a commutative pair of first- and second-order systems. Additional requirements are derived in the case of nonzero initial conditions. MATLAB simulations are used to verify the findings. The work is unique and is being published for the first time. It is critical from the standpoints of synthesis and/or design. Because many design techniques in engineering systems rely on tearing and reconstruction, this is the process of putting together simple components to create a finished product. Furthermore, it is demonstrated that regarding sensitivity to initial conditions, some combinations may be better than others. The results of this work can be extended for the decomposition of fourth-order discrete-time linear time-varying systems into lower-order commutative pairs, as two second-order commutative subsystems or one first-order and one third-order commutative subsystems.

Keywords: commutativity, decomposition, discrete time-varying systems, systems

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