In this paper, we establish some strong laws of large numbers (SLLN) for non-independent variables under the framework of sublinear expectations. One of our main results is for blockwise m-dependent random variables and another is for orthogonal random variables, both of which are the generalization of SLLN for independent random variables in sublinear expectation spaces.
Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory. The purpose of this paper is to study the splittings of operations of di-associative algebras and tri-associative algebras. First, we introduce the notion of a quadri-dendriform algebra, which is a splitting of a di-associative algebra. We show that a relative averaging operator on dendriform algebras gives rise to a quadri-dendriform algebra. Conversely, a quadri-dendriform algebra gives rise to a dendriform algebra and a representation such that the quotient map is a relative averaging operator. Furthermore, any quadri-dendriform algebra can be embedded into an averaging dendriform algebra. Finally, we introduce the notion of six-dendriform algebras, which are a splitting of tri-associative algebras, and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.
A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations. Let $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ be the set of permutations in the symmetric group $S_n$ which avoids patterns $\sigma_1, \sigma_2, \ldots, \sigma_r$. The aim of this paper is to investigate when, for certain patterns $\sigma_1, \sigma_2, \ldots, \sigma_r$, $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ is sign-balanced for every integer $n>1$. We prove that for any $\{\sigma_1, \sigma_2, \ldots, \sigma_r\}\subseteq S_3$, if $\{\sigma_1, \sigma_2, \ldots, \sigma_r\}$ is sign-balanced except $\{132, 213, 231, 312\}$, then $S_n(\sigma_1, \sigma_2, \ldots, \sigma_r)$ is sign-balanced for every integer $n>1$. In addition, we give some results in the case of avoiding some patterns of length $4$.
The main goal of this paper is to establish the boundedness of bilinear strongly singular operator (T) and its commutator (T)b1,b2 on generalized Morrey spaces Mup(μ)over non-homogeneous metric measure spaces.Under assumption that the Lebesgue measurable functions u,u1 and u2 belong to Wτ for τ ∈(0,2),and u1u2=u.The authors prove that (T) is bounded from product spaces Mu1p1(μ×Mu2p2(μ)into spaces Mup(μ),where 1/p=1/p1+1/p2 with 1＜p1,p2＜∞;and also bounded from product spaces Mu1p1(μ)×Mu2p2(μ)into generalized weak Morrey spaces WMup(μ).Furthermore,the author also show that commutator (T)b1,b2generated by b1,b2 ∈RBMO(μ)and (T) is bounded from product spaces Mu1p1(μ)× Mu2p2(μ)into spaces Mup(μ).
In this paper, we introduce the notion of embedding tensor on 3-Hom-Lie algebras and naturally induce 3-Hom-Leibniz algebras. Moreover, the cohomology theory of embedding tensors on 3-Hom-Lie algebras is defined. As an application, we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent, then their infinitesimals belong to the same cohomology class in the first cohomology group.
We show some existence results for the system of nonlocal Neumann problems with the Minkowski-curvature operator (r(N-1) u '/root 1-u '(2))' = r(N-1) f(r, u, u '), r is an element of(0, 1), u ' (0) = 0, u ' (1) = integral(1)(0) u ' (s) dg (s), where N >= 1 is an integer, f : [0, 1] x R-k x I-k -> R-k is continuous and bounded, I := (-1, 1), and g : [0, 1] -> R-k is a function of bounded variation. The proof is based on topological-degree arguments and extends to a larger class of nonlinearities.
In this paper, we consider compatible Hom-Lie triple systems. More precisely, compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-Lie triple systems. As applications of cohomology, we study linear deformations and abelian extensions of compatible Hom-Lie triple systems.
For given simple graphs H1,H2,…,Hc,the multicolor Ramsey number R(H1,H2,...,Hc)is defined as the smallest positive integer n such that for an arbitrary edge-decomposition{Gi}ci=1 of the complete graph Kn,at least one Gi has a subgraph isomorphic to Hi.Let m,n1,n2,...,nc be positive integers and Σ=Σci=1(ni-1).Some bounds and exact values of R(K1,n1,...,K1,nc,Pm)have been obtained in literature.Wang(Graphs Combin.,2020)conjec-tured that if Σ(≠)0(mod m-1)and Σ+1 ≥(m-3)2,then R(K1,n1,...,K1,nc,Pm)=Σ+m-1.In this note,we give a new lower bound and some exact values of R(K1,n1,...,K1,nc,Pm)pro-vided m ≤ Σ,Σ ≡ k(mod m-1),and 2 ≤ k ≤ m-2.These results partially confirm Wang's conjecture.
We say that a simple graph G is Seidel integral if its Seidel spectrum consists entirely of integers. If ?Ka,a ? ?Kb,b is Seidel integral, we show that it belongs the class of Seidel integral graphs [kt/? x0 + mt/?z]Ka,a ? [kt/? y0 + a/?z]nKb,b, where (i) a = (t+?n)k+?m and b = ?m; (ii) t, k, ?,m, n ? N such that (m, n) = 1, (n, t) = 1 and (?, t) = 1; (iii) ? = (a,mt) such that ? | kt; (iv) (x0, y0) is a particular solution of the linear Diophantine equation ax ? (mt)y = ? and (v) z ? z0 where z0 is the least integer such that (kt/? x0 + mt/?z0)? 1 and (kt/? y0 + a/?z0) ? 1. In particular, we demonstrate that ?Ka ? ?Kb is integral in respect to its ordinary adjacency matrix if and only if ?Ka,a ? ?Kb,b is Seidel integral.
This paper studies t-norms on the space L of all normal and convex fuzzy truth values. We first prove that the only non-convolution form type-2 t-norm constructed by Wu et al. satisfies the distributivity law for meet-convolution and show that t-norm in the sense of Walker and Walker is strictly stronger than tr-norm on L, which is strictly stronger than t-norm on L. Furthermore, we characterize some restrictive axioms of tr-norms for convolution operations on L and obtain some necessary conditions for tr-(co)norm convolution operations on L.
In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is proposed to solve this problem. An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples illustrate the validity and effectiveness of this method.
A coloring of edges of a graph G is injective if for any two distinct edges e1 and e2,the coloring of e1 and e2 are distinct if they are at distance 2 in G or in a common 3-cycle.The injective chromatic index of G is the minimum number of colors needed for an injective edge coloring of G.It was conjectured that the injective chromatic index of any subcubic graph is at most 6.In this paper,we partially confirm this conjecture by showing that the injective chromatic index of any claw-free subcubic graph is less than or equal to 6.The bound 6 is tight and our proof implies a linear-time algorithm for finding an injective edge coloring using at most 6 colors for such graphs.
The aim of this paper is to study the order of meromorphic solutions of linear difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0,where the coefficients Aj(z)(j=0,...,n)are entire functions.We obtain some results by giving some restrictions on coefficients of above equation with no dominating coefficient and partially answer a question of I.Laine and C.C.Yang.
A local convergence analysis of Chebyshev-Halley method having third order of convergence for approximating zero of non-linear operator f(v)=0 by using convex majorant function and their condition in B-space(Banach space),is presented in this article.We give the error estimate to show the efficiency of our study.Besides,we established the relation between majorant function and Kantorovich or Smale-type result as special cases of our general theory.
In this paper,we establish a characterization of the mixed radial-angular λ-central bounded mean oscillation spaces via the boundedness of the commutators Hb and its dual H*b with a function b ∈ CMOLp2,λradLp1ang(Rn).
In this paper,we consider the decomposition of the symmetric algebra F[V]into indecomposables with linear actions of a metacyclic group G=Cp × H,where H is a p'-group,and prove a periodicity property of the symmetric algebra F[V]if V is a direct sum of indecomposable G-module such that the norm polynomial of the simple H-module is the power of the product of the basis elements of the dual.
In this paper,we first introduce the notion of relative Rota-Baxter operators on Hom-Lie-Yamaguti algebras and give some characteristics of relative Rota-Baxter operators in terms of Nijenhuis operators and graphs.Then,the cohomology theory of relative Rota-Baxter operators on Hom-Lie-Yamaguti algebras is proposed.Finally,the deformation of the relative Rota-Baxter operator is explored by applying the cohomological approach.
In this work,we construct an efficient invariant energy quadratization(IEQ)method of unconditional energy stability to solve the Cahn-Hilliard equation.The constructed numerical scheme is linear,second-order accuracy in time and unconditional energy stability.We carefully analyze the unique solvability,stability and error estimate of the numerical scheme.The results show that the constructed scheme satisfies unique solvability,unconditional energy stability and the second-order convergence in time direction.Through a large number of 2D and 3D numerical experiments,we further verify the convergence order,unconditional energy stability and effectiveness of the scheme.
The point spectrum and non-degenerate symplectic structure of eigenfunction sys-tems of off-diagonal infinite dimensional Hamiltonian operator H=(0CB0)are studied in this article.The necessary and sufficient conditions for the eigenfunction systems of off-diagonal infi-nite dimensional Hamiltonian operator H to have non-degenerate symplectic structure are given.Further,the necessary and sufficient conditions for point spectrum to be contained in real axis,imaginary axis and other areas are obtained for off-diagonal infinite dimensional Hamiltonian operator H,respectively.As an illustrating example,off-diagonal infinite dimensional Hamilto-nian operators derived from the plate bending problem and string vibration problem are used to justify the conclusions.
