Search results for: hybrid of Adomian polynomial

Authors: Kamel Al-Khaled

Abstract:

Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

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Authors: Jaechun No

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This paper focuses on I/O optimizations of N-hybrid (New-Form of hybrid), which provides a hybrid file system space constructed on SSD and HDD. Although the promising potentials of SSD, such as the absence of mechanical moving overhead and high random I/O throughput, have drawn a lot of attentions from IT enterprises, its high ratio of cost/capacity makes it less desirable to build a large-scale data storage subsystem composed of only SSDs. In this paper, we present N-hybrid that attempts to integrate the strengths of SSD and HDD, to offer a single, large hybrid file system space. Several experiments were conducted to verify the performance of N-hybrid.

Keywords: SSD, data section, I/O optimizations, hybrid system

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Authors: Zuhier Altawallbeh

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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.

Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra

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Authors: Nevena Jakovčević Stor, Ivan Slapničar

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Any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen as real. By using accurate forward stable algorithm for computing eigen values of real symmetric arrowhead matrices we derive a forward stable algorithm for computation of roots of such polynomials in O(n^2 ) operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. Our examples include numerically difficult problems, like the well-known Wilkinson’s polynomials. Our algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method.

Keywords: roots of polynomials, eigenvalue decomposition, arrowhead matrix, high relative accuracy

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Authors: M. N. Ervina Efzan, H. J. Kong, C. K. Kok

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The present work deals with a study on the influences of hybrid modifier on LM 6 added through ladle metallurgy. In this study, LM 6 served as the reference alloy while Na2CO3 and Ti powders were used as the hybrid modifier. The effects of hybrid modifier on the micro structural enhancement of LM 6 were investigated using optical microscope (OM) and Scanning Electron Microscope (SEM). The results showed fragmented Si-rich needles and strength enhanced petal/ globular-like structures without obvious formation of soft primary α-Al and β-Fe-rich inter metallic compound (IMC) after the hybrid modification. Hardness test was conducted to examine the mechanical improvement of hybrid modified LM 6. 10% of hardness improvement was recorded in the hybrid modified LM 6 through ladle metallurgy.

Keywords: Al-Si, hybrid modifier, ladle metallurgy, hardness

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Authors: A. Brouri, F. Giri, A. Mkhida, A. Elkarkri, M. L. Chhibat

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Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. Presently, the linear subsystem is allowed to be parametric or not, continuous- or discrete-time. The input and output nonlinearities are polynomial and may be noninvertible. A two-stage identification method is developed such the parameters of all nonlinear elements are estimated first using the Kozen-Landau polynomial decomposition algorithm. The obtained estimates are then based upon in the identification of the linear subsystem, making use of suitable pre-ad post-compensators.

Keywords: nonlinear system identification, Hammerstein-Wiener systems, frequency identification, polynomial decomposition

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Authors: Ayubi Wirara, Ardya Suryadinata

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Improper application of the RSA algorithm scheme can cause vulnerability to attacks. The attack utilizes the relationship between broadcast messages sent to the user with some fixed polynomial functions that belong to each user. Scheme attacks carried out by applying the Chinese Remainder Theorem to obtain a general polynomial equation with the same modulus. The formation of the general polynomial becomes a first step to get back the original message. Furthermore, to solve these equations can use Coppersmith's theorem.

Keywords: RSA algorithm, broadcast message, Chinese Remainder Theorem, Coppersmith’s theorem

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Authors: Ogunrinde Roseline Bosede

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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Authors: Damir Latypov

Abstract:

A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: Neelam Singha

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The present work intends to analyze the system dynamics of Hashimoto’s thyroiditis with the assistance of fractional calculus. Hashimoto’s thyroiditis or chronic lymphocytic thyroiditis is an autoimmune disorder in which the immune system attacks the thyroid gland, which gradually results in interrupting the normal thyroid operation. Consequently, the feedback control of the system gets disrupted due to thyroid follicle cell lysis. And, the patient perceives life-threatening clinical conditions like goiter, hyperactivity, euthyroidism, hyperthyroidism, etc. In this work, we aim to obtain the approximate solution to the posed fractional-order problem describing Hashimoto’s thyroiditis. We employ the Adomian decomposition method to solve the system of fractional-order differential equations, and the solutions obtained shall be useful to provide information about the effect of medical care. The numerical technique is executed in an organized manner to furnish the associated details of the progression of the disease and to visualize it graphically with suitable plots.

Keywords: adomian decomposition method, fractional derivatives, Hashimoto's thyroiditis, mathematical modeling

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Authors: Zainab Yasir Abed Al-Rekaby, Abdul Jalil M. Khalaf

Abstract:

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.

Keywords: chromatic polynomial, chromatically equivalent, chromatically unique, wheel

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Authors: Alsaidi M. Altaher, Mohd Tahir Ismail

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Wavelet thresholding has been a power tool in curve estimation and data analysis. In the presence of outliers this non parametric estimator can not suppress the outliers involved. This study proposes a new two-stage combined method based on the use of the median filter as primary step before applying wavelet thresholding. After suppressing the outliers in a signal through the median filter, the classical wavelet thresholding is then applied for removing the remaining noise. We use automatic boundary corrections; using a low order polynomial model or local polynomial model as a more realistic rule to correct the bias at the boundary region; instead of using the classical assumptions such periodic or symmetric. A simulation experiment has been conducted to evaluate the numerical performance of the proposed method. Results show strong evidences that the proposed method is extremely effective in terms of correcting the boundary bias and eliminating outlier’s sensitivity.

Keywords: boundary correction, median filter, simulation, wavelet thresholding

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Authors: Zainab Yasir Al-Rekaby, Abdul Jalil M. Khalaf

Abstract:

Coloring the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W14 is chromatically unique.

Keywords: chromatic polynomial, chromatically Equivalent, chromatically unique, wheel

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Authors: Wajdi Mohamed Ratemi

Abstract:

The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities.

Keywords: pascal’s triangle, generalized pascal’s triangle, polynomial expansion, sierpinski’s triangle, combinatorics, probabilities

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Authors: Abdulhakeem Yusuf, Yomi Monday Aiyesimi, Mohammed Jiya

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The failure in an ordinary heat transfer fluid to meet up with today’s industrial cooling rate has resulted in the development of high thermal conductivity fluid which nanofluids belongs. In this work, the problem of unsteady one dimensional laminar flow of an incompressible fluid within a parallel wall is considered with one wall assumed to be wavy. The model is presented in its rectangular coordinate system and incorporates the effects of thermophoresis and Brownian motion. The local similarity solutions were also obtained which depends on Soret number, Dufour number, Biot number, Lewis number, and heat generation parameter. The analytical solution is obtained in a closed form via the Adomian decomposition method. It was found that the method has a good agreement with the numerical method, and it is also established that the heat generation parameter has to be kept low so that heat energy are easily evacuated from the system.

Keywords: Adomian decomposition method, Biot number, Dufour number, nanofluid

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Authors: Zainab Al-Maamari, Yassir Dinar

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The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds.

Keywords: invariant ring, Frobenius manifold, inversion, representation theory

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Authors: S. Dey, T. Mukhopadhyay, S. Adhikari

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This paper presents an exhaustive comparative investigation on sampling techniques of polynomial regression model based stochastic natural frequency of composite plates. Both individual and combined variations of input parameters are considered to map the computational time and accuracy of each modelling techniques. The finite element formulation of composites is capable to deal with both correlated and uncorrelated random input variables such as fibre parameters and material properties. The results obtained by Polynomial regression (PR) using different sampling techniques are compared. Depending on the suitability of sampling techniques such as 2k Factorial designs, Central composite design, A-Optimal design, I-Optimal, D-Optimal, Taguchi’s orthogonal array design, Box-Behnken design, Latin hypercube sampling, sobol sequence are illustrated. Statistical analysis of the first three natural frequencies is presented to compare the results and its performance.

Keywords: composite plate, natural frequency, polynomial regression model, sampling technique, uncertainty quantification

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Authors: Tareq Hamadneh, Jochen Merker, Hassan Al-Zoubi

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Bernstein's expansion for exponentials in Taylor functions provides lower and upper optimization values for the range of its original function. these values converge to the original functions if the degree is elevated or the domain subdivided. Taylor polynomial can be applied so that the exponential is a polynomial of finite degree over a given domain. Bernstein's basis has two main properties: its sum equals 1, and positive for all x 2 (0; 1). In this work, we prove the existence of fixed points for exponential functions in a given domain using the optimization values of Bernstein. The Bernstein basis of finite degree T over a domain D is defined non-negatively. Any polynomial p of degree t can be expanded into the Bernstein form of maximum degree t ≤ T, where we only need to compute the coefficients of Bernstein in order to optimize the original polynomial. The main property is that p(x) is approximated by the minimum and maximum Bernstein coefficients (Bernstein bound). If the bound is contained in the given domain, then we say that p(x) has fixed points in the same domain.

Keywords: Bernstein polynomials, Stability of control functions, numerical optimization, Taylor function

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points

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Authors: Prateeksha Sharma, V. Dinesh Kumar

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Performances of cylindrical multilayer hybrid plasmonic waveguides have been investigated in detail considering their structural and material aspects. Characteristics of hybrid metal insulator metal (HMIM) and hybrid insulator metal insulator (HIMI) waveguides have been compared on the basis of propagation length and confinement factor. Necessity of this study is to understand newer kind of waveguides that overcome the limitations of conventional waveguides. Investigation reveals that sub wavelength confinement can be obtained in two low dielectric spacer layers. This study provides gateway for many applications such as nano lasers, interconnects, bio sensors and optical trapping etc.

Keywords: hybrid insulator metal insulator, hybrid metal insulator metal, nano laser, surface plasmon polariton

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Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

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So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

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Authors: M. Mourad, K. Mahmoud

Abstract:

Recently hybrid vehicles have become a major concern as one alternative vehicles. This type of hybrid vehicle contributes greatly to reducing pollution. Therefore, this work studies the influence of electrification phase of hybrid electric vehicle on emission of vehicle at different road conditions. To accomplish this investigation, a simulation model was used to evaluate the external characteristics of the hybrid electric vehicle according to variant conditions of road resistances. Therefore, this paper reports a methodology to decrease the vehicle emission especially greenhouse gas emission inside cities. The results show the effect of electrification on vehicle performance characteristics. The results show that CO₂ emission of vehicle decreases up to 50.6% according to an urban driving cycle due to applying the electrification strategy for hybrid electric vehicle.

Keywords: electrification strategy, hybrid electric vehicle, driving cycle, CO2 emission

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Authors: Muhammad Bello Ibrahim, M. Auwal Zakari, Aliyu Usman

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Hybrid concrete construction (HCC) combines all the benefits of pre-casting with the advantages of cast in-situ construction. Merging the two, as a hybrid structure, results in even greater construction speed, value, and the overall economy. Its variety of uses has gained popularity in the United States and in Europe due to its distinctive benefits. However, the increase of its application in some countries (including Nigeria) has been relatively slow. Several researches have shown that hybrid construction offers an ultra-high performance concrete that offers superior strength, durability and aesthetics with design flexibility and within sustainability credentials, based on the available and economically visible technologies. This paper examines and documents the criterion that will help inform the process of deciding whether or not to adopt hybrid concrete construction (HCC) technology rather than more traditional alternatives. It also the present situation of design, construction and research on hybrid structures.

Keywords: hybrid concrete construction, Nigeria, sustainable infrastructure development, design flexibility

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Authors: Qiming Zhang, Youda Ye, Qinxue Jiang

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Accurate prediction of external flowfield and aero-heating at the wall of hypersonic vehicle is very crucial for the design of aircrafts. Unstructured/hybrid meshes have more powerful advantages than structured meshes in terms of pre-processing, parallel computing and mesh adaptation, so it is imperative to develop high-resolution numerical methods for the calculation of aerothermal environment on unstructured/hybrid meshes. The inviscid flux scheme is one of the most important factors affecting the accuracy of unstructured/ hybrid mesh heat flux calculation. Here, a new hybrid flux scheme is developed and the approach of interface type selection is proposed: i.e. 1) using the exact Riemann scheme solution to calculate the flux on the faces parallel to the wall; 2) employing Sterger-Warming (S-W) scheme to improve the stability of the numerical scheme in other interfaces. The results of the heat flux fit the one observed experimentally and have little dependence on grids, which show great application prospect in unstructured/ hybrid mesh.

Keywords: aero-heating prediction, computational fluid dynamics, hybrid meshes, hybrid schemes

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Authors: P. Hari Krishna, V. Ramana Murty

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Different types of foundations are subjected to pullout or tensile loads depending on the soil in which they are embedded or due to the structural loads coming on them. In those circumstances, anchors were generally used to resist these loads. This paper presents the field pullout studies on hybrid anchor piles embedded in different types of soils. The pullout capacity and resistance of the hybrid granular anchor piles installed in the native expansive soil which is available in the campus are compared with similar hybrid concrete anchor piles which were installed in similar field conditions.

Keywords: expansive soil, hybrid concrete anchor piles, hybrid granular anchor piles, pullout tests

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Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna

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Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

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Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis

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Authors: Tetsuya Yabuki, Yasunori Arizumi, Tetsuhiro Shimozato, Samy Guezouli, Hiroaki Matsusita, Masayuki Tai

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The main object of this paper is to present the research results of the development of a hybrid stainless steel girder system for bridge construction undertaken at University of Ryukyu. In order to prevent the corrosion damage and reduce the fabrication costs, a hybrid stainless steel girder in bridge construction is developed, the stainless steel girder of which is stiffened and braced by structural carbon steel materials. It is verified analytically and experimentally that the ultimate strength of the hybrid stainless steel girder is equal to or greater than that of conventional carbon steel girder. The benefit of the life-cycle cost of the hybrid stainless steel girder is also shown.

Keywords: smart structure, hybrid stainless steel members, ultimate strength, steel bridge, corrosion prevention

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Authors: S. B. Provost, Susan Sheng

Abstract:

An alternative bivariate density estimation methodology is introduced in this presentation. The proposed approach involves estimating the density function associated with the marginal distribution of each of the two variables by means of the saddlepoint approximation technique and applying a bivariate polynomial adjustment to the product of these density estimates. Since the saddlepoint approximation is utilized in the context of density estimation, such estimates are determined from empirical cumulant-generating functions. In the univariate case, the saddlepoint density estimate is itself adjusted by a polynomial. Given a set of observations, the coefficients of the polynomial adjustments are obtained from the sample moments. Several illustrative applications of the proposed methodology shall be presented. Since this approach relies essentially on a determinate number of sample moments, it is particularly well suited for modeling massive data sets.

Keywords: density estimation, empirical cumulant-generating function, moments, saddlepoint approximation

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Authors: Nabila Louai, Fouad Khaldi, Houria Benharchache

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In this paper, the case of meeting a household’s electrical energy demand with hybrid systems has been examined. The objective is to study technological feasibility and economic viability of the electrification project by a hybrid system (PV/ wind) of a residential home located in Batna-Algeria and to reduce the emissions from traditional power by using renewable energy. An autonomous hybrid wind/photovoltaic (PV)/battery power system and a PV/Wind grid connected system, has been carried out using Hybrid Optimization Model for Electric Renewable (HOMER) simulation software. As a result, it has been found that electricity from the grid can be supplied at a lower price than electricity from renewable energy at this moment.

Keywords: batna, household, hybrid system, renewable energy, techno-economy

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