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41.
卢广存 《数学物理学报(B辑英文版)》2002,22(4)
In this note a symplectic capacity of Hofer-Zehnder type that is only invariant under C1-symplectomorphisms is defined and all computation formulae for Hofer-Zehnder symplectic capacity obtained at present are proved still holding for it. As a consequence some results on Weinstein conjecture are generalized to C1-smooth hypersurface of contact type. 相似文献
42.
Let Xn,n 1,be a sequence of independent random variables satisfying P(Xn = O) = 1 - P(Xn = an) = 1 - 1/pn,where an,n 1,is a sequence of real numbers,andpn isthenthprime,setFN(x)=P(N∑Xnn=1 x).The authors investigate a conjecture of Erdos in probabilistic number theory and show that in order for the sequence FN to be weakly convergent,it is both sufficient and necessary that there exist three numbers x0 and x1 < x2 such that limsup(FN(x2) -FN(x1)) > 0 holds,and Lo =N→∞ lim FN(x0) exists.Moreover,the authors point ont that they can also obtain the same N→∞ result in the weakened case of liminfP(Xn = 0) > 0.n→∞ 相似文献
43.
Jakub Przybyło 《Random Structures and Algorithms》2015,47(4):776-791
Consider a simple graph G = (V,E) and its proper edge colouring c with the elements of the set {1,2,…,k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour sum distinguishing index of a graph and denoted by . The definition of this parameter, which makes sense for graphs containing no isolated edges, immediately implies that , where Δ is the maximum degree of G. On the other hand, it was conjectured by Flandrin et al. that for all those graphs, except for C5. We prove this bound to be asymptotically correct by showing that . The main idea of our argument relays on a random assignment of the colours, where the choice for every edge is biased by so called attractors, randomly assigned to the vertices. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 776–791, 2015 相似文献
44.
45.
In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that does not converge as (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices ). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture. 相似文献
46.
《Discrete Mathematics》2019,342(8):2445-2453
We prove Terao conjecture saying that the freeness is determined by the combinatorics for arrangements of 13 lines in the complex projective plane. 相似文献
47.
On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices 总被引:1,自引:0,他引:1
It is shown that the polynomialp(t) = Tr[(A+tB)m]has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa, and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to p(t) having positive coefficients for any m and any two n-by-n positive definite matrices. We show that, generally, the question in the real case reduces to that of singular A and B, and this is a key part of our proof. 相似文献
48.
We consider a single server loss system in which arrivals occur according to a doubly stochastic Poisson process with a stationary
ergodic intensity functionλ
t
. The service times are independent, exponentially distributed r.v.'s with meanμ
−1, and are independent of arrivals. We obtain monotonicity results for loss probabilities under time scaling as well as under
amplitude scaling ofλ
t
. Moreover, using these results we obtain both lower and upper bounds for the loss probability. 相似文献
49.
There is a 1941 conjecture of Erdos and Turán on what is now called additive basis that we restate:
Suppose that
If 0$"> for all , then is unbounded.
Conjecture 0.1(Erdos and Turán). Suppose that is an increasing sequence of integers and
Suppose that
If 0$"> for all , then is unbounded.
Our main purpose is to show that the sequence cannot be bounded by . There is a surprisingly simple, though computationally very intensive, algorithm that establishes this.
50.
ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE
ONAPAIROFNONISOMETRICISOSPECTRALDOMAINSWITHFRACTALBOUNDARIESANDTHEWEYLBERRYCONJECTURESLEEMAN,B.D.CHENHUAManuscriptrec... 相似文献