求一类函数最值的分式变形技巧

函数f(x)=ax+b/x(a>0,b>0)有较为广泛的应用,许多应用问题往往会归结为求这一函数的最值.本文列举分式函数化为上述函数形式的变形技巧.

Form Invariance of Lagrange System

To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.

Form Invariance of Routh Equations

The form invariance of Routh equations in holonomic systems is studied. The definition and criterion for the form invariance under the infinitesimal transformations are given. The relation of the form invariance with the Noether symmetry and the Lie symmetry is discussed.

On existence and uniqueness of the solution of elastoplastic contact problems

Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.

Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery

A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces.The cost function consists of a separable term, in which each component is modeled through its own potential,and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals.An algorithm with guaranteed weak convergence to a solution to the problem is provided.Various multicomponent signal decomposition and recovery applications are discussed.

Some problems of GPS RTK technique application to mining subsidence monitoring

Owing to the variability of mine surfaces, it is difficult to obtain the deformation monitoring data of the observation stations by traditional leveling technique. GPS RTK （Real-Time Kinematic） technique was employed to the subsidence observation in this paper, and its main sources of errors including rover pole deflection of the vertical, un-modeled systematic errors （gross error, multipath delay etc.） and the height transformation error, were analyzed systematically. Based on the fundamental theories of spherical fit- ting and Empirical Mode Decomposition （EMD）, the error reduction models were studied exhaustively. And two experiments were done in different environment to test the proposed models. The results show that the proposed methods can achieve a fourth-grade leveling accuracy, with （Root-Mean-Square） RMS in three orthogonal directions （N, E and H） of 4.1, 3.3 and 3.1 ram, respectively, by 3-5 rain continuous shaking of the observation GPS antenna, fully satisfying for mine surface subsidence deformation monitoring.

Jacquard image segmentation using Mumford-Shah model

Jacquard image segmentation is one of the primary steps in image analysis for jacquard pattern identification. The main aim is to recognize homogeneous regions within a jacquard image as distinct, which belongs to different patterns. Active contour models have become popular for finding the contours of a pattern with a complex shape. However, the performance of active contour models is often inadequate under noisy environment. In this paper, a robust algorithm based on the Mumford-Shah model is proposed for the segmentation of noisy jacquard images. First, the Mumford-Shah model is discretized on piecewise linear finite element spaces to yield greater stability. Then, an iterative relaxation algorithm for numerically solving the discrete version of the model is presented. In this algorithm, an adaptive triangular mesh is refined to generate Delaunay type triangular mesh defined on structured triangulations, and then a quasi-Newton numerical method is applied to find the absolute minimum of the discrete model. Experimental results on noisy jacquard images demonstrated the efficacy of the proposed algorithm.

Boundedness of Solutions for Elliptic Variational Inequalities

The boundedness is proved under more general structural conditions to solutions of elliptic variational inequalities and a priori estimates are obtained to maximum modulus of solutions for some special cases.

Analysis of the blunting line in ductile fracture toughness J_(IC) test method

The blunting line equation is very important in J-integral testing because of its indispensability in the determination of valid data and JIC value. The blunting line equation in current standard has had a larger relative error in depiction of the crack blunting compared to the experimentally measured results. By analyzing the blunting process of the crack tip according to the D-B model, a new form of blunting line was obtained on the base of the path independence of J-integral, i.e., J=1.25(σs+Sf)/(1+n)·WSZ. Experimental results show that this equation is more precise to describe the crack blunting than those in current standards.

Simplest Normal Forms of Generalized Neimark-Sacker Bifurcation

The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show that the conventional Neimark-Sacker bifurcation can be further simplified. The simplest normal forms of generalized Neimark-Sacker bifurcation are calculated. Based on the conventional normal form, using appropriate nonlinear transformations, it is found that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of the simplest normal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given.

The Discrete Horizontal Complex on Lattice Space

We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.

Mathieu Progressive Waves

A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.

New Activity of the Tanlu Fault Zone in the South of Huaihe to the Nvshanhu Segment since the Late Quaternary

Taking the Huaihe to the Nvshanhu segment of the Tanlu( Tancheng-Lujiang) fault zone as the main research target to explore whether there has been new activity since the late Quaternary,and based on the interpretation of remote sensing images and repeated surface investigations,we excavated trenches at the sections where the tectonic landform is significant,identified and recorded the deformation patterns of the fault and analyzed the activity behavior. Samples of new activity and deformation were collected and oriented slices were ground based on the samples ' original state to make the micro structural analysis and demonstration. All of the above research shows very clear linear tectonic geomorphology along the fault,three trenches across the fault zone all revealed new deformation traces since late Quaternary. The latest stratum dislocated by the fault is the late Quaternary and Holocene. The main slip mode is stick slip,as represented typically by fault scarps,wedge accumulation,the faults and the filled cracks and so on. In general,it shows the characteristics of brittle high-speed deformation and belongs to the prehistoric earthquake ruins. The above understanding was confirmed partially by microscopic analysis. In addition,the similarities and differences and the possible reasons for the characteristics of the latest activities of the Tancheng-Lujiang fault zone in the north and south of the Huaihe River regions are also discussed in this paper.

基于小波消噪的EMD模型在GPS振动信号处理中的应用

经验模式分解和小波分解是当前有效处理非平稳信号的两种时频分析方法,它们各具有其优缺点,适用于不同的应用。从对GPS振动信号的预处理、时域和频域处理入手,结果分析表明,对GPS振动信号先进行小波滤波消除随机噪声的干扰,再应用经验模式分解更有利于变形特征信息的分离和提取,提取的信号与振动平台记录数据更加吻合。

On the Kinetic Formulation of a Nonlinear Hyperbolic Variational Wave Equation

Motivated by [3], [4] and [5], we present the kinetic formulation of a nonlinear variational wave equation corresponding to some specific weak solutions . This equation arises from studies in nematic liquid crystals, long wave on a dipole chain and a few other fields.

单元目标测试答案

单元目标测试答案因式分解单元目标测试答案一、填空：１、略；２、略；３、（１）２５，（２）（３ａ＋１）（９ａ２－３ａ＋１），（３）（ｘ＋３ｙ）（７ｘ２＋６ｘｙ＋３ｙ２），（４）ｂ２４，ａｂ，（５）－１４ｘｙ，７ｘ，（６）（２ｘ－３ｙ）（ｘ＋５ｙ），４、...

单元目标测试答案

因式分解单元目标测试答案一、填空：１、略；２、略；３、（１）２５，（２）（３ａ＋１）（９ａ２－３ａ＋１），（３）（ｘ＋３ｙ）（７ｘ２＋６ｘｙ＋３ｙ２），（４）ｂ２４，ａｂ，（５）－１４ｘｙ，７ｘ，（６）（２ｘ－３ｙ）（ｘ＋５ｙ），４、ｍ＝－２，ｎ＝－...

Size-dependent transition of the deformation behavior of Au nanowires

Inspired by the controversy over tensile deformation modes of single-crystalline 〈110〉/{111} Au nanowires, we investigated the dependency of the deformation mode on diameters of nanowires using the molecular dynamics technique. A new criterion for assessing the preferred deformation mode-slip or twin propagation--of nanowires as a function of nanowire diameter is presented. The results demonstrate the size-dependent transition, from superplastic deformation mediated by twin propagation to the rupture by localized slips in deformed region as the nanowire diameter decreases. Moreover, the criterion was successfully applied to explain the superplastic deformation of Cu nanowires.

Comparisons between centrifuge and numerical modeling results for slope toppling failure

This paper presents series studies on the toppling mechanism by centrifuge tests and numerical simulations. Two different discrete element methods, i.e., the continuum-based discrete element method(CDEM) and the discontinuous deformation analysis(DDA), are adopted. The modeling results show that both the methods can accurately capture the failure modes of the centrifuge tests, including three distinct zones and two failure surfaces. Comparisons are made between the physical test and numerical simulation results. The critical inclination angle of the tilting table where the slope models are fixed on can be moderately predicted by the two methods, with different degrees of precision. The error between the test results and the simulated results is within 1% for the slope models without rock-bridges by both CDEM and DDA. However, it is amplified for the staggered-joint models that simulate the rock-bridges. With DDA, the average error is about 5%, and the maximum error is up to 17%. While with CDEM, the errors for the aligned-joint models are ranged from 1% to 6%, and it is from 10% to 29% for the staggered-joint models. The two numerical methods show the capability in simulating toppling failure of blocky rock mass with and without rock-bridges. The model with rock-bridges which provides a certain bending resistance is more stable than the one without any rock-bridge. In addition, the two failure surfaces were observed, which is different from the common understanding that only one failure surface appears.