58,517 research outputs found
Spectral flow and bifurcation of critical points of strongly indefinite functionals I
No full textSpectral flow is a well-known homotopy invariant of paths of self-adjoint Fredholm operators. We describe here a new construction of this invariant and prove the following theorem: Let f : I × U -> R be a C2 function defined on the product of a real interval I = [a, b] with a neighborhood U of the origin of a real separable Hilbert space H and such that for each t in I, 0 is a critical point of the functional f (t, ·). Assume that the Hessian L of f at 0 is Fredholm and moreover that L_a and L_b are nonsingular. If the spectral flow of the path L does not vanish, then the interval I contains at least one bifurcation point from the trivial branch for solutions of the equation Grad f (t, x) = 0. Equivalently: every neighborhood of I × {0} contains points of the form (t,x) where x is a critical point of f_t different from 0
Spectral flow and bifurcation of critical points of strongly indefinite functionals. II. Bifurcation of periodic orbits of Hamiltonian systems
No full textOur main results here are as follows: Let X* be a family of 2?-periodic Hamiltonian vectorfields that depend smoothly on a real parameter * in [a, b] and has a known, trivial, branch s* of 2?-periodic solutions. Let P* be the Poincare map of the linearization of X* at s* . If the ConleyZehnder index of the path P* does not vanish, then any neighborhood of the trivial branch of periodic solutions contains 2?-periodic solutions not on the branch. Moreover, if each solution s* is constant and each linearization A* of X* at s* is time independent, then bifurcation of 2?-periodic orbits from the branch of equilibria arises whenever i(Ab){i(Ab), where i(A) is the index of the linear Hamiltonian system Ju*=Au
Differential Acquisition of m-Sequences using Recursive Soft Sequential Estimation
No full textIn this contribution a novel sequential estimation method is proposed for the acquisition of -sequences. This sequential estimation method exploits the principle of iterative soft-in-soft-out (SISO) decoding for enhancing the acquisition performance, and that of differential pre-processing for the sake of achieving an enhanced acquisition performance, when communicating over various communication environments. Hence the advocated acquisition arrangement is referred to as the Differential Recursive Soft Sequential Estimation (DRSSE) acquisition scheme. The DRSSE acquisition scheme exhibits a low complexity, which is similar to that of an -sequence generator, while achieving an acquisition time that is linearly dependent on the number of stages in the -sequence generator. A low acquisition time is achieved with the advent of the property that the proposed DRSSE scheme is capable of determining the real-time reliabilities associated with the decision concerning a set of, say , consecutive chips. This set of consecutive chips constitutes the sufficient initial condition for enabling the local -sequence generator to produce a synchronized local despreading -sequence replica. Owing to these attractive characteristics, the DRSSE acquisition scheme constitutes a promising initial synchronization scheme for acquisition of long -sequences, when communicating over various propagation environments
∑_(l+m=k,l,m≥0) ((α+l-1)¦l) ((β+m-1)¦m)=((α+β+k-1)¦k) and its application to negative binomial distribution
No full textWe prove here the following equation: ∑_(l+m=k,l,m≥0) ((α+l-1)¦l) ((β+m-1)¦m)=((α+β+k-1)¦k) and give its application to prove the reproductive property of the negative binomial distribution.
These finite sum equation involving binomial coefficients and proof of the reproductive property are not known as far as the author knows.論文(Article)departmental bulletin pape
De Maiestate / Praeside M. Jacobo Thomasio, Moralis Philosoph. P. P., publice disputabit Johannes Dunte, R. L. Author & Respon: ad diem 9. Septembr. H L. Q. C.
No full textDE MAIESTATE / PRAESIDE M. JACOBO THOMASIO, MORALIS PHILOSOPH. P. P., PUBLICE DISPUTABIT JOHANNES DUNTE, R. L. AUTHOR & RESPON: AD DIEM 9. SEPTEMBR. H L. Q. C.
De Maiestate / Praeside M. Jacobo Thomasio, Moralis Philosoph. P. P., publice disputabit Johannes Dunte, R. L. Author & Respon: ad diem 9. Septembr. H L. Q. C. (1)
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Beiträge (21
Sulfate reduction in sulfuric material after re-flooding: effectiveness of organic carbon addition and pH increase depends on soil properties
No full textAbstract not availableChaolei Yuana, Rob Fitzpatrick, Luke M. Mosley, Petra Marschne
Changes in acidity and metal geochemistry in soils, groundwater, drain and river water in the Lower Murray River after a severe drought
No full textAbstract not availableLuke M. Mosley, Rob W. Fitzpatrick, David Palmer, Emily Leyden, Paul Shan
Amount of organic matter required to induce sulfate reduction in sulfuric material after re-flooding is affected by soil nitrate concentration
No full textAbstract not availableChaolei Yuan, Luke M. Mosley, Rob Fitzpatrick, Petra Marschne
Addition of organic material to sulfuric soil can reduce leaching of protons, iron and aluminium
No full textAbstract not availableTan Dang, Luke M. Mosley, Rob Fitzpatrick, Petra Marschne
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