The Theorem of Jentzsch--Szeg\H{o} on an analytic curve. Application to the irreducibility of truncations of power series

The theorem of Jentzsch--Szeg\H{o} describes the limit measure of a sequence of discrete measures associated to the zeroes of a sequence of polynomials in one variable. Following the presentation of this result by Andrievskii and Blatt in their book, we extend this theorem to compact Riemann surfaces, then to analytic curves over an ultrametric field. The particular case of the projective line over an ultrametric field gives as corollaries information about the irreducibility of the truncations of a power series in one variable.Comment: 16 pages; the application to irreducibility and the final example have been correcte

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

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

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

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

On Integrable Quantum Group Invariant Antiferromagnets

A new open spin chain hamiltonian is introduced. It is both integrable (Sklyanin`s type $K$ matrices are used to achieve this) and invariant under ${\cal U}_{\epsilon}(sl(2))$ transformations in nilpotent irreps for $\epsilon^3=1$. Some considerations on the centralizer of nilpotent representations and its representation theory are also presented.Comment: IFF-5/92, 13 pages, LaTex file, 8 figures available from author

The Yang-Baxter equation for PT invariant nineteen vertex models

We study the solutions of the Yang-Baxter equation associated to nineteen vertex models invariant by the parity-time symmetry from the perspective of algebraic geometry. We determine the form of the algebraic curves constraining the respective Boltzmann weights and found that they possess a universal structure. This allows us to classify the integrable manifolds in four different families reproducing three known models besides uncovering a novel nineteen vertex model in a unified way. The introduction of the spectral parameter on the weights is made via the parameterization of the fundamental algebraic curve which is a conic. The diagonalization of the transfer matrix of the new vertex model and its thermodynamic limit properties are discussed. We point out a connection between the form of the main curve and the nature of the excitations of the corresponding spin-1 chains.Comment: 43 pages, 6 figures and 5 table

Modelling the unfolding pathway of biomolecules: theoretical approach and experimental prospect

We analyse the unfolding pathway of biomolecules comprising several independent modules in pulling experiments. In a recently proposed model, a critical velocity $v_{c}$ has been predicted, such that for pulling speeds $v>v_{c}$ it is the module at the pulled end that opens first, whereas for $v<v_{c}$ it is the weakest. Here, we introduce a variant of the model that is closer to the experimental setup, and discuss the robustness of the emergence of the critical velocity and of its dependence on the model parameters. We also propose a possible experiment to test the theoretical predictions of the model, which seems feasible with state-of-art molecular engineering techniques.Comment: Accepted contribution for the Springer Book "Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications" (proceedings of the BIRS CMM16 Workshop held in Banff, Canada, August 2016), 16 pages, 6 figure

Steps towards Lattice Virasoro Algebras: su(1,1)

An explicit construction is presented for the action of the su(1,1) subalgebra of the Virasoro algebra on path spaces for the c(2,q) minimal models. In the case of the Lee-Yang edge singularity, we show how this action already fixes the central charge of the full Virasoro algebra. For this case, we additionally construct a representation in terms of generators of the corresponding Temperley-Lieb algebra.Comment: 15 pages, plain TeX, 4 typos correcte