微分分类数学模型在大数据分类系统优化算法的应用研究

针对大数据环境下的数据挖掘效率和精度不足的问题,提出了一种基于分类挖掘数学模型的评分方法,设计开发了大数据分类系统.首先利用融合算法模型的构建来解决大数据融合问题.在此过程中,把微分原理作为主要参考依据,并通过控制微分分类数据模型的双边界收敛,在偏微分数据集中进行分类数据模型的计算,在增加或减少数据量的支持下,完成模糊控制向量,再使用数据挖掘模型对聚类算法的数值约束,完成子序列的采集,并在迭代次数最少的情况下,利用测量信息进行收敛调节,最后采用高斯核关联数据挖掘序列.然后利用约束集差分延迟二阶和差分数学分类模型,从而构建了分类差分数学模型和大分类数据.结果及结论表明,所设计的系统大数据分类能够有效地提高准确率,降低内存占用率,具有较高的分类性能.

中空内压超滤膜丝的数学模型与运行特性

针对中空内压单支超滤膜的亲水短丝与疏水长丝,分别进行了丝壁透水系数与丝程阻力系数的压力及温度特性的测试分析;建立了膜丝运行的微分方程数学模型;分析了给水压力、给水温度、给水方式、膜丝长度、透水系数及阻力系数等内外因素变化时,各项膜丝沿程运行参数的变化分布规律,从而较为全面地揭示了中空内压超滤膜丝的运行规律。

大数据分类系统优化算法中微分分类数学模型的应用研究

本文深入探讨了大数据分类系统中微分分类数学模型的应用,并在偏微积分分类数学模型的基础上,对链接数据挖掘模型进行了改进。研究中特别提出了双边界收敛控制理论及其验证,以及关联挖掘方法的优化两大策略。在后续的应用部分,本文以A集团为例,利用Hadoop数据集群进行实证实验,并从接收器操作特征曲线(receiver operating characteristic curve,ROC)、精度测试和扩展性测试等多个角度对模型性能进行了详细分析。实验结果表明:微分分类法在分类能力和关联数据挖掘方面表现出高效性能,同时在误差率和扩展性方面也展现出优势,为大数据分类与挖掘提供了新的研究视角和策略。

仿真技术研究及其在气田管网改造中的应用

天然气管道系统在运行过程中,由于供气量和用气量的变化、阀门的开关、压缩机的启停等,往往会 使管网系统处于不稳定的运行状态,加上目前管网运行中存在着区域供用气不平衡、管网服役时间长、运行环境恶 劣、管线破漏频繁、事故隐患严重等问题。因此对管道系统进行动态分析是很有必要的。文章通过建立管道数学 微分模型以及管网中非管元件数学微分模型,并用隐式差分法将偏微分模型转换为有限的差分方程,然后用牛顿 迭代法求解有限差分方程组,最后通过自制软件对某气田管网进行了仿真。仿真结果表明:各管道中的压力没有 超过管道允许压力,管网内压降较小。因此,可以适当增加输气量;而部分管段流量很小,利用率很低,则需要调整 输气方案。仿真结果与实际情况对比表明,该方法具有仿真精度高、求解速度快的优点。

疫苗接种对传染病传播影响的仿真分析

目的提出了一个微分方程的传染病仿真模型,研究疫苗接种对抑制传染病疫情传播的影响。方法将疫苗接种这一影响因素划分为疫苗接种延迟时间和接种比例两个子因素,借鉴了传染病学研究的"仓室"模型思想,结合计算机仿真技术对传染病的传播机理进行仿真。在仿真中调整疫苗接种延迟时间的长短及疫苗接种的比例,研究疫苗接种对传染病疫情传播的影响。结果通过仿真得到疫苗接种对传染病疫情的传播具有明显的抑制作用。在传染病传播期间,对健康人群进行疫苗接种延迟的时间越短,疫苗接种的比例越大,越能够在一定程度上抑制传染病疫情的传播。结论将研究传染病的数学模型与计算机仿真技术相结合,是一种非常有效的方法,且更易于分析,为防治传染病传播提供了理论依据。

Progress in Pressure Swing Adsorption Models During the Recent 30 Years

The pressure swing adsorption (PSA) models discussed here are divided into three categories: partialdifferential equation model, electrical analogue model and neural network model. The partial differential equationmodel, including equilibrium and kinetic models, has provided an elementary viewpoint for PSA processes. Usingthe simplest equilibrium models, some influential factors, such as pressurization with product, incomplete purge,beds with dead volume and heat effects, are discussed respectively. With several approximate assumptions i.e.,concentration profile in adsorbent, 'frozen' column, symmetry and heat effects of bed wall, the more complexkinetic models can be simplified to a certain degree at the expense of a limited application. It has also been foundthat the electrical analogue model has great flexibility to handle more realistic PSA processes without any additionalhypothesis.

Cutting edge curve models for equal pitch cutters and their applications

A mathematic model is established using infinitesimal geometry for the cutting edge design of special milling cutters which use equal lead helix as cutting edges; equations are given for front-end and proclitic surface of revolution of ball pillar milling cutters, ball taper milling cutters and angularly conical milling cutters; and corresponding models are established for the continuity cutting edge curves of milling cutters. Typical examples are given to illustrate the applications of mathematic models, which prove the correctness and applicability of these geometric models.

Basic Numerical Computational Using Scilab Programming

Mathematics is very important for the engineering and scientist but to make understand the mathematics is very difficult if without proper tools and suitable measurement. A numerical method is one of the algorithms which involved with computer programming. In this paper, Scilab is used to carter the problems related the mathematical models such as Matrices, operation with ODE＇s and solving the Integration.

Application of differential equations in mathematical modeling

This paper introduces the main methods and steps of modeling principle by ordinary differential equations, and is used to explore the differential equation model to solve some practical problems, some features of the related problems. With the development of science and technology and production practice, differential equation is more closely connected with other subjects, and a mathematical model for some practical problems of good.

Stability of Motion ＂In the Large＂ of Some Class of Phase Systems

This article focuses on the study of stability of motion of the phase systems described by differential equations whose right-hand sides are periodic in the angular coordinate. The article deals with the mathematical model which has been investigated for stability ＂in the large＂ using the second Lyapunov method. Based on the theoretical results obtained in the work,the computational experiments on concrete examples of electric power systems, which showedthe sufficient efficacy of the proposed method for the studied phase system, were conducted.

The mathematical model and simulation of the electrostatic suspension system in the vertical direction

In order to research the vibration law of electrostatic suspension systems in the vertical direction, the mathematical model as a nonlinear differential equation is established. A series of simulation is carried out. The results show that the solution of the differential equation is a periodic function. The amplitude becomes bigger with the original velocity increased. The period becomes smaller with the original velocity increasing. The numerical methods are presented to derive the amplitude and the frequency, and the results coincide with that of the simulation. The condition during which the simple harmonic vibration arises is pointed out. The expressions for the amplitude and the period of simple harmonic vibration are derived respectively, and the results are the same with that of the simulation. This study is helpful for researching the vibration characteristics of the electrostatic suspension system. The external disturb should be controlled to lower the amplitude and the frequency of the vibration.

中空纤维膜机载制氮装置的数学建模分析

建立了考虑浓差极化现象的微分方程数学模型,并用正交配置法求解,对中空纤维膜机载制氮装置(OBIGGS)进行了分析,并对部分状态点的计算结果进行了实验验证.结果表明:富氮气体(NEA)中氧气的质量分数随着进气温度的升高而降低,在达到最小值后又呈上升趋势;在进气与排气压力差保持不变的情况下,随着中空纤维膜排气压力的下降,中空纤维膜的富氮气体质量流量逐渐增加;随着中空纤维膜丝长度的增加,丝内气体的压降和富氮气体质量流量均有所增加;中空纤维膜空气分离制得的富氮气体质量流量越大,则所需进气的质量流量越大,且富氮气体氧气质量分数越高.

PERMANENCE AND PERIODIC SOLUTION IN AN INTEGRODIFFERENTIAL SYSTEM WITH DISCRETE DIFFUSION

Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.

Fractional-Order Model of the Disease Psoriasis:A Control Based Mathematical Approach

Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epidermal Keratinocytes. Dendritic Cells and CD8＋ T-Cells have a significant role for the occurrence of this disease. In this paper, the authors have developed a mathematical model of Psoriasis involving CD4＋ T-Cells, Dendritic Ceils, CD8＋ T-Cells and Keratinocyte cell populations using the fractional differential equations with the effect of Cytokine release to observe the impact of memory on the cell-biological system. Using fractional calculus, the authors try to explore the suppressed memory, associated with the cell-biological system and to locate the position of Keratinocyte cell population as fractional derivative possess non-local property. Thus, the dynamics of Psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model. Finally, the authors introduce drug into the system to obstruct the interaction between CD4＋ T-Cells and Keratinocytes to restrict the disease Psoriasis. The authors derive the Euler-Lagrange conditions for the optimality made through Matlab by developing iterative of the drug induced system. Numerical simulations are schemes.

An analytical study of drug release kinetics from a degradable polymeric matrix

In modern days, biodegradable polymeric matrix used as the kingpin of local drug delivery system is in the center of attention. This work is concentrated on the formulation of mathematical model elucidating degradation of drug-loaded polymeric matrix followed by drug release to the adjacent biological tissues. Polymeric degradation is penciled with mass conservation equations. Drug release phenomenon is modeled by considering solubilization dynamics of drug particles, diffusion of the solubilized drug through polymeric matrix along with reversible dissociation/recrystallization process. In the tissue phase, reversible dissociation/association along with internalization processes of drug are taken into account. For this, a two-phase spatio-temporal model is postu- lated, which has ensued to a system of partial differential equations. They are solved analytically with appropriate choice of initial, interface and boundary conditions. In order to reflect the potency of the advocated model, the simulated results are analogized with corresponding experimental data and found laudable agreement so as to validate the applicability of the model considered. This model seems to foster the delicacy of the mantle enacted by important drug kinetic parameters such as diffusion coefficients, mass transfer coefficients, particle binding and internalization parameters, which is illustrated through local sensitivity analysis.

Dynamic Analysis of Vibrating Systems with Nonlinearities

The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,the strongly nonlinear Duffing oscillator with third,fifth,and seventh powers of the amplitude,the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration.The obtained results via the approach are compared with ones achieved utilizing other techniques.The results indicate that the approach has a good agreement with other well-known methods.He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.

Global dynamics of hepatitis C viral infection with logistic proliferation

A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson＇s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.

Shifted Boubaker Lagrangian approach for solving biological systems

Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus （HIV） infection model of CD4^＋T cells and the susceptible-infected-removed （SIR） epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian （SBL） method. This method reduces the solution of such system to a system of linear or non- linear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge-Kutta （RK4） method and with the solutions obtained by some other methods in the literature.

Hall Effect on Falkner–Skan Boundary Layer Flow of FENE-P Fluid over a Stretching Sheet

The Falkner-Skan boundary layer steady flow over a fiat stretching sheet is investigated in this paper. The mathematical model consists of continuity and the momentum equations, while a new model is proposed for MHD Finitely Extensible Nonlinear Elastic Peterlin （FENE-P） fluid. The effects of Hall current with the variation of intensity of non-zero pressure gradient are taken into account. The governing partial differential equations are first transformed to ordinary differential equations using appropriate similarity transformation and then solved by Adomian decomposition method （ADM）. The obtained results are validated by generalized collocation method （GCM） and found to be in good agreement. Effects of pertinent parameters are discussed through graphs and tables. Comparison with the existing studies is made as a limiting case of the considered problem at the end.

Method of directly defining the inverse mapping applied to prostate cancer immunotherapy --Mathematical model

In this paper, we apply the method of directly defining the inverse mapping introduced by Liao and Zhao [On the method of directly defining inverse mapping for nonlinear differential equations, Numer. Algorithms 72（4） （2016） 989-1020] to the problem of prostate cancer immunotherapy. We extend this method in two directions： first, we apply the method to a system of nonlinear ordinary differential equation, and second, we propose a new technique for finding the base functions in the considered algorithm.