Spin-1/2 Maxwell Fields

Requiring covariance of Maxwell's equations without a priori imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules, with new invariants, for all traditional Maxwell field and source quantities. The accompanying spin-1/2 representations of the Lorentz group employ the Minkowski metric, and consequently the primary spin-1/2 Maxwell invariants are also spin-1 invariants; for example, ²–A ², E ²–B ²+2i EB–(₀ +A)². The associated Maxwell Lagrangian density is also the same for both spin-1 and spin-1/2 fields. However, in the spin-1/2 case, standard field and source quantities are complex and both charge and gauge invariance are lost. Requiring the potentials to satisfy the Klein–Gordon equation equates the Maxwell and field-potential equations with two Dirac equations of the Klein–Gordon mass, and thus one complex Klein–Gordon Maxwell field describes either two real vector fields or two Dirac fields, all of the same mass.     

Weight Function Approach to q-Difference Equations for the q-Hypergeometric Polynomials

In this paper we define a new algebra generated by the difference operators D _q and D _q-1 with two analytic functions (x) and (x). Also, we define an operator M = J ₁ J ₂–J ₃ J ₄ s.t. all q-hypergeometric orthogonal polynomials Y _n(x), x cos(), are eigenfunctions of the operator M with eigenvalues _q [n] _q . The choice of (x) and (x) depend on the weight function of Y _n (x).     

湍流效应对光通信链路的影响研究与仿真

通过对大气湍流效应的分析,研究了激光在大气中传输时受大气随机信道的影响,通过软件实时显示光斑的闪烁、漂移,为进一步优化激光通信系统性能设计,最终实现全天候的大气激光通信做了有意义的探索。     

Undercooling and solidification of germanium melts studied by differential scanning calorimeter

~~Undercooling and solidification of germanium melts studied by differential scanning calorimeter~~     

Deficiency Indices of a Symmetric Ordinary Differential Operator with Infinitely Many Degeneration Points

Let H be the minimal symmetric operator in L ²() generated by the differential expression (-1) ⁿ (c(x)f ⁽ⁿ⁾)⁽ⁿ⁾, n 1, with a real coefficient c(x) that has countably many zeros without finite accumulation points and is infinitely smooth at all points x with c(x) 0. We study the value Def H of the deficiency indices of H. It is shown that DefH=+ if infinitely many zeros of c(x) have multiplicities p satisfying the inequality n – 1/2 < p < 2n – 1/2. Our second result pertains to the case in which the set of zeros of c(x) is bounded neither above nor below. Under this condition, Def H = 0 provided that the multiplicity of each zero is greater than or equal to 2n – 1/2. The multiplicities of zeros of c(x) are understood in the paper in a broader sense than in the standard definition.     

Self-similar solutions of the porous medium equation in a half-space with a nonlinear boundary condition: existence and symmetry

We find existence of a nonnegative compactly supported solution of the problem Δu=u^α in , ∂u/∂ν=u on . Moreover, we prove that every nonnegative solution with finite energy is compactly supported and radially symmetric in the tangential variables.     

Inheritance of surjectivity for partial differential operators on spaces of real analytic functions

For an open set let A(Ω) be the space of real analytic functions on Ω. Improving our previous results, we prove a new quantitative characterization of the linear partial differential operators P(D) which are surjective on A(Ω). This implies that P(D) is surjective on if P(D) is surjective on A(Ω) for some Ω≠∅. Further inheritance properties for the surjectivity of P(D) on A(Ω) are also obtained.     

Modeling,Mathematical and Numerical Analysis of Electrorheological Fluids

Many electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to a strong electric field the effective viscosity increases dramatically. In this paper we first derive a model which captures this behaviour. For the resulting system of equations we then prove local in time existence of strong solutions for large data. For these solutions we finally derive error estimates for a fully implicit time-discretization.     

Explicit Solution of a Non-Linear Filtering Problem for Lévy Processes with Application to Finance

In this paper we explicitly solve a non-linear filtering problem with mixed observations, modelled by a Brownian motion and a generalized Cox process, whose jump intensity is given in terms of a Lévy measure. Motivated by empirical observations of R. Cont and P. Tankov we propose a model for financial assets, which captures the phenomenon of time inhomogeneity of the jump size density. We apply the explicit formula to obtain the optimal filter for the corresponding filtering problem.     

On the Almost Intersections of Transient Brownian Motions

Let {B ₁ ^d (t)} and {B ^d ₂(t)} be independent Brownian motions in R ^d starting from 0 and nx respectively, and let w ^d _i (a,b) ={xR ^d : B ^d _i (t)=x for some t(a,b)}, i=1,2. Asymptotic expressions as n for the probability of dist(w ^d ₁(n ² t ₁, n ² t ₂), w ₂ ^d (0,n ² t ₃))1 with d4, respectively for the probability of dist(w ₁ ⁴(n ² t ₁,n ² t ₂),w ₂ ⁴(0,n ² t ₃))1 are obtained. As an application, an improvement of a result due to M. Aizenman concerning the intersections of Wiener sausages in R ⁴ is presented.