GRAPH-DIRECTED STRUCTURES OFSELF-SIMILAR SETS WITH OVERLAPSGRAPH-DIRECTED STRUCTURES OFSELF-SIMILAR SETS WITH OVERLAPSS

1. IntroductionThe self-similar sets (SSS) is one of the most important fractal classes, but the most properties such as dimensions, measures'' have been established upon the open set condition(OSC). It is a difficult problem to determine the structure and only a few results are knownwhen this condition is absent. On the other hand, for the graph-directed sets (GDS), ageneralization of SSS, if the OSC is satisfied, then analogous properties of the self-similarsets will hold still. The m…     

SINGULAR INTEGRAL EQUATIONS WITH COSECANT KERNEL IN SOLUTIONS WITH SINGULARITIES OF ORDER ONE

In this article, periodic Riemann boundary value problem with period 2aπalong closed smooth contours is discussed, and then singular integral equation with kernel csc t-t0/a along closed smooth contours restricted in the strip 0< Rez相似文献   

SUPERLINEAR CONSERVATION LAW WITH VISCOSITY

This paper gives some global existence results of the superlinear conservation law with viscosity.     

MELNIKOV VECTOR WITH HIGHER ORDER

ＭＥＬＮＩＫＯＶＶＥＣＴＯＲＷＩＴＨＨＩＧＨＥＲＯＲＤＥＲ￥ＺｈｕＤｅｍｉｎｇ（ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，２０００６２）Ａｂｓｔｒａｃｔ：Ｂｙｕｓｉｎｇｔｈｅｇｅｏｍｅｔｒｉｃａｌｍｅｔｈｏｄ，ｔｈｅｈｉｇｈｅｒｏｒｄｅｒＭ...     

BIVARIATE ESTIMATION WITH LEFT-TRUNCATED DATA

1. Introductionffendomly truncated data frequently arise in medical studies; other application areas include economics, insurance and astronomy in a broad senses random truncation correspondsto biased sampling, where only partial or incomplete data are aVailable about the variableof interest. A typical realization. can occur as follows: Suppose that individuals/items experience tWO consecutive events in time, an initiating eveal at t and a terminating eveal ats. Usuajly, statistical niterest …     

THE LINEARIZATION WITH ORDINARY DICHOTOMY

ＴＨＥ　ＬＩＮＥＡＲＩＺＡＴＩＯＮ　ＷＩＴＨ　ＯＲＤＩＮＡＲＹ　ＤＩＣＨＯＴＯＭＹＴＨＥＬＩＮＥＡＲＩＺＡＴＩＯＮＷＩＴＨＯＲＤＩＮＡＲＹＤＩＣＨＯＴＯＭＹ￥ＳｈｉＪｉｎｌｉｎ（ＦｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，）Ａｂｓｔｒａｃｔ：Ｈａｒｔｍａｎｈａ...     

HOMOCLINIC BIFURCATION WITH CODIMENSION 3

ＨＯＭＯＣＬＩＮＩＣＢＩＦＵＲＣＡＴＩＯＮＷＩＴＨＣＯＤＩＭＥＮＳＩＯＮ３￥ＺＨＵＤＥＭＩＮＧＡｂｓｔｒａｃｔ：ＦｉｒｓｔｉｔｉｓｐｒｏｖｅｄｔｈａｔｂｏｔｈｔｈｅｉｎｔｅｇｒａｌｏｆｔｈｅｄｉｖｅｒｇｅｎｃｅａｎｄｔｈｅＭｅｌｎｉｋｏｖｆｕｎｃｔｉ...     

MARKOV DECISION PROGRAMMING WITH CONSTRAINTS

ＭＡＲＫＯＶＤＥＣＩＳＩＯＮＰＲＯＧＲＡＭＭＩＮＧＷＩＴＨＣＯＮＳＴＲＡＩＮＴＳＬＩＵＪＩＡＮＹＯＮＧ（刘建庸）；ＬＩＵＫＥ（刘克）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，...     

A PARABOLIC EQUATION WITH HYSTERESIS

A parabolic equations with hysteresis is discussed. The existence of smoothstrong solution of one-dimension initial boundary problem of the equation isgiven.     

ON REACTION-DIFFUSION EQUATION WITH ABSORPTION

In this paper, we consider the dead core and some asymptotic behaviors of solutions to the initial boundary value problems of the equation u_t=△u-λupeu, where>0, 0相似文献   

Dynamics of Vortex Rossby Waves in Tropical Cyclones,Part 1: Linear Time‐Dependent Evolution on an f‐Plane

Analyses of observational data on hurricanes in the tropical atmosphere indicate the existence of spiral rainbands which propagate outward from the eye and affect the structure and intensity of the hurricane. These disturbances may be described as vortex Rossby waves. This paper describes the evolution of barotropic vortex Rossby waves in a cyclonic vortex in a two‐dimensional configuration where the variation of the Coriolis force with latitude is ignored. The waves are forced by a constant‐amplitude boundary condition at a fixed radius from the center of the vortex and propagate outward. The mean flow angular velocity profile is taken to be a quadratic function of the radial distance from the center of the vortex and there is a critical radius at which it is equal to the phase speed of the waves. For the case of waves with steady amplitude, an exact solution is derived for the steady linearized equations in terms of hypergeometric functions; this solution is valid in the outer region away from the critical radius. For the case of waves with time‐dependent amplitude, asymptotic solutions of the linearized equations, valid for late time, are obtained in the outer and inner regions. It is found that there are strong qualitative similarities between the conclusions on the evolution of the vortex waves in this configuration and those obtained in the case of Rossby waves in a rectangular configuration where the latitudinal gradient of the Coriolis parameter is taken into account. In particular, the amplitude of the steady‐state outer solution is greatly attenuated and there is a phase change of across the critical radius, and in the linear time‐dependent configuration, the outer solution approaches a steady state in the limit of infinite time, while the amplitude of the inner solution grows on a logarithmic time scale and the width of the critical layer approaches zero.     

Stability and instability of the standing waves for the Klein‐Gordon‐Zakharov system in one space dimension

The orbital instability of standing waves for the Klein‐Gordon‐Zakharov system has been established in two and three space dimensions under radially symmetric condition by Ohta‐Todorova in 2007. In the one space dimensional case, for the nondegenerate situation, we first check that the Klein‐Gordon‐Zakharov system satisfies Grillakis‐Shatah‐Strauss' assumptions on the stability and instability theorems for abstract Hamiltonian systems; see Grillakis‐Shatah‐Strauss (J. Funct. Anal. 1987). As to the degenerate case that the frequency , we follow the recent splendid work of Wu (2017) to prove the instability of the standing waves for the Klein‐Gordon‐Zakharov system, by using the modulation argument combining with the virial identity. For this purpose, we establish a modified virial identity to overcome several troublesome terms left in the traditional virial identity.     

Initial Time Layers and Kadomtsev–Petviashvili-Type Equations

The Kadomtsev–Petviashvili (KP) equation and generalizations (GKP) have temporal discontinuities at the initial instant of time. Motivated by the study of water waves, a generalized Boussinesq equation that contains the GKP equations as an "outer" limit is introduced. Within the context of matched asymptotic expansions the discontinuities are resolved. The linear system is analyzed in more detail and the limit process is rigorously established.     

Rational and Semirational Solutions of the Nonlocal Davey–Stewartson Equations

In this paper, the partially party‐time () symmetric nonlocal Davey–Stewartson (DS) equations with respect to x is called x‐nonlocal DS equations, while a fully symmetric nonlocal DSII equation is called nonlocal DSII equation. Three kinds of solutions, namely, breather, rational, and semirational solutions for these nonlocal DS equations are derived by employing the bilinear method. For the x‐nonlocal DS equations, the usual (2 + 1)‐dimensional breathers are periodic in x direction and localized in y direction. Nonsingular rational solutions are lumps, and semirational solutions are composed of lumps, breathers, and periodic line waves. For the nonlocal DSII equation, line breathers are periodic in both x and y directions with parallels in profile, but localized in time. Nonsingular rational solutions are (2 + 1)‐dimensional line rogue waves, which arise from a constant background and disappear into the same constant background, and this process only lasts for a short period of time. Semirational solutions describe interactions of line rogue waves and periodic line waves.     

Nonlinear Alfvén/Beltrami waves—An integrable structure built around the Casimir

We formulate a nonlinear wave equations that describe amplitude and pitch modulations of one-dimensional Alfvén waves propagating on a dispersive nonlinear plasma. The well-known fact that the ideal Alfvén wave can propagate on a homogeneous ambient magnetic field with conserving an arbitrary wave shape of any amplitude is explained by invoking the Casimirs stemming from a “topological defect” (or, a kernel) in the Poisson bracket operator of the ideal magnetohydrodynamic (MHD) system. Including the Hall term, however, the Alfvén waves are affected by the dispersive effect, and the aforementioned simplicity of the ideal Alfvén waves is greatly lost; an arbitrary wave can no longer propagate with a constant shape. Yet, we observe an integrable structure in the nonlinear modulation (induced by a compressible motion) of the Alfvén waves, which is described as nonlinear deformation of “Beltrami vortex” pertaining to the Casimirs.     

On a control problem for the wave equation in R<Superscript>3</Superscript>

Solutions of the wave equation (waves) initiated by infinitely distant sources (controls) are considered, and the L₂-completeness of reachable sets consisting of such waves is stidued. This problem is a natural analog of the control problem for a bounded domain where the completeness (local approximate controllability) in subdomains filled with waves generated by boundary controls occurs. It is shown that, in contrast to the latter case, the reachable sets formed by waves incoming from infinity are not complete in filled subdomains and describe the associated defect. Next, extending the class of controls to a set of special polynomials, the completeness is gained. A transform defined by jumps that arise in projecting functions to reachable sets is introduced. Its relevance to the Radon transform is clarified. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 19–37.     

Nonlinear behavior of electromagnetic waves on surface of antiferromagnet

The properties of the nonlinear TM waves on the interface between a dielectric and an antiferromagnet are studied. The relationship between the field components of TM wave is discussed in detail, and the dispersion characteristics as well as the position of the peak field are exposed. The theoretical analysis shows that for the nonlinear TM waves there exist passband(s) and stopband(s) which can be switched into each other by varying the power. It is revealed that, in the case of , the nonlinear TM waves on the interface are backward surface waves with the group and phase velocities opposite. Project supported by the National Natural Science Foundation of China (Grant No. 69477020).     

Reflection and transmission of the surface <Emphasis Type="Italic">P</Emphasis>-waves on the line of jump in elastic parameters

Problems of diffraction of elastic surface waves of horizontal polarization (P-waves) on a line of jump in elastic parameters are considered. The corresponding coefficients of reflection, refraction, and transmission are obtained by means of the parabolic equation method. A comparison of the Rayleigh waves, SV-waves, and P-waves is carried out. Numerical values of the transformation matrix are found in the case where the whispering gallery wave transforms to a sum of whispering gallery waves and a homogeneous wave transforms to the first five modes of whispering gallery waves. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 106–137.     

H 1-perturbations of Smooth Solutions for a Weakly Dissipative Hyperelastic-rod Wave Equation

We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa–Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. We fix a smooth solution and establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from In particular, the supersonic solitary shock waves [8] are included in the analysis. Dedicated to the memory of Professor Aldo Cossu The research of K.H. Karlsen is supported by an Outstanding Young Investigators Award from the Research Council of Norway. The current address of G.M. Coclite is Department of Mathematics, University of Bari, Via E. Orabona 4, 70125 Bari, Italy     

On the stability of the solitary waves to the (generalized) Kawahara equation

In this paper we investigate the orbital stability of solitary waves to the (generalized) Kawahara equation (gKW) which is a fifth order dispersive equation. For some values of the power of the nonlinearity, we prove the orbital stability in the energy space $H^2(\mathbb{R})$ of two branches of even solitary waves of gKW by combining the well-known spectral method introduced by Benjamin [4] with continuity arguments. We construct the first family of even solitons by applying the implicit function theorem in the neighborhood of the explicit solitons of gKW found by Dey et al. [9]. The second family consists of even traveling waves with low speeds. They are solutions of a constraint minimization problem on the line and rescaling of perturbations of the soliton of gKdV with speed 1.