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Analyzing the service availability of mobile cloud computing systems by fluid-flow approximation

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Frontiers of Information Technology & Electronic Engineering 2015年第7期16卷 553-567页

作者： Hong-wu LV Jun-yu LIN Hui-qiang WANG Guang-sheng FENG Mo ZHOU College of Computer Science and Technology Harbin Engineering University Harbin 150001 China

Mobile cloud computing （MCC） has become a promising technique to deal with computation- or data-intensive tasks. It overcomes the limited processing power, poor storage capacity, and short battery life of mobile devices. Providing continuous and on-demand services, MCC argues that the service must be available for users at anytime and anywhere. However, at present, the service availability of MCC is usually measured by some certain metrics of a real-world system, and the results do not have broad representation since different systems have different load levels, different deployments, and many other random factors. Meanwhile, for large-scale and complex types of services in MCC systems, simulation-based methods （such as Monte- Carlo simulation） may be costly and the traditional state-based methods always suffer from the problem of state-space explosion. In this paper, to overcome these shortcomings, fluid-flow approximation, a breakthrough to avoid state-space explosion, is adopted to analyze the service availability of MCC. Four critical metrics, including response time of service, minimum sensing time of devices, minimum number of nodes chosen, and action throughput, are def＇med to estimate the availability by solving a group of ordinary differential equations even before the MCC system is fully deployed. Experimental results show that our method costs less time in analyzing the service availability of MCC than the Markov- or simulation-based methods.

关键词： Service availability Mobile cloud computing Fluid-flow approximation ordinary differential equations

A Stability Theory in Nonlinear Programming

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The Journal of China Universities of Posts and Telecommunications 2001年第1期8卷 72-74页

作者： ZHOUZong-fang SHIYong ManagementCollege UniversityofElectronicScienceandTechnologyChengdu610054P.RChina UniversityofNebraskaatOmaha NE68182USA

We propose a new method for finding the local optimal points of the constrained nonlinear programming by ordinary differential equations (ODE) , and prove asymptotic stability of the singular points of partial vari... 详细信息

关键词： constrained nonlinear programming ordinary differential equations asymptotic stability partial variables

ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF A CERTAIN FOURTH-ORDER differential EQUATION

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Annals of differential equations 2004年第3期20卷 221-234页

作者： A.I.Sadek A.S.AL-Elaiw Dept.of Math. Faculty of ScienceAssiut University71516 AssiutEayptFaculty of Education for GirlsScientific DepartmentsAk-Hassa P.O.Box 180Pin Code 31982Al-HassaK.S.A.

The present paper establishes sufficient conditions for the uniformly bounded of any solution of (1.1) and which tend to zero as t → ∞.

关键词： ordinary differential equations asymptotic behaviour uniformly bounded

Modelling the Dynamical State of the Projected Primary and Secondary Intra-Solution-Particle Movement System of Efavirenz In-Vivo

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International Journal of Modern Nonlinear Theory and Application 2016年第4期5卷 235-247页

作者： Tafireyi Nemaura Department of Clinical Pharmacology University of Zimbabwe Harare Zimbabwe Department of Applied Mathematics National University of Science and Technology Bulawayo Zimbabwe

This work seeks to describe intra-solution particle movement system. It makes use of data obtained from simulations of patients on efavirenz. A system of ordinary differential equations is used to model movement state at some particular concentration. The movement states’ description is found for the primary and secondary level. The primary system is found to be predominantly an unstable system while the secondary system is stable. This is derived from the state of dynamic eigenvalues associated with the system. The saturated solution-particle is projected to be stable both for the primary potential and secondary state. A volume conserving linear system has been suggested to describe the dynamical state of movement of a solution particle.

关键词： ordinary differential equations Stability Nonautonomous Linear System Concentration-Varying Eigenvalues Solution Particle

Laplace Transform, Non-Constant Coefficients differential equations and Applications to Riccati Equation

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Applied Mathematics 2020年第7期11卷 639-649页

作者： Malick Ndiaye Mathematics and Computer Sciences Department at Marist College Poughkeepsie NY USA

In this paper, the Laplace Transform is used to find explicit solutions of a fam-ily of second order differential equations with non-constant coefficients. For some of these equations, it is possible to find the solutions using standard tech-niques of solving ordinary differential equations. For others, it seems to be very difficult indeed impossible to find explicit solutions using traditional methods. The Laplace transform could be an alternative way. An application on solving a Riccati Equation is given. Recall that the Riccati Equation is a non-linear differential equation that arises in many topics of Quantum Me-chanics and Physics.

关键词： ordinary differential equations Laplace Transform

An Explicit Single-Step Nonlinear Numerical Method for First Order Initial Value Problems (IVPs)

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Journal of Applied Mathematics and Physics 2020年第9期8卷 1729-1735页

作者： Omolara Fatimah Bakre Ashiribo Senapon Wusu Moses Adebowale Akanbi Department of Mathematics & Statistics Federal College of Education (Technical) Lagos Nigeria Department of Mathematics Lagos State University Lagos Nigeria

Interest in the construction of efficient methods for solving initial value problems that have some peculiar properties with it or its solution is recently gaining wide popularity. Based on the assumption that the solution is representable by nonlinear trigonometric expressions, this work presents an explicit single-step nonlinear method for solving first order initial value problems whose solution possesses singularity. The stability and convergence properties of the constructed scheme are also presented. Implementation of the new method on some standard test problems compared with those discussed in the literature proved its accuracy and efficiency.

关键词： ordinary differential equations First Order Initial Value Problems Nonlinear Singularities

Applications of Non-Classical equations and Their Approaches to the Solution of Some of Classes equations Arise in the Kelvin-Helmholtz Mechanism and Instability

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Open Journal of Applied Sciences 2022年第11期12卷 1873-1891页

作者： Mahammad A. Nurmammadov Shamakhi Astropysical Observatory Named after Nasreddin Tusi of Ministry of Sciences and Education of the Republic Azerbaijan Shamakhi Azerbaijan

In the presented work, we consider applications of non-classical equations and their approaches to the solution of some classes of equations that arise in the Kelvin-Helmholtz Mechanism (KHM) and instability. In all areas where the Kelvin-Helmholtz instability (KHI) problem is investigated with the corresponding data unchanged, the solution can be taken directly in a specific form (for example, to determine the horizontal structure of a perturbation in a barotropic rotational flow, which is a boundary condition taken, as well as other types of Kelvin-Helmholtz instability problems). In another example, the shear flow along the magnetic field in the Z direction, which is the width of the contact layer between fast and slow flows, has a velocity gradient along the X axis with wind shear. The most difficult problems arise when the above unmentioned equation has singularities simultaneously at points and in this case, our results also remain valid. In the case of linear wave analysis of Kelvin-Helmholtz instability (KHI) at a tangential discontinuity (TD) of ideal magneto-hydro-dynamic (MHD) plasma, it can be attributed to the presented class, and in this case, as far as we know, solutions for eigen modes of instability KH in MHD plasma that satisfy suitable homogeneous boundary conditions. Based on the above mentioned area of application for degenerating ordinary differential equations in this work, the method of functional analysis in order to prove the generalized solution is used. The investigated equation covers a class of a number of difficult-to-solve problems, namely, generalized solutions are found for classes of problems that have analytical and mathematical descriptions. With the aid of lemmas and theorems, the existence and uniqueness of generalized solutions in the weight space are proved, and then general and particular exact solutions are found for the considered problems that are expressed analytically explicitly. Obtained our results may be used for all

关键词： Kelvin-Helmholtz Mechanism and Instability ordinary differential equations Weighted Space Degenerating Planetary Jupiter Non-Classical Approaches

A Filtered Milne-Simpson ODE Method with Enhanced Stability Properties

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Journal of Applied Mathematics and Physics 2023年第1期11卷 192-208页

作者： Ari Aluthge Scott A. Sarra Marshall University Huntington WV USA

The Milne-Simpson method is a two-step implicit linear multistep method for the numerical solution of ODEs that obtains the theoretically highest order of convergence for such a method. The stability region of the method is only an interval on the imaginary axis and the method is classified as weakly stable which causes non-physical oscillations to appear in numerical solutions. For this reason, the method is seldom used in applications. This work examines filtering techniques that improve the stability properties of the Milne-Simpson method while retaining its fourth-order convergence rate. The resulting filtered Milne-Simpson method is attractive as a method of lines integrator of linear time-dependent partial differential equations.

关键词： ordinary differential equations Numerical Methods Weak Instability

Modeling and Optimization of Interaction between Small Coastal Pelagic Fish, their Biological Predators and Fishermen

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Open Journal of Optimization 2021年第1期10卷 13-27页

作者： Ibrahima Diedhiou Salimata Gueye Diagne Fambaye Ngom Sow Coumba Diallo Diop Ndiaga Thiam Gabriel Birame Ndiaye Aissatou Fall Ndoye Gueye Cheikh Anta Diop University of Dakar (UCAD) Dakar Senegal Department of Mathematics and Computer Science (DMI) UCAD Dakar Senegal Oceanographic Research Center Dakar Thiaroye (CRODT) Dakar Senegal Direction of Maritime Fisheries (DPM) Dakar Senegal

Small coastal pelagic fish are one of the fish families most affected by sea fishing. This man-made phenomenon leads to an imbalance in the marine and coastal ecosystem and is one of the main causes of migration north and offshore of the ranges. We used the ordinary differential equations to model the interactions existing between small pelagic resources and fishermen. Modelling follows the same of the Lotka-Volterra equations with a difference in the number of variables. This study confirmed the instability of the marine ecosystem. The objective is first of all to model a system of three interacting individuals composed of two distinct types of predators and two types of prey, and then optimise this interaction with the aim of conserving biodiversity in the ecosystem under study. Determining the Jacobian matrix made it possible to calculate the reproduction rate basic (R0). The study of the strong connectedness has made it possible to reduce the number of variables without losing the objective of the study. A computer program implemented on the language computer python facilitated the visualisation of the results.

关键词： Small Coastal Pelagics ordinary differential equations Modelling Optimisation Basic Reproduction Rate