Abstract: Zhao and Ho asked in a recent paper that for each T0 space X, whether KB(X) (the set of all irreducible closed sets of X whose suprema exist) is the canonical k-bounded sobrification of X in the sense of Keimel and Lawson. In this paper, we construct a counterexample to give a negative answer. We also consider the subcategory Topκ of the category Top0 of T0 spaces, and prove that the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category Topκ. PubDate: 2019-03-01

Abstract: The main purpose of this paper is using the analytic methods, the solutions of the congruence equation mod p and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 3-dimensional Kloostermann sums mod p, and give a sharp asymptotic formula for it. PubDate: 2019-03-01

Abstract: In this paper, we first generalize Gerstewitz’s functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order principle [Qiu, J. H.: A pre-order principle and set-valued Ekeland variational principle. J. Math. Anal. Appl., 419, 904–937 (2014)]. By using the generalized Gerstewitz’s functions and the partial order principle, we obtain a vector EVP for ε-efficient solutions in the sense of Németh, which essentially improves the earlier results by completely removing a usual assumption for boundedness of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results. PubDate: 2019-03-01

Abstract: Let X be a Banach space over \(\mathbb{F} (=\mathbb{R} \rm{or} \mathbb{C})\) with dimension greater than 2. Let \(\mathcal{N}(X)\) be the set of all nilpotent operators and \(\mathcal{B}_0(X)\) the set spanned by \(\mathcal{N}(X)\) . We give a structure result to the additive maps on \(\mathbb{F}I+\mathcal{B}_0(X)\) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on \(\mathbb{F}I+\mathcal{B}_0(X)\) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A−1 +ϕ(T)I for all \(T\in\mathbb{F}I+\mathcal{B}_0(X)\) or Φ(T) = cAT* A−1 + ϕ(T)I for all \(T\in\mathbb{F}I+\mathcal{B}_0(X)\) , where c is a nonzero scalar, A is a τ-linear bijective transformation for some automorphism τ of F and ϕ is an additive functional. In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator. PubDate: 2019-03-01

Abstract: Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n ≠ 0. An additive mapping δ from R into M is called an (m, n)-Jordan derivation if (m + n)δ(A2) = 2mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every (m, n)-Jordan derivation with m ≠ n from a C* -algebra into its Banach bimodule is zero. An additive mapping δ from R into M is called a (m, n)-Jordan derivable mapping at W in R if (m + n)δ(AB + BA) = 2mδ(A)B + 2mδ(B)A + 2nAδ(B) + 2nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and \(\mathcal{U}=\begin{bmatrix}\mathcal{A} & \mathcal{M} \\\mathcal{N} & \mathcal{B} \end{bmatrix}\) is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero. PubDate: 2019-03-01

Abstract: In this article, we investigate the arithmetic behavior of the function D3(n) which counts the number of 3-regular tripartitions of n. For example, we show that for α ≥ 1 and n ≥ 0, $${D_3}\left( {{3^{2\alpha }}n + \frac{{11 \cdot {3^{2\alpha - 1}} - 1}}{4}} \right) \equiv 0\left( {\bmod {3^{2\alpha + 3}}} \right)$$ and $${D_3}\left( {{3^{2\alpha }}n + \frac{{7 \cdot {3^{2\alpha - 1}} - 1}}{4}} \right) \equiv 0\left( {\bmod {3^{2\alpha + 2}}} \right)$$ . PubDate: 2019-03-01

Abstract: Let G be a basic classical Lie superalgebra except A(n, n) and D(2, 1, α) over the complex number field ℂ. Using existence of a non-degenerate invariant bilinear form and root space decomposition, we prove that every 2-local automorphism on G is an automorphism. Furthermore, we give an example of a 2-local automorphism which is not an automorphism on a subalgebra of Lie superalgebra spl(3, 3). PubDate: 2019-03-01

Abstract: Let \(X= \{X(t) \in \mathbb{R}^d, t\in \mathbb{R}^N\}\) be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in ℝd, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version. PubDate: 2019-03-01

Abstract: We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial \(B(G;x):={\sum}_{k=-n}^{\partial(G)}B_k(G)x^{n+k}\) , where Bk(G) denotes the number of vertex subsets of G with differential equal to k. We state some properties of B(G; x) and its coefficients. In particular, we compute the differential polynomial for complete, empty, path, cycle, wheel and double star graphs. We also establish some relationships between B(G; x) and the differential polynomials of graphs which result by removing, adding, and subdividing an edge from G. PubDate: 2019-03-01

Abstract: In this paper we pursue the study of the best approximation operator extended from LΦ to Lφ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calderón–Zygmund class t m p (x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ. PubDate: 2019-02-01

Abstract: In this paper, we study the reconstruction of spline functions from their nonuniform samples. We investigate the existence and uniqueness of the solution of the following problem: for given data {(xn, yn): n ∈ ℤ}, find a cardinal spline f(x), of a given degree, satisfying yn = f(xn), n ∈ ℤ. Several necessary and/or sufficient conditions for the existence and uniqueness of the solution of the problem are derived. Finally, an example and some applications are presented to illustrate the main results. PubDate: 2019-02-01

Abstract: Let \(f,g : X \rightarrow Y\) be maps from a compact infra-nilmanifold X to a compact nilmanifold Y with \(X \geq \rm{dim}\it{Y}\) . In this note, we show that a certain Wecken type property holds, i.e., if the Nielsen number N(f, g) vanishes then f and g are deformable to be coincidence free. We also show that if X is a connected finite complex X and the Reidemeister coincidence number R(f, g) = ∞ then f ~ f′ so that \(C(f',g)= \{x \in X f'(x)=g(x)\}\) is empty. PubDate: 2019-02-01

Abstract: Balinsky–Novikov superalgebras were introduced by Balinsky for constructing super-Vira-soro type Lie superalgebras. In this paper, we give sufficient and necessary conditions for a Lie superalgebra generalized by a Balinsky–Novikov superalgebra with dimension 2 2 to be a quadratic Lie superalgebra. PubDate: 2019-02-01

Abstract: Empirical likelihood inference for parametric and nonparametric parts in functional coefficient ARCH-M models is investigated in this paper. Firstly, the kernel smoothing technique is used to estimate coefficient function δ(x). In this way we obtain an estimated function with parameter β. Secondly, the empirical likelihood method is developed to estimate the parameter β. An estimated empirical log-likelohood ratio is proved to be asymptotically standard chi-squred, and the maximum empirical likelihood estimation (MELE) for β is shown to be asymptotically normal. Finally, based on the MELE of β, the empirical likelihood approach is again applied to reestimate the nonparametric part δ(x). The empirical log-likelohood ratio for δ(x) is proved to be also asymptotically standard chi-squred. Simulation study shows that the proposed method works better than the normal approximation method in terms of average areas of confidence regions for β, and the empirical likelihood confidence belt for δ(x) performs well. PubDate: 2019-02-01

Abstract: The authors recently defined a new graph invariant denoted by Ω(G) only in terms of a given degree sequence which is also related to the Euler characteristic. It has many important combinatorial applications in graph theory and gives direct information compared to the better known Euler characteristic on the realizability, connectedness, cyclicness, components, chords, loops etc. Many similar classification problems can be solved by means of Ω. All graphs G so that \(\Omega(G)\leq-4\) are shown to be disconnected, and if \(\Omega(G)\geq-2\) , then the graph is potentially connected. It is also shown that if the realization is a connected graph and \(\Omega(G)\geq-2\) , then certainly the graph should be a tree. Similarly, it is shown that if the realization is a connected graph G and \(\Omega(G)\geq0\) , then certainly the graph should be cyclic. Also, when \(\Omega(G)\geq-4\) , the components of the disconnected graph could not all be cyclic and if all the components of G are cyclic, then \(\Omega(G)\geq0\) . In this paper, we study an extremal problem regarding graphs. We find the maximum number of loops for three possible classes of graphs. We also state a result giving the maximum number of components amongst all possible realizations of a given degree sequence. PubDate: 2019-02-01

Abstract: In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz’s strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive. PubDate: 2019-02-01

Abstract: Let G be an extension of ℚ by a direct sum of r copies of ℚ. (1) If G is abelian, then G is a direct sum of r + 1 copies of ℚ and AutG ≅ GL(r + 1, Q); (2) If G is non-abelian, then G is a direct product of an extraspecial ℚ-group E and m copies of ℚ, where E/ζE is a linear space over Q with dimension 2n and m + 2n = r. Furthermore, let AutG′G be the normal subgroup of AutG consisting of all elements of AutG which act trivially on the derived subgroup G′ of G, and AutG/ζG,ζGG be the normal subgroup of AutG consisting of all central automorphisms of G which also act trivially on the center ζG of G. Then (i) The extension 1 → AutG′G → AutG → AutG′ → 1 is split; (ii) AutG′G/AutG/ζG,ζGG ≅ Sp(2n,Q) × (GL(m, Q) ⋉ ℚ(m)); (iii) AutG/ζG,ζGG/InnG ≅ ℚ(2nm). PubDate: 2019-02-01

Abstract: Let X be a compact metric space, F: X×ℝ → X be a continuous flow and x ∈ X a proper quasi-weakly almost periodic point, that is, x is quasi-weakly almost periodic but not weakly almost periodic. The aim of this paper is to investigate whether there exists an invariant measure generated by the orbit of x such that the support of this measure coincides with the minimal center of attraction of x' In order to solve the problem, two continuous flows are constructed. In one continuous flow, there exist a proper quasi-weakly almost periodic point and an invariant measure generated by its orbit such that the support of this measure coincides with its minimal center of attraction; and in the other, there is a proper quasi-weakly almost periodic point such that the support of any invariant measure generated by its orbit is properly contained in its minimal center of attraction. So the mentioned problem is sufficiently answered in the paper. PubDate: 2019-02-01

Abstract: In this paper, we study radial operators in Toeplitz algebra on the weighted Bergman spaces over the polydisk by the (m, λ)-Berezin transform and find that a radial operator can be approximated in norm by Toeplitz operators without any conditions. We prove that the compactness of a radial operator is equivalent to the property of vanishing of its (0, λ)-Berezin transform on the boundary. In addition, we show that an operator S is radial if and only if its (m, λ)-Berezin transform is a separately radial function. PubDate: 2019-02-01

Authors:Yong Hu; Lei Zhang Abstract: Let S be a smooth minimal projective surface of general type with p g (S) = q(S) = 1, K S 2 = 6. We prove that the degree of the bicanonical map of S is 1 or 2. So if S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface. PubDate: 2018-05-18 DOI: 10.1007/s10114-018-7262-z