Geometry,topology, and vacuum energy

Quantum corrections are investigated in multidimensional models for which the internal manifold is a squashed three-dimensional sphere orS ³/Z _p . It is shown that the divergences which arise in the summation over topologies disappear when quantum matter is taken into account.Leningrad State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 12–20, January, 1992.     

Euler数，Bernoulli数及有序Bell数的渐近估计

利用特殊函数的发生函数为亚纯函数的特点,给出Euler数、Bernoulli数、有序Bell数等几个组合数的带有余项的渐进估计．     

含测量误差的部分线性模型的发散参数估计(英文)

本文考虑了部分线性模型中,线性部分协变量含有测量误差,并且线性部分的参数随着样本量的增大而发散的估计问题.我们考虑了用可观测的替代变量来替代不可观察到的真实变量,这种替代变量的期望与真实变量存在线性关系.我们提出了估计方法,并研究了估计量的相合性与渐进正态性.此外,我们研究了发散参数的发散速度.我们通过模拟来说明该估计的实际效果.     

Electrostatics, Hyperbolic Geometry and Wandering Vectors

A family of planar discrete electrostatic systems on the unitcircle with finitely atomic external fields is considered. Thegeometry of particles in the external field yielding a givenminimum energy configuration is studied. As an application,the wandering vectors of the shift operator in the Dirichletspaces associated with finitely atomic measures are also studied.In particular, the zero locus of a wandering vector is discussed.     

Cubic Curves,Finite Geometry and Cryptography

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a ‘shared secret’ related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.     

Quasigroups, Geometry and Nonlinear Geometric Algebra

A survey of the methods of the theory of quasigroups and loops in algebra and geometry is presented in order to attract the attention of mathematicians and physicists to promising applications of this new branch of mathematics in applied sciences.     

圈钱偏好、非流通股与IPO定价

在传统信号理论基础上，本文建立了一个用于解释股票市场上的圈钱偏好与IPO定价问题的模型。模型主要基于一个新的假设——发行者对从一级和二级市场得到的资金总额具有特定的偏好，并且发行者出于某种考虑将保留一定股份作为非流通股。本文研究了该假设下，如果投资者自始至终无法知道项目的真实价值，而只能根据发行份额和折价程度来判断项目的真实情况时的IPO定价问题。发行者的这种偏好的实际意义，就是通常所说的圈钱偏好。     

PBW Degeneration: Algebra,Geometry, and Combinatorics

We review the recent progress in the theory of Poincaré–Birkhoff–Witt degenerations of irreducible representations of simple Lie algebras. We describe algebraic, geometric, and combinatorial aspects of the theory.     

Unit Balls, Lorentz Boosts, and Hyperbolic Geometry

The bounded symmetric spaces naturally associated with the Poincaré and Beltrami-Klein models of hyperbolic geometry on the open unit ball B in ${\mathbb{R}^n}$ and with the automorphism group of biholomorphic maps on the open ball in ${\mathbb{C}^n}$ give rise by a standard construction to specialized loop structures (nonassociative groups), which we use to define canonical metrics, called rapidity metrics. We show that this rapidity metric agrees with the classical Poincaré metric resp. the Cayley-Klein metric resp. the Bergman metric. We introduce the Lorentz boost of vectors in B, which turns out to be a loop isomorphism. It induces a similarity of metrics between the rapidity metric of the Einstein or Möbius loop and the trace metric on positive definite matrices restricted to the Lorentz boosts.     

两种四角系统的Wiener数和Hyper-Wiener数(英文)

我们推导出两类四角系统的Wiener数和Hyper-Wiener数的计算公式.     

Quantum Spacetime,Quantum Geometry and Planck scales

The Principles of Quantum Mechanics and of Classical General Relativity indicate that Spacetime in the small (Planck scale) ought to be described by a noncommutative C* Algebra, implementing spacetime uncertainty relations. A model C* algebra of Quantum Spacetime and its Quantum Geometry is described. Interacting Quantum Field Theory on such a background is discussed, with open problems and recent progress. Applications to cosmology suggest that the Planck scale ought to depend upon dynamics, and possible consequences in the large of the quantum structure in the small are outlined.     

Jones Invariant,Cantorian Geometry and Quantum Spacetime

The relation between Jones knot polynominals and statistical mechanics is discussed in the light of Cantorian geometry. It is further shown that von Neumanns continuous geometry may be regarded as being a quantum spacetime akin to Cantorian space E ^(∞) and noncommutative geometry.