正则表达式方程组的最小解

网络安全检测中,正则表达式匹配是深度包检测的主要手段,匹配算法则是其关键技术。目前,正则表达式匹配算法可以大体分为转换压缩、状态压缩和字母表压缩三类。文章讨论正则表达式方程组最小解及其求解算法,证明了正则表达式方程组的最小解的存在性和基于Gauss消元法的求解算法的正确性,给出了最小解的构造,分析了求解算法的时间复杂度,为规则压缩奠定了理论基础。

求解正则表达式方程组高斯消元法的矩阵方法

本文在分析现有求解正则表达式方程组最小不动点的高斯消元法基础上，提出了一种利用系数矩阵进行消元变换求解正则表达式方程组的高斯消元法，并给出易编程的实现算法。

计算机控制系统的数学模型与优化控制方法

1 建立数学模型的目的 1.1 模型用于控制系统的分析和设计过程的数学模型通常属于动态模型范畴,它的最基本形式是系统的状态方程表达式: X(K+1)=ƒ(X(K),U(K),K)或X(K+1)=A(K) X(K)+B(K)U(K)

印刷速度与油墨转移率关系的研究

印刷过程中,印刷速度的变化往往会引起油墨转移、纸张定位等多方面的变化,印刷机操作人员必须熟悉因印刷速度改变带来的各种影响,从而采取相应的措施来维持印刷过程和印刷质量的稳定性,其中,印刷速度对油墨转移率的影响最为严重。印刷中油墨转移实质上就是墨层在橡皮布和承印物之间分裂并转移的过程,油墨转移率的高低取决于墨层的分裂位置。分裂位置越靠近橡皮布,则转移到纸张上的油墨越多,油墨转移率越高,反之,

Preserving Coherence of Coherent State Studied via Weyl-Wigner Correspondence

By means of the Weyl correspondence and the explicit normally ordered expression of the Wigner operatorwe convert the time evolution equation of coherent states,governed by some Hamiltonian operators,into seeking forconsistent solution of a set of evolution equtions of classical variables which can meet the requirment that an initialcoherent state remains coherent all the time.

Investigation on characteristics of liquid self-diffusion in slit nanopores using simple quasicrystal model of liquid

Dynamical properties of liquid in nano-channels attract much interest because of their applications in engineering and biological systems. The transfer behavior of liquid confined within nanopores differs significantly from that in the bulk. Based on the simple quasicrystal model of liquid, analytical expressions of self-diffusion coefficient both in bulk and in slit nanopore are derived from the Stokes–Einstein equation and the modified Eyring's equation for viscosity. The local self-diffusion coefficient in different layers of liquid and the global self-diffusion coefficient in the slit nanopore are deduced from these expressions. The influences of confinement by pore walls,pore widths, liquid density, and temperature on the self-diffusion coefficient are investigated. The results indicate that the self-diffusion coefficient in nanopore increases with the pore width and approaches the bulk value as the pore width is sufficiently large. Similar to that in bulk state, the self-diffusion coefficient in nanopore decreases with the increase of density and the decrease of temperature, but these dependences are weaker than that in bulk state and become even weaker as the pore width decreases. This work provides a simple method to capture the physical behavior and to investigate the dynamic properties of liquid in nanopores.

Free vibration of vibrating device coupling two pendulums using multiple time scales method

A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis. Based on energy analysis, dynamic equations with cubic nonlinearities were established using Lagrange's equation. In order to obtain approximate solution, multiple time scales method, one of perturbation technique, was applied. Cases of non-resonant and 1:1:2:2 internal resonant were discussed. In the non-resonant case, the validity of multiple time scales method is confirmed, comparing numerical results derived from fourth order Runge-Kutta method with analytical results derived from first order approximate expression. In the 1:1:2:2 internal resonant case, modal amplitudes of Aa1 and Ab2 increase, respectively, from 0.38 to 0.63 and from 0.19 to 0.32, while the corresponding frequencies have an increase of almost 1.6 times with changes of initial conditions, indicating the existence of typical nonlinear phenomenon. In addition, the chaotic motion is found under this condition.

Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates

The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coetficient Korteweg-de Vries （KdV） equation. The reduction to the （KdV） equation may be useful to understand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.

Solutions of the Schrdinger Equation for PT-Symmetric Coupled Quintic Potentials in Two Dimensions

This paper deals with the solutions of time independent Schrodinger wave equation for a two-dimensional PT-symmetric coupled quintic potential in its most general form. Employing wavefunction ansatz method, general analytic expressions for eigenvalues and eigenfunctions for first four states are obtained. Solutions of a particular case are also presented.

Three Semi-empirical Analytic Expressions for the Radial Distribution Function of Hard Spheres

Three simple analytic expressions satisfying the limitation condition at low densities for the radial distribution function of hard spheres are developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan-Starling equation of state. The simplicity and precision for these expressions are superior to the well-known Percus Yevick expression. The coefficients contained in these expressions have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of PercusYevick expression for the second coordination shell. One of the expressions has been applied to develop an analytic equation of state for the square-well fluid, and the numerical results are in good agreement with the computer simulation data.

Evolution of Arbitrary States under Fock-Darwin Hamiltonian and a Time-Dependent Electric Field

The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin(FD) Hamiltonian subjected to a time-dependent electric field in the plane of the system.An exact analytical expression is established for the evolution of the eigenstates.This result then provides a general solution to the time-dependent Schro¨dinger equation.

Modeling of shear wave velocity in limestone by soft computing methods

The main purpose of current study is development of an intelligent model for estimation of shear wave velocity in limestone. Shear wave velocity is one of the most important rock dynamic parameters. Because rocks have complicated structure, direct determination of this parameter takes time, spends expenditure and requires accuracy. On the other hand, there are no precise equations for indirect determination of it; most of them are empirical. By using data sets of several dams of Iran and neuro-genetic, adaptive neuro-fuzzy inference system （ANFIS）, and gene expression programming （GEP） methods, models are rendered for prediction of shear wave velocity in limestone. Totally, 516 sets of data has been used for modeling. From these data sets, 413 ones have been utilized for building the intelligent model, and 103 have been used for their performance evaluation. Compressional wave velocity （Vp）, density （7） and porosity （.n）, were considered as input parameters. Respectively, the amount of R for neuro-genetic and ANFIS networks was 0.959 and 0.963. In addition, by using GEP, three equations are obtained; the best of them has 0.958R. ANFIS shows the best prediction results, whereas GEP indicates proper equations. Because these equations have accuracy, they could be used for prediction of shear wave velocity for limestone in the future.

On the Product of Integro Differential Equations and Their Solutions in Direct Sum Spaces

In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.

Potentials of Cellular Vortex Element Modeling of Fluid Flow in Confined 2D Aquifer

Numerical methods such as finite difference, finite volume, finite element or hybrid methods have been globally used to successfully study fluid flow in porous stratum of which aquifers are typical examples. Those methods involve mathematical expressions which increases computation time with requirement of specific human expertise. In this paper, numerical models for single phase flow in 1D and 2D using the conservation of mass principles, Darcy＇s flow equation, equation of state, continuity equation and the STB/CFB （stock tank barrel/cubic feet barrel） balance were developed. The models were then recast into pressure vorticity equations using convectional algorithms. Derived equations were used to formulate transport equations which resemble the conventional vorticity transport equation. Formulated numerical models were used to investigate the daily instantaneous aquifer pressure drawdowns and pressure heads for 365 days. The developed equations were subsequently solved using cellular vortex element technique. The developed computer program was used to investigate confined aquifer of dimensions 10× 10 × 75 m with single vertex image. For the aquifer rate of 0.5 m3/s, 0.1 m3/s, 0.15 m3/s, 0.2 m3/s, 0.25 m3/s, 1.0 m3/s, 2.0 m3/s, 2.5 m3/s, 3.0 m3/s, 4.0 m3/s, the respective average head drawdowns and heads were, 1.127 ±0.0141 m, 1.317 ±0.0104 m, 1.412± 0.0041 m, 1.427 ± 0.116 m,1.527 ± 0.0141 m, 2.107 ± 0.0171 m, 2.197 ±0.0191 m, 3.007±0.0171 m, 3.127 ± 0.0041 m, 3.626 ± 0.0121 m, and 25 kN/m2, 35 kN/m2, 33 kN/m2, 5 kN/m2, 6 kN/m2, 11 kN/m2, 25 kN/m2, 42 kN/m2, 50 kN/m2, 62 kN/m2, respectively. Cellular vortex technique with relative little mathematics has been established to have recorded successes in numerical modeling of fluid flow in aquifer simulation.

高中数学教学中如何培养创造性思维

新时代下,高中数学教学中已经将创造性思维的培养列为一个非常重要的教学目标.培养创造性思维对于学生的独立思考能力将会有非常大的促进,有助于提高学生发现问题、分析问题、解决问题的能力以及他们对于学习的兴趣和积极性.在解决数学问题方面,创造性思维也可以为他们提供更有效的方法.所以,在高中数学教学中。

Riemann-Hilbert Boundary Value Problem for the Cauchy-Riemann Equation

The Riemann-Hilbert boundary value problem for the inhomogeneous Cauchy-Riemann equation in the polydomain is considered. The sufficient and necessary solvable conditions and integral expressions of solution for the above problem are given.

SEMI-LINEAR SYSTEMS OF BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN R^n

This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.

On Recursion Operator of the q-KP Hierarchy

It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.

Orbit control strategy for Lagrange point orbits based on an analytical method

The periodic or quasi-periodic orbits around collinear Lagrange points present many properties that are advantageous for space missions. These Lagrange point orbits are exponentially unstable. On the basis of an analytical method, an orbit control strategy that is designed to eliminate the dominant unstable components of Lagrange point orbits is developed. The proposed strategy enables the derivation of the analytical expression of nonlinear control force. The control parameter of this strategy can be arbitrarily selected provided that the parameter is considerably lower than the negative eigenvalue of motion equations, and that the energy required keeps the same order of magnitude. The periodic or quasi-periodic orbit of controlled equations remains near the periodic or quasi-periodic orbit of uncontrolled equations.