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91.
We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers. 相似文献
92.
93.
Chi‐Cheung Su Meinan He Jiayan Shi Rachid Amine Jian Zhang Khalil Amine 《Angewandte Chemie (International ed. in English)》2020,59(41):18229-18233
Despite the exceptionally high energy density of lithium metal anodes, the practical application of lithium‐metal batteries (LMBs) is still impeded by the instability of the interphase between the lithium metal and the electrolyte. To formulate a functional electrolyte system that can stabilize the lithium‐metal anode, the solvation behavior of the solvent molecules must be understood because the electrochemical properties of a solvent can be heavily influenced by its solvation status. We unambiguously demonstrated the solvation rule for the solid‐electrolyte interphase (SEI) enabler in an electrolyte system. In this study, fluoroethylene carbonate was used as the SEI enabler due to its ability to form a robust SEI on the lithium metal surface, allowing relatively stable LMB cycling. The results revealed that the solvation number of fluoroethylene carbonate must be ≥1 to ensure the formation of a stable SEI in which the sacrificial reduction of the SEI enabler subsequently leads to the stable cycling of LMBs. 相似文献
94.
The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function , Gauss, who estimated the rate at which prime numbers increase, and Riemann, who extended to the complex plane z and conjectured that all nontrivial zeros are in the axis. The nonadditive entropy , where BG stands for Boltzmann-Gibbs) on which nonextensive statistical mechanics is based, involves the function . It is already known that this function paves the way for the emergence of a q-generalized algebra, using q-numbers defined as , which recover the number x for . The q-prime numbers are then defined as the q-natural numbers , where n is a prime number We show that, for any value of q, infinitely many q-prime numbers exist; for they diverge for increasing prime number, whereas they converge for ; the standard prime numbers are recovered for . For , we generalize the function as follows: (). We show that this function appears to diverge at , . Also, we alternatively define, for , and , which, for , generically satisfy , in variance with the case, where of course . 相似文献
95.
Min-qiangYu Zhi-pingZhou De-yueYan 《高分子科学》2004,(2):155-167
This work deals with the kinetics of co-condensation polymerization of AB2 and AB monomers, giving expressions of the two-dimensional molecular weight distribution function and the number/weight average molecular weights of the resulting copolymers. The two-dimensional molecular weight distribution depends on two indices, n and l, which are the respective numbers of AB2 and AB units in a copolymer species. The evolution of the two-dimensional weight and z distributions during the co-condensation polymerization has been evaluated systematically. Finally, the two-dimensional distribution was transformed into a one-dimensional molecular weight distribution with only one variable (the molecular weight of the products instead of the degree of polymerization). The calculated results show that the highly branched copolymer has a very broad molecular weight distribution when the co-condensation polymerization approaches completion. 相似文献
96.
对一类有界独立或相依的随机变量序列|ξn|,获得了它的伯努利大数定律、波雷尔强大数定律及常返性定理.作为应用,得出了Loève专著[1]中的推广的伯努利大数定律、常返性定理,改进了[1]中的推广的波雷尔强大数定律. 相似文献
97.
98.
For each n and k, we examine bounds on the largest number m so that for any k‐coloring of the edges of Kn there exists a copy of Km whose edges receive at most k?1 colors. We show that for , the largest value of m is asymptotically equal to the Turá number , while for any constant then the largest m is asymptotically larger than that Turá number. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 120–129, 2002 相似文献
99.
We investigate the small ball problem for d-dimensional fractional Brownian sheets by functional analytic methods. For this reason we show that integration operators of Riemann–Liouville and Weyl type are very close in the sense of their approximation properties, i.e., the Kolmogorov and entropy numbers of their difference tend to zero exponentially. This allows us to carry over properties of the Weyl operator to the Riemann–Liouville one, leading to sharp small ball estimates for some fractional Brownian sheets. In particular, we extend Talagrand's estimate for the 2-dimensional Brownian sheet to the fractional case. When passing from dimension 1 to dimension d2, we use a quite general estimate for the Kolmogorov numbers of the tensor products of linear operators. 相似文献
100.
André Adler 《Journal of Theoretical Probability》2002,15(4):939-949
Consider independent and identically distributed random variables {X,X
nj
, 1jn,n1} with density f(x)=px
–p–1
I(x1), where p>0. We show that there exist unusual generalized Laws of the Iterated Logarithm involving the larger order statistics from our array. 相似文献