The Dimension of the Hilbert Scheme of Special Threefolds #

The Hilbert scheme of 3-folds in ? ⁿ , n ≥  6 , that are scrolls over ? ² or over a smooth quadric surface Q  ? ? ³ or that are quadric or cubic fibrations over ? ¹ is studied. All known such threefolds of degree 7  ≤ d ≤  11 are shown to correspond to smooth points of an irreducible component of their Hilbert scheme, whose dimension is computed.     

A Few Remarks About the Hilbert Scheme of Smooth Projective Curves

We discuss two conjectures by Francesco Severi and Joe Harris about the irreducibility and the dimension of the Hilbert scheme parameterizing smooth projective curves of given degree and genus.     

三维热传导型半导体器件问题在局部加密网格上的有限差分格式

局部网格加密技术能很好地解决局部性很强的问题,半导体器件问题的解在半导体的p-n结附近有很强的局部性质.热传导型半导体器件瞬态问题的数学模型由四个方程组成的非线性偏微分方程组的初边值问题决定,电场位势方程是椭圆型的,电子和空穴浓度方程是抛物型的,温度方程是热传导型的.依据实际数值模拟的需要,提出了一类三维热传导型半导体问题在时间上进行局部加密的复合网格上的有限差分格式,并给出了电子、空穴浓度和温度的最大模误差估计以及数值算例.这些研究结果对半导体器件数值模拟的算法理论、实际应用和工程软件系统的研制,均具有重要的价值.     

Bicomplex Quantum Mechanics: II. The Hilbert Space

Using the bicomplex numbers

一类非线性反应-扩散方程有限差分格式的稳定性研究

In the article,the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established.Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space.The approach used is of a simple characteristic in gaining the stability condition of the scheme.     

实Hilbert空间中点到有限余维子空间的距离问题

本文讨论实Ｈｉｌｂｅｒｔ空间中一点到有限余维子空间的距离，将一点到超平面的距离公式推广到一点到余维ｎ子空间Ｍ以及仿射集Ｑ的距离公式，并对Ｍ或Ｑ闭的情形表示出最佳逼近元。     

有限群共轭类长的一个问题

设A和B都是有限群G的子群且G=AB.若A是G的次正规子群,且对每个p∈π(G)以及每个素数幂阶的p′-元x∈A∪B,p~2均不整除|x~G|,则G为超可解群.这个结果正面解答了由石向东,韦华全和马儇龙于2013年提出的一个问题,统一推广了由刘晓蕾于2011年得到的三个定理.     

On the free implicative semilattice extension of a Hilbert algebra

Hilbert algebras provide the equivalent algebraic semantics in the sense of Blok and Pigozzi to the implication fragment of intuitionistic logic. They are closely related to implicative semilattices. Porta proved that every Hilbert algebra has a free implicative semilattice extension. In this paper we introduce the notion of an optimal deductive filter of a Hilbert algebra and use it to provide a different proof of the existence of the free implicative semilattice extension of a Hilbert algebra as well as a simplified characterization of it. The optimal deductive filters turn out to be the traces in the Hilbert algebra of the prime filters of the distributive lattice free extension of the free implicative semilattice extension of the Hilbert algebra. To define the concept of optimal deductive filter we need to introduce the concept of a strong Frink ideal for Hilbert algebras which generalizes the concept of a Frink ideal for posets.     

Hilbert Module Realization of the Square of White Noise and Finite Difference Algebras

We develop an approach to the representations theory of the algebra of the square of white noise based on the construction of Hilbert modules. We find the unique Fock representation and show that the representation space is the usual symmetric Fock space. Although we started with one degree of freedom we end up with countably many degrees of freedom. Surprisingly, our representation turns out to have a close relation to Feinsilver's finite difference algebra. In fact, there exists a holomorphic image of the finite difference algebra in the algebra of square of white noise. Our representation restricted to this image is the Boukas representation on the finite difference Fock space. Thus we extend the Boukas representation to a bigger algebra, which is generated by creators, annihilators, and number operators.     

On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol

For some class of two-dimensional Toeplitz operators with locally sectorial symbol, we establish a criterion for the projection method to possess the Fredholm property.     

Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System

In this paper, we derive and analyze a conservative Crank-Nicolson-type finite difference scheme for the Klein-Gordon-Dirac (KGD) system. Differing from the derivation of the existing numerical methods given in literature where the numerical schemes are proposed by directly discretizing the KGD system, we translate the KGD equations into an equivalent system by introducing an auxiliary function, then derive a nonlinear Crank-Nicolson-type finite difference scheme for solving the equivalent system. The scheme perfectly inherits the mass and energy conservative properties possessed by the KGD, while the energy preserved by the existing conservative numerical schemes expressed by two-level's solution at each time step. By using energy method together with the 'cut-off' function technique, we establish the optimal error estimate of the numerical solution, and the convergence rate is $\mathcal{O}(τ^2 + h^2)$ in $l^∞$-norm with time step $τ$ and mesh size $h.$ Numerical experiments are carried out to support our theoretical conclusions.     

一道曲线积分题目的六种解法

给出了一道曲线积分题目的六种解法,这有利于提高学生对综合运用数学知识的能力,同时也可以启发学生思维和开阔他们的思路.     

正则轨道的存在性与有限群的幂零长

本文给出了一些正则轨道存在性的条件，结合Ａ．Ｔｕｒｕｌｌ的近期定理，得到了关于有限可解群的幂零长的一些结论．     

共轭类的长和有限群的结构

设Ｇ是有限群，并设Ｃｏｎ（Ｇ）是由Ｇ的一切共轭类组成的集合。本文目的是考察Ｃｏｎ（Ｇ）的算术结构对Ｇ的群结构的影响。我们着重于Ｃｏｎ（Ｇ）的ｐ－部分结构，并得到关于ｐ－幂零群的两个定理。这里，ｐ表示一个有限群的最小素因子。用这两个定理，我们还得到若干结果，其中两个改进了Ｄ．Ｃｈｉｌｌａｇ和Ｍ．Ｈｅｒｚｏｇ关于共轭类长的两个结果。     

非线性Sobolev-Galpern方程有限差分格式在t＞0时的长时间收敛性和稳定性

本文讨论了非线性Sobolev-Galpern初边值问题,给出了Sobolev-Galpern方程的有限差分格式在t>0时的长时间收敛性和稳定性的证明．     

Extension of Finite Rank Operators and Operator Ideals with the Property (I)

We present criteria and related techniques which help to decide whether the adjoint operator ideal (𝔄*, A *) of an injective and totally accessible maximal Banach ideal (𝔄, A ) is itself also totally accessible. This approach (which involves the transfer of the principle of local reflexivity to operator ideals) is based on the extension of finite rank operators, viewed as elements of the adjoint ideal (𝔄*, A *). Using the local properties (I) and (S) of the corresponding product ideal 𝔄* ∘ 𝔏_∞, these methods even enable us to show that 𝔏_∞ and 𝔏₁ cannot be totally accessible – answering an open question of Defant and Floret .