The inverse scattering problem for Schrödinger and Klein–Gordon equations with a nonlocal nonlinearity

We study the inverse scattering problem for the nonlinear Schrödinger equation and for the nonlinear Klein–Gordon equation with the generalized Hartree type nonlinearity. We reconstruct the nonlinearity from knowledge of the scattering operator, which improves the known results.     

Multiple harmonic series related to multiple Euler numbers

In this paper, we define the multiple Euler numbers and consider some multiple harmonic series of Mordell-Tornheim's type, which is a partial sum of the Mordell-Tornheim zeta series defined by Matsumoto. Indeed, we prove a certain reducibility of these series as well as the multiple zeta values.     

The Solow model improved through the logistic manpower growth law

In this paper the neo-classical economic Solow-Swan model (1956) has been improved replacing its Malthusian manpower law with the Verhulst (logistic) one. The relevant ordinary differential equation for the ratio capital/work has been then integrated in closed form via the Hypergeometric function₂ F ₁. The logistic growth injection for the manpower is detected to induce a more slow dynamics onto the Solow-Swan system, which keeps its stability. Increasing developments are displayed as the technologic progress rises. Further sceneries are tested and the congruence of the new solution with the classical one is shown switching to zero the selflimitation coefficent in the logistic law. Research supported by MURST grant:Metodi matematici in economia     

Electronic structure of the wrong-bond states in amorphous germanium sulphides

First-principles calculations of the electronic structures of the wrong bonds were performed for amorphous germanium sulphides in order to explain their compositional dependence. Model cluster calculations of the density of states using a set of geometry similar to the crystalline-GeS₂ coordination can reproduce the peak structure of the experimental valence band photoemission spectra. The bonding and anti-bonding states of the covalent Ge-S bonds form valence and conduction band respectively, and the top of the valence band is occupied with S 3p lone-pair states. The bonding states are modified by S-S bonds and the anti-bonding states are modified by Ge-Ge bonds, mainly through their hybridization with the wrong-bond states between p-orbitals. The lone-pair states do not interact either of them to form a different band, and obscure the modification induced by the S-S wrong bonds. Therefore, we can conclude that the narrowing of the bandgap with increasing Ge content from GeS₂ composition is due to that of the conduction-band bottom with increasing germanium wrong bonds, though the narrowing with increasing S content is moderate due to the presence of the lone-pair states at the valence-band top.     

Some 3-manifolds with 2-generated fundamental group

We describe a family of graph manifolds that have 2-generated fundamental group but do not admit a Heegaard splitting of genus 2. They are closely related to the examples provided by Boileau and Zieschang if these are considered as (non-proper) graph manifolds.Received: 14 August 2002     

Inner Radius of Univalence for a Strongly Starlike Domain

 The inner radius of univalence of a domain D with Poincaré density ρ _D is the possible largest number σ such that the condition ∥ S _f ∥ _D  = sup _{w∈ D} ρ _D (w) ⁻²∥ S _f (z) ∥ ≤ σ implies univalence of f for a nonconstant meromorphic function f on D, where S _f is the Schwarzian derivative of f. In this note, we give a lower bound of the inner radius of univalence for strongly starlike domains of order α in terms of the order α. The author was partially supported by the Ministry of Education, Grant-in-Aid for Encouragement of Young Scientists, 11740088. A part of this work was carried out during his visit to the University of Helsinki under the exchange programme of scientists between the Academy of Finland and the JSPS. Received November 26, 2001; in revised form September 24, 2002 Published online May 9, 2003     

π1-classification of real arrangements with up to eight lines

One of the open questions in the geometry of line arrangements is to what extent does the incidence lattice of an arrangement determine its fundamental group. Line arrangements of up to 6 lines were recently classified by K.M. Fan (Michigan Math. J. 44(2) (1997) 283), and it turns out that the incidence lattice of such arrangements determines the projective fundamental group. We use actions on the set of wiring diagrams, introduced in (Garber et al. (J. Knot Theory Ramf.), to classify real arrangements of up to 8 lines. In particular, we show that the incidence lattice of such arrangements determines both the affine and the projective fundamental groups.     

Nonlinear electron transport properties of InAlAs/InGaAs based Y-branch junctions for microwave rectification at room temperature

A detailed analysis of nonlinear effects-electron switching and rectification, in InAlAs/InGaAs based Y-branch junction (YBJ) devices is presented to investigate the potential of YBJ for high frequency applications at 300 K. Results based on semi-classical simulations yield good qualitative agreement with measurements and previously reported theoretical and experimental results. The nonlinear parabolic behaviour of our device is attributed to device geometry and space charge effects. RF analysis shows that the YBJ has tremendous intrinsic potential to function as a frequency doubler and microwave rectifier when operated in the parabolic regime. The present analysis serves as a tool to optimize the bias conditions for RF measurements and to estimate the effect of interconnects and parasitic elements on the RF performance of real devices.     

Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models

Parameters of Gaussian multivariate models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical when the sample size is very large, as, for example, in the case of massive georeferenced data sets. In this paper, we study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, designed to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first-order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations.     

Arithmetic expressions of Selberg's zeta functions for congruence subgroups

In [P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982) 229-247], it was proved that the Selberg zeta function for SL₂(Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms. The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg zeta functions for congruence subgroups of SL₂(Z). As applications, we study the Brun-Titchmarsh type prime geodesic theorem and the asymptotic formula of the sum of the class number.