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1.
具Hardy-Sobolev临界指数的奇异椭圆方程多解的存在性 总被引:1,自引:0,他引:1
运用变分方法研究了下面问题-Δpu=μupx(s)s-2u f(x,u),x∈Ω,u=0,x∈Ω,多重解的存在性,其中Ω是一个具有光滑边界的有界区域. 相似文献
2.
P. E. Cladis 《Journal of statistical physics》1991,62(5-6):899-925
We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems. 相似文献
3.
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
4.
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
5.
K. S. Birdi 《Colloid and polymer science》1997,275(6):561-566
The surface tension versus temperature data of homologous series of n-alkanes and n-alkenes is analyzed. Critical temperatures are shown to be predicted from these data, with a very high precision, after some
corrections are made. The corrections are shown to arise from the effect of the critical pressure on the extrapolated data
to surface tension approaching zero.
Received: 29 October 1996 Accepted: 13 December 1996 相似文献
6.
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
7.
周焕松 《数学物理学报(B辑英文版)》1998,(2)
1IntroductionIntillspaper,weare(follccrlledwitlltileexistellccofPositly(tsollltiollsoftilefollowillgnonhonlogelleousellipticProblclll:whereg(x)EL'(R'),g(:v)Z0alldg(x)t0,f(x,t)=h(x,t).hi=withb>0,h(x,t)EC(R=xR,R)alldtilefollowing(CI)-(C3)11old:(CI)sliphillM0.linljfl- x,h(T,t)(t--if-=011llif'orllllyforxeR2.hill}t:l-:,t)(axle(~ltJ')= lx,11lliforllllyl'Ora:6RZ.ltl~la(C3)ThereexistM>0,aE(0,1]sucllthatFOllowing[1,5],wesaythatf(x,t)=h(x,f… 相似文献
8.
E. Hatta H. Hosoi H. Akiyama T. Ishii K. Mukasa 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,2(3):347-349
We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface
by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes
itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is
caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure.
The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There
are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions.
Received: 8 July 1997 / Accepted: 4 November 1997 相似文献
9.
10.
Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions. 相似文献