480 research outputs found
Baxter operator formalism for Macdonald polynomials
We develop basic constructions of the Baxter operator formalism for the
Macdonald polynomials associated with root systems of type A. Precisely we
construct a dual pair of mutually commuting Baxter operators such that the
Macdonald polynomials are their common eigenfunctions. The dual pair of Baxter
operators is closely related to the dual pair of recursive operators for
Macdonald polynomials leading to various families of their integral
representations. We also construct the Baxter operator formalism for the
q-deformed gl(l+1)-Whittaker functions and the Jack polynomials obtained by
degenerations of the Macdonald polynomials associated with the type A_l root
system. This note provides a generalization of our previous results on the
Baxter operator formalism for the Whittaker functions. It was demonstrated
previously that Baxter operator formalism for the Whittaker functions has deep
connections with representation theory. In particular the Baxter operators
should be considered as elements of appropriate spherical Hecke algebras and
their eigenvalues are identified with local Archimedean L-factors associated
with admissible representations of reductive groups over R. We expect that the
Baxter operator formalism for the Macdonald polynomials has an interpretation
in representation theory of higher-dimensional arithmetic fields.Comment: 22 pages, typos are fixe
O desenvolvimento de um sistema computacional de sumarização multidocumento com base em um método linguisticamente motivado
This paper presents the studies conducted in the area of Natural Language Processing, more specifically, in Automatic Multi-document Summarization. We describe the steps for the production of a computational prototype, based on a linguistically motivated method, for summarizing news texts in Portuguese.Este trabalho apresenta os estudos realizados na área de Processamento de Linguagem Natural, mais especificamente, em Sumarização Automática Multidocumento. São descritos os passos para a produção de um protótipo computacional, baseado em um método linguisticamente motivado, para a produção de sumários de notícias jornalísticas escritas em português.FAPESPICMCPró-reitoria de Pesquis
The Interplay of Landau Level Broadening and Temperature on Two-Dimensional Electron Systems
This work investigates the influence of low temperature and broadened Landau
levels on the thermodynamic properties of two-dimensional electron systems. The
interplay between these two physical parameters on the magnetic field
dependence of the chemical potential, the specific heat and the magnetization
is calculated. In the absence of a complete theory that explains the Landau
level broadening, experimental and theoretical studies in literature perform
different model calculations of this parameter. Here it is presented that
different broadening parameters of Gaussian-shaped Landau levels cause width
variations in their contributions to interlevel and intralevel excitations.
Below a characteristic temperature, the interlevel excitations become
negligible. Likewise, at this temperature range, the effect of the Landau level
broadening vanishes.Comment: 5 pages, 5 figures, submitted to Solid State Communication
Exact operator solution of the Calogero-Sutherland model
The wave functions of the Calogero-Sutherland model are known to be
expressible in terms of Jack polynomials. A formula which allows to obtain the
wave functions of the excited states by acting with a string of creation
operators on the wave function of the ground state is presented and derived.
The creation operators that enter in this formula of Rodrigues-type for the
Jack polynomials involve Dunkl operators.Comment: 35 pages, LaTeX2e with amslate
Exact perturbative solution of the Kondo problem
We explicitly evaluate the infinite series of integrals that appears in the
"Anderson-Yuval" reformulation of the anisotropic Kondo problem in terms of a
one-dimensional Coulomb gas. We do this by developing a general approach
relating the anisotropic Kondo problem of arbitrary spin with the boundary
sine-Gordon model, which describes impurity tunneling in a Luttinger liquid and
in the fractional quantum Hall effect. The Kondo solution then follows from the
exact perturbative solution of the latter model in terms of Jack polynomials.Comment: 4 pages in revtex two-colum
Hopf algebras and Markov chains: Two examples and a theory
The operation of squaring (coproduct followed by product) in a combinatorial
Hopf algebra is shown to induce a Markov chain in natural bases. Chains
constructed in this way include widely studied methods of card shuffling, a
natural "rock-breaking" process, and Markov chains on simplicial complexes.
Many of these chains can be explictly diagonalized using the primitive elements
of the algebra and the combinatorics of the free Lie algebra. For card
shuffling, this gives an explicit description of the eigenvectors. For
rock-breaking, an explicit description of the quasi-stationary distribution and
sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes
will only appear on the version on Amy Pang's website, the arXiv version will
not be updated.
Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by
certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of
the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is
invariant under the action of certain differential operators which include half
the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit
clusters of size at most k: they vanish when k+1 of their variables are
identified, and they do not vanish when only k of them are identified. We
generalize most of these properties to superspace using orthogonal
eigenfunctions of the supersymmetric extension of the trigonometric
Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular,
we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at
\alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span
an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N
commuting variables and N anticommuting variables. We prove that the ideal
{\mathcal I}^{(k,r)}_N is stable with respect to the action of the
negative-half of the super-Virasoro algebra. In addition, we show that the Jack
superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting
variables are equal, and conjecture that they do not vanish when only k of them
are identified. This allows us to conclude that the standard Jack polynomials
with prescribed symmetry should satisfy similar clustering properties. Finally,
we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for
the subspace of symmetric superpolynomials in N variables that vanish when k+1
commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we
present exceptions to an often made statement concerning the clustering
property of the ordinary Jack polynomials for (k,r,N)-admissible partitions
(see Footnote 2); 2) Conjecture 14 is substantiated with the extensive
computational evidence presented in the new appendix C; 3) the various tests
supporting Conjecture 16 are reporte
Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the -Adics-Quantum Group Connection
We establish a previously conjectured connection between -adics and
quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra
and its generalizations, the conceptual basis for the Macdonald polynomials,
which ``interpolate'' between the zonal spherical functions of related real and
\--adic symmetric spaces. The elliptic quantum algebras underlie the
\--Baxter models. We show that in the n \air \infty limit, the Jost
function for the scattering of {\em first} level excitations in the
\--Baxter model coincides with the Harish\--Chandra\--like \--function
constructed from the Macdonald polynomials associated to the root system .
The partition function of the \--Baxter model itself is also expressed in
terms of this Macdonald\--Harish\--Chandra\ \--function, albeit in a less
simple way. We relate the two parameters and of the Macdonald
polynomials to the anisotropy and modular parameters of the Baxter model. In
particular the \--adic ``regimes'' in the Macdonald polynomials correspond
to a discrete sequence of XXZ models. We also discuss the possibility of
``\--deforming'' Euler products.Comment: 25 page
Permeability analysis in bisized porous media: wall effect between particles of different size
The permeability of binary packings of glass beads with different size ratio – 13.3, 20, and 26.7, was investigated. In the Kozeny–Carman equation, the dependence of the tortuosity τ on the mixture porosity ε(xD) was described according to τ = 1/εn for different volume fraction of large particles in the mixture, xD. Obtained data on packing permeability shows that the parameter n is a function of the volume fraction and particle size ratio, with values between 0.5 and 0.4. This can be explained by the wall effect resulting from the arrangement of the small particles occurring near the large particle surface. A model taking in account this effect was suggested that can be useful in the characterization of transport phenomena in granular beds as well as in engineering applications.Fundação para a Ciência e a Tecnologia (FCT) - SFRH/BPD/18128/2004; Project POCI_EQU_58337/2004
Evaluating the function of wildcat faecal marks in relation to the defence of favourable hunting areas
This is an Accepted Manuscript of an article published by Taylor & Francis in Ethology Ecology and Evolution on 2015, available online: http://www.tandfonline.com/10.1080/03949370.2014.905499To date, there have been no studies of carnivores that have been specifically designed to examine the function of scent marks in trophic resource defence, although several chemical communication studies have discussed other functions of these marks. The aim of this study was to test the hypothesis that faecal marks deposited by wildcats (Felis silvestris) serve to defend their primary trophic resource, small mammals. Field data were collected over a 2-year period in a protected area in northwestern Spain. To determine the small mammal abundance in different habitat types, a seasonal live trapping campaign was undertaken in deciduous forests, mature pine forests and scrublands. In each habitat, we trapped in three widely separated Universal Transverse Mercator (UTM) cells. At the same time that the trapping was being performed, transects were conducted on foot along forest roads in each trapping cell and in one adjacent cell to detect fresh wildcat scats that did or did not have a scent-marking function. A scat was considered to have a presumed marking function when it was located on a conspicuous substrate, above ground level, at a crossroad or in a latrine. The number of faecal marks and the small mammal abundance varied by habitat type but not by seasons. The results of the analysis of covariance (ANCOVA) indicated that small mammal abundance and habitat type were the factors that explained the largest degrees of variation in the faecal marking index (number of faecal marks in each cell/number of kilometres surveyed in each cell). This result suggests that wildcats defended favourable hunting areas. They mark most often where their main prey lives and so where they spend the most time hunting (in areas where their main prey is more abundant). This practice would allow wildcats to protect their main trophic resource and would reduce intraspecific trophic competitio
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