Authors:Paul Norbury Pages: 1163 - 1183 Abstract: Abstract We represent stationary descendant Gromov–Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of the large degree behaviour of stationary descendant Gromov–Witten invariants in terms of intersection numbers over the moduli space of curves. We also show that primary Gromov–Witten invariants are “virtual” stationary descendants and hence the string and divisor equations can be understood purely in terms of stationary invariants. PubDate: 2017-09-01 DOI: 10.1007/s10114-017-5314-4 Issue No:Vol. 33, No. 9 (2017)

Authors:Yun Fan Pages: 1184 - 1192 Abstract: Abstract In this paper, we prove that if a c.e. Turing degree d is non-low2, then there are two left-c.e. reals β 0, β 1 in d, such that, if β 0 is wtt-reducible to a left-c.e. real α, then β 1 is not computable Lipschitz (cl-) reducible to α. As a corollary, d contains a left-c.e. real which is not cl-reducible to any complex (wtt-complete) left-c.e. real. PubDate: 2017-09-01 DOI: 10.1007/s10114-017-6585-5 Issue No:Vol. 33, No. 9 (2017)

Authors:Xiang Mao Ding; Yu Ping Li; Ling Xian Meng Pages: 1193 - 1205 Abstract: Abstract Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory (CFT) method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra. PubDate: 2017-09-01 DOI: 10.1007/s10114-017-6268-2 Issue No:Vol. 33, No. 9 (2017)

Authors:Jing Lu; Xing Dong Tang Pages: 1206 - 1224 Abstract: Abstract In this paper, we study the global scattering result of the solution for the generalized Davey–Stewartson system $$\left\{ {\begin{array}{*{20}{c}} {i{\partial _t}u + \Delta u = {{\left u \right }^2}u + u{v_{{x_1}}},\left( {t,x} \right) \in \mathbb{R} \times {\mathbb{R}^3},} \\ { - \Delta u = {{\left( {{{\left u \right }^2}} \right)}_{{x_1}}}.} \end{array}} \right.$$ The main difficulties are the failure of the interaction Morawetz estimate and the asymmetrical structure of nonlinearity (in particular, the nonlinearity is non-local). To compensate, we utilize the strategy derived from concentration-compactness idea, which was first introduced by Kenig and Merle [Invent. Math., 166, 645–675 (2006)]. PubDate: 2017-09-01 DOI: 10.1007/s10114-017-6301-5 Issue No:Vol. 33, No. 9 (2017)

Authors:Mourad Oudghiri; Khalid Souilah Pages: 1225 - 1241 Abstract: Abstract Let B(X) be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. Given an integer n ≥ 1, we show that an additive surjective map Φ on B(X) preserves Drazin invertible operators of index non-greater than n in both directions if and only if Φ is either of the form Φ(T) = αATA −1 or of the form Φ(T) = αBT *B −1 where α is a non-zero scalar, A: X → X and B: X* → X are two bounded invertible linear or conjugate linear operators. PubDate: 2017-09-01 DOI: 10.1007/s10114-017-6534-3 Issue No:Vol. 33, No. 9 (2017)

Authors:Xiao Fei Zhang; Tai Shun Liu; Yong Hong Xie Pages: 1242 - 1248 Abstract: Abstract In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball B n respectively. PubDate: 2017-09-01 DOI: 10.1007/s10114-017-6220-5 Issue No:Vol. 33, No. 9 (2017)

Authors:Mohamed Akel; Fatimah Alabbad Pages: 1249 - 1266 Abstract: Abstract In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann–Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are obtained. The boundary behavior of these operators is discussed. Finally, we investigate the Schwarz problem and the Riemann–Hilbert problem for inhomogeneous Cauchy–Riemann equations. PubDate: 2017-09-01 DOI: 10.1007/s10114-016-6127-6 Issue No:Vol. 33, No. 9 (2017)

Authors:Sheng Yang; Sheng Gao; Chong Bin Xu Pages: 1267 - 1274 Abstract: Abstract Let B be a 3-block of a finite group G with a defect group D. In this paper, we are mainly concerned with the number of characters in a particular block, so we shall use Isaacs’ approach to block structure. We consider the block B of a group G as a union of two sets, namely a set of irreducible ordinary characters of G having cardinality k(B) and a set of irreducible Brauer characters of G having cardinality l(B). We calculate k(B) and l(B) provided that D is normal in G and \(D \cong \left\langle {x,y,z x^{3^n } = y^{3^m } = z^3 = \left[ {x,z} \right] = \left[ {y,z} \right] = 1,\left[ {x,y} \right] = z} \right\rangle \left( {n > m \geqslant 2} \right)\) . PubDate: 2017-09-01 DOI: 10.1007/s10114-017-5792-4 Issue No:Vol. 33, No. 9 (2017)

Authors:Pai Yang; Lei Qiao Pages: 1275 - 1286 Abstract: Abstract Let f(z) be a meromorphic function in the complex plane, whose zeros have multiplicity at least k + 1 (k ≥ 2). If sin z is a small function with respect to f(z), then f(k)(z) − P(z) sinz has infinitely many zeros in the complex plane, where P(z) is a nonzero polynomial of deg(P(z)) ≠ 1. PubDate: 2017-09-01 DOI: 10.1007/s10114-017-6137-z Issue No:Vol. 33, No. 9 (2017)

Authors:Chang Sen Yang; Feng Hui Wang Pages: 1287 - 1296 Abstract: Abstract For a non-trivial Banach space X, let J(X), C NJ(X), C NJ (p) (X) respectively stand for the James constant, the von Neumann–Jordan constant and the generalized von Neumann–Jordan constant recently inroduced by Cui et al. In this paper, we discuss the relation between the James and the generalized von Neumann–Jordan constants, and establish an inequality between them: C NJ (p) (X) ≤ J(X) with p ≥ 2, which covers the well-known inequality C NJ(X) ≤ J(X). We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al. PubDate: 2017-09-01 DOI: 10.1007/s10114-017-6211-6 Issue No:Vol. 33, No. 9 (2017)

Authors:Youngsoo Seol Pages: 1297 - 1304 Abstract: Abstract We consider a linear Hawkes process with random marks. Some limit theorems have been studied by Karabash and Zhu [Stoch. Models, 31, 433–451 (2015)]. In this paper, we obtain a moderate deviation principle for marked Hawkes processes. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-6433-7 Issue No:Vol. 33, No. 10 (2017)

Authors:Huan Huan Li Pages: 1305 - 1320 Abstract: Abstract By assigning to each complex over a semi-simple ring two acyclicizations, we construct an explicit recollement for homotopy categories of a certain triangular matrix ring such that all the six triangle functors of the recollement preserve acyclic complexes. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-6565-9 Issue No:Vol. 33, No. 10 (2017)

Authors:Tao Cheng; Hui Qiang Shi; Shanshuang Yang Pages: 1321 - 1338 Abstract: Abstract This paper is devoted to the study of some fundamental properties of the sewing homeomorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sufficient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Hölder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-6481-z Issue No:Vol. 33, No. 10 (2017)

Authors:Jian Ping Zhang; Yun Zhang Li Pages: 1339 - 1351 Abstract: Abstract For refinable function-based affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame (WNABF). Under the setting of reducing subspaces of L 2(R d ), we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-6445-3 Issue No:Vol. 33, No. 10 (2017)

Authors:Liang Jin; Xiaojun Cui Pages: 1352 - 1360 Abstract: Abstract In this paper, we classify the set of Lorentzian metrics on T2, analyse the topological structure of some subclasses and study whether a subclass could admit certain weak solutions to the eikonal equations. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-6348-3 Issue No:Vol. 33, No. 10 (2017)

Authors:Xing Xiao Li; Hong Ru Song Pages: 1361 - 1381 Abstract: Abstract In this paper, we give a complete conformal classification of the regular space-like hypersurfaces in the de Sitter Space S m+1 1 with parallel para-Blaschke tensors. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-6208-1 Issue No:Vol. 33, No. 10 (2017)

Authors:Pei Ma; Feng Quan Li; Yan Li Pages: 1382 - 1396 Abstract: Abstract In this paper, we study the Pohozaev identity associated with a H´enon–Lane–Emden system involving the fractional Laplacian: $$\left\{ {\begin{array}{*{20}{c}} {{{\left( { - \Delta } \right)}^s}u = {{\left x \right }^a}{v^p},}&{x \in \Omega ,} \\ {{{\left( { - \Delta } \right)}^s}u = {{\left x \right }^b}{v^q},}&{x \in \Omega ,} \\ {u = v = 0,}&{x \in {\mathbb{R}^n}\backslash \Omega ,} \end{array}} \right.$$ in a star-shaped and bounded domain Ω for s ∈ (0, 1). As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-6556-x Issue No:Vol. 33, No. 10 (2017)

Authors:Jing Zhang; Huo Xiong Wu Pages: 1397 - 1420 Abstract: Abstract This paper is devoted to investigating the weighted L p -mapping properties of oscillation and variation operators related to the families of singular integrals and their commutators in higher dimension. We establish the weighted type (p, p) estimates for 1 < p < ∞ and the weighted weak type (1, 1) estimate for the oscillation and variation operators of singular integrals with kernels satisfying certain Hörmander type conditions, which contain the Riesz transforms, singular integrals with more general homogeneous kernels satisfying the Lipschitz conditions and the classical Dini’s conditions as model examples. Meanwhile, we also obtain the weighted L p -boundeness for such operators associated to the family of commutators generated by the singular integrals above with BMO(Rd)-functions. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-6379-9 Issue No:Vol. 33, No. 10 (2017)

Authors:Xin Luo; Ying Qing Xiao; Yue Ping Jiang Pages: 1421 - 1430 Abstract: Abstract In this note, first, we show that the asymptotic subcone, the ultralimit, the completion of an asymptotically PT−1 space are still an asymptotically PT−1 space. Secondly, we consider two kinds of metric spaces, which have been considered by Ibragimov and Gromov, respectively. We show that they are asymptotically PT−1 spaces under particular conditions, which provide some concrete examples of asymptotically PT−1 spaces. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-5257-9 Issue No:Vol. 33, No. 10 (2017)

Authors:Rui Dong Wang; Xu Jian Huang Pages: 1431 - 1442 Abstract: Abstract In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres. PubDate: 2017-10-01 DOI: 10.1007/s10114-017-6589-1 Issue No:Vol. 33, No. 10 (2017)