W^(l,p)(R^n)(1

由文献[1]我们知道,每个函数f,是L^p连续的,即 (integral from n=R^n to ∞(|f(x+h)-f(x)|~pdx))^(1/p)ljt→0,当h→0。 在文献[2]§Ⅰ.4中,关于L^p连续性获得了更深入结果:命题

状态空间E为可列的情形下标准三点转移函数族的可微性质的进一步探讨

§1 引言[1,2]中,我们对两参数马尔科夫过程的三点转移函数族{Pijkr（s,t）}的解析性质进行了研究,包括可测性,连续性,可微分性等,以及恒正性及状态对的分解定理等。我们发现,两参数马尔科夫过程与单参数马尔科夫过程虽然有某些相似,但更重要的是本质上的不同。本文对两参数马尔科夫过程的三点转移函数族的解析性质作进一步的探讨。

The Solvability of the Degenerate Differential Systems with Delay

In this paper we study the degenerate differential system with delay:E(t)=Ax(t)+Bx(t-1)+f(t),give the canonical form of this systems and study this form of degeneration system with delay,have some results for the solvability of such systems and the uniqueness of their solutions.

New Exact Solutions for （2＋1）-Dimensional Breaking Soliton Equation

New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutionsand triangular periodic wave solutions are obtained.

The Qualitative Analysis of a Solution of a Series Maintenance System with Two Components

In this paper, firstly we study the series ma intenance system with two components, obtain its exsistence and uniqueness of a dynamic state nonnegative solution by strongly continuous semigroups of operator s theory. Then we prove that 0 is the eigenvalue of the system’s host operators, a nd finally we study the eigenvector of the eigenvalue 0.

Solitary Wave in Linear ODE with Variable Coefficients

In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.

Controllability, Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems

The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.

Research present situation and analysis on classification of rock drillability

Rock drillability reflects the drill bit fragments rock hardly or easily. At present, rock drillability classification indexes have rock single axle compressive strength, point load intensity, fracture stress during chiseling, drill speed, chiseling specific work, acoustic parameter, cutting magnitude and so on. Every index reflects rock drillability but isnt overall. It is feasible that using many indexes of fuzzy mathematics method etc. to evaluate rock drillability.

A New (2+1)-Dimensional Integrable Equation

A new nonlinear partial differential equation （PDE） in 2＋1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal resealing. In order to demonstrate integrability property of the new equation, the corresponding Lax pair is obtained by applying the reduction technique to the Lax pair of the mKP equation.

THE STOCHASTIC ESTIMATION OF SATELLITE CLOCK CORRECTION INFORMATION IN WADGPS

Using autocorrelation information of the pseudorange errors generated by se- lective availability (SA) frequency dithering, we have constructed a simple first order stochas- tic model for SA effects. This model has been used in a Kalman filter to account for the stochastic behavior of SA dithering in estimating satellite clock information in wide area dif- ferential GPS. We have obtained fifteen percent improvement in the user positioning using the correlation information on the satellite clock information in a Kalman filter, when comparing the results obtained using a regular least square estimation.

Solvability of Boundary Value Problems for Some Functional Differential Equations

This paper considers the following boundary value problems for functional differential equations: x' (t) = f(t, xt) (0<t<b) ,x0 = x1, and x'(t) = f(t,xt, x' (t)) (0<t<b) , x0 = , x(b) = B. By using certain fixed point theorem based on degree theory,some sufficient conditions for solvability of the above problems are given.

The theoretical analysis of dynamic response on cantilever beam of variable stiffness

The paper presents the theoretical analysis of a variable stiffness beam. The bending stiffness EI varies continuously along the length of the beam. Dynamic equation yields differential equation with variable co- efficients based on the model of the Euler-Bernoulli beam. Then differential equation with variable coefficients becomes that with constant coefficients by variable substitution. At last, the study obtains the solution of dy- namic equation. The cantilever beam is an object for analysis. When the flexural rigidity at free end is a constant and that at clamped end is varied, the dynamic characteristics are analyzed under several cases. The results dem- onstrate that the natural angular frequency reduces as the fiexural rigidity reduces. When the rigidity of clamped end is higher than that of free end, low-level mode contributes the larger displacement response to the total re- sponse. On the contrary, the contribution of low-level mode is lesser than that of hi^h-level mode.

Existence of almost periodic solutions to a class of non- autonomous functional integro-differential stochastic equations

In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A（t） satisfy Acquistapace-Terreni conditions, and with some suitable assumptions, the existence and uniqueness of a square-mean almost periodic mild solution to the equations are obtained.

Design and analysis of the reliability of on-board computer system based on Markov-model

An on-board computer system should have such advantages as light weight,small volume and low power to meet the demand of micro-satellites. This paper, based on specific characteristics of Stereo Mapping Micro-Satellite (SMMS), describes the on-board computer system with its advantage of having centralized and distributed control in the same system and analyzes its reliability based on a Markov model in order to provide a theoretical foundation for a reliable design. The on-board computer system has been put into use in principle prototype model of Stereo Mapping Micro-Satellite and has already been debugged. All indexes meet the requirements of the design.

SS-SERA:An improved framework for architectural level soft error reliability analysis

Integrated with an improved architectural vulnerability factor （AVF） computing model, a new architectural level soft error reliability analysis framework, SS-SERA （soft error reliability analysis based on SimpleScalar）, was developed. SS-SERA was used to estimate the AVFs for various on-chip structures accurately. Experimental results show that the AVFs of issue queue （IQ）, register update units （RUU）, load store queue （LSQ） and functional unit （FU） are 38.11%, 22.17%, 23.05% and 24.43%, respectively. For address-based structures, i.e., levell data cache （LID）, DTLB, level2 unified cache （L2U）, levell instruction cache （LII） and ITLB, AVFs of their data arrays are 22.86%, 27.57%, 14.80%, 8.25% and 12.58%, lower than their tag arrays＇ AVFs which are 30.01%, 28.89%, 17.69%, 10.26% and 13.84%, respectively. Furthermore, using the AVF values obtained with SS-SERA, a qualitative and quantitative analysis of the AVF variation and predictability was performed for the structures studied. Experimental results show that the AVF exhibits significant variations across different structures and workloads, and is influenced by multiple microarchitectural metrics and their interactions. Besides, AVFs of SPEC2K floating point programs exhibit better predictability than SPEC2K integer programs.

Stochastic differential equation software reliability growth model with change-point

This paper presents software reliability growth models(SRGMs) with change-point based on the stochastic differential equation(SDE).Although SRGMs based on SDE have been developed in a large scale software system,considering the variation of failure distribution in the existing models during testing time is limited.These SDE SRGMs assume that failures have the same distribution.However,in practice,the fault detection rate can be affected by some factors and may be changed at certain point as time proceeds.With respect to this issue,in this paper,SDE SRGMs with changepoint are proposed to precisely reflect the variations of the failure distribution.A real data set is used to evaluate the new models.The experimental results show that the proposed models have a fairly accurate prediction capability.

Similarity Solutions for Generalized Variable Coefficients Zakharov-Kuznetsov Equation under Some Integrability Conditions

In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.

Microhabitat Effect on Iron Distribution and Transfer in Carex pseudocuraica in Sanjiang Plain Wetlands

Ten clonal units of Carex pseudocuraica growing in four different microhabitats (perennial flooded ditch water,perennial flooded ditch sediment,seasonal flooded ditch sediment and perennial flooded soil) of the Sanjiang Plain,Northeast China,were collected randomly for phenotypic plasticity analysis.Iron content,chemical and physical properties of substrates and the total Fe of nine plant modules were measured as well.The results show that the performance of the C.pseudocuraica is affected by the microhabitat,with the greatest performance score in perennial flooded ditch water,and the lowest in perennial flooded soil.The biomass allocation indexes indicate that much more mass is allocated to stems and roots to expand colonization area.The distribution of the total Fe in plant modules appears as pyramids from the tip to the root,while marked differences are observed in the distribution proportion of stems,tillering nodes and roots that are allometrically growing.Iron transfer from substrates to the plant is mainly controlled by the substrate type.The differences of iron distribution and transfer in the plant in different microhabitats are attributed to the iron contents of the substrates as well as the phenotypic plasticity of the plant.

Double-Pole Solution and SolitonAntisoliton Pair Solution of MNLSE/DNLSE Based upon Hirota Method

Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.

Differentiability of stochastic differential equations driven by the G-Brownian motion

In this paper,we study the differentiability of the solutions of stochastic differential equations driven by the G-Brownian motion with respect to the initial data and the parameter.