Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Laguerre polynomials as Jensen polynomials of Laguerre-Polya entire functions

We prove that the only Jensen polynomials associated with an entire function in the Laguerre-Polya class that are orthogonal are the Laguerre polynomials. (C) 2009 Elsevier B.V. All rights reserved.

Composition and invertibility for a class of generalized functions in the Colombeau's theory

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

Equivalence of many-photon Green's functions in the Duffin-Kemmer-Petiau and Klein-Gordon-Fock statistical quantum field theories

Using the functional integral formalism for the statistical generating functional in the statistical (finite temperature) quantum field theory, we prove the equivalence of many-photon Greens functions in the Duffin-Kennner-Petiau and Klein-Gordon-Fock statistical quantum field theories. As an illustration, we calculate the one-loop polarization operators in both theories and demonstrate their coincidence.

Equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories

We prove the equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.

GENERALIZED HEAVISIDE FUNCTIONS IN THE COLOMBEAU THEORY CONTEXT

We defined generalized Heaviside functions for a variable x in R-n, and for variables (x, t) in R-n x R-m. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

Higher order turän inequalities

The celebrated Turân inequalities P 2 n(x)-P n-x(x)P n+1(x) ≥ 0, x ε[-1,1], n ≥ 1, where P n(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ 2 n - γ n-1γ n+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pölya class, ψ(x) = ∑ ∞ n=0 γ nx n / n!. ©1998 American Mathematical Society.

Schur-SzegA composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Schur-Szegö composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Search for doubly charged Higgs boson pair production in the decay to mu(+)mu(+)mu(-)mu(-) in p(p)over-bar collisions at root s=1.96 TeV

A search for pair production of doubly charged Higgs bosons in the process p (p) over bar -->H++H---->mu(+)mu(+)mu(-)mu(-) is performed with the D0 run II detector at the Fermilab Tevatron. The analysis is based on a sample of inclusive dimuon data collected at an energy of roots=1.96 TeV, corresponding to an integrated luminosity of 113 pb(-1). In the absence of a signal, 95% confidence level mass limits of M(H-L(+/-+/-))>118.4 GeV/c(2) and M(H-R(+/-+/-))>98.2 GeV/c(2) are set for left-handed and right-handed doubly charged Higgs bosons, respectively, assuming 100% branching into muon pairs.

GCHF basis sets and their application in the electronic structure study of PrMnO3

The approach called generator coordinate Hartree-Fock (GCHF) method is used in the selection of Gaussian basis set [25s18p for O ((3)p), 31s21p14d for Mn (S-6), and 33s22p16d9f for Pr ((4)J)] for atoms. The role of the weight functions in the assessment of the numerical integration range of the GCHF equations is shown. These basis sets are contracted to (25s18p/9s5p), (31s21p14d/9s6p4d), and (33s22pl6d9f118sl2p5d3f) by segmented contraction scheme of Dunning and they are utilized in calculations of Restricted-Open-HF (ROHF) Total and Orbital energies of the (MnO+1)-Mn-3 and (PrO+1)-Pr-1 fragments, to evaluate their quality in molecular studies. The addition of one d polarization function in the contracted (9s5p) basis set for O(P-3) atom and their application with the contracted (9s6p4d), (18s21p5d3f) basis sets for Mn (S-6) and Pr-Pr ((4)j) atoms lead to the electronic structure study of PrMnO3. The dipole moment, the total energy, and total atomic charges properties were calculated and were carried out at ROHF level with the [PrMnO3](2) fragment. The calculated values show that PrMnO3 does not present piezoelectric properties. (C) 2004 Elsevier B.V. All rights reserved.

Anxiolytic effect of estradiol in the median raphe nucleus mediated by 5-HT1A receptors

Estrogen deficiency has been associated with stress, anxiety and depression. Estrogen receptors have been identified in the median raphe nucleus (MRN). This structure is the main source of serotonergic projections to the hippocampus, a forebrain area implicated in the regulation of defensive responses and in the resistance to chronic stress. There is evidence showing that estrogen modulates 5-HT1A receptor functions. In the MRN, somatodendritic 5-HT1A receptors control the activity of serotonergic neurones by negative feedback. The present study evaluated the effect of intra-MRN injection of estradiol benzoate (EB) (600 or 1200 ng/0.2 mu l) on the performance of ovariectomised rats submitted to the elevated plus-maze test of anxiety and to the open-field test. Additionally, the same effect was evaluated with a previous intra-MRN injection of WAY 100635 (100 ng/0.2 mu l), an antagonist of 5-HT1A receptors. The results showed that both doses of EB increased the percentage of entries and the percentage of time spent into the open arms, suggestive of an anxiolytic effect. The highest dose of the drug also increased the number of entries into the enclosed arm and locomotion in the open field, indicating a stimulatory motor effect. WAY 100635 antagonised the effect of estradiol in the elevated plus-maze and in the open-field. The results show that estrogen receptors of the MRN are implicated in the regulation of anxiety-related behaviour. The results also support claims that the effect of estrogen involves a change in 5-HT1A receptor function. (C) 2005 Elsevier B.V. All rights reserved.

Spin, charge, and orbital correlations in the one-dimensional t(2g)-orbital Hubbard model

We present the zero-temperature phase diagram of the one-dimensional t(2g)-orbital Hubbard model, obtained using the density-matrix renormalization group and Lanczos techniques. Emphasis is given to the case of the electron density n=5 corresponding to five electrons per site, while several other cases for electron densities between n=3 and 6 are also studied. At n=5, our results indicate a first-order transition between a paramagnetic (PM) insulator phase, with power-law slowly decaying correlations, and a fully polarized ferromagnetic (FM) state by tuning the Hund's coupling. The results also suggest a transition from the n=5 PM insulator phase to a metallic regime by changing the electron density, either via hole or electron doping. The behavior of the spin, charge, and orbital correlation functions in the FM and PM states are also described in the text and discussed. The robustness of these two states against varying parameters suggests that they may be of relevance in quasi-one-dimensional Co-oxide materials, or even in higher dimensional cobaltite systems as well.

Electromagnetic form factor of the pion in the space- and time-like regions within the front-form dynamics

The pion electromagnetic form factor is calculated in the space- and time-like regions from -10 (GeV/c)2 up to 10 (GeV/c)2, within a front-form model. The dressed photon vertex where a photon decays in a quark-antiquark pair is depicted generalizing the vector meson dominance ansatz, by means of the vector meson vertex functions. An important feature of our model is the description of the on-mass-shell vertex functions in the valence sector, for the pion and the vector mesons, through the front-form wave functions obtained within a realistic quark model. The theoretical results show an excellent agreement with the data in the space-like region, while in the time-like region the description is quite encouraging. © 2003 Elsevier B.V. All rights reserved.

Insertion of the superior head of the lateral pterigoid muscle in the human fetuses

The lateral pterygoid muscle, more specifically its superior head, as we know, is closely related to the temporomandibular joint (TMJ). Particularly in children, in contrast with what was observed in adults, these joints have been rarely studied, by the anatomic functional aspect, little knowing about its functions in the embryonic and fetal periods. We used, in this work, 12 fetuses ranging in age from 16 to 39 weeks of intrauterine life, where we observed that the superior head of the lateral pterygoid muscle is inserted in the disc and in the articular capsule, in all age groups studied, and also, that the fibers and the thickness of the articular disc is, as well as the articular capsule suffer modifications in accordance with the period of development. © 2007 Sociedad Chilena de Anatom•br>.