Search results for: locus equations

Authors: Meimei Shi

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Objectives: The identification of endangered species, especially simultaneous detection of multiple species in complex samples, plays a critical role in alleged wildlife crime incidents and prevents illegal trade. This study was to develop a multi-locus DNA metabarcoding method for endangered animal species identification. Methods: Several pairs of universal primers were designed according to the mitochondria conserved gene regions. Experimental mixtures were artificially prepared by mixing well-defined species, including endangered species, e.g., forest musk, bear, tiger, pangolin, and sika deer. The artificial samples were prepared with 1-16 well-characterized species at 1% to 100% DNA concentrations. After multiplex-PCR amplification and parameter modification, the amplified products were analyzed by capillary electrophoresis and used for NGS library preparation. The DNA metabarcoding was carried out based on Illumina MiSeq amplicon sequencing. The data was processed with quality trimming, reads filtering, and OTU clustering; representative sequences were blasted using BLASTn. Results: According to the parameter modification and multiplex-PCR amplification results, five primer sets targeting COI, Cytb, 12S, and 16S, respectively, were selected as the NGS library amplification primer panel. High-throughput sequencing data analysis showed that the established multi-locus DNA metabarcoding method was sensitive and could accurately identify all species in artificial mixtures, including endangered animal species Moschus berezovskii, Ursus thibetanus, Panthera tigris, Manis pentadactyla, Cervus nippon at 1% (DNA concentration). In conclusion, the established species identification method provides technical support for customs and forensic scientists to prevent the illegal trade of endangered animals and their products.

Keywords: DNA metabarcoding, endangered animal species, mitochondria nucleic acid, multi-locus

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Divij Gupta

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Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: Josephine Aikpitanyi, Friday Okonofua, Lorrettantoimo, Sandy Tubeuf

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Every day, 800 women die from conditions related to pregnancy and childbirth, resulting in an estimated 300,000 maternal deaths worldwide per year. Over 99 percent of all maternal deaths occur in developing countries, with more than half of them occurring in sub-Saharan Africa. Nigeria being the most populous nation in sub-Saharan Africa bears a significant burden of worsening maternal and child health outcomes with a maternal mortality rate of 917 per 100,000 live births and child mortality rate of 117 per 1,000 live births. While several studies have documented that financial barriers disproportionately discourage poor women from seeking needed maternal and child healthcare, other studies have indicated otherwise. Evidence shows that there are instances where health facilities with skilled healthcare providers exist, and yet maternal, and child health outcomes remain abysmally low, indicating the presence of non-cognitive and behavioural factors that may affect the utilization of healthcare services. This study investigated the influence of locus of control and self-esteem on utilization of maternal and child healthcare services in Nigeria. Specifically, it explored the differences in utilization of antenatal care, skilled birth care, postnatal care, and child vaccination by women having an internal and external locus of control and women having high and low self-esteem. We collected information on non-cognitive traits of 1411 randomly selected women, along with information on utilization of the various indicators of maternal and child healthcare. Estimating logistic regression models for various components of healthcare services utilization, we found that women’s internal locus of control was a significant predictor of utilization of antenatal care, skilled birth care, and completion of child vaccination. We also found that having high self-esteem was a significant predictor of utilization of antenatal care, postnatal care, and completion of child vaccination after adjusting for other control variables. By improving our understanding of non-cognitive traits as possible barriers to maternal and child healthcare utilization, our findings offer important insights for enhancing participant engagement in intervention programs that are initiated to improve maternal and child health outcomes in low-and-middle-income countries.

Keywords: behavioural economics, health-seeking behaviour, locus of control and self-esteem, maternal and child healthcare, non-cognitive traits, and healthcare utilization

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Mahmoud Huleihil

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In this study, the performance of a thermodynamic gas cycle of magnetohydrodynamic (MHD) power generation is considered and presented in terms of power efficiency curves. The dissipation mechanisms considered include: fluid friction modeled by means of the isentropic efficiency of the compressor, heat transfer leakage directly from the hot reservoir to the cold heat reservoir, and constant velocity of the MHD generator. The study demonstrates that power and efficiency vanish at the extremes of both slow and fast operating conditions. These points are demonstrated on power efficiency curves and the locus of efficiency at maximum power and the locus of maximum efficiency. Qualitatively, the considered loss mechanisms have a similar effect on the efficiency at maximum power operation and on maximum efficiency operation, thus these efficiencies are reduced, even for small values of the loss mechanisms.

Keywords: magnetohydrodynamic generator, electrical efficiency, maximum power, maximum efficiency, heat engine

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Geir Sigurðsson

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This paper compares ancient Daoist and Confucian approaches to the human body as a locus for learning, edification or personal cultivation. While pointing out some major differences between ancient Chinese and mainstream Western visions of the body, it seeks at the same time inspiration in some seminal Western phenomenological and post-structuralist writings, in particular from Maurice Merleau-Ponty and Pierre Bourdieu. By clarifying the somewhat dissimilar scopes of foci found in Daoist and Confucian philosophies with regard to the role of and attitude to the body, the conclusion is nevertheless that their approaches are comparable, and that both traditions take the physical body to play a vital role in the cultivation of excellence. Lastly, it will be argued that cosmological underpinnings prevent the Confucian li from being rigid and invariable and that it rather emerges as a flexible learning device to train through active embodiment a refined sensibility for one’s cultural environment.

Keywords: body, Confucianism, Daoism, li (ritual), phenomenology

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Zhanar Imanova

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Masses of real celestial bodies change anisotropically and reactive forces appear, and they need to be taken into account in the study of these bodies' dynamics. We studied the two-planet problem of three bodies with variable masses in the presence of reactive forces and obtained the equations of perturbed motion in Newton’s form equations. The motion equations in the orbital coordinate system, unlike the Lagrange equation, are convenient for taking into account the reactive forces. The perturbing force is expanded in terms of osculating elements. The expansion of perturbing functions is a time-consuming analytical calculation and results in very cumber some analytical expressions. In the considered problem, we obtained expansions of perturbing functions by small parameters up to and including the second degree. In the non resonant case, we obtained evolution equations in the Newton equation form. All symbolic calculations were done in Wolfram Mathematica.

Keywords: two-planet, three-body problem, variable mass, evolutionary equations

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Authors: Matevž Breška, Iztok Peruš, Vlado Stankovski

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Systematic overview of existing Ground Motion Prediction Equations (GMPEs) has been published by Douglas. The number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration (PGA) the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works.

Keywords: Ground Motion Prediction Equations, Levenberg-Marquardt algorithm, refitting PF-L database, peak ground acceleration

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Authors: Zahid Ullah, Atlas Khan

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The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: Wathig Hashim Mohamed Ibrahim

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Twenty Five polymorphic microsatellite out of 50 Loci were used to genotype some camel (Camelus dromedarius) types and subtypes in Sudan (Naylawi, Shanapla, Lahawi, Kinani, Rashaydi, Bani-Aamir, Annafi, Bishari Shallagyai and Bishari Arririt) and that from Qatar (OmmaniHJ, OmmaniKH, Majaheem, Pakistani Sindi, Pakistani Punjabi and Pakistani) and for comparative; one type from Somalia (Aarhou) and another from Chad (Spotted) were investigated. The highest number of alleles were 23 in Locus CVRL 01, and lowest were 2 in YWLL 59. The observed heterozygosity (Hobs) were 0.950 and 0.049 for VOLP08 and YWLL09, respectively, while the expected heterozygosity (HExp) were 0.915 and 0.362 for Locus VOLP67 and YWLL58, respectively, and the HExp mean was 0.7378. Polymorphic Information Content (PIC) ranged between 0.907 - 0.345 in Locus VOLP67 and YWLL58, and the PIC mean was 0.7002. The genetic distance ranged between 0.545 – 0.098 for Shallagyai (Bishari subtype) – Pakistani Sindi subtype and between Annafi - Rashaydi, respectively. The genetic distance between spotted and all types ranged between 0.223 with Arririt (Bishari subtype) and 0.463 with Punjabi (Pakistani subtype) that found in Qatar, while all types with Aarhou ranged between 0.215 for Arririt and 0.469 with Punjabi (Pakistani subtype). The dondrogram shows that there is a relationship between the genetic makeup and geographical distributions and also between the genetic makeup and phenotypic characteristic. Individual assignment was calculated, 46.62% correctly assigned and 46.87% quality index. Hardy Weinberg Equivalent (HWE) was also calculated. Key words: Camel, genotype, polymorphic microsatellite

Keywords: camel, genotype, polymorphic microsatellite, types and subtypes

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: Muhammad Ali, Aamir Sohail, Umair Malik

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Research in entrepreneurship has gained much attention in current academic environment. Youngsters are taking interest to start their own business in spite of risk matter. The objective of the study is to explain how various personality traits (personal attitude, locus of control, instrumental readiness and perceived behavioral control) are affecting entrepreneurial intention of students. The theory of planned behavior supports out study which explains that personal attractiveness, social norms and feasibility are the main factors that affect intentions of an individual. The sample data of 120 is collected from graduating batch of three reputed universities of Islamabad through questionnaires. Our results support the hypothesis that personality traits positively influence the entrepreneurial intention. We conclude from the study that many graduating students are willing to start a new venture, but most of them are likely to do a job in their respective fields. Risk factor also exists in their minds because in our country most people are risk-averse and they do not want to lose their money in case of loss.

Keywords: entrepreneurship, instrumental readiness, locus of control, personal attitude

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Authors: Minas Balyan

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Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: T. Bouchabchoub, A. Bendahmane, A. Haouriqui, N. Attou

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This paper presents simulation results of Forex predicting model equations in order to give approximately a prevision of interest rates. First, Hall-Taylor (HT) equations have been used with Taylor rule (TR) to adapt them to European and American Forex Markets. Indeed, initial Taylor Rule equation is conceived for all Forex transactions in every States: It includes only one equation and six parameters. Here, the model has been used with Hall-Taylor equations, initially including twelve equations which have been reduced to only three equations. Analysis has been developed on the following base macroeconomic variables: Real change rate, investment wages, anticipated inflation, realized inflation, real production, interest rates, gap production and potential production. This model has been used to specifically study the impact of an inflation shock on macroeconomic director interest rates.

Keywords: interest rate, Forex, Taylor rule, production, European Central Bank (ECB), Federal Reserve System (FED).

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: H. Sakamoto, S. Kurosawa, M. Suzuki, S. Oguri

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In Arabidopsis, several genes encoding proteins with ankyrin repeats and trans-membrane domains (AtANKTM) have been identified as mediators of biotic and abiotic stress responses. It has been known that the expression of an AtANKTM gene, At2g24600, is induced in response to abiotic stress and that there are four splicing variants derived from this locus. In this study, by RT-PCR and sequencing analysis, an unknown splicing variant of the At2g24600 transcript was identified. Based on differences in the predicted amino acid sequences, the five splicing variants are divided into three groups. The three predicted proteins are highly homologous, yet have different numbers of ankyrin repeats and trans-membrane domains. It is generally considered that ankyrin repeats mediate protein-protein interaction and that the number of trans-membrane domains affects membrane topology of proteins. The protein variants derived from the At2g24600 locus may have different molecular functions each other.

Keywords: alternative splicing, ankyrin repeats, trans-membrane domains, arabidopsis

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Authors: Huseyi̇n Das, Bülent Tarim, Sunay Demi̇r, Nurçi̇n Küçükkent, Sevi̇l Cengi̇z, Engi̇n Tülek, Veci̇hi̇ Aksakal

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Atak-S laying hens are a high-performance strain obtained by crossing of the Rhode Island Red (RIR) X the Barred Plymouth Rock (BR) and are being produced in the Ankara Poultry Research Institute since 1997. Phenotypic and genetic improving studies are continued for this strain. In this study, 2 from IGF and 1 from IGFBP2, totally 3 different SNP polymorphisms were examined in 200 Atak-S chickens. Genotypes of SNPs were compared using ANOVA to body weight and egg number thorough 32 weeks of age, body weight at sexual maturity, age at sexual maturity and also egg quality traits such as egg shell breaking strength, shell thickness, Haugh unit, albumen index, yolk index, shape index. Only IGF(a) locus was in agreement with Hardy-Weinberg equilibrium, while, the other loci were not. As a result of the performance comparisons to the 3 SNP loci, it was determined that there has a significant association (P<0.05) between only TC genotypes of the IGF(b) locus and body weight at 32 weeks of age, but there was not any association to the other traits.

Keywords: Atak-S, Igf, Igfbp2, single nucleotide polymorphism

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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