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आयतन 5, मुद्दा 1 (2016)

शोध आलेख

Cavities Identification from Partially Overdetermined Boundary Data in Linear Elasticity

Jaiem E, Abda AB and Rjaibi B

Our main interest in this work is an analysis of geometrical inverse problem related to the detection of cavities, in elasticity framework from partially overdetermined boundary data in two spatial dimensions. For the reconstruction, we have only access to the displacement field and to the normal component of the normal stress. We propose an identification method based on the Kohn-Vogelius formulation combined with the topological gradient method. An asymptotic expansion for an energy function is derived with respect to the creation of a small hole. A one-shot reconstruction algorithm based on the topological sensitivity analysis is implemented. Some numerical experiments concerning the cavities identification are finally reported, highlighting the ability of the method to identify multiple cavities.

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A Direct Method for Determining a P-Solution of Linear Parametric Systems

Kolev L

Recently, a new type of solution to a linear interval parametric (LIP) system (called parameterized or p-solution) has been introduced. An iterative method for determining such a solution has also been proposed. In the present paper, a direct method for determining the p-solution is suggested. Its functional characteristics are compared with those of: (i) a direct method for computing an outer interval (nonparametric) solution of LIP systems, (ii) the known iterative method.

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A Fast Analytic Simulation of Stochastic Mutation and its Application to Modeling Cancer Drug Resistance

Colborn JA

Random “Darwinian” mutation is a primary mechanism by which cancer and pathogens develop resistance to drugs, and this process has been mathematically modeled extensively. Analytic models employ simple equations and allow for very fast computation, but do not accurately predict mutation times or survival probabilities of resistant populations. Stochastic models provide a distribution of probable outcomes but involve more complex mathematics. We present here an analytic method that simulates stochastic mutation with much better accuracy than that of the standard analytic equations. This method is based on an observation that the median stochastic solution emerges at a time close to when the cumulative probability of a first mutant birth approaches unity, which can be calculated analytically. We compare our model to the median stochastic resistant population versus time for varying rates of cell division, natural death, mutation, and drug kill. Generally we find at least an order-of-magnitude reduction in the error of the birth time and the RMS normalized error relative to the standard analytic solution. This method’s speed, accuracy, and simple results make it well-suited as a tool in software and mutation models to survey the resistant heterogeneity of cancers under various treatment plans or to guide a probabilistic analysis with a stochastic model. Such models could advance progress toward a better understanding of the dynamics of resistant subpopulations, better personalized treatment plans, and longer patient survival given the complex and ever-changing sets of drugs, doses, schedules, and cancer genomics of each patient in the clinical setting.

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Modeling Open Channel Fluid Flow with Trapezoidal Cross Section and a Segment Base

Marangu PK, Mwenda E and Theuri DM

This study investigates the suitability of trapezoidal cross-section with segment base in drainage system design. The study has considered steady uniform open channel flow. The saint-Venant partial differential equations of continuity and momentum governing free surface flow in open channels have been solved using finite difference approximation method. We investigate the effects of the channel radius, area of the cross section, the flow depth and the manning coefficient on the flow velocity. The flow variables are velocity and the flow depth while the flow parameters are cross section area of flow, channel radius, slope of the channel and manning coefficient. The study has established that increase in cross section area of flow leads to a decrease in flow velocity. Further, increase in channel radius and cross section area of flow leads to a decrease in flow velocity and increase in roughness coefficient cause flow velocity to decrease. Additionally, increase in flow depth increases velocity. The physical conditions of the flow channel have been applied to conservation equations to arrive at specific governing equations. The results of the study have been presented graphically.

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Mathematical Modelling and Computer Simulation

Huang Y, Zhang H and Laibin G

This article adopts and analyzes a stochastic collocation method to approximate the solution of four order elliptic partial differential equations with random coefficients and forcing terms, which are applied for some mathematicalbiology model. The method is composed of a Galerkin finite approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space, and natural brings on the solution of uncoupled deterministic problems. The well-posedness of the elliptic partial differential equations is investigated as well under some regular assumptions. Strong error estimates for the fully discrete solution using L2 norms are obtained in this work.

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The Role of Family in Initiating Methamphetamine Abuse Treatment: Insights through a Mathematical Model

Mushanyuzy J, Nyabadza F, Muchatibayaz G and Stewartz AGR

Methamphetamine addiction can be considered a family disease", and family involvement in helping a methamphetamine addict seek assistance is essential in combating the methamphetamine epidemic. We develop a mathematical model that takes into account the roles played by families in initiating methamphetamine treatment. An incidence term of newly admitted rehabilitants with probabilities β2 and β3 for joining inpatient and outpatient rehabilitation respectively, have been employed to this effect. Results indicate that family involvement is very crucial in lowering the threshold value a. Hence efforts targeted at encouraging family members to make appropriate referrals would be helpful in controlling the methamphetamine epidemic. The qualitative analysis of the model includes local and Lyapunov global stability of equilibrium. The approach of this paper is to suggest an extension of the drug abuse models which consider only one treatment option for drug users. It will be shown that the proposed model: (i) allows the drug users to choose between in-patient and out-patient rehabilitation, and (ii) is analyzed in the context of real data.

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A New Number Theory-Algebra Analysis II

Sonaglioni L

The basis of this quaternions algebra. The problem of the j k   ⋅ product. 3d (and 4d) product and division in algebraic form; also, the algebraic forms of the product and of the division are differentiable. Questions about the possibility of extend this algebra to more dimensions.

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Cryptographic Schemes Based on Elliptic Curves over the Ring Zp[i]

Kumar M and Gupta P

Elliptic Curve Cryptography recently gained a lot of attention in industry. The principal attraction of ECC compared to RSA is that it offers equal security for a smaller key size. The present paper includes the study of two elliptic curve Ea,b and Ea,-b defined over the ring Zp[i] where i2 = -1. After showing isomorphism between Ea,b and Ea,-b. We define a composition operation (in the form of a mapping) on their union set. Then we have discussed our proposed cryptographic schemes based on the elliptic curve E = Ea,b∪Ea,-b. We also illustrate the coding of points over E, secret key exchange and encryption/decryption methods based on above said elliptic curve. Since our proposed scheme are based on elliptic curve of the particular type therefore the proposed schemes provides a highest strength-per-bit of any cryptosystem known today with smaller key size resulting in faster computations, lower power assumption and memory. Another advantage is that authentication protocols based on ECC are secure enough even if a small key size is used.

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Common Fixed Points of Generalized α-ψ-contractive Type Self-mappings and Multivalued Mappings

Mohammadi B

In this paper, mutivated by the recent work of samet et al. (Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Anal. we give some new results on existence of common fixed points for a pair of generalized α-ψ-contractive self-mappings and multivalued mappings. This results extend and improve many existing results in the literature. Some examples are given to illustrate the results.

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Two-step Explicit Methods for the Numerical Integration of a System of Second Order Initial Value Problems

Gul MN

In this paper, authors present a new family of two-step explicit fourth order methods, for the numerical integration of second order periodic initial-value problems. These methods are explicit in nature and we intend to use them, in future, as a predictor for the family of direct hybrid methods. Their stability properties and the efficiency are also discussed. Considering some numerical results, authors saw that the new methods are superior to the existing explicit methods.

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A Computational Method for the Solution of Nonlinear Burgers Equation Arising in Longitudinal Dispersion Phenomena in Fluid Flow through Porous Media

Olayiwola MO

This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

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The Adomian Decomposition Method for Eigenvalue Problems

Nhawu G, Mafuta P and Mushanyu J

The Adomian decomposition method (ADM) is a powerful method which considers the approximate solution of a non-linear equation as an infinite series which usually converges to the exact solution. In this paper, this method is proposed to solve some eigenvalue problems. It is shown that the series solutions converges to the exact solution for each problem. Then we obtain the eigenvalues of these problems.

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New Type of Riesz Sequence Space of Non-absolute Type

Ganie AH, Ahmad M, Sheikh NA and Jalal T

The aim of this paper is to introduce the space rq (u, p) ∞ , we show its completeness property, show that the spaces rq (u, p) ∞ , are linearly isomorphic to the spaces l∞(p), respectively and compute their α-, β- and γ- duals.

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Study on the Model of Insurer’s Solvency Ratio under Levy Process

Xia D and Fei W

This paper studies the insurer’s solvency ratio model with the Levy process in the presence of financial distress cost. By an option pricing formula for the Levy process, the explicit formula for the expected present value of shareholder’s terminal payoff is given.

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Expert System for Detecting and Diagnosing Car Engine Brake Failure Fault using Dynamic Control System (DCS)

Ibitayo LD, Mohammed GU, Rabiu I and Abdulrahman A

Dynamic Control Systems (DCS) can be applied in detecting and diagnosing car engine brake failure faults which has continuously being implemented to serve different branches such as Mechanical Engineering and many others. Car engine Brake Failure is a sequence of diagnostic processes that brings about the deployment of expertise. It is very important to note that Expert System (ES) is one of the leading Artificial Intelligence techniques that have been adopted to handle such task. This paper presents the imperatives for an Expert System in developing Dynamic Control Systems for detecting and diagnosing car engine Brake Failure faults through input and output requirements of constructing successful Knowledge-Based Systems. Furthermore, diagnosis of car engine Brake Failure faults requires high technical skills and experienced mechanics which are typically scarce and expensive to get. Thus, DCS provides input and output equations in form of Matrix/Vector State Space Representation (MSSR) which is useful in assisting mechanical technicians for car brake failure detection and diagnosis via mathematical Differential Equations in form of DCS.

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