Modules of Abelian integrals and Picard-Fuchs systems

We give a simple proof of an isomorphism between the two $\mathbb{C}[t]$-modules: the module of relative cohomologies $\Lambda^2/dH\land \Lambda^1$ and the module of Abelian integrals corresponding to a regular at infinity polynomial $H$ in two variables. Using this isomorphism, we prove existence and deduce some properties of the corresponding Picard-Fuchs system.Comment: A separate section discusses Fuchsian properties of the Picard-Fuchs system, Morse condition exterminated. Few errors were correcte

On the Number of Zeros of Abelian Integrals: A Constructive Solution of the Infinitesimal Hilbert Sixteenth Problem

We prove that the number of limit cycles generated by a small non-conservative perturbation of a Hamiltonian polynomial vector field on the plane, is bounded by a double exponential of the degree of the fields. This solves the long-standing tangential Hilbert 16th problem. The proof uses only the fact that Abelian integrals of a given degree are horizontal sections of a regular flat meromorphic connection (Gauss-Manin connection) with a quasiunipotent monodromy group.Comment: Final revisio

On a computer-aided approach to the computation of Abelian integrals

An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is applied to the study of bifurcations of limit cycles arising from a cubic perturbation of an elliptic Hamiltonian of degree four

Algebraic and analytical tools for the study of the period function

In this paper we consider analytic planar differential systems having a first integral of the form H(x, y) = A(x) + B(x)y + C(x)y2 and an integrating factor κ(x) not depending on y. Our aim is to provide tools to study the period function of the centers of this type of differential system and to this end we prove three results. Theorem A gives a characterization of isochronicity, a criterion to bound the number of critical periods and a necessary condition for the period function to be monotone. Theorem B is intended for being applied in combination with Theorem A in an algebraic setting that we shall specify. Finally, Theorem C is devoted to study the number of critical periods bifurcating from the period annulus of an isochrone perturbed linearly inside a family of centers. Four different applications are given to illustrate these results

Search for CP Violation in the Decay Z -> b (b bar) g

About three million hadronic decays of the Z collected by ALEPH in the years 1991-1994 are used to search for anomalous CP violation beyond the Standard Model in the decay Z -> b \bar{b} g. The study is performed by analyzing angular correlations between the two quarks and the gluon in three-jet events and by measuring the differential two-jet rate. No signal of CP violation is found. For the combinations of anomalous CP violating couplings, ${\hat{h}}_b = {\hat{h}}_{Ab}g_{Vb}-{\hat{h}}_{Vb}g_{Ab}$ and $h^{\ast}_b = \sqrt{\hat{h}_{Vb}^{2}+\hat{h}_{Ab}^{2}}$, limits of \hat{h}_b < 0.59$and$h^{\ast}_{b} < 3.02$ are given at 95\% CL.Comment: 8 pages, 1 postscript figure, uses here.sty, epsfig.st

Search for the glueball candidates f0(1500) and fJ(1710) in gamma gamma collisions

Data taken with the ALEPH detector at LEP1 have been used to search for gamma gamma production of the glueball candidates f0(1500) and fJ(1710) via their decay to pi+pi-. No signal is observed and upper limits to the product of gamma gamma width and pi+pi- branching ratio of the f0(1500) and the fJ(1710) have been measured to be Gamma_(gamma gamma -> f0(1500)). BR(f0(1500)->pi+pi-) < 0.31 keV and Gamma_(gamma gamma -> fJ(1710)). BR(fJ(1710)->pi+pi-) < 0.55 keV at 95% confidence level.Comment: 10 pages, 3 figure

Structural and ultrastructural alterations in human olfactory pathways and possible associations with herpesvirus 6 infection

Publisher Copyright: © 2017 Skuja et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Structural and ultrastructural alterations in human olfactory pathways and putative associations with human herpesvirus 6 (HHV-6) infection were studied. The olfactory bulb/tract samples from 20 subjects with an unspecified encephalopathy determined by pathomorphological examination of the brain autopsy, 17 healthy age-matched and 16 younger controls were used. HHV-6 DNA was detected in 60, 29, and 19% of cases in these groups, respectively. In the whole encephalopathy group, significantly more HHV-6 positive neurons and oligodendrocytes were found in the gray matter, whereas, significantly more HHV-6 positive astrocytes, oligodendrocytes, microglia/macrophages and endothelial cells were found in the white matter. Additionally, significantly more HHV-6 positive astrocytes and, in particular, oligodendrocytes were found in the white matter when compared to the gray matter. Furthermore, when only HHV-6 PCR+ encephalopathy cases were studied, we observed similar but stronger associations between HHV-6 positive oligodendrocytes and CD68 positive cells in the white matter. Cellular alterations were additionally evidenced by anti-S100 immunostaining, demonstrating a significantly higher number of S100 positive cells in the gray matter of the whole encephalopathy group when compared to the young controls, and in the white matter when compared to both control groups. In spite the decreased S100 expression in the PCR+ encephalopathy group when compared to PCR- cases and controls, groups demonstrated significantly higher number of S100 positive cells in the white compared to the gray matter. Ultrastructural changes confirming the damage of myelin included irregularity of membranes and ballooning of paranodal loops. This study shows that among the cellular targets of the nervous system, HHV-6 most severely affects oligodendrocytes and the myelin made by them.publishersversionPeer reviewe

Observation of charmless hadronic B decays

Four candidates for charmless hadronic B decay are observed in a data sample of four million hadronic Z decays recorded by the ALEPH detector at LEP. The probability that these events come from background sources is estimated to be less than 10(-6). The average branching of weakly decaying B hadrons (a mixture of B-d(0), B-s(0) and Lambda(b) weighted by their production The average branching ratio of weakly decaying B hadrons (a mixture of B-d(0) cross sections and lifetimes, here denoted B) into two long-lived charged hadrons (pions, kaons or protons) is measured to be Br(B-->h(+)h(-))=(1.7(-0.7)(+1.0)+/-0.2)x10(-5). The relative branching fraction Br(B-d(s)(0)-->pi(+)pi(-)(K-))/Br(B-d(s)(0)-->h(+)h(-)) is measured to be 1.0(-0.3-0.1)(+0.0+0.0). In addition, branching ratio upper limits are obtained for a variety of exclusive charmless hadronic two-body decays of B hadrons