Search results for: structured parity equations

Authors: Kamel Al-Khaled

Abstract:

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: A. M. Sagir

Abstract:

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: Lourdita Llanto

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This study described and assessed the implementation of artificial insemination (AI) for cattle and carabaos in the Bicol Region, Philippines: Albay, Sorsogon and Camarines Sur. Three hundred respondents were interviewed. Results were analyzed using frequency counts, means, percentages and chi-square test. Semen samples from different stations were analyzed for motility, viability and morphology. T-test was used in semen quality evaluation. Provincial AI coordinators (PAIC) were male, averaging 59 years old, married, had college education, served in government service for 34 years, but as PAIC for 5.7 years. All had other designations. Mean AI operation was 11.33 years with annual support from the local government unit of Php76,666.67. AI technicians were males, married, with college education, and trained on AI. Problems were on mobility; inadequate knowledge of farmers in animal raising and AI; and lack of liquid nitrogen and frozen semen supply. There was 2.95 municipalities and breedable cattle/carabaos of 3,091.25 per AI technician. Mean number of artificially inseminated animals per AI technician for 2011 was 28.57 heads for carabaos and 8.64 heads for cattle. There was very low participation rate among farmers. Carabaos were 6.52 years with parity 1.53. Cattle were 5.61 years, with parity of 1.51. Semen quality significantly (p ≤ 0.05) deteriorated in normal and live sperm with storage and handling at the provincial and field stations. Breed, AI technicians practices and AI operation significantly affected conception rate. Mean conception rate was 57.62%.

Keywords: artificial insemination, carabao, parity, mother tanks, frozen semen

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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: 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: Rafsan Al Mamun, Md. Motaharul Islam, Rabana Tajrin, Nabiha Noor, Shafinaz Qader

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In an attempt to enrich the lives of billions of people by providing proper information, security and a way of communicating with others, the need for efficient and improved satellites is constantly growing. Thus, there is an increasing demand for better error detection and correction (EDAC) schemes, which are capable of protecting the data onboard the satellites. The paper is aimed towards detecting and correcting such errors using a special algorithm called the Hamming Code, which uses the concept of parity and parity bits to prevent single-bit errors onboard a satellite in Low Earth Orbit. This paper focuses on the study of Low Earth Orbit satellites and the process of generating the Hamming Code matrix to be used for EDAC using computer programs. The most effective version of Hamming Code generated was the Hamming (16, 11, 4) version using MATLAB, and the paper compares this particular scheme with other EDAC mechanisms, including other versions of Hamming Codes and Cyclic Redundancy Check (CRC), and the limitations of this scheme. This particular version of the Hamming Code guarantees single-bit error corrections as well as double-bit error detections. Furthermore, this version of Hamming Code has proved to be fast with a checking time of 5.669 nanoseconds, that has a relatively higher code rate and lower bit overhead compared to the other versions and can detect a greater percentage of errors per length of code than other EDAC schemes with similar capabilities. In conclusion, with the proper implementation of the system, it is quite possible to ensure a relatively uncorrupted satellite storage system.

Keywords: bit-flips, Hamming code, low earth orbit, parity bits, satellite, single error upset

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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: O. S. Asaolu, A. Bolorunduro

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Background: Unwanted, mistimed and unintended pregnancy is an important public health issue and the most common cause of maternal mortality in developing countries. Unintended pregnancy is a potential hazard for every sexually active woman as it most times ends in unsafe abortion. The study aimed at assessing the pre-conception contraceptive use, prevalence of unintended pregnancies and the non-contraceptive factors associated with unintended pregnancy amongst currently married women in Osun state. Methodology: A descriptive cross-sectional study among randomly selected 341 currently married pregnant women attending antenatal clinics in Ilesa town of Osun state was conducted in 5 health facilities. A random selection of 5 of the 22 health facilities in the state was done. Data was collected through a self-administered questionnaire and all completed questionnaires were analyzed with SPSS. Result: About two-fifth of the currently pregnant women (40%) who has never used an FP method reported that their current pregnancy was unintended. The results indicate that age of women, age at first sex, substance use, total children ever born of children, religion, and extramarital affairs were key predictors of unintended pregnancy. Women who have higher parity are more likely to experience unintended pregnancy compared to women with lower parity (odds ratio, 0.25). Furthermore, those women who don’t engage in extra marital affairs were less likely to experience unintended pregnancy (odds ratio, 0.3) compared to those who do not. Contribution to knowledge: The predicted probability, using logistic regression, has shown that women who engage in extramarital affairs and women with high parity are more likely to have unintended pregnancy. Conclusion: Behaviour change programs should aim to reduce unintended pregnancy by focusing mostly on identified factors so that the need for abortion is decreased and the overall well-being of the family is maintained and enhanced.

Keywords: unintended pregnancy, factors, pregnant women, Nigeria

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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: Sanan Raza, Tariq Abbas, Ahmad Yar Qamar, Muhammad Younus, Hamayun Khan, Mujahid Zafar

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Water Buffaloes contribute significantly in Asian agriculture. The objective of this study was to evaluate the efficacy of two synchronization protocols in enhancing pregnancy rate in 105 mixed parity buffaloes particularly in summer season. Buffaloes are seasonal breeders showing more fertility from October to January in subtropical environment of Pakistan. In current study 105 lactating buffaloes of mixed parity were used having normal estrous cycle, age ranging 5-9 years, weighing between 400-650 kg, BCS 4 ± 0.5 (1-5) and lactation varied from first to 5th. Experimental animals were divided into three groups based on corpus leteummorphometry. Morphometry of C.L was done using rectal population and ultrasonography. All animals were injected 25mg of PGi.m. (Cloprostenol). In Group-1 (n=35) hCG was administered at follicular size of 10mm having scanned after detection of heat. Similarly Group-2 (n=35) received 25 mg EB i.m (Estradiol Benzoate) after confirmation of follicular size of 10mm with ultrasound. Likewise, buffaloes of Group-3 (n=35) were administered normal saline respectively using as control. All buffaloes of three groups were inseminated after 12h of hCG, EB, and normal saline administration respectively. Pregnancy was assessed by ultrasound at 18th and 45th day post insemination. Pregnancy rates at 18th day were 38.2%, 34.5%, and 27.3% for G1, G2, and G3 respectively indicating that hCG and EB administered groups have no difference in results except control group having lower conception rate than both groups respectively. Similarly on 42nd day, these were 40.4%, 32.7% for G1 and G2 which are significantly higher than G3= 26.6 (control Group). Also, hCG and EB treated buffaloes have more probability of pregnancy than control group. Based on the findings of current study, it seems reasonable that the use of hCG and EB has been associated with improving pregnancy rates in non-breeding season of buffaloes.

Keywords: buffalo, hCG, EB, pregnancy rate, follicle, insemination

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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: Seyed Saeid Nabavi

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Background: Many infants with intrauterine growth disorder are screened for TORCH infections. This action has no economic justification in terms of the imposed costs. In this regard, due to the research gap in this field, this study aimed to investigate the relationship between intrauterine growth disorder and TORCH infection in neonates referred to Milad hospital in 2019 and 2020. Materials and Methods: In this cross-sectional study, 41IUGR newborns were selected and evaluated based on diagnostic and clinical studies in Milad Hospital in 2019 and 2020. TORCH results found in IgG and IgM antibody titer assay were tested in mother and infant. Antibody titers of toxoplasmosis, rubella, cytomegalovirus, herpes, and syphilis were determined in cases, and other variables were compared. The collected data were entered in SPSS software 25 and analyzed at a significant level of 0.05 using the statistical tests of Kolmogorov–Smirnov, Shapiro–Wilk, chi-square, and Mann–Whitney. Results: Most of the IUGR infants studied were girls (68.3%), Gravida and Parity were reported to be 68.3% and 80%, respectively, in the study. Mean weight, APGAR score, and neonatal gestational age are reported as 1710.62±334.43 g, 7.71±1.47, and 35.7+ 1.98 weeks, respectively. Most of the newborns were born by cesarean section (92.7%). TORCH infection was reported in three patients, 7.3%. The mean gestational age of IUGR infants with TORCH infection was reported to be less than other babies with IUGR. Therefore, the mean gestational age of subjects with TORCH infection was 33±1.4 weeks and in others 35.94±1.91 weeks (p-value = 0.038). No significant relationship between TORCH infection and gender, gravidity, and parity of newborns was found (p-value > 0.05). Conclusion: TORCH infection was reported in 3 patients( 7.3%). No significant relationship between TORCH infection and gender, gravidity, and parity of newborns was found. p-value > 0.05

Keywords: congenital infection, intrauterine growth restriction, TORCH infections, neonates

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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: Nkiru Nnaemezie, J. O. Okafor

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The high mortality as a result of pregnancy related illnesses is a global public health problem and a source of concern to most countries including Nigeria. This study was therefore designed to determine the Demographic Variables associated with common pregnancy related illnesses among pregnant mothers in Awka South Local Government Area of Anambra State. The design of the study was an expost-facto research design. All the folders of the pregnant mothers that were studied from 2010-2014 formed the population of the study which included 10,250 folders. Based on the content of the folders, a researcher developed pro-forma (RDP) was used for data collection. Five research questions and five hypotheses were postulated for the study. Research questions postulated were answered using simple percentage. Hypotheses stated were analyzed at 0.05 level of significance using chi-square (X²) statistics. The result among others showed that pregnant mothers within 15-29 years had the most pregnancy related illnesses than mothers on other age brackets. Pregnant mothers with 0-1 parity level experienced the most pregnancy related illnesses than mothers on other parity levels. Public servants experienced the most pregnancy related illnesses than mothers in other occupations. Married pregnant mothers experienced the most pregnancy related illnesses than single mothers. Pregnant mothers with secondary education had the most pregnancy related illnesses than mothers in other education levels. There were significant differences in the common pregnancy related illnesses among the pregnant mothers of the study in relation to the demographic variables of the study which included age, parity, occupation, marital status and educational level. Based on the findings, conclusions were drawn, and the following recommendations among others were made: there is need for health education in terms of educating those pregnant mothers during antenatal clinics; single mothers should be advised to register for antenatal early enough.

Keywords: analysis, demographic variables, pregnancy related illnesses, pregnant mothers

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Authors: Muhammad Umar Kiani, Muhammad Shahbaz, Hassan Akbar

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Simulation of a high speed inviscid steady ideal air flow around a 2D/axial-symmetry body was carried out by the use of mb_cns code. mb_cns is a program for the time-integration of the Navier-Stokes equations for two-dimensional compressible flows on a multiple-block structured mesh. The flow geometry may be either planar or axisymmetric and multiply-connected domains can be modeled by patching together several blocks. The main simulation code is accompanied by a set of pre and post-processing programs. The pre-processing programs scriptit and mb_prep start with a short script describing the geometry, initial flow state and boundary conditions and produce a discretized version of the initial flow state. The main flow simulation program (or solver as it is sometimes called) is mb_cns. It takes the files prepared by scriptit and mb_prep, integrates the discrete form of the gas flow equations in time and writes the evolved flow data to a set of output files. This output data may consist of the flow state (over the whole domain) at a number of instants in time. After integration in time, the post-processing programs mb_post and mb_cont can be used to reformat the flow state data and produce GIF or postscript plots of flow quantities such as pressure, temperature and Mach number. The current problem is an example of supersonic inviscid flow. The flow domain for the current problem (strake configuration wing) is discretized by a structured grid and a finite-volume approach is used to discretize the conservation equations. The flow field is recorded as cell-average values at cell centers and explicit time stepping is used to update conserved quantities. MUSCL-type interpolation and one of three flux calculation methods (Riemann solver, AUSMDV flux splitting and the Equilibrium Flux Method, EFM) are used to calculate inviscid fluxes across cell faces.

Keywords: steady flow simulation, processing programs, simulation code, inviscid flux

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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: 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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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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