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1.
2.
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual. 相似文献
3.
Nikolaos V. Tsekos Michael Garwood Kmil Ugurbil 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2002,156(2):187
A new technique is presented for generating myocardial tagging using the signal intensity minima of the transition zones between the bands of 0° and 360° rotations, induced by a tandem of two adiabatic delays alternating with nutations for tailored excitation (DANTE) inversion sequences. With this approach, the underlying matrix corresponds to magnetization that has experienced 0° or 360° rotations. The DANTE sequences were implemented from adiabatic parent pulses for insensitivity of the underlying matrix to B1 inhomogeneity. The performance of the proposed tagging technique is demonstrated theoretically with computer simulations and experimentally on phantom and on the canine heart, using a surface coil for both RF transmission and signal reception. The simulations and the experimental data demonstrated uniform grid contrast and sharp tagging profiles over a twofold variation of the B1 field magnitude. 相似文献
4.
David B. Wilson 《Random Structures and Algorithms》2002,21(2):182-195
There has been much recent interest in the satisfiability of random Boolean formulas. A random k‐SAT formula is the conjunction of m random clauses, each of which is the disjunction of k literals (a variable or its negation). It is known that when the number of variables n is large, there is a sharp transition from satisfiability to unsatisfiability; in the case of 2‐SAT this happens when m/n → 1, for 3‐SAT the critical ratio is thought to be m/n ≈ 4.2. The sharpness of this transition is characterized by a critical exponent, sometimes called ν = νk (the smaller the value of ν the sharper the transition). Experiments have suggested that ν3 = 1.5 ± 0.1. ν4 = 1.25 ± 0.05, ν5 = 1.1 ± 0.05, ν6 = 1.05 ± 0.05, and heuristics have suggested that νk → 1 as k → ∞. We give here a simple proof that each of these exponents is at least 2 (provided the exponent is well defined). This result holds for each of the three standard ensembles of random k‐SAT formulas: m clauses selected uniformly at random without replacement, m clauses selected uniformly at random with replacement, and each clause selected with probability p independent of the other clauses. We also obtain similar results for q‐colorability and the appearance of a q‐core in a random graph. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 182–195, 2002 相似文献
5.
The binding energy of excitonium negative ion for ground 1S-state in bulk conductors: Ge, Si, CdSe and for green and yellow lines of Cu2O in hyperspherical coordinate method are found. Angular and radial correlations between electrons are taken into account by the channel functions, which are the eigen-functions of operator on the surface of sphere in six-dimensional sphere. The calculation of energies have been done using the adiabatic and Born-Oppenheimer approximations. In Born-Oppenheimer approximation is enough to give a binding energy with only 1.2% error, in adiabatic approximation this error drops to 0.7 %. 相似文献
6.
袁文俊 《数学物理学报(A辑)》2003,23(2):224-230
该文考虑具有控制系数 A\-0 和系数仅有有限个极点的高阶线性齐次微分方程(1.1)。得到了一个复振荡结果,该结果是J. K. Langley[11]等作者在整系数下相应结果的推广。 相似文献
7.
稀疏过程在破产问题中的应用 总被引:5,自引:0,他引:5
本讨论一类人寿保险的风险过程,其中保单到达服从齐次Poisson过程。而描述退保及索赔发生的计数过程分别为这一过程的q-稀疏与p-稀疏.对此模型给出其破产概率的具体上界,并与其它一类风险模型进行比较. 相似文献
8.
Anatoliy Samoilenko Manuel Pinto Sergei Trofimchuk 《Proceedings of the American Mathematical Society》2005,133(1):145-154
We apply the Krylov and Bogolyubov asymptotic integration procedure to asymptotically autonomous systems. First, we consider linear systems with quasi-periodic coefficient matrix multiplied by a scalar factor vanishing at infinity. Next, we study the asymptotically autonomous Van-der-Pol oscillator.
9.
Franois Lavaud Michel Fontanille Yves Gnanou 《Journal of polymer science. Part A, Polymer chemistry》2004,42(19):4964-4975
Studies on the anionic polymerization of methyl methacrylate in tetrahydrofuran and in the presence of sparteine have revealed a beneficial effect due to this additive, resulting in a decrease in the extent of termination. Better control of the definition of the polymers formed can thus be achieved in the presence of this additive. On the other hand, macromolecular engineering requires a range of active species concentrations lower than 10?3 mol L?1 and particularly the synthesis of polymers of high molar masses. For a better understanding of the mechanism of chain growth under such concentration conditions, the kinetics of polymerization have been investigated with a technique based on adiabatic calorimetry. Sparteine has been found to lack sufficient cation‐binding power to prevent the propagating enolate ion pairs from aggregating. The rate constant of propagation of nonaggregated species has been estimated, as well as the aggregation constant of equilibrium. For very low initiator concentrations, termination reactions have been shown to profoundly alter the control of the polymerization and to prevent a quantitative monomer conversion. Theoretical maximal conversions have been calculated from kinetic data and compare well with the experimental values. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4964–4975, 2004 相似文献
10.
A model of two interacting (chemically different) linear polymer chains is solved exactly using the real-space renormalization
group transformation on a family of Sierpinski gasket type fractals and on a truncated 4-simplex lattice. The members of the
family of the Sierpinski gasket-type fractals are characterized by an integer scale factorb which runs from 2 to ∞. The Hausdorff dimensiond
F of these fractals tends to 2 from below asb → ∞. We calculate the contact exponenty for the transition from the State of segregation to a State in which the two chains are entangled forb = 2-5. Using arguments based on the finite-size scaling theory, we show that forb→∞, y = 2 - v(b) d
F, wherev is the end-toend distance exponent of a chain. For a truncated 4-simplex lattice it is shown that the system of two chains
either remains in a State in which these chains are intermingled in such a way that they cannot be told apart, in the sense
that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system, or in a State
in which they are either zipped or entangled. We show the region of existence of these different phases separated by tricritical
lines. The value of the contact exponenty is calculated at the tricritical points. 相似文献