Search results for: Polynomial Differentiation

Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.

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Authors: LI qiu-min, TIAN yi-xiang, ZHANG gao-xun

Abstract:

GMDH algorithm can well describe the internal structure of objects. In the process of modeling, automatic screening of model structure and variables ensure the convergence rate.This paper studied a new GMDH model based on polynomial spline  stimation. The polynomial spline function was used to instead of the transfer function of GMDH to characterize the relationship between the input variables and output variables. It has proved that the algorithm has the optimal convergence rate under some conditions. The empirical results show that the algorithm can well forecast Consumer Price Index (CPI).

Keywords: spline, GMDH, nonparametric, bias, forecast.

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Authors: Wint Thida Zaw, Thinn Thu Naing

Abstract:

One of the essential sectors of Myanmar economy is agriculture which is sensitive to climate variation. The most important climatic element which impacts on agriculture sector is rainfall. Thus rainfall prediction becomes an important issue in agriculture country. Multi variables polynomial regression (MPR) provides an effective way to describe complex nonlinear input output relationships so that an outcome variable can be predicted from the other or others. In this paper, the modeling of monthly rainfall prediction over Myanmar is described in detail by applying the polynomial regression equation. The proposed model results are compared to the results produced by multiple linear regression model (MLR). Experiments indicate that the prediction model based on MPR has higher accuracy than using MLR.

Keywords: Polynomial Regression, Rainfall Forecasting, Statistical forecasting.

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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: Generalized Pascal’s triangle, Pascal’s triangle, polynomial expansion, Sierpinski’s triangle, staircase horizontal vertical method.

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Authors: Mayada Alqaisi, Nasser Al-Shanti, Quiyu Wang, William S. Gilmore

Abstract:

In-vitro mouse co-culture of E14 embryonic stem cells (ESCs) and OP9 stromal cells can recapitulate the earliest stages of haematopoietic development, not accessible in human embryos, supporting both haemogenic precursors and their primitive haematopoietic progeny. 1α, 25-Dihydroxy-vitamin D3 (VD3) has been demonstrated to be a powerful differentiation inducer for a wide variety of neoplastic cells, and could enhance early differentiation of ESCs into blood cells in E14/OP9 co-culture. This study aims to ascertain whether VD3 is key in promoting differentiation and suppressing proliferation, by separately investigating the effects of VD3 on the proliferation phase of the E14 cell line and on stromal OP9 cells.The results showed that VD3 inhibited the proliferation of the cells in a dose-dependent manner, quantitatively by decreased cell number, and qualitatively by alkaline-phosphatase staining that revealed significant differences between VD3-treated and untreated cells, characterised by decreased enzyme expression (colourless cells). Propidium-iodide cell-cycle analyses showed no significant percentage change in VD3-treated E14 and OP9 cells within their G and S-phases, compared to the untreated controls, despite the increased percentage of G-phase compared to the S-phase in a dosedependent manner. These results with E14 and OP9 cells indicate that adequate VD3 concentration enhances cellular differentiation and inhibits proliferation. The results also suggest that if E14 and OP9 cells were co-cultured andVD3-treated, there would be furtherenhanced differentiation of ESCs into blood cells.

Keywords: Differentiation, embryonic stem cells, OP9 stromal cells, 1α, 25-dihydroxy-vitamin D3

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Authors: U.K. Saha, L.K. Arora

Abstract:

The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration with multiindex Mittag-Leffler function.

Keywords: Multiindex Mittag-Leffler function, Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration, Riemann-Liouville fractional integrals and derivatives.

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Authors: Attapon Charoenpon, Ekkarach Pankeaw

Abstract:

This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (╬¢ ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ╬¢ <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: Aerodynamic, Characteristic Equation, Angle ofAttack, Polynomial interpolation, Trajectories

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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 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, stability analysis.

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Authors: A. Chillali, M. Sahmoudi

Abstract:

In this paper, we will give a cryptographic application over the integral closure O_Lof sextic extension L, namely L is an extension of Q of degree 6 in the form Q(a,b), which is a rational quadratic and monogenic extension over a pure monogenic cubic subfield K generated by a who is a root of monic irreducible polynomial of degree 2 andb is a root of irreducible polynomial of degree 3.

Keywords: Integral bases, Cryptography, Discrete logarithm problem.

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Authors: S. K. Tomar, R. Prasad, S. Panda, C. Ardil

Abstract:

Reduction of Single Input Single Output (SISO) discrete systems into lower order model, using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Modified Cauer Form (MCF) and differentiation are used. In this method the original discrete system is, first, converted into equivalent continuous system by applying bilinear transformation. The denominator of the equivalent continuous system and its reciprocal are differentiated successively, the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. The reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.

Keywords: Discrete System, Single Input Single Output (SISO), Bilinear Transformation, Reduced Order Model, Modified CauerForm, Polynomial Differentiation, Particle Swarm Optimization, Integral Squared Error.

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Authors: M. Zarebnia, M. Hoshyar, M. Sedaghati

Abstract:

In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Non-polynomial spline functions; Numerical method

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Authors: Olusheye Akinfenwa, Samuel Jator, Nianmin Yoa

Abstract:

A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.

Keywords: Stiff IVPs, System of ODEs, Backward differentiationformulas, Block methods, Stability.

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Authors: Navdeep Goel, Salvador Gabarda

Abstract:

Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Multiplexing involves packing signals together whose representations are compact in the working domain. In order to optimize transmission resources each 4 × 4 pixel block of the image is transformed by a suitable polynomial approximation, into a minimal number of coefficients. Less than 4 × 4 coefficients in one block spares a significant amount of transmitted information, but some information is lost. Different approximations for image transformation have been evaluated as polynomial representation (Vandermonde matrix), least squares + gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev polynomials or singular value decomposition (SVD). Results have been compared in terms of nominal compression rate (NCR), compression ratio (CR) and peak signal-to-noise ratio (PSNR) in order to minimize the error function defined as the difference between the original pixel gray levels and the approximated polynomial output. Polynomial coefficients have been later encoded and handled for generating chirps in a target rate of about two chirps per 4 × 4 pixel block and then submitted to a transmission multiplexing operation in the time-frequency domain.

Keywords: Chirp signals, Image multiplexing, Image transformation, Linear canonical transform, Polynomial approximation.

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Authors: S. Deswal, M. Pal

Abstract:

Presently various computational techniques are used in modeling and analyzing environmental engineering data. In the present study, an intra-comparison of polynomial and radial basis kernel functions based on Support Vector Regression and, in turn, an inter-comparison with Multi Linear Regression has been attempted in modeling mass transfer capacity of vertical (θ = 90O) and inclined (θ multiple plunging jets (varying from 1 to 16 numbers). The data set used in this study consists of four input parameters with a total of eighty eight cases, forty four each for vertical and inclined multiple plunging jets. For testing, tenfold cross validation was used. Correlation coefficient values of 0.971 and 0.981 along with corresponding root mean square error values of 0.0025 and 0.0020 were achieved by using polynomial and radial basis kernel functions based Support Vector Regression respectively. An intra-comparison suggests improved performance by radial basis function in comparison to polynomial kernel based Support Vector Regression. Further, an inter-comparison with Multi Linear Regression (correlation coefficient = 0.973 and root mean square error = 0.0024) reveals that radial basis kernel functions based Support Vector Regression performs better in modeling and estimating mass transfer by multiple plunging jets.

Keywords: Mass transfer, multiple plunging jets, polynomial and radial basis kernel functions, Support Vector Regression.

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Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman

Abstract:

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.

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Authors: Adam Roman

Abstract:

Finding synchronizing sequences for the finite automata is a very important problem in many practical applications (part orienters in industry, reset problem in biocomputing theory, network issues etc). Problem of finding the shortest synchronizing sequence is NP-hard, so polynomial algorithms probably can work only as heuristic ones. In this paper we propose two versions of polynomial algorithms which work better than well-known Eppstein-s Greedy and Cycle algorithms.

Keywords: Synchronizing words, reset sequences, Černý Conjecture

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Authors: S.A.M. Yatim, Z.B. Ibrahim, K.I. Othman, F. Ismail

Abstract:

The implicit block methods based on the backward differentiation formulae (BDF) for the solution of stiff initial value problems (IVPs) using variable step size is derived. We construct a variable step size block methods which will store all the coefficients of the method with a simplified strategy in controlling the step size with the intention of optimizing the performance in terms of precision and computation time. The strategy involves constant, halving or increasing the step size by 1.9 times the previous step size. Decision of changing the step size is determined by the local truncation error (LTE). Numerical results are provided to support the enhancement of method applied.

Keywords: Backward differentiation formulae, block backwarddifferentiation formulae, stiff ordinary differential equation, variablestep size.

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Authors: Kyunghoon Kim, Sungjoon Shim, Jun Tae Kim, Jong Tae Kim

Abstract:

In a wireless communication system, a predistorter(PD) is often employed to alleviate nonlinear distortions due to operating a power amplifier near saturation, thereby improving the system performance and reducing the interference to adjacent channels. This paper presents a new adaptive polynomial digital predistorter(DPD). The proposed DPD uses Coordinate Rotation Digital Computing(CORDIC) processors and PD process by pipelined architecture. It is simpler and faster than conventional adaptive polynomial DPD. The performance of the proposed DPD is proved by MATLAB simulation.

Keywords: DPD, CORDIC.

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Authors: Jeng-Wen Lin, Simon Chien-Yuan Chen

Abstract:

Based on assumptions of neo-classical economics and rational choice / public choice theory, this paper investigates the regulation of industrial land use in Taiwan by homeowners associations (HOAs) as opposed to traditional government administration. The comparison, which applies the transaction cost theory and a polynomial regression analysis, manifested that HOAs are superior to conventional government administration in terms of transaction costs and overall efficiency. A case study that compares Taiwan-s commonhold industrial park, NangKang Software Park, to traditional government counterparts using limited data on the costs and returns was analyzed. This empirical study on the relative efficiency of governmental and private institutions justified the important theoretical proposition. Numerical results prove the efficiency of the established model.

Keywords: Homeowners Associations, Institutional Efficiency, Polynomial Regression, Transaction Cost.

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Authors: Z. Liu, K. Cao

Abstract:

Strategic spatial planning, which is taken as an effective and competitive way for the governors of the city to improve the development and management level of a city, has been blooming in recent years all over the world. In the context of globalization and informatization, strategic spatial planning must transfer its focus on three different levels: global, regional and urban. Internal and external changes in environmental conditions lead to new advances in strategic planning both theoretically and practically. However, such advances or changes respond differently to cities on account of different dynamic mechanisms. This article aims at two cities of Tianjin in China and Melbourne in Australia, through a comparative study on strategic planning, to explore the differentiation of mechanisms in urban planning making. By comparison and exploration, the purpose of this article is to exhibit two different planning worlds between western and Chinese in a new way nowadays.

Keywords: Differentiation, Tianjin China, Melbourne Australia, strategic planning.

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Authors: N. M. A. Nik Long, Z. K. Eshkuvatov, M. Yaghobifar, M. Hasan

Abstract:

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

Keywords: Approximation, Galerkin method, Integral equations, Laguerre polynomial.

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Authors: Amir Azizi, Amir Yazid b. Ali, Loh Wei Ping, Mohsen Mohammadzadeh

Abstract:

Uncertainties of a serial production line affect on the production throughput. The uncertainties cannot be prevented in a real production line. However the uncertain conditions can be controlled by a robust prediction model. Thus, a hybrid model including autoregressive integrated moving average (ARIMA) and multiple polynomial regression, is proposed to model the nonlinear relationship of production uncertainties with throughput. The uncertainties under consideration of this study are demand, breaktime, scrap, and lead-time. The nonlinear relationship of production uncertainties with throughput are examined in the form of quadratic and cubic regression models, where the adjusted R-squared for quadratic and cubic regressions was 98.3% and 98.2%. We optimized the multiple quadratic regression (MQR) by considering the time series trend of the uncertainties using ARIMA model. Finally the hybrid model of ARIMA and MQR is formulated by better adjusted R-squared, which is 98.9%.

Keywords: ARIMA, multiple polynomial regression, production throughput, uncertainties

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Authors: R.Marsalek

Abstract:

This paper present a new way to find the aerodynamic characteristic equation of missile for the numerical trajectories prediction more accurate. The goal is to obtain the polynomial equation based on two missile characteristic parameters, angle of attack (α ) and flight speed (ν ). First, the understudied missile is modeled and used for flow computational model to compute aerodynamic force and moment. Assume that performance range of understudied missile where range -10< α <10 and 0< ν <200. After completely obtained results of all cases, the data are fit by polynomial interpolation to create equation of each case and then combine all equations to form aerodynamic characteristic equation, which will be used for trajectories simulation.

Keywords: ferro-precipitate, adsorption, SDS, zeta potential

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Authors: Deogratius Musiige, François Anton, Vital Yatskevich, Laulagnet Vincent, Darka Mioc, Nguyen Pierre

Abstract:

This paper presents a methodology towards the emulation of the electrical power consumption of the RF device during the cellular phone/handset transmission mode using the LTE technology. The emulation methodology takes the physical environmental variables and the logical interface between the baseband and the RF system as inputs to compute the emulated power dissipation of the RF device. The emulated power, in between the measured points corresponding to the discrete values of the logical interface parameters is computed as a polynomial interpolation using polynomial basis functions. The evaluation of polynomial and spline curve fitting models showed a respective divergence (test error) of 8% and 0.02% from the physically measured power consumption. The precisions of the instruments used for the physical measurements have been modeled as intervals. We have been able to model the power consumption of the RF device operating at 5MHz using homotopy between 2 continuous power consumptions of the RF device operating at the bandwidths 3MHz and 10MHz.

Keywords: Radio frequency, high power amplifier, baseband, LTE, power, emulation, homotopy, interval analysis, Tx power, register-transfer level.

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Authors: Pavel K. Lopatin, Artyom S. Yegorov

Abstract:

The Algorithm 2 for a n-link manipulator movement amidst arbitrary unknown static obstacles for a case when a sensor system supplies information about local neighborhoods of different points in the configuration space is presented. The Algorithm 2 guarantees the reaching of a target position in a finite number of steps. The Algorithm 2 is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the Algorithm2 implementation are given.

Keywords: Manipulator, trajectory planning, unknown obstacles.

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Authors: R. B. Ogunrinde

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, Initial value problem, Polynomials.

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Authors: Gints Jekabsons

Abstract:

The approach of subset selection in polynomial regression model building assumes that the chosen fixed full set of predefined basis functions contains a subset that is sufficient to describe the target relation sufficiently well. However, in most cases the necessary set of basis functions is not known and needs to be guessed – a potentially non-trivial (and long) trial and error process. In our research we consider a potentially more efficient approach – Adaptive Basis Function Construction (ABFC). It lets the model building method itself construct the basis functions necessary for creating a model of arbitrary complexity with adequate predictive performance. However, there are two issues that to some extent plague the methods of both the subset selection and the ABFC, especially when working with relatively small data samples: the selection bias and the selection instability. We try to correct these issues by model post-evaluation using Cross-Validation and model ensembling. To evaluate the proposed method, we empirically compare it to ABFC methods without ensembling, to a widely used method of subset selection, as well as to some other well-known regression modeling methods, using publicly available data sets.

Keywords: Basis function construction, heuristic search, modelensembles, polynomial regression.

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Authors: Matthias Dehmer1 Jürgen Kilian

Abstract:

Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated.Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds for the moduli of the zeros of complex polynomials. That means, we provide disks in the complex plane where all zeros of a complex polynomial are situated. Such bounds are extremely useful for obtaining a priori assertations regarding the location of zeros of polynomials. Based on the proven bounds and a test set of polynomials, we present an experimental study to examine which bound is optimal.

Keywords: complex polynomials, zeros, inequalities

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Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: Operational matrix of differentiation, Similarity transformation, Shifted second kind Chebyshev wavelets, Stefan problem.

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Authors: Mughal Yar M, Israr Ul Haq, Bushra Noman

Abstract:

The stem cells have ability to differentiated themselves through mitotic cell division and various range of specialized cell types. Cellular differentiation is a way by which few specialized cell develops into more specialized.This paper studies the fundamental problem of computational schema for an artificial neural network based on chemical, physical and biological variables of state. By doing this type of study system could be model for a viable propagation of various economically important stem cells differentiation. This paper proposes various differentiation outcomes of artificial neural network into variety of potential specialized cells on implementing MATLAB version 2009. A feed-forward back propagation kind of network was created to input vector (five input elements) with single hidden layer and one output unit in output layer. The efficiency of neural network was done by the assessment of results achieved from this study with that of experimental data input and chosen target data. The propose solution for the efficiency of artificial neural network assessed by the comparatative analysis of “Mean Square Error" at zero epochs. There are different variables of data in order to test the targeted results.

Keywords: Computational shcmin, meiosis, mitosis, neuralnetwork, Stem cell SOM;

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