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1.
What is the largest number of edges in a graph of order n and girth g? For d-regular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular
graphs as well, yielding an affirmative answer to an old open problem ([4] p. 163, problem 10).
Received: June 27, 2000 Final version received: July 3, 2001 相似文献
2.
The nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K nm , which is directly related to the curvature of the nuclear matter equation of state, is a very important physical quantity in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. We review the current status of K nm and the experimental and theoretical methods used to determine the value of K nm from the excitation crosssections σ(E) and the transition strength distributions S(E) of compression modes in nuclei. In particular, we will consider the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) and provide a simple explanation to the long standing problem of the conflicting results obtained for K nm , deduced from experimental data on excitation cross sections for the ISGMR and data for the ISGDR. 相似文献
3.
We present some asymptotic results for the family of pausing time densities having the asymptotic (t) property(t) [t ln1+(t/T)]–1. In particular, we show that for this class of pausing time densities the mean-squared displacement r
2(t) is asymptotically proportional to ln(t/T), and the asymptotic distribution of the displacement has a negative exponential form. 相似文献
4.
We calculate the moments t
q
, whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t
q
~L
(q) asL, then we show that there is a phase transition atq=q
c
such that whenq<q
c
,(g)=0, and forq>q
c
, (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions. 相似文献
5.
Michal Shahar Haim Meshulam Shlomo Margel 《Journal of polymer science. Part A, Polymer chemistry》1986,24(2):203-213
Two sytrene derivatives formylstyrene and styrene sulfonylcholoride, were synthesized. Polymeric microspheres in diameters ranging from 0.1 to 2 μm were synthesized by polymerization of chlormoethylstyrene, formylstyrene, and styrene sulfonylcholoride in organic solvents, in the presence of appropriate surfactants. The kinetics of microsphere formation were studied. The molecular weight distribution of the products was determined by gel permeation chromatography. Conditions for binding various amino ligands to the microspheres were also established. 相似文献
6.
Cyclic voltammetry and electrolysis studies were carried out in dimethyl sulfoxide, diglyme and liquid ammonia. The depolarizers were diethyl fumarate, ethyl cinnamate, stilbene and anthracene. The reduction reactions were carried out in the presence of organic halides, phenol, acids and water. The rates of the reactions were measured. The main solvent effect was noticed with water which reacts 100 times faster in diglyme than in liquid ammonia or DMSO. The results of electrolytic experiments with two reactants simultaneously were compared with those predicted from the kinetic data. 相似文献
7.
Single bacterial cells, each expressing a different library variant, were compartmentalized in aqueous droplets of water-in-oil (w/o) emulsions, thus maintaining a linkage between a plasmid-borne gene, the encoded enzyme variant, and the fluorescent product this enzyme may generate. Conversion into a double, water-in-oil-in-water (w/o/w) emulsion enabled the sorting of these compartments by FACS, as well as the isolation of living bacteria cells and their enzyme-coding genes. We demonstrate the directed evolution of new enzyme variants by screening >10(7) serum paraoxonase (PON1) mutants, to yield 100-fold improvements in thiolactonase activity. In vitro compartmentalization (IVC) of single cells, each carrying >10(4) enzyme molecules, in a volume of <10 femtoliter (fl), enabled detection and selection despite the fast, spontaneous hydrolysis of the substrate, the very low initial thiolactonase activity of PON1, and the use of difusable fluorescent products. 相似文献
8.
Shlomo Havlin James E. Kiefer George H. Weiss Daniel Benavraham Yehoshua Glazer 《Journal of statistical physics》1985,41(3-4):489-496
We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l
dl
. For the suggested model, the corresponding exponent for the mass of the skeleton,d
l
s
, can be expressed in terms ofd
l
asd
l
s
= 1,d
l
d
l
c
= 2;d
l
s
= d
l
–1,d
1
d
l
c
= 2, which implies that the tree is finitely ramified ford
l
2 and infinitely ramified whend
l
2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees. 相似文献
9.
10.
Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability ton steps is O((
2n)–1/3), where =–ln(1–c), andc is the trap concentration. (2) The short time form for the survival probability is found to be exp[–a(c)n
1/2], wherea(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go liken
2/3for largen. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn. One such model is studied. 相似文献