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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.
3.
We prove that for every fixed k and ? ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2 ?. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k‐edge coloring of a sufficiently large Qn contains a monochromatic copy of H. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 196–208, 2006 相似文献
4.
M. Noga 《Czechoslovak Journal of Physics》1992,42(8):823-841
The representation of the electron field operators separating charge from spin and providing transmutations between spin and isospin quantum numbers has been derived for any dimension. In this representation the interaction term in the Hubbard model is expressed in a bilinear form of quasiparticle field operators. The quasiparticles are spinless fermions with the electron electric charge. The consequence of this representation is that superconductivity in the strong coupling Hubbard model is due to odd wave pairings of electrons.The author expresses his sincere gratitude to Professor S. Stenholm for discussions and for the warm hospitality at the Research Institute for Theoretical Physics, University of Helsinki where this work has began. He would especially like to thank Professor C. Cronström who played an important role in the early and final stages of this work. Professor Anderson is acknowledged for providing the author with two chapters of his book (not yet published) quoted in the Discussion. 相似文献
5.
Noga Alon Oded Goldreich Johan Hstad Ren Peralta 《Random Structures and Algorithms》1992,3(3):289-304
We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1)) (log log n + k/2 + log k + log 1/?), where ? is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ? < 1/(k log n)). An additional advantage of our constructions is their simplicity. 相似文献
6.
A. Hotzel P. Thirolf Ch. Ender D. Schwalm M. Mutterer P. Singer M. Klemens J. P. Theobald M. Hesse F. Gönnenwein H. v. d. Ploeg 《Zeitschrift für Physik A Hadrons and Nuclei》1987,356(3):299-308
The γ-ray spectrum of 252Cf(sf) was measured in the Darmstadt-Heidelberg Crystal Ball spectrometer, with a double ionization chamber mounted inside to detect the fission fragments. The measurement was aimed at a better understanding of an unusual component found in the high-energy region between 3 and 8 MeV, with fragment mass splits near symmetry. This component was proved to be predominantly emitted by the heavier fragment, to reach its highest intensity at a fragment mass split of 132:120, and to have an almost isotropic angular distribution. Calculations with the statistical code CASCADE could reproduce the main features. 相似文献
7.
Letm 3 andk 1 be two given integers. Asub-k-coloring of [n] = {1, 2,...,n} is an assignment of colors to the numbers of [n] in which each color is used at mostk times. Call an
arainbow set if no two of its elements have the same color. Thesub-k-Ramsey number sr(m, k) is defined as the minimumn such that every sub-k-coloring of [n] contains a rainbow arithmetic progression ofm terms. We prove that((k – 1)m
2/logmk) sr(m, k) O((k – 1)m
2 logmk) asm , and apply the same method to improve a previously known upper bound for a problem concerning mappings from [n] to [n] without fixed points.Research supported in part by Allon Fellowship and by a Bat Sheva de-Rothschild grant.Research supported in part by the AKA Research Fund of the Hungarian Academy of Sciences, grant No. 1-3-86-264. 相似文献
8.
Novel types of ground states associated with properties of heavy fermion systems are derived for crystals with covalent bonds generated by short-range exchange forces between valence electrons of atoms localized at lattice sites. It is shown that the short-range exchange forces can give rise to a narrow energy band in which electrons can exhibit an enormous effective mass. The same exchange forces provide the microscopic mechanism for spin-singlet pairing of electrons into Cooper pairs which are responsible for superconductivity in these systems. This superconductivity exhibits several different anisotropic superconducting states. The effective mass, Fermi energy, specific heat, Pauli susceptibility, critical temperatures and critical magnetic field of heavy fermion systems are calculated and compared with experimental data.The authors thank Dr. . Jano for discussions. 相似文献
9.
A regressive function (also called a regression or contractive mapping) on a partial order P is a function mapping P to itself such that (x)x. A monotone k-chain for is a k-chain on which is order-preserving; i.e., a chain x
1<...ksuch that (x
1)...(xk). Let P
nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P
nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x
t(x,j–1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) < f(K) <t( + k, k) , where k 0 as k. Alternatively, the largest k such that every regression on P
nis guaranteed to have a monotone k-chain lies between lg*(n) and lg*(n)–2, inclusive, where lg*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element. 相似文献
10.
Gertraud Chiste Helmut Egg Klemens Kraus Elisabeth Pipitz Elisabeth Spanyar 《Monatshefte für Chemie / Chemical Monthly》1991,122(6-7):537-544
Summary A new method for the synthesis of 1,2-diaryl-1,2-dihydro-5-methyl-3H-pyrazol-3-ones3 and 4-acetyl-1,2-diaryl-1,2-dihydro-5-methyl-3H-pyrazol-3-ones5 is presented. The reaction of 4,4-disubstituted 1,2-diarylhydrazines1 with acetic anhydride in the presence of an equimolar amount of 4-(dimethylamino)pyridine leads to mixtures of the corresponding acetyl derivatives2 and3. Under the same conditions, 2,2-disubstituted 1,2-diarylhydrazines yield mixtures of3 and5.
4-(Dimethylamino)pyridin-katalysierte Reaktion von 1,2-Diarylhydrazinen mit Essigsäureanhydrid
Zusammenfassung Eine neue Methode zur Synthese von 1,2-Diaryl-1,2-dihydro-5-methyl-3H-pyrazol-3-onen3 und 4-Acetyl-1,2-diaryl-1,2-dihydro-5-methyl-3H-pyrazol-3-onen5 wird beschrieben. Die Reaktion von 4,4-disubstituierten 1,2-Diaryl-hydrazinen1 mit Essigsäureanhydrid führt in Gegenwart eines Äquivalentes 4-(Dimethylamino)pyridin zu Gemischen der entsprechenden Acetylderivate2 und3. Unter den gleichen Bedingungen werden aus 2,2-disubstituierten 1,2-Diarylhydrazinen Gemische aus3 und5 erhalten.相似文献