15 March 2019, Volume 35 Issue 3

    

• Select all
  |

Articles
• Select
  Generalized Gerstewitz's Functions and Vector Variational Principle for ε-Efficient Solutions in the Sense of Németh

  Jing Hui QIU

  Acta Mathematica Sinica. 2019, 35(3): 297-320. https://doi.org/10.1007/s10114-018-7159-x

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  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.
• Select
  Surfaces with p_g=q=1, K²=6 and Non-birational Bicanonical Maps

  Yong HU, Lei ZHANG

  Acta Mathematica Sinica. 2019, 35(3): 321-337. https://doi.org/10.1007/s10114-018-7262-z

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let S be a smooth minimal projective surface of general type with p_g(S)=q(S)=1, K_S²=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.
• Select
  On the Differential Polynomial of a Graph

  Ludwin A. BASILIO-HERNÁNDEZ, Walter CARBALLOSA, Jesús LEAÑOS, José M. SIGARRETA

  Acta Mathematica Sinica. 2019, 35(3): 338-354. https://doi.org/10.1007/s10114-018-7307-3

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial B(G; x):=Σ_k=-n^∂(G) B_k(G) x^n+k, where B_k(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.
• Select
  On 3-Regular Tripartitions

  Chandrashekar ADIGA, Ranganatha DASAPPA

  Acta Mathematica Sinica. 2019, 35(3): 355-368. https://doi.org/10.1007/s10114-018-7111-0

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  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, 
  

• Select
  The Fourth Power Mean of the General 3-dimensional Kloostermann Sums mod p

  Wen Peng ZHANG, Xing Xing LV

  Acta Mathematica Sinica. 2019, 35(3): 369-377. https://doi.org/10.1007/s10114-018-7455-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  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.
• Select
  Characterizations of (m, n)-Jordan Derivations and (m, n)-Jordan Derivable Mappings on Some Algebras

  Guang Yu AN, Jun HE

  Acta Mathematica Sinica. 2019, 35(3): 378-390. https://doi.org/10.1007/s10114-018-7495-x

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  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 U=[_N^A_B^M] is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero.
• Select
  Dimension Results for Space-anisotropic Gaussian Random Fields

  Wen Qing NI, Zhen Long CHEN, Wei Gang WANG

  Acta Mathematica Sinica. 2019, 35(3): 391-406. https://doi.org/10.1007/s10114-018-8016-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let X={X(t) ∈ R^d, t ∈ R^N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R^d, 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.
• Select
  Additive Maps Preserving Nilpotent Perturbation of Scalars

  Ting ZHANG, Jin Chuan HOU

  Acta Mathematica Sinica. 2019, 35(3): 407-426. https://doi.org/10.1007/s10114-018-8048-z

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let X be a Banach space over F (=R or C) with dimension greater than 2. Let N (X) be the set of all nilpotent operators and B₀(X) the set spanned by N (X). We give a structure result to the additive maps on FI + B₀(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI + B₀(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T)=cATA^-1 +φ(T)I for all T ∈ FI + B₀(X) or Φ(T)=cAT^* A^-1 + φ(T)I for all T ∈ FI + B₀(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.
• Select
  2-Local Automorphisms on Basic Classical Lie Superalgebras

  Li YU, Ying WANG, Hai Xian CHEN, Ji Zhu NAN

  Acta Mathematica Sinica. 2019, 35(3): 427-437. https://doi.org/10.1007/s10114-018-7519-6

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  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).
• Select
  The Answer to a Problem Posed by Zhao and Ho

  Bin ZHAO, Jing LU, Kai Yun WANG

  Acta Mathematica Sinica. 2019, 35(3): 438-444. https://doi.org/10.1007/s10114-018-7535-6

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  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 Top_κ 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 Top_κ.