An imaginary potential with universal normalization for dissipative processes in heavy-ion reactions

In this work we present new coupled channel calculations with the São Paulo potential (SPP) as the bare interaction, and an imaginary potential with system and energy independent normalization that has been developed to take into account dissipative processes in heavy-ion reactions. This imaginary potential is based on high-energy nucleon interaction in nuclear medium. Our theoretical predictions for energies up to ≈100 MeV/nucleon agree very well with the experimental data for the p,n+nucleus, ¹⁶O + ²⁷Al, ¹⁶O + ⁶⁰Ni, ⁵⁸Ni + ¹²⁴Sn, and weakly bound projectile ⁷Li + ¹²⁰Sn systems.     

Migration of protons in a chain of tyrosine residues

This article deals with the proton migration in a tyrosine stack, which models the proton channels existing in a number of proteins, including tubulin. The magnesium ion Mg²⁺ within the complex with guanosine triphosphate facilitates dissociation of a water molecule through initiating a shift of protons along the chain composed of relatively distant tyrosine residues. The process is thermodynamically stable (ΔG₂₉₈<0). The energy barrier for the protein shift does not exceed 3.15 kJ/mole. A relatively weak electrostatic field mimicking electret properties of proteins facilitates long‐distance proton migration. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 409–415, 2001     

Two-vibron bound states in the β--Fermi--Pasta--Ulam model

This paper studies the two-vibron bound states in the β- Fermi Pasta-Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site and mixed two-vibron bound states may exist in the model. Specially, wave number has a significant effect on such bound states, which may be considered as the quantum effects of the localized states in quantum systems.     

Perturbation theory for velocity-dependent potentials

In the presence of a velocity-dependent Kisslinger potential, the partial-wave, time-independent Schr?dinger equation with real boundary conditions is written as an equation for the probability density. The changes in the bound-state energy eigenvalues due to the addition of small perturbations in the local as well as the Kisslinger potentials are determined up to second order in the perturbation. These changes are determined purely in terms of the unperturbed probability density, the perturbing local potential, as well as the Kisslinger perturbing potential and its gradient. The dependence on the gradient of the Kisslinger potential stresses the importance of a diffuse edge in nuclei. Two explicit examples are presented to examine the validity of the perturbation formulas. The first assumes each of the local and velocity-dependent parts of the potential to be a finite square well. In the second example, the velocity-dependent potential takes the form of a harmonic oscillator. In both cases the energy eigenvalues are determined exactly and then by using perturbation theory. The agreement between the exact energy eigenvalues and those obtained by perturbation theory is very satisfactory. Received: 24 May 2002 / Accepted: 15 July 2002 / Published online: 3 December 2002 RID="a" ID="a"e-mail: mij@hu.edu.jo Communicated by V. Vento     

Simple bounds for closed queueing networks

Consider a closed Jackson type network in which each queue has a single exponential server. Assume that N customers are moving among k queues. We establish simple closed form bounds on the network throughput (both lower and upper), which are sharper than those that are currently available. Numerical evaluation indicates that the improvements are significant.     

Some Upper Bounds on the Covering Radii of Linear Codes Over Fq and Their Applications

We show that the covering radius R of an [n,k,d] code over F_q is bounded above by R n-n _q(k, d/q). We strengthen this bound when R d and find conditions under which equality holds.As applications of this and other bounds, we show that all binary linear codes of lengths up to 15, or codimension up to 9, are normal. We also establish the normality of most codes of length 16 and many of codimension 10. These results have applications in the construction of codes that attain t[n,k,/it>], the smallest covering radius of any binary linear [n,k].We also prove some new results on the amalgamated direct sum (ADS) construction of Graham and Sloane. We find new conditions assuring normality of the ADS; covering radius 1 less than previously guaranteed for ADS of codes with even norms; good covering codes as ADS without the hypothesis of normality, from concepts p- stable and s- stable; codes with best known covering radii as ADS of two, often cyclic, codes (thus retaining structure so as to be suitable for practical applications).     

On lower bounds for theL 2-Wasserstein metric in a Hilbert space

We provide two families of lower bounds for theL ²-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02.     

An exact construction of digital convex polygons with minimal diameter

Given a natural number n, an exact formula is derived for the minimal possible size MD(n) of a square grid, in which a digital convex n-gon can be inscribed. An exact construction of a digital convex n-gon which can be inscribed into a square grid of size MD(n) is also given.     

An asymptotic minimax risk bound for estimation of a linear functional relationship

We consider estimation of the parameter B in a multivariate linear functional relationship X_i=ξ_i+ξ_1i, Y_i=Bξ_i+ξ_2i, i=1,…,n, where the errors (ζ_1i^′, ζ_2i^′) are independent standard normal and (ξ_i, i ) is a sequence of unknown nonrandom vectors (incidental parameters). If there are no substantial a priori restrictions on the infinite sequence of incidental parameters then asymptotically the model is nonparametric but does not fit into common settings presupposing a parameter from a metric function space. A special result of the local asymptotic minimax type for the m.1.e. of B is proved. The accuracy of the normal approximation for the m.l.e. of order n^−1/2 is also established.     

Electrostatic self-energy and Bekenstein entropy bound in the massive Schwinger model

We obtain the electrostatic energy of two opposite charges near the horizon of stationary black holes in the massive Schwinger model. Besides the confining aspects of the model, we discuss the Bekenstein entropy upper bound of a charged object using the generalized second law. We show that despite the massless case, in the massive Schwinger model the entropy of the black hole and consequently the Bekenstein bound are altered by the vacuum polarization.