Search results for: Chapman Kolmogorov forward differential equations

Authors: Nader Parsazadeh

Abstract:

The variety of bed sediment load relationships, insufficient information and data, and the influence of river conditions make the selection of an optimum relationship for a given river extremely difficult. Hence, in order to select the best formulae, the bed load equations should be evaluated. The affecting factors need to be scrutinized, and equations should be verified. Also, re-evaluation may be needed. In this research, sediment bed load of Dez Dam at Tal-e Zang Station has been studied. After reviewing the available references, the most common formulae were selected that included Meir-Peter and Muller, using MS Excel to compute and evaluate data. Then, 52 series of already measured data at the station were re-measured, and the sediment bed load was determined. 1. The calculated bed load obtained by different equations showed a great difference with that of measured data. 2. r difference ratio from 0.5 to 2.00 was 0% for all equations except for Nilsson and Shields equations while it was 61.5 and 59.6% for Nilsson and Shields equations, respectively. 3. By reviewing results and discarding probably erroneous measured data measurements (by human or machine), one may use Nilsson Equation due to its r value higher than 1 as an effective equation for estimating bed load at Tal-e Zang Station in order to predict activities that depend upon bed sediment load estimate to be determined. Also, since only few studies have been conducted so far, these results may be of assistance to the operators and consulting companies.

Keywords: bed load, empirical relation ship, sediment, Tale Zang Station

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: equivalent martingale measure, European put option, girsanov theorem, martingales, monte carlo method, option price valuation formula

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita

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This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.

Keywords: dynamic response, nonlinear impact response, finite element analysis, numerical analysis

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Authors: M. N. Abu Seman, L. M. Kei, M. A. Yusoff

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Forward Osmosis (FO) polyamide thin-film composite membranes have been prepared by inter facial polymerization using commercial UF polyethersulfone as membrane support. Different inter facial polymerization times (10s, 30s and 60s) in the organic solution containing trimesoyl chloride (TMC) at constant m-phenylenediamine (MPD) concentration (2% w/v) were studied. The synthesized polyamide membranes then tested for treatment of natural organic matter (NOM) and compared to commercial Cellulose TriAcetate (CTA) membrane. It was found that membrane prepared with higher reaction time (30 s and 60 s) exhibited better membrane performance (flux and humic acid removal) over commercial CTA membrane.

Keywords: cellulose triacetate, forward osmosis, humic acid, polyamide

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Authors: Sidrah Ahmed

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The river and lakes flows are modeled mathematically by shallow water equations that are depth-averaged Reynolds Averaged Navier-Stokes equations under Boussinesq approximation. The temperature stratification dynamics influence the water quality and mixing characteristics. It is mainly due to the atmospheric conditions including air temperature, wind velocity, and radiative forcing. The experimental observations are commonly taken along vertical scales and are not sufficient to estimate small turbulence effects of temperature variations induced characteristics of shallow flows. Wind shear stress over the water surface influence flow patterns, heat fluxes and thermodynamics of water bodies as well. Hence it is crucial to couple temperature gradients with shallow water model to estimate the atmospheric effects on flow patterns. The Ripa system has been introduced to study ocean currents as a variant of shallow water equations with addition of temperature variations within the flow. Ripa model is a hyperbolic system of partial differential equations because all the eigenvalues of the system’s Jacobian matrix are real and distinct. The time steps of a numerical scheme are estimated with the eigenvalues of the system. The solution to Riemann problem of the Ripa model is composed of shocks, contact and rarefaction waves. Solving Ripa model with Riemann initial data with the central schemes is difficult due to the eigen structure of the system.This works presents the comparison of four different finite difference schemes for the numerical solution of Riemann problem for Ripa model. These schemes include Lax-Friedrichs, Lax-Wendroff, MacCormack scheme and a higher order finite difference scheme with WENO method. The numerical flux functions in both dimensions are approximated according to these methods. The temporal accuracy is achieved by employing TVD Runge Kutta method. The numerical tests are presented to examine the accuracy and robustness of the applied methods. It is revealed that Lax-Freidrichs scheme produces results with oscillations while Lax-Wendroff and higher order difference scheme produce quite better results.

Keywords: finite difference schemes, Riemann problem, shallow water equations, temperature gradients

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Authors: Hassen M. Ouakad

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In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin

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Authors: Yuanhao Gao, Pin Lin, Kees Weijer

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In this paper, we will determine the external body force distribution with analysis of stokes fluid motion using mathematical modelling and numerical approaching. The body force distribution is regarded as the unknown variable and could be determined by the idea of optimal control theory. The Stokes flow motion and its velocity are generated by given forces in a unit square domain. A regularized objective functional is built to match the numerical result of flow velocity with the generated velocity data. So that the force distribution could be determined by minimizing the value of objective functional, which is also the difference between the numerical and experimental velocity. Then after utilizing the Lagrange multiplier method, some partial differential equations are formulated consisting the optimal control system to solve. Finite element method and conjugate gradient method are used to discretize equations and deduce the iterative expression of target body force to compute the velocity numerically and body force distribution. Programming environment FreeFEM++ supports the implementation of this model.

Keywords: optimal control model, Stokes equation, finite element method, conjugate gradient method

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Authors: Vandana N. Purav

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Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials.

Keywords:

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Authors: Bandari Shankar, Yohannes Yirga

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In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement

Keywords: unsteady, heat and mass transfer, manetohydrodynamics, nanofluid, non-uniform heat source/sink, stretching sheet

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Authors: Libo Jiang, Huan Li, Rongling Wu

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Ordinary differentiation equations (ODE) have proven to be powerful for reconstructing precise and informative gene regulatory networks (GRNs) from dynamic gene expression data. However, joint modeling and analysis of all genes, essential for the systematical characterization of genetic interactions, are challenging due to high dimensionality and a complex pattern of genetic regulation including activation, repression, and antitermination. Here, we address these challenges by unifying variable selection and game theory through ODE. Each gene within a GRN is co-expressed with its partner genes in a way like a game of multiple players, each of which tends to choose an optimal strategy to maximize its “fitness” across the whole network. Based on this unifying theory, we designed and conducted a real experiment to infer salt tolerance-related GRNs for Euphrates poplar, a hero tree that can grow in the saline desert. The pattern and magnitude of interactions between several hub genes within these GRNs were found to determine the capacity of Euphrates poplar to resist to saline stress.

Keywords: gene regulatory network, ordinary differential equation, game theory, LASSO, saline resistance

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Authors: Khalil Ur Rehman, M. Y. Malik, Usman Ali

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In this paper, the problem proposed by Von Karman is treated in the attendance of additional flow field effects when the liquid is spaced above the rotating rigid disk. To be more specific, a purely viscous fluid flow yield by rotating rigid disk with Navier’s condition is considered in both magnetohydrodynamic and hydrodynamic frames. The rotating flow regime is manifested with heat source/sink and chemically reactive species. Moreover, the features of thermophoresis and Brownian motion are reported by considering nanofluid model. The flow field formulation is obtained mathematically in terms of high order differential equations. The reduced system of equations is solved numerically through self-coded computational algorithm. The pertinent outcomes are discussed systematically and provided through graphical and tabular practices. A simultaneous way of study makes this attempt attractive in this sense that the article contains dual framework and validation of results with existing work confirms the execution of self-coded algorithm for fluid flow regime over a rotating rigid disk.

Keywords: Navier’s condition, Newtonian fluid model, chemical reaction, heat source/sink

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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: Si-Gwan Kim

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In Delay Tolerant Networks (DTN), there may not exist an end-to-end path between source and destination at the time of message transmission. Employing ‘Store Carry and Forward’ delivery mechanism for message transmission in such networks usually incurs long message delays. In this paper, we present the modified Binary Spray and Wait (BSW) routing protocol that enhances the performance of the original one. Our proposed algorithm adjusts the number of forward messages depending on the number of neighbor nodes. By using beacon messages periodically, the number of neighbor nodes can be managed. The simulation using ONE simulator results shows that our modified version gives higher delivery ratio and less latency as compared to BSW.

Keywords: delay tolerant networks, store carry and forward, one simulator, binary spray and wait

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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: Muhammad Zubair Akbar Qureshi, Abdul Bari Farooq

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The intention of the current study to analyze the significance of nano-layer in incompressible magneto-hydrodynamics (MHD) flow of a Newtonian nano-fluid consisting of carbon nano-materials has been considered through an absorbent channel with moving porous walls. Using applicable similarity transforms, the governing equations are converted into a system of nonlinear ordinary differential equations which are solved by using the 4th-order Runge-Kutta technique together with shooting methodology. The phenomena of nano-layer have also been modeled mathematically. The inspiration behind this segment is to reveal the behavior of involved parameters on velocity and temperature profiles. A detailed table is presented in which the effects of involved parameters on shear stress and heat transfer rate are discussed. Specially presented the impact of the thickness of the nano-layer and radius of the particle on the temperature profile. We observed that due to an increase in the thickness of the nano-layer, the heat transfer rate increases rapidly. The consequences of this research may be advantageous to the applications of biotechnology and industrial motive.

Keywords: carbon nano-tubes, magneto-hydrodynamics, nano-layer, thermal conductivity

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Authors: N. Smaoui, B. Chentouf

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The boundary stabilization problem of the rotating disk-beam system is a topic of interest in research studies. This system involves a flexible beam attached to the center of a disk, and the control and stabilization of this system have been extensively studied. This research focuses on the case where the center of mass is fixed in an inertial frame, and the rotation of the center is non-uniform. The system is represented by a set of nonlinear coupled partial differential equations and ordinary differential equations. The boundary stabilization problem of this system via a delayed boundary control is considered. We assume that the boundary control is either of a force type control or a moment type control and is subject to the presence of a constant time-delay. The aim of this research is threefold: First, we demonstrate that the rotating disk-beam system is well-posed in an appropriate functional space. Then, we establish the exponential stability property of the system. Finally, we provide numerical simulations that illustrate the theoretical findings. The research utilizes the semigroup theory to establish the well-posedness of the system. The resolvent method is then employed to prove the exponential stability property. Finally, the finite element method is used to demonstrate the theoretical results through numerical simulations. The research findings indicate that the rotating disk-beam system can be stabilized using a boundary control with a time delay. The proof of stability is based on the resolvent method and a variation of constants formula. The numerical simulations further illustrate the theoretical results. The findings have potential implications for the design and implementation of control strategies in similar systems. In conclusion, this research demonstrates that the rotating disk-beam system can be stabilized using a boundary control with time delay. The well-posedness and exponential stability properties are established through theoretical analysis, and these findings are further supported by numerical simulations. The research contributes to the understanding and practical application of control strategies for flexible structures, providing insights into the stability of rotating disk-beam systems.

Keywords: rotating disk-beam, delayed force control, delayed moment control, torque control, exponential stability

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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: Razieh Karimian, Kim Burton, Mohammad Mehdi Naghizadeh, Maryam Karimian

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Introduction: Habitual upper body postures are associated with online learning during the COVID-19 pandemic. This study explored whether adding an exercise routine to an ergonomic advice intervention improves these postures. Methods: In this randomized trial, 42 male adolescent students with a forward head posture were randomly divided into two equal groups, one allocated to ergonomic advice alone and the other to ergonomic advice plus an exercise routine. The angles of forward head, shoulder, and back postures were measured with a photogrammetric profile technique before and after the 8-week intervention period. Findings: During home quarantine, 76% of the students used their mobile phones, while 35% used a table-chair-computer for online learning. While significant reductions of the forward, shoulder, and back angles were found in both groups (P < 0.001), the effect was significantly greater in the exercise group (P < 0.001: forward head, shoulder, and back angles reduced by some 9, 6, and 5 degrees respectively, compared with 4 degrees in the forward head, and 2 degrees in the shoulder and back angles for ergonomic advice alone. Conclusion: The exercise routine produced a greater improvement in habitual upper body postures than ergonomic advice alone, a finding that may extend beyond online learning at home.

Keywords: randomized trial, online learning, adolescent, posture, exercise, ergonomic advice

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Authors: Ese Urhie, Olabisi Popoola, Obindah Gershon

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Several policies and programs initiated to address the challenge of unemployment in Nigeria seem to be inadequate. The desired structural transformation which is expected to absorb the excess labour in the economy is yet to be achieved. The agricultural sector accounts for almost half of the labour force with very low productivity. This could partly explain why the much anticipated structural transformation has not been achieved. A major reason for the low productivity is the fact that the production process is predominantly based on the use of traditional tools. In view of the underdeveloped nature of the agricultural sector, Nigeria still has huge potentials for productivity enhancement through modern technology. Aside from productivity enhancement, modern agriculture also stimulates both backward and forward linkages that promote investment and thus generate employment. Contrary to the apprehension usually expressed by many stake-holders about the adoption of modern technology by labour-abundant less-developed countries, this study showed that though there will be job loss initially, the reverse will be the case in the long-run. The outcome of this study will enhance the understanding of all stakeholders in the sector and also encourage them to adopt modern techniques of farming. It will also aid policy formulation at both sectoral and national levels. The recursive model and analysis adopted in the study is useful because it exhibits a unilateral cause-and-effect relationship which most simultaneous equation models do not. It enables the structural equations to be ordered in such a way that the first equation includes only predetermined variables on the right-hand side, while the solution for the final endogenous variable is completely determined by all equations of the system. The study examines the transmission channels and effect of modern agriculture on agricultural productivity and employment growth in Nigeria, via its forward and backward linkages. Using time series data spanning 1980 to 2014, the result of the analyses shows that: (i) a significant and positive relationship between agricultural productivity growth and modern agriculture; (ii) a significant and negative relationship between export price index and agricultural productivity growth; (iii) a significant and positive relationship between export and investment; and (iv) a significant and positive relationship between investment and employment growth. The unbalanced growth theory will be a good strategy to adopt by developing countries such as Nigeria.

Keywords: employment, modern agriculture, productivity, recursive model

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot

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Authors: Eugene Stepanov, Arkadi Ponossov

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Ordinary differential equations with switching nonlinearities constitute a very useful tool in many applications. The solutions of such equations can usually be calculated analytically if they cross the discontinuities transversally. Otherwise, one has trajectories that slides along the discontinuity, and the calculations become less straightforward in this case. For instance, one of the problems one faces is non-uniqueness of the sliding modes. In the presentation, it is proposed to apply the theory of hybrid dynamical systems to calculate the solutions that are ‘hidden’ in the discontinuities. Roughly, one equips the underlying switched system with an explicitly designed discrete dynamical system (‘automaton’), which governs the dynamics of the switched system. This construction ‘splits’ the dynamics, which, as it is shown in the presentation, gives uniqueness of the resulting hybrid trajectories and at the same time provides explicit formulae for them. Projecting the hybrid trajectories back onto the original continuous system explains non-uniqueness of its trajectories. The automaton is designed with the help of the attractors of the specially constructed adjoint dynamical system. Several examples are provided in the presentation, which supports the efficiency of the suggested scheme. The method can be of interest in control theory, gene regulatory networks, neural field models and other fields, where switched dynamics is a part of the analysis.

Keywords: hybrid dynamical systems, singular perturbation analysis, sliding modes, switched dynamics

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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: Salah Alrabeei, Mohammad Yousuf

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The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, , L-stable methods, pricing European options, Jump–diffusion model

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Authors: Maja Andrić, Josip Pečarić

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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.

Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality

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Authors: Qinghua Zhang, Yanhe Zhu, Xiang Zhao, Yeqin Yang, Hongwei Jing, Guoan Zhang, Jie Zhao

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This paper presents a wearable reconfigurable supernumerary robotic limb with differential actuated joints, which is lightweight, compact and comfortable for the wearers. Compared to the existing supernumerary robotic limbs which mostly adopted series structure with large movement space but poor carrying capacity, a prototype with the series-parallel configuration to better adapt to different task requirements has been developed in this design. To achieve a compact structure, two kinds of cable-driven mechanical structures based on guide pulleys and differential actuated joints were designed. Moreover, two different tension devices were also designed to ensure the reliability and accuracy of the cable-driven transmission. The proposed device also employed self-designed bearings which greatly simplified the structure and reduced the cost.

Keywords: cable-driven, differential actuated joints, reconfigurable, supernumerary robotic limb

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Shafiullah Soomro

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Active contour is one of the image segmentation techniques and its goal is to capture required object boundaries within an image. In this paper, we propose a novel image segmentation method by using an active contour method based on anisotropic diffusion feature enhancement technique. The traditional active contour methods use only pixel information to perform segmentation, which produces inaccurate results when an image has some noise or complex background. We use Perona and Malik diffusion scheme for feature enhancement, which sharpens the object boundaries and blurs the background variations. Our main contribution is the formulation of a new SPF (signed pressure force) function, which uses global intensity information across the regions. By minimizing an energy function using partial differential framework the proposed method captures semantically meaningful boundaries instead of catching uninterested regions. Finally, we use a Gaussian kernel which eliminates the problem of reinitialization in level set function. We use several synthetic and real images from different modalities to validate the performance of the proposed method. In the experimental section, we have found the proposed method performance is better qualitatively and quantitatively and yield results with higher accuracy compared to other state-of-the-art methods.

Keywords: active contours, anisotropic diffusion, level-set, partial differential equations

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Authors: Nevena Jakovčević Stor, Ivan Slapničar

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

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

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Authors: 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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