Hom-Lie algebras were introduced by J. Hartwig, D. Larsson, and S. Silvestrov as a generalized Lie algebra. When studying the homology and cohomology theory of Hom-Lie algebras, the authors find that the lowdimensional cohomology theory of Hom-Lie algebras is not well studied because of the Hom-Jacobi identity. In this paper, the authors compute the first and second cohomology groups of the
Two kinds of eigentime identity for asymmetric finite Markov chains are proved both in the ergodic case and the transient case.
In this article, we apply the localization techniques to right (?)-serial coalgebras and obtain some interesting results. In particular, we give a characterization of right (?)-serial coalgebras by means of its ‘local structure’, which is the localized right (?)-serial coalgebras, and we get a main result—the periodicity theorem.
Let
It is an interesting topic to determine the structure of a finite group with a given number of elements of maximal order. In this article, we classify finite groups with 24 elements of maximal order.
In this paper, we first analyze the structure of a finite nonsolvable group in which every cyclic subgroup of order 2 and 4 of every second maximal subgroup is an NE-subgroup. Next, we prove that a finite group
Suppose that cause-effect relationships between variables can be described by a causal network with a linear structural equation model. Kuroki and Miyakawa proposed a graphical criterion for selecting covariates to identify the effect of a conditional plan with one control variable [J. Roy. Statist. Soc. Ser. B, 2003, 65: 209-222]. In this paper, we study a particular type of conditional plan with more than one control variable and propose a graphical criterion for selecting covariates to identify the effect of a conditional plan of the studied type.
In this paper, we use the general quantization method by Drinfel’d twists to quantize the Schr?dinger-Virasoro Lie algebra whose Lie bialgebra structures were recently discovered by Han-Li-Su. We give two different kinds of Drinfel’d twists, which are then used to construct the corresponding Hopf algebraic structures. Our results extend the class of examples of noncommutative and noncocommutative Hopf algebras.
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We derive the gradient estimates and Harnack inequalities for positive solutions of the diffusion equation
J. Wei recently proposed a concept of
Let
The aim of this paper is to study the boundedness of the windowed-Kontorovich-Lebedev transforms. For this purpose, we first define the translation associated to the Kontorovich-Lebedev transform and a generalized convolution product, then obtain some harmonic analysis results. We present a sufficient and necessary condition for the boundedness of the windowed-Kontorovich-Lebedev transform. Finally, we define the corresponding Weyl operator, and study the boundedness and compactedness of the Weyl operator with symbols in
In this paper, we characterize the nilpotency and supersolvability of a finite group
In this paper, we establish an exact asymptotic formula for the finite-time ruin probability of a nonstandard compound renewal risk model with constant force of interest in which claims arrive in groups, their sizes in one group are identically distributed but negatively dependent, and the inter-arrival times between groups are negatively dependent too.