On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002     

Moments of an exponential functional of random walks and permutations with given descent sets

The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial Y = 1 + ξ₁ + ξ₁ξ₂ + ξ₁ξ₂ξ₃ + ⋯ of independent and identically distributed non-negative random variables. It has moments that are rational functions of the variables μ _k = E(ξ ^k ) < 1 with universal coefficients. It turns out that such a coefficient is equal to the number of permutations with descent set defined by the multiindex of the coefficient. A recursion enumerates all numbers of permutations with given descent sets in the form of a Pascal-type triangle. This revised version was published online in August 2006 with corrections to the Cover Date.     

A Verified Optimization Technique to Locate Chaotic Regions of Hénon Systems

We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located by the new technique.     

Widrow-cellular neural network and optoelectronic implementation

A new type of optoelectronic cellular neural network has been developed by providing the capability of coefficients adjusment of cellular neural network (CNN) using Widrow based perceptron learning algorithm. The new supervised cellular neural network is called Widrow-CNN. Despite the unsupervised CNN, the proposed learning algorithm allows to use the Widrow-CNN for various image processing applications easily. Also, the capability of CNN for image processing and feature extraction has been improved using basic joint transform correlation architecture. This hardware application presents high speed processing capability compared to digital applications. The optoelectronic Widrow-CNN has been tested for classic CNN feature extraction problems. It yields the best results even in case of hard feature extraction problems such as diagonal line detection and vertical line determination.     

Multiple Shocks in Bricklayers' Model

In bricklayers' model, which is a generalization of the misanthrope processes, we show that a nontrivial class of product distributions is closed under the time-evolution of the process. This class also includes measures fitting to shock data of the limiting PDE. In particular, we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting, in an attractive way, via their jump rates. Our results are related to those of Belitsky and Schütz⁽⁴⁾ on the simple exclusion process, although we do not use quantum formalism as they do. The structures we find are described from a fixed position. Similar ones were found in Balázs,⁽²⁾ valak as seen from the random position of the second class particle.     

Influence of solute mobility on dislocation motion I. Basic model

Dislocation motion in the real lattice of alloys is highly complex. In a certain temperature range the dynamic strain ageing phenomena have been reported. In this paper the influence of mobile solute atoms (as obstacles) on the motion of dislocation is analysed. Both processes are assumed to be thermally activated. A new model based on this assumption is proposed. The dislocation velocity and the friction stress (due to solute-dislocation interactions) are calculated. A change in the friction stress caused by solute mobility is discussed.     

Low-density close-closed loop burst error detecting codes

In this paper, we study cyclic codes detecting a subclass of close-closed loop bursts viz. low-density close-closed loop bursts. A sub-class of CT close-closed loop bursts called CT low-density close-closed loop bursts is also studied.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Density functional study of the conformational space of 4C1 D-glucuronic acid

The conformational space of (4)C(1) alpha- and beta-d-glucuronic acid was scanned by HF/3-21G(p) calculations followed by optimization of the 15 most stable structures for each, using the B3LYP density functional theory method in conjunction with a diffuse polarized valence triple-zeta basis set. We found a general preference of the alpha anomers in the isolated molecules in agreement with the large endo-anomeric hyperconjugation effects in these structures. From the other intramolecular interactions (exo-anomeric hyperconjugation, hydrogen-bonding, dipole-dipole, and steric interactions), the effect of the hydrogen bonding is the most pronounced and plays a major role in determining the stability order within the alpha and beta series. The most stable conformer of both alpha and beta (4)C(1) d-glucuronic acid is the structure with the maximum number (5) of intramolecular hydrogen bonds. Introduction of solvent (water) effects by the SCI-PCM model resulted in two characteristic changes of the energetic properties: the gas-phase stability order changed considerably, and the energy range of the 15 most stable conformers decreased from 30 to 15 kJ/mol. The geometrical parameters reflect well the superimposed effects of hyperconjugation and hydrogen-bonding interactions. Most characteristics are the variations of the C-O bond distances (within a range of 0.04 A) upon the combined intramolecular effects.