Analytic continuation at first-order phase transitions

We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH 0. This new function is used for numerical calculation of the coefficients C_n in the power series expansions of the magnetizationm in the form m(H)=1 + C_n(H-H ₀ )ⁿ for various H₀ 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=H_sp(Ti < 0.     

Existence and regularity of solution to the generalized Tricomi equation with a singular initial datum at a point

In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type domain. We suppose that an initial datum on the degenerate plane is smooth away from the origin, and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity.     

A rigid inclusion in an elastic space under the action of a uniform heat flow in the inclusion plane

A solution is presented for the three dimensional static thermoelastic problem of an absolutely rigid inclusion (anticrack) in the case when a uniform heat flow is directed along the inclusion plane. By using the potential method and the Fourier transform technique, the problem is reduced to a system of coupled two-dimensional singular integral equations for the shear stress jumps across the inclusion. As an illustration, a typical application to the circular anticrack is presented. Explicit expressions for the thermal stresses in the inclusion plane are obtained and discussed from the point of view of material failure.     

Keller–Osserman estimates and removability result for the anisotropic porous medium equation with gradient absorption term

We study “large” nonnegative solutions for a class of quasilinear equations model of which is We give a sufficient condition on the exponents and for the removability of isolated singularities.     

纯奇点范畴中的Buchweitz定理

我们定义纯奇点范畴D_(psg)~b(R)为有界纯导出范畴D_(pur)~b(R)与纯投射模构成的有界同伦范畴K~b(■)的Verdier商,得到了纯奇点范畴D_(psg)~b(R)三角等价于相对纯投射模的Gorenstein范畴的稳定范畴■的一个充分必要条件.同时,还给出三角等价D_(psg)~b(R)≌D_(psg)~b(S)的充分条件,这里R和S都是环.     

Multiple positive solutions for Schrödinger‐Poisson system involving singularity and critical exponent

In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form where 0 ∈ Ω is a smooth bounded domain in , , and λ > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained.     

Non-singular Brans–Dicke collapse in deformed phase space

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.     

Time-periodic solutions of the Einstein's field equations Ⅰ:general framework

In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.     

纳米磁流体动态散斑干涉场的奇异场分布

通过对由纳米磁流体运动引起的双扫描激光散斑干涉光场及其变化做拉盖尔-高斯滤波下的傅里叶变换,获得动态散斑干涉图对应的光学涡旋分布及变化特征。分析认为,光学涡旋分布及变化对应着由纳米磁微粒及其团族的运动所引起的动态散斑变化。当纳米磁微粒聚集到分散的过程中,动态激光散斑光场的奇异场分布发生相应变化,说明了磁流体运动过程对应涡旋密度有先大后小,再由小变大的两个变化;并且光学涡旋密度高,对应较小颗粒的散斑场,磁流体处于稳态的状况;光学涡旋密度低,对应较大颗粒的散斑场,对应着磁流体激烈的运动。研究结果体现了奇异场分布变化和纳米磁流体动后趋稳的过程存在对应关系。     

二阶差分方程的奇性边值问题

主要采用上下解方法,研究了一类带有奇性的二阶差分方程的两点边值问题,给出了一系列正解的存在条件.