A Class of Affine Processes Arising as Fluctuation Limits of Super-Brownian Motion in a Super-Brownian Catalytic Medium

A class of infinite dimensional Ornstein-Uhlenbeck processes that arise as solutions of stochastic partial differential equations with noise generated by measure-valued catalytic processes is investigated. It will be shown that the catalytic Ornstein-Uhlenbeck process with super-Brownian catalyst in one dimension arises as a high density fluctuation limit of a super-Brownian motion in a super-Brownian catalyst with immigration. The main tools include Laplace transformations of stochastic processes, analysis of a non-linear partial differential equation and techniques on continuity and regularity based on properties of the Sobolev spaces.     

Schrödinger’s Equation with Gauge Coupling Derived from a Continuity Equation

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ? S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out.     

Attribute dependency functions considering data efficiency

Pawlak’s attribute dependency degree model is applicable to feature selection in pattern recognition. However, the dependency degrees given by the model are often inadequately computed as a result of the indiscernibility relation. This paper discusses an improvement to Pawlak’s model and presents a new attribute dependency function. The proposed model is based on decision-relative discernibility matrices and measures how many times condition attributes are used to determine the decision value by referring to the matrix. The proposed dependency degree is computed by considering the two cases that two decision values are equal or unequal. A feature of the proposed model is that attribute dependency degrees have significant properties related to those of Armstrong’s axioms. An advantage of the proposed model is that data efficiency is considered in the computation of dependency degrees. It is shown through examples that the proposed model is able to compute dependency degrees more strictly than Pawlak’s model.     

Spectral Scattering Theory for Automorphic Forms

We construct a scattering process for L²-automorphic forms on the quotient of the upper half plane by a cofinite discrete subgroup Γ of . The construction is algebraic besides being analytic in the sense that we use some relations satisfied by real-analytic Eisenstein series with a complex parameter. Thanks to this feature, the construction of our operators and spaces is explicit. We show some properties of the Lax-Phillips generator on a scattering subspace carved out from this process. We prove that the spectrum of this operator consists only of eigenvalues, which correspond to the nontrivial zeros, counted with multiplicity, of the Dirichlet series appearing in the functional equation of the Eisenstein series. In particular, in the case of the (full) modular group , the Dirichlet series reduces to the Riemann zeta function ζ, thereby we obtain a spectral interpretation of the nontrivial zeros of ζ.      

左(右)零模

为了更好地描述信息的聚合,左（右）零模的概念被引入。然后,各种连续的左（右）零模的结构定理被给出,即给出了一个二元运算是连续的左（右）零模的充要条件。     

非线性光电导开关载流子碰撞电离分析

对非线性GaAs光电导开关在锁定期间的电流成丝现象、具有负微分迁移率的速场特性、深能级的陷阱效应、光子的再吸收等因素进行分析,建立了非线性光电导开关锁定期间的连续性方程和电中性方程.基于该方程组,用有限差分法计算了偏压为2 200 V的3.5 mm GaAs∶EL2非线性光电导开关的电流实验数据,得到电流丝内载流子瞬态特性为：载流子浓度约为1017 cm－3,EL2电子陷阱近似饱和;电子电流随锁定时间明显下降,空穴电流基本不变;单位寿命时间载流子雪崩倍增因子的均值约为1.2,其统计起伏随锁定时间增大.     

Regularly open sets in fuzzy topological spaces

This paper is devoted to the study of the role of fuzzy regularly open sets. We prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings. We prove that under a fuzzy almost continuous and fuzzy almost open map, the inverse image of a fuzzy regularly open set is fuzzy regularly open. Further we define a new type of fuzzy separation axioms, fuzzy almost separation axioms. It is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology. For example, in a fuzzy almost T₁ space not every fuzzy singleton is δ-closed. Also a fuzzy space which is fuzzy almost as well as fuzzy almost T₀ is fuzzy almost regular. While in general topology we have to take an almost T₂ space in place of almost T₀ space.     

On the continuity of the magnetization and energy in Ising ferromagnets

We investigate the phase diagram of ferromagnetic Ising spin systems satisfying the G.H.S. inequality. We show that they cannot have a normal first-order phase transition as the temperatureT is varied, i.e., one where the magnetization is discontinuous and there are three coexisting phases. Furthermore, for n.n. interactions, discontinuity in the magnetization at 0 <T ₀ T _c implies an uncountable infinity of pure phases atT ₀.     

Continuity of K-theory: An example in equal characteristics

If is a perfect field of characteristic , we show that the Quillen K-groups are uniquely -divisible for . In fact, the Milnor K-groups are uniquely -divisible for all . This implies that is -connected after profinite completion for a complete discrete valuation ring with perfect residue field.

     

In what sense is the rational interpolation problem well posed

It is well known that the nonlinear problem of interpolatingm+n+1 data by a rational function of type (m, n) may have no solution, but that the corresponding linearized problem (obtained by multiplying through by the denominator) always leads to a unique rational function, which is often still called the rational interpolant. For fixedm andn, and fixed (possibly multiple) interpolation points, the dependence of this interpolant on the prescribed function values is studied here. For ten notions of convergence in the space _{m, n} the question of the continuity of this interpolation operator is investigated.Communicated by William B. Gragg.AMS classification: 41A24, 30E05, 41A20, 65D05.