A double bounded key identity for Goellnitz's (big) partition theorem

Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computation

Central Charge and the Andrews-Bailey Construction

From the equivalence of the bosonic and fermionic representations of finitized characters in conformal field theory, one can extract mathematical objects known as Bailey pairs. Recently Berkovich, McCoy and Schilling have constructed a `generalized' character formula depending on two parameters \ra and $\r2$, using the Bailey pairs of the unitary model $M(p-1,p)$. By taking appropriate limits of these parameters, they were able to obtain the characters of model $M(p,p+1)$, $N=1$ model $SM(p,p+2)$, and the unitary $N=2$ model with central charge $c=3(1-{\frac{2}{p}})$. In this letter we computed the effective central charge associated with this `generalized' character formula using a saddle point method. The result is a simple expression in dilogarithms which interpolates between the central charges of these unitary models.Comment: Latex2e, requires cite.sty package, 13 pages. Additional footnote, citation and reference

Supersymmetric pairing of kinks for polynomial nonlinearities

We show how one can obtain kink solutions of ordinary differential equations with polynomial nonlinearities by an efficient factorization procedure directly related to the factorization of their nonlinear polynomial part. We focus on reaction-diffusion equations in the travelling frame and damped-anharmonic-oscillator equations. We also report an interesting pairing of the kink solutions, a result obtained by reversing the factorization brackets in the supersymmetric quantum mechanical style. In this way, one gets ordinary differential equations with a different polynomial nonlinearity possessing kink solutions of different width but propagating at the same velocity as the kinks of the original equation. This pairing of kinks could have many applications. We illustrate the mathematical procedure with several important cases, among which the generalized Fisher equation, the FitzHugh-Nagumo equation, and the polymerization fronts of microtubulesComment: 13 pages, 2 figures, revised during the 2nd week of Dec. 200

Quasi-Lie schemes and Emden--Fowler equations

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from this new perspective. Finally some t-dependent constants of the motion for equations of Emden type satisfying certain conditions are recovered

Riccati-parameter solutions of nonlinear second-order ODEs

It has been proven by Rosu and Cornejo-Perez in 2005 that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a `growth' parameter from the trivial null solution up to the particular solution found through the factorization procedureComment: 5 pages, 3 figures, change of title and more tex

Quantum Clifford-Hopf Algebras for Even Dimensions

In this paper we study the quantum Clifford-Hopf algebras $\widehat{CH_q(D)}$ for even dimensions $D$ and obtain their intertwiner $R-$matrices, which are elliptic solutions to the Yang- Baxter equation. In the trigonometric limit of these new algebras we find the possibility to connect with extended supersymmetry. We also analyze the corresponding spin chain hamiltonian, which leads to Suzuki's generalized $XY$ model.Comment: 12 pages, LaTeX, IMAFF-12/93 (final version to be published, 2 uuencoded figures added

Degenerating families of dendrograms

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist $p$-adic representation of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the $p$-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are $p$-adic parameter spaces of (families of) dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.Comment: 13 pages, 8 figure

Event Stream Processing with Multiple Threads

Current runtime verification tools seldom make use of multi-threading to speed up the evaluation of a property on a large event trace. In this paper, we present an extension to the BeepBeep 3 event stream engine that allows the use of multiple threads during the evaluation of a query. Various parallelization strategies are presented and described on simple examples. The implementation of these strategies is then evaluated empirically on a sample of problems. Compared to the previous, single-threaded version of the BeepBeep engine, the allocation of just a few threads to specific portions of a query provides dramatic improvement in terms of running time

Espaces de Berkovich sur Z : \'etude locale

We investigate the local properties of Berkovich spaces over Z. Using Weierstrass theorems, we prove that the local rings of those spaces are noetherian, regular in the case of affine spaces and excellent. We also show that the structure sheaf is coherent. Our methods work over other base rings (valued fields, discrete valuation rings, rings of integers of number fields, etc.) and provide a unified treatment of complex and p-adic spaces.Comment: v3: Corrected a few mistakes. Corrected the proof of the Weierstrass division theorem 7.3 in the case where the base field is imperfect and trivially value