Second order parabolic equations in Banach spaces with dynamic boundary conditions

In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.

     

Some Further Properties of the Accelerated Kerr-Schild Metrics

We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.     

S3上阿诺德弦猜想中的变分方法

本文使用变分方法证明了三维标准切触球的标准勒让德扭结，至少存在一个弦连结适应于标准切触结构的任何选定切触形式，这部分证明了著名的阿诺德弦猜想。     

氯柱硼镁石在氯化镁水溶液中相转化平衡液相的红外光谱分析

采用差示FTIR光谱技术,研究了氯柱硼镁石在30℃下浓度为0.5,12和18％MgCl_2水溶液中溶解及相转化平衡饱和水溶液中硼氧配阴离子的FTIR光谱。给出了溶液中硼氧配阴离子的FTIR光谱振动频率的归属,515cm~(-1)为单和二硼氧配阴离子特征峰,630cm~(-1)为三硼氧配阴离子特征峰,550cm~(-1)为四硼氧配阴离子特征峰。对饱和水溶液中硼氧配阴离子的存在形式及其相互作用以及与相转化析出固相的关系进行了讨论。     

Silane photoabsorption spectra mear the Si 2p thresholds：the geometry of Si 2p excited SiH4

Based on the multiple-scattering self-consistent-field method, we have studied the photoabsorption spectra near the Si 2p thresholds of silane. According to our calculations, the clear assignments of the inner-shell photoabsorption spectra are provided. In comparison with the high-resolution experimental spectra, the geometric structure of the Si 2p-excited SiH_{4}^{**} is recommended to be of a C_{2v} symmetry. More specifically, the Si 2p-excited SiH_{4}^{**} have two bond lengths of 2.50 a.u. and another two bond lengths of 2.77 a.u., and the corresponding two bond angles are 104.0° and 112.5° respectively.     

Second order three boundary value problem in Banach spaces via Henstock and Henstock-Kurzweil-Pettis integral

Existence theorems and some properties of solutions set of three boundary value second order differential equations and inclusions in Banach spaces are obtained under Henstock, respectively Henstock-Kurzweil-Pettis integrability assumptions. Our results extend those obtained by Azzam, Castaing and Thibault in the Bochner integrability setting and in the Pettis integrability one. The continuity of the (unique) solution with respect to a parameter in the single-valued case is also studied.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa^[6], G. Gundersen^[7] and J.K. Langley^[8], Li Chun-hong^[11].     

Diameter graphs of polygons and the proof of a conjecture of Graham

We show that for an n-gon with unit diameter to have maximum area, its diameter graph must contain a cycle, and we derive an isodiametric theorem for such n-gons in terms of the length of the cycle. We then apply this theorem to prove Graham's 1975 conjecture that the diameter graph of a maximal 2m-gon (m?3) must be a cycle of length 2m−1 with one additional edge attached to it.     

The function of graphs and gestures in algorithmatization

The purpose of this paper is to present evidence supporting the conjecture that graphs and gestures may function in different capacities depending on whether they are used to develop an algorithm or whether they extend or apply a previously developed algorithm in a new context. I illustrate these ideas using an example from undergraduate differential equations in which students move through a sequence of Realistic Mathematics Education (RME)-inspired instructional materials to create the Euler method algorithm for approximating solutions to differential equations. The function of graphs and gestures in the creation and subsequent use of the Euler method algorithm is explored. If students’ primary goal was algorithmatizing ‘from scratch’, they used imagery of graphing and gesturing as a tool for reasoning. However if students’ primary goal was to make predictions in a new context, they used their previously developed Euler algorithm to reason and used graphs and gestures to clarify their ideas.     

Mixed methods on quadrilaterals and hexahedra

We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.