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41.
Summary We consider the Cauchy problem for the generalized porous medium equation ut=(u) where u=u(x, t), xRn and t>0, and the initial datum u(x, 0) is assumed to be nonnegative, integrable mid to nave compact support. The nonlinearity (u) is a C1 function defined for uO which grows like a power of u. Our assumptions generalize the porous medium case, (u)=um, m>1, and also include the equation of the Marshak waves. This problem has finite speed of propagation. We estimate the rate of growth of the support of the solution with precise estimates for t 0 and t. Our main result deals with the regularity of the solutions. We show that after a certain time t0 the pressure, defined by v=(u), with (u)=(u)/u and (0)=0, is a Lipschitz-continuous function of x and t and the interface is a Lipschitz-continuous surface in RN+1; the solution u is Hölder continuous for all times t> 0.Both authors partially supported by CAICYT, Project 2805-83. The second author also supported by USA-Spain Joint Research Grant CCB-8402023. 相似文献
42.
Pablo A. Ferrari 《Probability Theory and Related Fields》1992,91(1):81-101
Summary The one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the Burgers equation. We study the process with rates of jumpsp>q to the right and left, respectively, and with initial product measure with densities < to the left and right of the origin, respectively (with shock initial conditions). We prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times. If this particle is added at another site, then it describes the behavior of a characteristic of the Burgers equation. For vanishing left density (=0) we prove, in the scale t1/2, that the position of the shock at timet depends only on the initial configuration in a region depending ont. The proofs are based on laws of large numbers for the second class particle. 相似文献
43.
Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad 《Numerical Algorithms》1992,3(1):91-104
Leta 1,...,a p be distinct points in the finite complex plane ?, such that |a j|>1,j=1,..., p and let \(b_j = 1/\bar \alpha _j ,\) j=1,..., p. Let μ0, μ π (j) , ν π (j) j=1,..., p;n=1, 2,... be given complex numbers. We consider the following moment problem. Find a distribution ψ on [?π, π], with infinitely many points of increase, such that $$\begin{array}{l} \int_{ - \pi }^\pi {d\psi (\theta ) = \mu _0 ,} \\ \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - a_j )^n }} = \mu _n^{(j)} ,} \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - b_j )^n }} = v_n^{(j)} ,} j = 1,...,p;n = 1,2,.... \\ \end{array}$$ It will be shown that this problem has a unique solution if the moments generate a positive-definite Hermitian inner product on the linear space of rational functions with no poles in the extended complex plane ?* outside {a 1,...,a p,b 1,...,b p}. 相似文献
44.
We have studied the efficiency of parallel tempering simulations for a variety of systems including a coarse-grained protein, an atomistic model polypeptide, and the Lennard-Jones fluid. A scheme is proposed for the optimal allocation of temperatures in these simulations. The method is compared to the existing empirical approaches used for this purpose. Accuracy associated with the computed thermodynamic quantities such as specific heat is also computed and their dependence on the trial-exchange acceptance rate is reported. 相似文献
45.
Mauleón P Núñez AA Alonso I Carretero JC 《Chemistry (Weinheim an der Bergstrasse, Germany)》2003,9(7):1511-1520
Unlike traditionally used acyclic 1,2-disubstituted alkenes, the reaction of alpha,beta-unsaturated phenyl sulfones with aryl iodides under Heck reaction conditions (Pd(OAc)(2) as catalyst, Ag(2)CO(3) as base in DMF at 120 (0)C) takes place mainly by a cascade process, involving one unit of the alkene and three units of the aryl iodide, to afford a substituted 9-phenylsulfonyl-9,10-dihydrophenanthrene. The dominant formation of this 3:1 coupling product, instead of the Heck trisubstituted olefin, shows that aromatic C-H bond activation processes can compete with the usually fast syn beta-hydrogen elimination step in the Heck arylation of an acyclic olefin. The structural scope of this palladium-catalyzed cascade arylation of alpha,beta-unsaturated sulfones has proved to be wide with regard to substitution at the beta-position (alkyl, aryl, or alkenyl substitution), substitution at the sulfone unit (alkyl or phenyl sulfones), and configuration at the CdoublebondC bond (trans or cis). Moreover, although less favored than in the case of the arylation of alpha,beta-unsaturated sulfones, similarly substituted 9,10-dihydrophenanthrenes have also been obtained in the case of alpha,beta-unsaturated phosphine oxides and alpha,beta-unsaturated phosphonate esters. A Pd(0)-Pd(II)-Pd(IV) mechanistic pathway involving the successive formation of highly electrophilic sigma-alkylpalladium intermediates and palladacycles is proposed for this multicomponent arylation. 相似文献
46.
Yin J Aviles P Lee W Ly C Guillen MJ Munt S Cuevas C Faircloth G 《Rapid communications in mass spectrometry : RCM》2005,19(5):689-695
A rapid and sensitive liquid chromatography/tandem mass spectrometry (LC/MS/MS) assay was developed and validated to quantify a novel antineoplastic agent, PM00104, in mouse, rat, dog, and human plasma. The method was validated to demonstrate the specificity, limit of quantification (LOQ), accuracy, and precision of measurements. The calibration range for PM00104 was established using PM00104 standards from 0.01-5.0 ng/mL in blank plasma. The selected reaction monitoring (SRM), based on the m/z 692.2 --> 218.2 transition, was specific for PM00104, and that based on the m/z 697.2 --> 218.2 transition was specific for PM00104 ((13)C(2),(2)H(3)) (the internal standard, IS); no endogenous materials interfered with the analysis of PM00104 and IS from blank plasma. The assay was linear over the concentration range 0.01-5.0 ng/mL. The correlation coefficients for the calibration curves ranged from 0.9981-0.9999. The mean intra-day and inter-day accuracies for all calibration standards (n = 8) ranged from 97-105% (< or =5% bias) in human plasma, and the mean inter-day precision for all calibration standards was less than 8.5%. The mean intra- and inter-day assay accuracy for all quality control (QC) replicates in human plasma (n = 9), determined at each QC level throughout the validated runs, ranged from 96-112% (< or =12% bias) and from 102-105% (< or =5% bias), respectively. The mean intra- and inter-day assay precision was less than 15.0 and 11.8% for all QC levels, respectively. For the QC samples prepared in animal species plasma, the %CV values of the assays ranged from 1.8-8.8% in mouse plasma, from 3.7-13.8% in rat plasma, and from 3.0-7.2% in dog plasma. The assay accuracies ranged from 92-102% (< or =8% bias) for all QC levels prepared in mouse plasma; ranged from 93-106% (< or =7% bias) in rat plasma; and ranged from 95-114% (< or =14% bias) in dog plasma. The assay has been used to support preclinical pharmacokinetic and toxicokinetic studies and is currently used to measure PM00104 plasma concentrations to support clinical trials. 相似文献
47.
Manuel Gadella Sebastin Fortín Juan Pablo Jorge Marcelo Losada 《Entropy (Basel, Switzerland)》2022,24(6)
We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo. 相似文献
48.
Pablo Spiga 《Journal of Algebraic Combinatorics》2016,43(3):715-734
We determine all finite primitive groups that are automorphism groups of edge-transitive hypergraphs. This gives an answer to a problem proposed by Babai and Cameron. 相似文献
49.
50.