We study several kinds of Hausdorff operators on Campanato spaces and obtain the sharp bounds for them. Furthermore, we also discuss the boundedness of multilinear Hausdorff operator on Morrey space.

We introduce a catastrophe risk model with variable premium rates and obtain a local result of the ruin probability under heavy-tailed claims. In addition, we extend the risk model and propose a regression-type size-dependence one under the framework of web Markov skeleton process, which has some theoretic and practical value in the field of actuarial, and allows applications in various areas.

We discuss the existing relaxed alternating projection method for solving the linear matrix equation AXB=C under some closed convex constraints to X. The considered closed convex constrained set, denoted by R, is (1) the set of bounded matrices, (2) the set of Q-positive definite matrices, (3) the solution set of a linear matrix inequality. We prove the weak convergence of the matrix sequence generated by the proposed algorithm, and present some numerical examples for solving AXB=C under symmetric nonnegative and symmetric positive semidefinite matrices constraint to illustrate the feasibility and efficiency of the proposed algorithm, and to show its clear superiority comparing with alternating projection method and spectral projected gradient method.

We present the necessary and sufficient conditions for the element after perturbing and investigate the perturbation bounds for the generalized Drazin inverse by using block technology in Banach algebra.

We study the totally umbilical property of compact closed equal-distance immersed hyper-surfaces Mⁿ in the positive curvature space form Sⁿ⁺¹(c) (c>0) and the higher order mean curvatures, and obtain a result which improves the relevant recent theorems in this research field.

We consider the random intervals I_n(ω)=ω_n+(-l_n/2,l_n/2) (mod 1), where {l_n}_n≥1 is a sequence of positive real numbers which is decreasing to zero and {ω_n}_n≥1 is an i.i.d. sequence with Gibbs distribution measure on the circle T= R/Z. Using the tools from multi-fractal analysis, we estimate the Hausdorff dimension of sets which are covered finitely or infinitely many times by {I_n(ω)}.

In this paper, the automorphism group of the generalized orthogonal graph ΓGO_2ν+δ(q,m,S) over F_q of odd characteristic is determined, where 1<m<ν.

We first introduce a new type of neural network operators with sigmoidal functions, and give the pointwise and global estimates of the approximation by the networks. The new neural network operators can approximate the functions with a very good rate which can not be obtained by polynomial approximation. To further improve the approximation rate for functions of smoothness, we also introduce a new type of combinations of neural network operators, and give pointwise and global estimates of the approximation by the combinations. A numerical example is given to demonstrate our new method.

For congruence ρ on an inverse semigroup, there are maximal element ρT and minimal element ρt in a trace class; by the same token, there are maximal element ρK and minimal element ρk in a kernel class. So we can find four operators Γ= {K, k, T, t} on congruence lattice C(S) of an inverse semigroup S. Inthis paper,we gained extremum congruence which is not identity relation on free monogenic inverse semigroup I_x. Then establishing relations in Γ on congruence lattice C(S), we obtain trace-kernel operator semigroup Γ+/Σ^* of I_x finally.

In a recent paper, Lie bialgebra structures on generalized Heisenberg- Virasoro algebra L are considered by the authors. In this paper, the explicit formula of the quantization on generalized Heisenberg-Virasoro algebra is presented.

We obtain a necessary and sufficient condition for that there exists a nontrivial self-orthogonal or self-dual cyclic codes over finite fields and the explicit enumerating formula. As a corollary, a simple and easy criterion for several classes of non-trivial self-orthogonal cyclic codes is given.

We study the nonexistence of solutions for a singular semilinear elliptic equations. The results improve and implement a work by Arcoya et al. [Existence and nonexistence of solutions for singular quadratic quasilinear equations, J. Differential Equations, 2009, 246: 4006-4042], whose proofs are very simple and based on Poincaré inequality, Lusin theorem and Egoroff theorem.

In this paper, we consider the quasilinear elliptic systems with the nonlinear boundary condition and weight function. With the help of the Nehari manifold, we obtain the system has at least two nontrival positive solutions under the proper region of parameters.

This paper considers the evolution by mean curvature vector plus a forcing field in the direction of its position vector of a closed submanifold of dimension n (≥ 2) in R^n+p. Suppose that mean curvature vector is nonzero everywhere and that the full norm of the second fundamental form is bounded by a fixed multiple (depending only on n) of the length of the mean curvature vector at every point. It is shown that such submanifolds may contract to a point in finite time if the forcing field is small, or exist for all time and expand to infinity if it is large enough. Moreover, if the evolving submanifolds undergo suitable homotheties and the time parameter is transformed appropriately into a parameter t, 0 ≤ t < ∞, it is also shown the normalized submanifolds in any case converge smoothly to a round sphere in some (n + 1)-dimensional subspace of R^n+p as t→∞.

The complete convergence for weighted sums of arrays ρ-mixing random variables is discussed under general conditions by utilizing the Rosenthal type inequality of ρ-mixing random variables. General complete convergence theorems and convergence for moving average processes generated by sequences of ρ-mixing random variables are obtained, which improve and extend the related known works in the literature.

We provide a mean-square convergence rate of stochastic theta methods for a class of stochastic differential delay equations whose coefficients are not Lipschitz but only Hölder continuous.

We introduce real vector cone metric spaces, where cone metric is the mapping on a real vector space without topological structures. We also prove some new fixed point theorems in real vector cone metric spaces. By using nonlinear scalarization functions, we establish the equivalence between these and some other fixed point results in metric and in real vector cone metric spaces. Our results improve and generalize some results from the literature.

We investigate the properties of meromorphic solutions of Painlevé Ⅲ difference equations. In particular, we study the existence of Borel exceptional value, the exponent of convergence of zeros, poles and fixed points of a transcendental meromorphic solution. Several sharp examples of meromorphic solutions of some Painlevé Ⅲ difference equations are given.

We study the existence of nodal solutions for the p-Laplacian problems with jumping nonlinearities at zero and infinity. More precisely, we show that there exists at least one nodal solution to the problems if nonlinearities crossing the Fučik spectrum.

In this paper, for some choices of integers B, we give all the integer solutions of equation x²+By^2p=z³ with xyz≠0 and x, y, z pairwise coprime for prime p ≥ 11.

We discuss some relationship of the numerical upper bounds for the mean values of smooth Weyl sums of fractional moments. Some new results on the numerical upper bounds of the mean values are given when the moments are in the interval [4, 5].

Let a, n ≥ 1 be integers, p a prime. We prove that, under some conditions the Diophantine equations X²- a² + 4p²ⁿ)Y⁴ = -4p²ⁿ and X²-(a²+p²ⁿ)Y⁴ = -p²ⁿ have at most two coprime positive integer solutions (X, Y).

A new construction of fractal interpolation surfaces (FISs) on rectangular grids using iterated function systems (IFSs) is proposed and some of their properties are studied in this paper. The IFSs employed are endowed with variable free parameters and are proved that they can generate continuous bivariate FISs, which can be used as self-affine and non-self-affine fractal interpolation models on arbitrary data points. Some inequalities concerning the sensitivity of the resulting bivariate fractal interpolation functions (FIFs) are deduced in two metric senses. The estimation of the error between the bivariate FIF and a bivariate data generating function is given. Finally, under certain conditions, the uniform convergence of the bivariate FIFs to the data generating function is proved.

The R₀-implication operator is a new implication operator that was proposed by Wang Guojun in 2000. In the present, the R₀-implication operator has been applied to studying of fuzzy controlling, approximate reasoning, fuzzy recognition, fuzzy systems, quantitative logic. The common point of applications is that the function determined by a formula through R₀-implication operator plays a key role. In this paper, the characteristics of the function determined by a formula through R₀-implication operator are investigated intensively in R₀-style propositional logic system. The necessary and sufficient conditions are obtained for a function f: [0, 1]ⁿ → [0, 1] to be induced by a formula through the R₀-implication operator in R₀-style propositional logic system.

Let B_d be the unit ball ofd-dimensional complex Euclid space C^d, H_d^g (B_d^√R) the reproducing kernel Hilbert space with U-invariant reproducing kernel K(z,w) = g(<z,w>), where g(z) = ∑_n=0^∞ a_nz_n (a_n ≥ 0) is the generating function of the space H_d^g (B_d^√R). In this paper, we show that the multiplier algebra of the space H_d^g (B_d^√R) is a proper subset of H^∞(B_d^√R), and there exists a holomorphic self-mapping ø from B_d^√Rinto B_d^√Rsuch that the multiplication operator M_øis not bounded when the sequence {a_n}_n^∞=0 is bounded andd ≥ 2. Furthermore, we prove that if the coefficients sequence {a_n}_n^∞=0 of the generating function g is a bounded, non-decreasing sequence, i.e. there exists a positive number M such that 0 ≤ a₀ ≤ a₁ ≤ … ≤ M, n = 0, 1, 2, …, then the space H_d^g (B_d^√R) is not subnormal, in other words, there is not any positive measure μ on C^d such that ||f|| H_d^g2 =∫ _C^d |f(z)|²dμ(z), for each f∈H_d^g (B_d^√R), and then von Neumann's inequality does not hold on the space H_d^g (B_d^√R).

We investigate a class of N-Laplacian equations with subcritical growth. Based on Trudinger-Moser inequality and Morse theory, we prove the existence of nontrivial solutions when there is no Mountain Pass geometry, without imposing the Ambrosetti-Rabinowitz condition or a global sign condition.

We prove that if λ₁, λ₂, λ₃, λ₄ are positive real numbers, and at least one of λ_i/λ_j (1 ≤ i < j ≤ 4) is irrational, then, the integer parts of λ₁x₁² +λ₂x₂³ +λ₃x₃⁴ +λ₄x₄⁴ are prime infinitely often for natural numbers x₁, x₂, x₃, x₄. This greatly improves of the former result.

We consider the following singular elliptic equation
,
which involves the Caffarelli-Kohn-Nirenberg inequalities. By virtue of the Ljusternik-Schnirelaman theory and a Pohozaev-type identity, we obtain the existence and nonexistence results of sing-changing solutions for the above problem.

In this paper, the characteristic inequalities ofL^pBanach space is extended to Orlicz spaces partially. Using the method of Orlicz spaces theory, we establish some inequalities in Orlicz spaces.

A ratio-dependent predator-prey model incorporating a prey refuge is investigated and a series of sufficient conditions on global stability, limit cycle and Hopf bifurcation are obtained. The results show that when the transformation rate, mortality and the half-saturation constant of predator population satisfy certain conditions,prey refuge has no influence on the coexistence of predator and prey species. Once the condition is not satisfied, then prey refuge has stabilization effect. Numerical simulations are performed to illustrate the feasibility of our results.

In this paper, the set of m-th equal partition points of n-simplex is defined by recursion. A necessary and sufficient condition for deciding the zero polynomial is presented, i.e., for a polynomial f of m degree in n variables, it is the zero polynomial iff it vanishes at m-th equal partition points of an arbitrary n-simplex. As applications, this result is presented on the properly posed set of nodes for interpolation and the parallel numerical method of mechanical theorem proving.

The generalized connectivity of a graph G was introduced by Chartrand et al. Let S be a nonempty set of vertices of G, and k(S) denote the largest number of internally disjoint trees connecting S in G. Then for an integer r with 2 ≤ r ≤ n, the generalized r-connectivity k_r(G) of G is the minimum k(S) where S runs over all the r-subsets of the vertex set of G. Obviously, k₂(G) = k(G), is the vertex connectivity of G, and hence the generalized connectivity is a natural generalization of the vertex connectivity. In this paper, we study the generalized 3-connectivity of random graphs and prove that for every fixed integer k ≥ 1, p = (logn + (k + 1) loglogn - logloglogn)/n is a sharp threshold function for the property k₃(G(n, p)) ≥ k, which could be seen as a counterpart of Bollobás and Thomason's result for vertex connectivity.

We study the automorphism groups of vertex operator algebras associated with Ĥ₄ and give a complete description.

We consider the asymptotic properties of the nearest neighbor estimation for functional data. Under α-mixing and some regularity assumptions, we investigate the consistency and asymptotic normality of the nearest neighbor estimation for the nonparametric regression models with functional data. For the empirical data analysis, we consider three different distributions of the errors. The results show that the advantages of the nearest neighbor estimation lie in its easy computation, robustness and good performance under finite sample.

In this apper, we establish the boundedness of commutators generated by the n-dimensional Hausdorff operator and weighted Lipschitz or CO functions on some function spaces, such as weighted Lebesgue spaces and weighted Herz type spaces.

In this paper, two improved conjugate gradient methods are proposed for unconstrained optimization. The two presented methods can generate sufficient decent directions at every iteration depending on no line search, moreover, the global convergence of the two proposed methods are proved under the standard Wolfe line search. Some elementary numerical experiments are reported, which show that the two proposed methods are promising.

We first present several generic uniqueness theorems for set-valued mappings, then apply them to investigate the uniqueness of the solutions of max-min problems, vector optimization problems and fixed point problems etc. As results, we prove that, in the sense of Baire's category, most of the problems in the space consisting of max-min problems (respectively, vector optimization problems and fixed point problems) have unique solution.

We analyze a three-step iterative scheme for mappings of asymptotically nonexpansive type in uniformly convex hyperbolic spaces. The new iterative scheme includes Ishikawa-type and Krasnoselski-Mann iteration as special cases. As an application, we obtain a Δ-convergence theorem of the three-step iterative scheme for mappings of asymptotically nonexpansive type in CAT(0) spaces. The results obtained in this paper represent an extension as well as refinement of previous known results.

For OU processes driven by α-stable motions, its transition density function has no explicit form, while the conditional characteristic function is known. In this paper, we present an quasi-likelihood estimation procedure for parameters of the discretely sampled process of OU processes driven by α-stable motions. The proposed procedure is based on the conditional characteristic function, and the quasi-likelihood estimator is proved to be consistent and asymptotically efficient under some mild conditions. Finally, Monte Carlo simulations are conducted to demonstrate the accuracy and stability of proposed estimator.

We characterize the linear map Φ: Alg_Mα → Alg_Mβ which statisfies the property that Φ(I) = I and AB = ζBA ⇔ Φ(A)Φ(B) = ζΦ(B)Φ(A) for A,B ∈ Alg_Mα and for some scalar ζ. It is proved that every surjective weakly continuous linear map preserving identity and commutativity up to a factor in both directions between two nest subalgebras with non-trivial nests of any factor von Neumann algebra is either an isomorphism or an anti-isomorphism.