First exit times for compound Poisson dams with a general release rule

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. For this dam, we solve Kolmogorov’s backward differential equation to obtain the Laplace transforms of the first exit times in terms of a certain positive kernel. This allows us to provide an explicit expression for the Laplace transform of the wet period for a finite dam.     

Transcendence conjectures about periods of modular forms and rational structures on spaces of modular forms

The conjecture is made that the rational structures on spaces of modular forms coming from the rationality of Fourier coefficients and the rationality of periods are not compatible. A consequence would be that ζ(2k-1)/π ^2k-1 (ζ(s)=Riemann zeta function;k∈ℕ,k≥2) is irrational or even transcendental.     

Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations

A general method of constructing families of cyclic polynomials over with more than one parameter will be discussed, which may be called a geometric generalization of the Gaussian period relations. Using this, we obtain explicit multi-parametric families of cyclic polynomials over of degree . We also give a simple family of cyclic polynomials with one parameter in each case, by specializing our parameters.

     

On the Number of Appearances of a Word in a Sequence of I.I.D. Trials

Let X ₁,...,X _n be a sequence of i.i.d. random variables taking values in an alphabet =₁,...,_q,q 2, with probabilities P(X _a=_i)=p _i,a=1,...,n,i=1,...,q. We consider a fixed h-letter word W=w₁...w_h which is produced under the above scheme. We define by R(W) the number of appearances of W as Renewal (which is equal with the maximum number of non-overlapping appearances) and by N(W) the number of total appearances of W (overlapping ones) in the sequence X _{a 1} a1n under the i.i.d. hypothesis. We derive a bound on the total variation distance between the distribution (R(W)) of the r.v. R(W) and that of a Poisson with parameter E(R(W)). We use the Stein-Chen method and related results from Barbour et al. (1992), as well as, combinatorial results from Schbath (1995b) concerning the periodic structure of the word W. Analogous results are obtained for the total variation distance between the distribution of the r.v. N(W) and that of an appropriate Compound Poisson r.v. Related limit theorems are obtained and via numerical computations our bounds are presented in tables.     

The derivation of the quantum kinetic equation and the two-time resolvent method

Van Hove's partial density matrix, _E (t), in his generalized master equation is interpreted as a Wigner representation of two-time dyad for energy E and time t. This interpretation enables us to integrate the energyE in Van Hove's master equation. The resultant equation is of non-Markov type on two time parameters. Starting with this master equation, the derivation of quantum kinetic equations, including the second-order approximation in the density expansion, is discussed. The scaling of the quantum kinetic equation is examined in detail for a system in which particles interact through the delta shell potential. It is shown that the quantum kinetic equation, including three-particle scattering, may exist for the physical situations of low-energy scattering,high-energy scattering, and for resonance scattering for time scales of the system sufficiently separated. In deriving the quantum kinetic equation, a factorization theorem form-particle distribution functions is proved to arbitrary order in perturbation expansion.     

坡上矩阵的逆与幂(英文)

Invertible conditions,indices and periods of matrices over an incline are considered.In all proofs multiplicative commutativity is not used.Some results about invertibility, indices and periods in a commutative incline are proved to be correct also for any incline.     

The First Principle Calculation of Green—Kubo Formula with the Two—Time Ensemble Technique

For weak-coupling electronic plasmas in the presence of small fluctuations,we calculate Green-Kuboformula for transport coefficients employing the ab initio theory,i.e.,the two-time ensemble technique.The microscopic interpretations of Onsager‘s hypothesis on fluctuations are presented in the framework.     

Combinatorics on partial word correlations

Partial words are strings over a finite alphabet that may contain a number of “do not know” symbols. In this paper, we consider the period and weak period sets of partial words of length n over a finite alphabet, and study the combinatorics of specific representations of them, called correlations, which are binary and ternary vectors of length n indicating the periods and weak periods. We characterize precisely which vectors represent the period and weak period sets of partial words and prove that all valid correlations may be taken over the binary alphabet. We show that the sets of all such vectors of a given length form distributive lattices under suitably defined partial orderings. We show that there is a well-defined minimal set of generators for any binary correlation of length n and demonstrate that these generating sets are the primitive subsets of {1,2,…,n−1}. We also investigate the number of partial word correlations of length n. Finally, we compute the population size, that is, the number of partial words sharing a given correlation, and obtain recurrences to compute it. Our results generalize those of Guibas, Odlyzko, Rivals and Rahmann.