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In this paper we consider a general action principle for mechanics written by means of the elements of a Lie algebra. We study the physical reasons why we have to choose precisely a Lie algebra to write the action principle. By means of such an action principle we work out the equations of motion and a technique to evaluate perturbations in a general mechanics that is equivalent to a general interaction picture. Classical or quantum mechanics come out as particular cases when we make realizat...
In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m - 1) time derivatives of the Hamiltonian at the initial and final time insta...
In this paper we study under which circumstances there exists a general change of gross variables that transforms any FokkerPlanck equation into another of the OrnsteinUhlenbeck class that, therefore, has an exact solution. We find that any FokkerPlanck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo a...
In this paper we give some ideas that can be useful to solve SchrÃ¶dinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.
This paper discusses the interest of binary partition
trees as a region-oriented image representation. Binary partition
trees concentrate in a compact and structured representation a set
of meaningful regions that can be extracted from an image. They
offer a multiscale representation of the image and define a translation
invariant 2-connectivity rule among regions. As shown in this
paper, this representation can be used for a large number of processing
goals such as filte...
Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.
Connected operators [4] and Region Growing [2] algorithms have been created in different context and applications. However, they all are based on the same fundamental merging process. This paper discusses the basic issues of the merging algorithm and presents different applications ranging from simple frame segmentation to video sequence analysis.
Peer Reviewed
In this paper we present, in a unified way, several results af uniform
approximation for real-valued continuous and uniformly continuous
functions an a space X. We obtain all of them by applying a general
method af proof that involves certain kind of cauntable covers af
X, the so-called 2-finite covers. For instance, if X is endowed with
the weak uniformity given by a vector lattice $\mathfrak{F}$ of real-valued
functions an X containing all the real constant functions then,...
CERN-LEP. Measurement of the cross section for Z0 Z0 production in E+ E- collisions at centre of mass energies from 192 to 209 GeV using a data sample of total integrated luminosity 452 pb-1.
CERN-LEP. Measurement of the fragmentation function of b quarks into B mesons at the Z0 energy. The data consisting of about 4M hadronic Z0 decays were taken during the 1991 - 1995 running period.. The mean value of X for the Weakly Decaying B-meson data is found to be 0.716 +- 0.006(stat) +- 0.006(syst) and for the Leading B-meson data 0.736 +- 0.006(stat) +- 0.006(syst).
CERN-LEP. Measurement of the cross section for exclusive production of pion and kaon pairs in two photon collisions. The data come from the LEP running periods between 1992 and 2000 with centre of mass energies between 88 and 209 GeV. The total integrated luminosity is 837.5 pb-1.
CERN-LEP. Measurement of the multiplicities and cross sections for the inclusive production of PI0, ETA, ETAPRIME, K0S and LAMBDA mesons in two- and three-jet events from hadronic Z0 decays produced the E+ E- collisions. The analysis is based on 3.7M hadronic events.
CERN-LEP. Measurement of event shape variable distributions and charged particle spectra in E+ E- collisions at c.m. energies from 91 to 209 GeV. The previously published data at 91.2 GeV and 133 GeV have been re-processed and the higher energy data are presented here for the first time. The total data sample has an integrated luminosity of 730 pb-1.. Numerical values supplied by Hasko Stenzel.. This part contains the multiplicities and charged particle distributions.
CERN-LEP. Measurement...
CERN-LEP. Measurement of the production of charmed D and D* mesons using the full data sample of LEPI data collected between 1991 and 1995. The fractional energy spectrum of D*+- mesons is presented and the probability of a c-quark to hadronize into a D*+- is found to be 0.233 +- 0.010 +- 0.011. Using the D*+- energy and the hemisphere mass imbalance distributions the fraction of Z0 decays inwhich a gluon splits into a ccbar pair is found to be (3.23 +- 0.48 +- 0.53) PC T. The ratio ofVector/...
CERN-LEP. Measurement of the fraction of hadronic Z0 decays (R_c) with charm quark pairs using a sample of 3.7 million hadronic decays collected between 1992 and 1995. R is determined by three methods, one using the inclusive electron spectrum and the other two using a double-tagging technique which is independent of the charm tagging efficiency. The average value is quoted here.
CERN-LEP. A measurement of the spectral functions of non-strange $\tau$ vector current final states is presented, using 124358 $\tau$ pairs recorded by the ALEPH detector at LEP during the years 1991 to 1994. The spectral functions of the dominant two- and four-pion $\tau$ decay channels are compared to published results of $e^+e^-$ annihilation experiments via isospin rotation. A combined fit of the pion form factor from $\tau$ decays and $e^+e^-$ data is performed using different parame...