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We show that in an ordered matroid the partial derivative ∂p+qt/∂xp∂yq of the Tutte polynomial is p!q! times the generating function of activities of subsets with corank p and nullity q. More generally, this property holds for the 3-variable Tutte polynomial of a matroid perspective. 相似文献
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This paper investigates the relationship between the minimal Hellinger martingale measure of order q (MHM measure hereafter) and the q-optimal martingale measure for any q≠1. First, we provide more results for the MHM measure; in particular we establish its complete characterization in two manners. Then we derive two equivalent conditions for both martingale measures to coincide. These conditions are in particular fulfilled in the case of markets driven by Lévy processes. Finally, we analyze the MHM measure as well as its relationship to the q-optimal martingale measure for the case of a discrete-time market model. 相似文献
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A group-word w is called concise if whenever the set of w-values in a group G is finite it always follows that the verbal subgroup w(G) is finite. More generally, a word w is said to be concise in a class of groups X if whenever the set of w-values is finite for a group G∈X, it always follows that w(G) is finite. P. Hall asked whether every word is concise. Due to Ivanov the answer to this problem is known to be negative. Dan Segal asked whether every word is concise in the class of residually finite groups. In this direction we prove that if w is a multilinear commutator and q is a prime-power, then the word wq is indeed concise in the class of residually finite groups. Further, we show that in the case where w=γk the word wq is boundedly concise in the class of residually finite groups. It remains unknown whether the word wq is actually concise in the class of all groups. 相似文献
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This article concerns the MP inverse of the differences and the products of projections in a ring R with involution. Some equivalent conditions are obtained. As applications, the MP invertibility of the commutator pq−qp and the anti-commutator pq+qp are characterized, where p and q are projections in R . Some related known results in C?-algebra are generalized. 相似文献
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In this paper we generalize classical Lq, q≥p, estimates of the gradient to the Orlicz space for weak solutions of quasilinear elliptic equations of p-Laplacian type. 相似文献
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This paper is devoted to investigation of the Cauchy problem for nonlinear equations with a small parameter. They are actually small perturbations of linear elliptic equations in which case the Cauchy problem is ill-posed. To study the Cauchy problem we invoke purely nonlinear methods, such as successive iterations and Lq Sobolev spaces with large q. We also discuss linearisable problems. 相似文献
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A multivariate Lévy-driven continuous time autoregressive moving average (CARMA) model of order (p,q), q<p, is introduced. It extends the well-known univariate CARMA and multivariate discrete time ARMA models. We give an explicit construction using a state space representation and a spectral representation of the driving Lévy process. Furthermore, various probabilistic properties of the state space model and the multivariate CARMA process itself are discussed in detail. 相似文献