We obtain relations among boundary states in bosonic minimal open string theory using the boundary ground ring. We also obtain a difference equation that boundary correlators must satisfy. email: [email protected], Address after Sep 11, 2005: School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA email: [email protected]

We use the theory of vertex operator algebras and intertwining operators to obtain systems of q-difference equations satisfied by the graded dimensions of the principal subspaces of certain level k standard modules for ŝl(3). As a consequence we establish new formulas for the graded dimensions of the principal subspaces corresponding to the highest weights iΛ1 + (k − i)Λ2, where 1 ≤ i ≤ k and Λ...

and T (r, f), which is only true for finite order meromorphic functions. We have also obtained the proximity function and pointwise estimates of f(z+η)/f(z) which is a discrete version of the classical logarithmic derivative estimates of f(z). We apply these results to give new growth estimates of meromorphic solutions to higher order linear difference equations. This also allows us to solve an...

The discrete Painlevé I equation (dPI) is an integrable difference equation which has the classical first Painlevé equation (PI) as a continuum limit. dPI is believed to be integrable because it is the discrete isomonodromy condition for an associated (single-valued) linear problem. In this paper, we derive higher-order difference equations as isomonodromy conditions that are associated to the ...

In this paper some new sufficient conditions for the oscillation of solutions of the third order half-linear difference equations ∆ ( an(∆ (xn + bnh(xn−δ))) α ) + qnf(xn+1−τ ) = 0 and ∆ ( an(∆ (xn − bnh(xn−δ))) α ) + qnf(xn+1−τ ) = 0 are established. Some examples are presented to illustrate the main results.

This article continues investigation of ways to obtain pseudo-random sequences over Galois field via generating LRS over Galois ring and complication it. Previous work is available at http://eprint.iacr.org/2016/212 In this work we provide low rank estimations for sequences generated by two different designs based on coordinate sequences of linear recurrent sequences (LRS) of maximal period (MP...

We show that the first-order system of difference equations zn+1 = αz a nw b n, wn+1 = βz c nw d n, n ∈ N0, where a, b, c, d ∈ Z, α, β ∈ C \ {0}, z0, w0 ∈ C \ {0}, is solvable in closed form, by finding closed form formulas of its solutions.

In this work, oscillatory behavior of solutions of a class of fourth order neutral functional difference equations of the form ∆ ( r(n)∆(y(n) + p(n)y(n−m)) ) + q(n)G(y(n− k)) = 0 is studied under the assumption ∞ ∑

and Applied Analysis 3 The coefficients {ci ki (z)}, {di ti (z)} are meromorphic functions and small functions, S (r) = ∑T (r, a (i) ) +∑T(r, b (j) )

1 College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 2 Key Laboratory of Network Control & Intelligent Instrument, Chongqing University of Posts and Telecommunications, Ministry of Education, Chongqing 400065, China 3 College of Applied Sciences, Beijing University of Technology, Beijing 100124, China 4 School of Communication and I...