Search results for: fractional Black-Scholes equations

Authors: A. Boulanoir, B. Ould Bouamama, A. Debiane, N. Achour

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The paper deals with robust Fault Detection and isolation with respect to parameter uncertainties based on linear fractional transformation form (LFT) Bond graph. The innovative interest of the proposed methodology is the use only one representation for systematic generation of robust analytical redundancy relations and adaptive residual thresholds for sensibility analysis. Furthermore, the parameter uncertainties are introduced graphically in the bond graph model. The methodology applied to the nonlinear industrial Electro-Mechanical Actuators (EMA) used in avionic systems, has determined first the structural monitorability analysis (which component can be monitored) with given instrumentation architecture with any need of complex calculation and secondly robust fault indicators for online supervision.

Keywords: bond graph (BG), electro mechanical actuators (EMA), fault detection and isolation (FDI), linear fractional transformation (LFT), mechatronic systems, parameter uncertainties, avionic system

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Artion Kashuri, Rozana Liko

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In this paper, the authors establish an integral identity using delta differentiable functions. By applying this identity, some new results via a general class of convex functions with respect to two nonnegative functions on a time scale are given. Also, for suitable choices of nonnegative functions, some special cases are deduced. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtained as well. We hope that current work using our idea and technique will attract the attention of researchers working in mathematical analysis, mathematical inequalities, numerical analysis, special functions, fractional calculus, quantum mechanics, quantum calculus, physics, probability and statistics, differential and difference equations, optimization theory, and other related fields in pure and applied sciences.

Keywords: convex functions, Hermite-Hadamard inequality, special means, time scale

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

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

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: N. Fusun Oyman Serteller

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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

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Authors: A. Giniatoulline

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A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

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Authors: Ritu Rani

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In this paper, we apply minimalistically upheld linear semi-orthogonal B-spline wavelets, exceptionally developed for the limited interim to rough the obscure function present in the integral equations. Semi-orthogonal wavelets utilizing B-spline uniquely developed for the limited interim and these wavelets can be spoken to in a shut frame. This gives a minimized help. Semi-orthogonal wavelets frame the premise in the space L²(R). Utilizing this premise, an arbitrary function in L²(R) can be communicated as the wavelet arrangement. For the limited interim, the wavelet arrangement cannot be totally introduced by utilizing this premise. This is on the grounds that backings of some premise are truncated at the left or right end purposes of the interim. Subsequently, an uncommon premise must be brought into the wavelet development on the limited interim. These functions are alluded to as the limit scaling functions and limit wavelet functions. B-spline wavelet method has been connected to fathom linear and nonlinear integral equations and their systems. The above method diminishes the integral equations to systems of algebraic equations and afterward these systems can be illuminated by any standard numerical methods. Here, we have connected Newton's method with suitable starting speculation for solving these systems.

Keywords: semi-orthogonal, wavelet arrangement, integral equations, wavelet development

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Authors: Irfan Ali, Srikant Gupta, Aquil Ahmed

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Every country needs a sustainable development (SD) for its economic growth by forming suitable policies and initiative programs for the development of different sectors of the country. This paper is comprised of modeling and optimization of different sectors of India that form a multi-criterion model. In this paper, we developed a fractional goal programming (FGP) model that helps in providing the efficient allocation of resources simultaneously by achieving the sustainable goals in gross domestic product (GDP), electricity consumption (EC) and greenhouse gasses (GHG) emission by the year 2030. Also, a weighted model of FGP is presented to obtain varying solution according to the priorities set by the policy maker for achieving future goals of GDP growth, EC, and GHG emission. The presented models provide a useful insight to the decision makers for implementing strategies in a different sector.

Keywords: sustainable and economic development, multi-objective fractional programming, fuzzy goal programming, weighted fuzzy goal programming

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: R. Rama Kishore, Sunesh

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Recent development in the usage of internet for different purposes creates a great threat for the copyright protection of the digital images. Digital watermarking can be used to address the problem. This paper presents detailed review of the different watermarking techniques, latest trends in the field of secured, robust and imperceptible watermarking. It also discusses the different optimization techniques used in the field of watermarking in order to improve the robustness and imperceptibility of the method. Different measures are discussed to evaluate the performance of the watermarking algorithm. At the end, this paper proposes a watermarking algorithm using (2, 2) share visual cryptography and Bezier curve based algorithm to improve the security of the watermark. The proposed method uses fractional transformation to improve the robustness of the copyright protection of the method. The algorithm is optimized using fuzzy entropy for better results.

Keywords: digital watermarking, fractional transform, visual cryptography, Bezier curve, fuzzy entropy

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Authors: Xijun Yu, Zhenzhen Li, Zupeng Jia

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This paper presents a new cell-centered Lagrangian scheme for two-dimensional compressible flow. The new scheme uses a semi-Lagrangian form of the Euler equations. The system of equations is discretized by Discontinuous Galerkin (DG) method using the Taylor basis in Eulerian space. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently by a nodal solver. The mesh moves with the fluid flow. The time marching is implemented by a class of the Runge-Kutta (RK) methods. A WENO reconstruction is used as a limiter for the RKDG method. The scheme is conservative for the mass, momentum and total energy. The scheme maintains second-order accuracy and has free parameters. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme.

Keywords: cell-centered Lagrangian scheme, compressible Euler equations, RKDG method

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Authors: Payel Das, Gnaneshwar Nelakanti

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In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain superconvergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and $L^2$-norm. Numerical examples are given to illustrate the theoretical results.

Keywords: hammerstein integral equations, spectral method, discrete galerkin, numerical quadrature, superconvergence

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Authors: Ogunrinde Roseline Bosede

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

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

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Authors: Mohd. Akram, A. A. M. Saeed

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Surfactants are widely used in our daily life either directly in household and personal care products or indirectly in the industrial processes. The kinetics of the interaction of glycyl-DL-aspartic acid (Gly-DL-Asp) with ninhydrin has been investigated spectrophotometrically in aqueous and organic-solvent media in the absence and presence of cationic surfactant of tetradecyltrimethylammonium bromide (TTAB). The study was carried out under different experimental conditions. The first and fractional order-rate were observed for [Gly-DL-Asp] and [ninhydrin], respectively. The reaction was enhanced about four-fold by TTAB micelles. The effect of organic solvents was studied at a constant concentration of TTAB and showed an increase in the absorbance as well as the rate constant for the formation of product (Ruhemann's purple). The results obtained in micellar media are treated quantitatively in terms of pseudo-phase and Piszkiewicz cooperativity models. The Arrhenius and Eyring equations are valid for the reaction over the range of temperatures used and different activation parameters (Ea, ∆H#, ∆S#, and ∆G#) have been evaluated.

Keywords: glycyl-DL-aspartic acid, ninhydrin, organic solvents, TTAB

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.

Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle

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Authors: M. R. Akbari, S. Akbari, L. Abdollahpour

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The present paper is concerned with calculating the 2-dimensional velocity profile of a viscous flow for an incompressible fluid along the leading edge of a flat plate by using the continuity and motion equations with a simple and innovative approach. A Comparison between Numerical method and AGM has been made and the results have been revealed that AGM is very accurate and easy and can be applied for a wide variety of nonlinear problems. It is notable that most of the differential equations can be solved in this approach which in the other approaches they do not have this capability. Moreover, there are some valuable benefits in this method of solving differential equations, for instance: Without any dimensionless procedure, we can solve many differential equation(s), that is, differential equations are directly solvable by this method. In addition, it is not necessary to convert variables into new ones. According to the afore-mentioned expressions which will be proved in this literature, the process of solving nonlinear differential equation(s) will be very simple and convenient in contrast to the other approaches.

Keywords: leading edge, new idea, flat plate, incompressible fluid

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Authors: Alia Alghosoun, Nabil El Moçayd, Mohammed Seaid

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Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Keywords: erodible beds, finite element method, finite volume method, nonlinear elasticity, shallow water equations, stresses in soil

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Authors: Hassan Manouzi

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We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: least squares, wick product, SPDEs, finite element, wiener chaos expansion, gradient method

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Authors: Y. J. Zhou, G. Lu

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In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: analytical method, mechanical responses, spherical wave propagation, traumatic brain injury

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Authors: Nabila Jaman, K. E. Hoque, S. Sawall, M. Ferdows

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Coronary artery disease (CAD) is one of the most lethal diseases of the cardiovascular diseases. Coronary arteries stenosis and bifurcation angles closely interact for myocardial infarction. We want to use computer-aided design model coupled with computational hemodynamics (CHD) simulation for detecting several types of coronary artery stenosis with different locations in an idealized model for identifying virtual fractional flow reserve (vFFR). The vFFR provides us the information about the severity of stenosis in the computational models. Another goal is that we want to imitate patient-specific computed tomography coronary artery angiography model for constructing our idealized models with different left anterior descending (LAD) and left circumflex (LCx) bifurcation angles. Further, we want to analyze whether the bifurcation angles has an impact on the creation of narrowness in coronary arteries or not. The numerical simulation provides the CHD parameters such as wall shear stress (WSS), velocity magnitude and pressure gradient (PGD) that allow us the information of stenosis condition in the computational domain.

Keywords: CAD, CHD, vFFR, bifurcation angles, coronary stenosis

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: Saurabh Rawat, Anushree Sah

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K Maps are generally and ideally, thought to be simplest form for obtaining solution of Boolean equations. Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws, and different traits of Karnaugh Maps. Largest possible k- cubes that exist for a given function are equivalent to its prime implicants. A technique of minimization of Logic functions is tried to be achieved through cubical methods. The main purpose is to make aware and utilise the advantages of cubical techniques in minimization of Logic functions. All this is done with an aim to achieve minimal cost solution.r

Keywords: K-maps, don’t care conditions, Boolean equations, cubes

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Authors: Maali Kachouri, Anis Jarboui

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We focus on the causal relationship between governance and information transparency as well as interrelation among the various governance mechanisms. This paper employs a simultaneous equations approach to show this relationship in the Tunisian context. Based on an 8-year dataset, our sample covers 28 listed companies over 2006-2013. Our findings suggest that internal and external governance mechanisms are interdependent. Moreover, in order to analyze the causal effect between information transparency and governance mechanisms, we found evidence that information transparency tends to increase good corporate governance practices.

Keywords: simultaneous equations approach, transparency, causal relationship, corporate governance

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Authors: M. Shaban, A. Alibeigloo

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This paper studies free vibration behavior of single-walled carbon nanotubes (SWCNTs) embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, nonlocal theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radius-to-length ratio.

Keywords: carbon nanotubes, embedded, nonlocal, free vibration

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Authors: Abdelghani Choucha, Lakhdar Chaib, Salem Arif

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This paper treated the problem of power system stability with the aid of Static Synchronous Series Compensator (SSSC) installed in the transmission line of single machine infinite bus (SMIB) power system. A fractional order PID (FOPID) controller has been applied as a robust controller for optimal SSSC design to control the power system characteristics. Additionally, the SSSC based FOPID parameters are smoothly tuned using Invasive Weed Optimization algorithm (IWO). To verify the strength of the proposed controller, SSSC based FOPID controller is validated in a wide range of operating condition and compared with the conventional scheme SSSC-POD controller. The main purpose of the proposed process is greatly enhanced the dynamic states of the tested system. Simulation results clearly prove the superiority and performance of the proposed controller design.

Keywords: SSSC-FOPID, SSSC-POD, SMIB power system, invasive weed optimization algorithm

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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Authors: S. Srednyak

Abstract:

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

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

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Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo

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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.

Keywords: chemical reaction, MHD, double-diffusive, stretching plate

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