We give a monoidal category approach to Hom-coassociative coalgebra by imposing the Hom-coassociative law up to some isomorphisms on the comultiplication map and requiring that these isomorphisms satisfy the copentagon axiom and obtain a Hom-coassociative 2-coalgebra, which is a 2- category. Second, we characterize Hom-bialgebras in terms of their categories of modules. Finally, we give a categorical realization of Hom-quasi-Hopf algebras using Hom-coassociative 2-coalgebra.
We give an easy proof of Andrews and Clutterbuck’s main results [J. Amer. Math. Soc., 2011, 24(3): 899−916], which gives both a sharp lower bound for the spectral gap of a Schrödinger operator and a sharp modulus of concavity for the logarithm of the corresponding first eigenfunction. We arrive directly at the same estimates by the ‘double coordinate’ approach and asymptotic behavior of parabolic flows. Although using the techniques appeared in the above paper, we partly simplify the method and argument. This maybe help to provide an easy way for estimating spectral gap. Besides, we also get a new lower bound of spectral gap for a class of Schödinger operator.
We prove that the local times of a sequence of Sinai’s random walks converge to those of Brox’s diffusion by proper scaling. Our proof is based on the intrinsic branching structure of the random walk and the convergence of the branching processes in random environment.
Let L(s, sym2f) be the symmetric-square L-function associated to a primitive holomorphic cusp form f for SL(2,
Let G be a graph of maximum degree Δ. A proper vertex coloring of G is acyclic if there is no bichromatic cycle. It was proved by Alon et al. [Acyclic coloring of graphs. Random Structures Algorithms, 1991, 2(3): 277−288] that G admits an acyclic coloring with O(Δ4/3) colors and a proper coloring with O(Δ(k−1)/(k−2)) colors such that no path with k vertices is bichromatic for a fixed integer k≥5. In this paper, we combine above two colorings and show that if k≥5 and G does not contain cycles of length 4, then G admits an acyclic coloring with O(Δ(k−1)/(k−2)) colors such that no path with k vertices is bichromatic.
We give the explicit formulas of the minimizers of the anisotropic Rudin-Osher-Fatemi models
where
A pricing model for a corporate bond with rating migration risk is established in this article. With the technology of utility-indifference valuation under the Markov-modulated framework, we analyze the price of a multi-rating bond and obtain closed formulae in a three-rating case. Based on the pricing formulae, the impacts of the parameters on the indifference price are analyzed and some reasonable financial explanations are provided as well.
A subgroup H of a finite group G is said to be s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. We say that a subgroup H of a finite group G is S-semiembedded in G if there exists an s-permutable subgroup T of G such that TH is s-permutable in G and
We study the Hopf *-algebra structures on the Hopf algebra H(1, q) over
This article deals with the ruin probability in a Sparre Andersen risk process with the inter-claim times being Erlang distributed in the framework of piecewise deterministic Markov process (PDMP). We construct an exponential martingale by virtue of the extended generator of the PDMP to change the measure. Some results are derived for the ruin probabilities, such as the general expressions for ruin probability, Lundberg bounds, Cramér-Lundberg approximations, and finite-horizon ruin probability.
value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For any (C, c) well-spaced sequence
has no solution in primes p1, p2. It is shown that for any ε>0,we have E(
Let
We investigate the properties of nil-Coxeter algebras and nil-Ariki-Koike algebras. To be precise, from the view of standardly based algebras introduced by J. Du, H. Rui [Trans. Amer. Math. Soc, 1998, 350: 3207–3235], we give a description of simple modules of nil-Coxeter algebras and nil-Ariki-Koike algebras. Then we determine the representation type of nil-Coxeter algebras and nil-Ariki-Koike algebras. We also give a description of the center of nil-Ariki-Koike algebras.