34 research outputs found
Polynomial Bounds for Oscillation of Solutions of Fuchsian Systems
We study the problem of placing effective upper bounds for the number of
zeros of solutions of Fuchsian systems on the Riemann sphere. The principal
result is an explicit (non-uniform) upper bound, polynomially growing on the
frontier of the class of Fuchsian systems of given dimension n having m
singular points. As a function of n,m, this bound turns out to be double
exponential in the precise sense explained in the paper. As a corollary, we
obtain a solution of the so called restricted infinitesimal Hilbert 16th
problem, an explicit upper bound for the number of isolated zeros of Abelian
integrals which is polynomially growing as the Hamiltonian tends to the
degeneracy locus. This improves the exponential bounds recently established by
A. Glutsyuk and Yu. Ilyashenko.Comment: Will appear in Annales de l'institut Fourier vol. 60 (2010
Bounded decomposition in the Brieskorn lattice and Pfaffian Picard--Fuchs systems for Abelian integrals
We suggest an algorithm for derivation of the Picard--Fuchs system of
Pfaffian equations for Abelian integrals corresponding to semiquasihomogeneous
Hamiltonians. It is based on an effective decomposition of polynomial forms in
the Brieskorn lattice. The construction allows for an explicit upper bound on
the norms of the polynomial coefficients, an important ingredient in studying
zeros of these integrals.Comment: 17 pages in LaTeX2
Details of large-panel buildings seismic analysis
The normative requirements of different European countries, USA, CIS, Canada, etc. codes on ensuring of buildings and structures safety at earthquakes are analyzed. The methodology based on non-elastic response spectrum of buildings and allows taking into account non-linear behaviour of structure are proposed in elaboration of Eurocode 8 requirements. The report provides the calculation examples of non-linear displacements of framed and frameless concrete buildings with application of that methodology
Oscillation of linear ordinary differential equations: on a theorem by A. Grigoriev
We give a simplified proof and an improvement of a recent theorem by A.
Grigoriev, placing an upper bound for the number of roots of linear
combinations of solutions to systems of linear equations with polynomial or
rational coefficients.Comment: 16 page
Simulation of fuel injection through a nozzle having different position of the spray holes
In the article, a method of hydraulic calculation of working process of a diesel fuel feed system having a nozzle with different positions of its spray holes was investigated. A research of diesel engine injector nozzle design which had two groups of holes was carried out. Entering edges of the first group with the coefficient of flow μhl were located in the sack volume and entering edges of the second group (coefficient of flow μhu) – on the locking taper surface of the nozzle body. The coefficients of flow μhl and μhu differ considerably and depend on the valve needle position. This enables to distribute rationally the injection quantity by injection holes taking into account operating conditions of the diesel engine and hence – by the combustion chamber zones