Applications of Reflection Amplitudes in Toda-Type Theories

Reflection amplitudes are defined as two-point functions of certain class of conformal field theories where primary fields are given by vertex operators with real couplings. Among these, we consider (Super-) Liouville theory and simply and non-simply laced Toda theories. In this paper we show how to compute the scaling functions of effective central charge for the models perturbed by some primary fields which maintains integrability. This new derivation of the scaling functions are compared with the results from conventional TBA approach and confirms our approach along with other non-perturbative results such as exact expressions of the on-shell masses in terms of the parameters in the action, exact free energies. Another important application of the reflection amplitudes is a computation of one-point functions for the integrable models. Introducing functional relations between the one-point functions in terms of the reflection amplitudes, we obtain explicit expressions for simply-laced and non-simply-laced affine Toda theories. These nonperturbative results are confirmed numerically by comparing the free energies from the scaling functions with exact expressions we obtain from the one-point functions.     

Combinatorics of Rational Functions and Poincaré- Birchoff-Witt Expansions of the Canonical U ({\frak n}\_)-Valued Differential Form

We study the canonical U -valued differential form, whose projections to different Kac-Moody algebras are key ingredients of the hypergeometric integral solutions of KZ-type differential equations and Bethe ansatz constructions. We explicitly determine the coefficients of the projections in the simple Lie algebras A_r, B_r, C_r, D_r in a conveniently chosen Poincaré- Birchoff-Witt basis.Received June 28, 2004     

A note on p-adic Euler measure on ℤp

In this paper, we give some p-adic approximation of E _n,x for certain n. Finally we will treat p-adic l-function of Kubota-Leopoldt’s type Euler numbers and p-adic measure for Euler numbers.     

Local edge detectors using a sigmoidal transformation for piecewise smooth data

For piecewise smooth data, edges can be recognized by jump discontinuities in the data. Successful edge detection is essential in digital signal processing as the most relevant information is often observed near the edges in each segmented region. In this paper, using the concentration property of existing local edge detectors and the clustering property of sigmoidal transformations, we provide enhanced edge detectors which diminish the oscillations of the local detector near jump discontinuities as well as highly improve rate of convergence away from the discontinuities. Numerical results of some examples illustrate efficiency of the presented method.     

On classical artinian localizations

ABSTRACT

We present some results about Lie algebras, which can be written as the sum of two subalgebras in two cases: where both subalgebras are simple or both are nilpotent. In the first case we suggest new examples of simple Lie algebras admitting decomposition into the sum of simple subalgebras and give explicit realizations where the existence of such decompositions was established earlier. We single out cases where such decomposition is not possible. We also construct examples of solvable Lie algebras, which are the sums of two nilpotent subalgebras, and the derived length of the sum is greater than the sum of the nilpotent indexes of the summands.     

Stabilization of an asymmetric bolaamphiphilic sugar-based crown ether hydrogel by hydrogen bonding interaction and its sol-gel transcription

Asymmetric bolaamphiphilic sugar-based hydrogelators (1-3) were synthesized and their gelation ability with and without alkylammonium ions was investigated by CD, TEM, FTIR and NMR. These compounds acted as versatile gelators for organic solvents and water. The xerogels 1-3 obtained from water showed well-developed structures of fibrils with diameters of 10-38 nm and length of several hundred micrometers. Particularly, the gelation ability of crown-appended gelator 1 was drastically enhanced by addition of alkylammonium ions 4 and 5, suggesting that the bridging effect of alkyldiammonium ions could be the primary driving-force for the stabilization due to the intermolecular hydrogen bonding and electrostatic interactions. The present result is a rare case of a hydrogel being stabilized by a host-guest interaction. In addition, the hydrogel 1 with AgNO₃ and KClO₄ induced the formation of nanotubular and vesicular structures of silica by sol-gel polymerization of TEOS, respectively. These results indicate that hydrogel 1 acted as a template to produce inorganic nanomaterials.     

Products of Bergman space Toeplitz operators on the polydisk

Motivated by recent works of Ahern and uković on the disk, we study the generalized zero product problem for Toeplitz operators acting on the Bergman space of the polydisk. First, we extend the results to the polydisk. Next, we study the generalized compact product problem. Our results are new even on the disk. As a consequence on higher dimensional polydisks, we show that the generalized zero and compact product properties are the same for Toeplitz operators in a certain case.The first three authors were partially supported by KOSEF(R01-2003-000-10243-0) and the last author was partially supported by the National Science Foundation.     

An experimental and theoretical study of the formation of nanostructures of self-assembled cyanuric acid through hydrogen bond networks on graphite

The self-assembly of cyanuric acid into ordered nanostructures on a crystalline substrate, highly ordered pyrolytic graphite (HOPG), has been investigated at low temperature under ultrahigh vacuum (UHV) conditions by means of scanning tunneling microscopy in conjunction with theoretical simulations. Many domains with different self-assembly patterns were observed. One such domain represents the formation of an open 2D rosette (cyclic) structure from the self-assembly process, the first observation of this type of structure for pure cyanuric acid on a graphite substrate. Each self-assembled domain exhibits characteristic superstructures formed through different hydrogen bond networks at low coverage and low deposition rate. Experimental observation of coexistent, two-dimensional crystalline structures with distinct hydrogen bond patterns is supported by energy minimizations and molecular dynamics calculations, which show multiple stable structures for this molecule when self-assembled on graphite.     

Mean first passage time for the contact between the ends of a chain polymer

We investigate the first passage times for the contact between the ends of a Rouse chain, whose initial separation is greater than a predefined contact distance, sigma, and equilibrium-distributed. An approximate analytic expression for the mean first passage time is obtained and compared with the results of previous theories and Brownian dynamics simulations. We find that the results of the present theory are in better agreement with Brownian dynamics simulation results than those of previously reported theories.