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71.
David John Benson 《Archiv der Mathematik》2017,109(5):413-414
Let K be a field of characteristic zero, and let R be a ring containing K. Then either \(R^\times = K^\times \) or \(K^\times \) is a subgroup of infinite index in \(R^\times \). 相似文献
72.
John R. Britnell Neil Saunders Tony Skyner 《Journal of Pure and Applied Algebra》2017,221(11):2647-2665
A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient.The smallest examples of exceptional p-groups have order . For an odd prime p, we classify all pairs where G has order and Q is a distinguished quotient. (The case has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order with at least one exceptional quotient tends to 1/2. 相似文献
73.
Longlu Wang Xia Liu Jinming Luo Xidong Duan Prof. John Crittenden Prof. Chengbin Liu Shuqu Zhang Prof. Yong Pei Yunxiong Zeng Prof. Xiangfeng Duan 《Angewandte Chemie (International ed. in English)》2017,56(26):7610-7614
The metallic 1T-MoS2 has attracted considerable attention as an effective catalyst for hydrogen evolution reactions (HERs). However, the fundamental mechanism about the catalytic activity of 1T-MoS2 and the associated phase evolution remain elusive and controversial. Herein, we prepared the most stable 1T-MoS2 by hydrothermal exfoliation of MoS2 nanosheets vertically rooted into rigid one-dimensional TiO2 nanofibers. The 1T-MoS2 can keep highly stable over one year, presenting an ideal model system for investigating the HER catalytic activities as a function of the phase evolution. Both experimental studies and theoretical calculations suggest that 1T phase can be irreversibly transformed into a more active 1T′ phase as true active sites in photocatalytic HERs, resulting in a “catalytic site self-optimization”. Hydrogen atom adsorption is the major driving force for this phase transition. 相似文献
74.
John Engbers 《Journal of Graph Theory》2017,85(4):780-787
For graphs G and H , an H‐coloring of G is a map from the vertices of G to the vertices of H that preserves edge adjacency. We consider the following extremal enumerative question: for a given H , which connected n‐vertex graph with minimum degree δ maximizes the number of H‐colorings? We show that for nonregular H and sufficiently large n , the complete bipartite graph is the unique maximizer. As a corollary, for nonregular H and sufficiently large n the graph is the unique k‐connected graph that maximizes the number of H‐colorings among all k‐connected graphs. Finally, we show that this conclusion does not hold for all regular H by exhibiting a connected n‐vertex graph with minimum degree δ that has more ‐colorings (for sufficiently large q and n ) than . 相似文献
75.
We find a formula for the number of directed 5‐cycles in a tournament in terms of its edge scores and use the formula to find upper and lower bounds on the number of 5‐cycles in any n‐tournament. In particular, we show that the maximum number of 5‐cycles is asymptotically equal to , the expected number 5‐cycles in a random tournament (), with equality (up to order of magnitude) for almost all tournaments. 相似文献
76.
Convergence analysis for second‐order accurate schemes for the periodic nonlocal Allen‐Cahn and Cahn‐Hilliard equations 下载免费PDF全文
Zhen Guan John Lowengrub Cheng Wang 《Mathematical Methods in the Applied Sciences》2017,40(18):6836-6863
In this paper, we provide a detailed convergence analysis for fully discrete second‐order (in both time and space) numerical schemes for nonlocal Allen‐Cahn and nonlocal Cahn‐Hilliard equations. The unconditional unique solvability and energy stability ensures ? 4 stability. The convergence analysis for the nonlocal Allen‐Cahn equation follows the standard procedure of consistency and stability estimate for the numerical error function. For the nonlocal Cahn‐Hilliard equation, because of the complicated form of the nonlinear term, a careful expansion of its discrete gradient is undertaken, and an H ?1 inner‐product estimate of this nonlinear numerical error is derived to establish convergence. In addition, an a priori bound of the numerical solution at the discrete level is needed in the error estimate. Such a bound can be obtained by performing a higher order consistency analysis by using asymptotic expansions for the numerical solution. Following the technique originally proposed by Strang (eg, 1964), instead of the standard comparison between the exact and numerical solutions, an error estimate between the numerical solution and the constructed approximate solution yields an O (s 3+h 4) convergence in norm, in which s and h denote the time step and spatial mesh sizes, respectively. This in turn leads to the necessary bound under a standard constraint s ≤C h . Here, we also prove convergence of the scheme in the maximum norm under the same constraint. 相似文献
77.
In this work, we study the pseudomonotonicity of multivalued operators from the point of view of polarity, in an analogous way as the well-known monotone polar due to Martínez-Legaz and Svaiter, and the quasimonotone polar recently introduced by Bueno and Cotrina. We show that this new polar, adapted for pseudomonotonicity, possesses analogous properties to the monotone and quasimonotone polar, among which are a characterization of pseudomonotonicity, maximality and pre-maximality. Furthermore, we characterize the notion of D-maximal pseudomonotonicity introduced by Hadjisavvas. We conclude this work studying the connections between pseudomonotonicity, variational inequality problems and upper sign-continuity. 相似文献
78.
John?M.?BallEmail author Arghir?Zarnescu 《Calculus of Variations and Partial Differential Equations》2017,56(1):13
For a bounded domain \(\Omega \subset {\mathbb R}^m, m\ge 2,\) of class \(C^0\), the properties are studied of fields of ‘good directions’, that is the directions with respect to which \(\partial \Omega \) can be locally represented as the graph of a continuous function. For any such domain there is a canonical smooth field of good directions defined in a suitable neighbourhood of \(\partial \Omega \), in terms of which a corresponding flow can be defined. Using this flow it is shown that \(\Omega \) can be approximated from the inside and the outside by diffeomorphic domains of class \(C^\infty \). Whether or not the image of a general continuous field of good directions (pseudonormals) defined on \(\partial \Omega \) is the whole of \(S^{m-1}\) is shown to depend on the topology of \(\Omega \). These considerations are used to prove that if \(m=2,3\), or if \(\Omega \) has nonzero Euler characteristic, there is a point \(P\in \partial \Omega \) in the neighbourhood of which \(\partial \Omega \) is Lipschitz. The results provide new information even for more regular domains, with Lipschitz or smooth boundaries. 相似文献
79.
John T. Conway 《Integral Transforms and Special Functions》2017,28(6):488-503
A method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete elliptic integrals. This gives a total of 27 integrals for the complete integral of the third kind, including the single integral given in the literature. Some typographical errors in a previous related paper are corrected. 相似文献
80.