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31.
In this paper, we show that if G is a finite group with three supersolvable subgroups of pairwise relatively prime indices in G and G′ is nilpotent, then G is supersolvable. Let π(G) denote the set of prime divisors of |G| and max(π(G)) denote the largest prime divisor of |G|. We also establish that if G is a finite group such that G has three supersolvable subgroups H, K, and L whose indices in G are pairwise relatively prime,
q \nmid p-1{q \nmid p-1} where p = max(π(G)) and q = max(π(L)) with L a Hall p′-subgroup of G, then G is supersolvable. 相似文献
32.
Neil Marcus 《General Relativity and Gravitation》1990,22(8):873-881
An exact solution of Einstein gravity coupled to a dilaton field is found. The solution is conformally flat and is invariant under Lorentz transformations. The singularities and conformal structure of the metric are examined. 相似文献
33.
Neil A. Watling 《Communications in Mathematical Physics》1990,134(2):321-345
Monodromy fields on ?2 are a family of lattice fields in two dimensions which are a natural generalization of the two dimensional Ising field occurring in theC *-algebra approach to Statistical Mechanics. A criterion for the critical limit one point correlation of the monodromy field σa(M) at a ∈ ?2, $$\mathop {\lim }\limits_{s \uparrow 1} \left\langle {\sigma _a (M)} \right\rangle ,$$ is deduced for matrices M ∈ GL(p,?) having non-negative eigenvalues. Using this criterion non-identity 2×2 matrices are found with finite critical limit one point correlation. The general set ofp×p matrices with finite critical limit one point correlations is also considered and a conjecture for the critical limitn point correlations postulated. 相似文献
34.
Mathias Beiglbö ck Vitaly Bergelson Neil Hindman Dona Strauss 《Transactions of the American Mathematical Society》2008,360(2):819-847
There are several notions of largeness that make sense in any semigroup, and others such as the various kinds of density that make sense in sufficiently well-behaved semigroups including and . It was recently shown that sets in which are multiplicatively large must contain arbitrarily large geoarithmetic progressions, that is, sets of the form , as well as sets of the form . Consequently, given a finite partition of , one cell must contain such configurations. In the partition case we show that we can get substantially stronger conclusions. We establish some combined additive and multiplicative Ramsey theoretic consequences of known algebraic results in the semigroups and , derive some new algebraic results, and derive consequences of them involving geoarithmetic progressions. For example, we show that given any finite partition of there must be, for each , sets of the form together with , the arithmetic progression , and the geometric progression in one cell of the partition. More generally, we show that, if is a commutative semigroup and a partition regular family of finite subsets of , then for any finite partition of and any , there exist and such that is contained in a cell of the partition. Also, we show that for certain partition regular families and of subsets of , given any finite partition of some cell contains structures of the form for some .
35.
36.
We consider a problem related to Hadwiger's Conjecture. Let D=(d1, d2, …, dn) be a graphic sequence with 0?d1?d2?···?dn?n?1. Any simple graph G with D its degree sequence is called a realization of D. Let R[D] denote the set of all realizations of D. Define h(D)=max{h(G): G∈R[D]} and χ(D)=max{χ(G): G∈R[D]}, where h(G) and χ(G) are Hadwiger number and chromatic number of a graph G, respectively. Hadwiger's Conjecture implies that h(D)?χ(D). In this paper, we establish the above inequality for near regular degree sequences. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 175–183, 2010 相似文献
37.
38.
We report a study of the 4 A 2g →2 T 1g absorption band of Mn4+ in Cs2SiF6. The band shows several lines or groups of lines associated with transitions from the 4 A 2g ground state to the spin-orbit components (2 T 1g )Γ8 and (2 T 1g )Γ6 coupled to the three odd-parity vibrations v 6(t 2u ), v 4(t 1u ) and v 3(t 1u ). The absorptions associated with the (2 T 1g )Γ8 electronic state have structure whereas those associated with the (2 T 1g )Γ6 do not. It is shown that the structure is a consequence of splitting of the Γ8 × v vibronic multiplets by electron-vibration interaction. The intensity of the 4 A 2g →(2 T 1g )Γ i + vj vibronic transitions are expressed in terms of a small number of parameters; two parameters for v(t 1u ) modes and three for v(t 2u ) modes. Plausible but not good fits to the low temperature Zeeman data and vibronic splitting patterns are obtained. The excitation spectrum of the Cs2SiF6 : Mn4+ in the region of the 4 A 2g →2 Eg and 4 A 2g →2 T 1g is recorded using a c.w. dye laser. This reveals numerous weaker lines involving combinational modes and even-parity modes v5 (t 2g ), v 2(eg ) and v 1(a 1g ). Several interesting electron-vibrational effects are observed. These are illustrated and discussed qualitatively. 相似文献
39.
The reaction of 2,5-dimethylfuran (DMF) with H-atoms was studied using a potential energy surface calculated at the CBS-QB3 level of theory and master equation/RRKM modeling. Hydrogen abstraction by H-atom and hydrogen additions on DMF were considered. As the decomposition pathways of the initial adducts were unknown, a large number of decomposition routes was explored for these adducts. An important number of interconnected product channels were found and preliminary master equation calculations were performed to select the crucial wells and exit channels. The ipso substitution DMF + H → methylfuran (MF) + CH3 and the formation of 1,3-butadiene and acetyl radical (CH3CO) were found to be the major product channels in the addition process. The total calculated rate constant was found in good agreement with experimental data and is nearly pressure-independent. A small sensitivity to pressure was found for the computed branching ratios. At 1 bar, the yields of the two product channels of the addition process are maximal at 1100 K with computed branching ratios of 39% (MF + CH3) and 27% (1,3-C4H6 + CH3CO). Above 1300 K, hydrogen abstraction by H-atom becomes dominant and reaches a branching ratio of 56% at 2000 K. 相似文献
40.
The purpose of this paper is to introduce, for a finite Coxeter groupW, the mod 2 boundary operator on the space of all Coxeter matroids (also known asWP-matroids) forWandP, wherePvaries through all the proper standard parabolic subgroups ofW(Theorem 3 of the paper). A remarkably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter groupW(Theorem 1) yields a natural definition of the boundary of a Coxeter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroupsQiofP(Theorem 2). These results have very natural interpretations in the case of ordinary matroids and flag-matroids (Section 3). 相似文献