Authors:Jerod Michel Pages: 591 - 606 Abstract: Abstract Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets (and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns (which were recently coined by Cunsheng Ding in “Codes from Difference Sets” (2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-6151-6 Issue No:Vol. 33, No. 5 (2017)

Authors:Yan Yun Su; Heng Jian Cui; Kai Can Li Pages: 607 - 619 Abstract: Abstract In this paper, the parameters of a p-dimensional linear structural EV (error-in-variable) model are estimated when the coefficients vary with a real variable and the model error is time series. The adjust weighted least squares (AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-3187-6 Issue No:Vol. 33, No. 5 (2017)

Authors:Wen Wang Pages: 620 - 634 Abstract: Abstract In this paper, let (M n , g) be an n-dimensional complete Riemannian manifold with the m-dimensional Bakry–Émery Ricci curvature bounded below. By using the maximum principle, we first prove a Li–Yau type Harnack differential inequality for positive solutions to the parabolic equation $${u_t} = LF\left( u \right) = \Delta F\left( u \right) - \nabla f \cdot \nabla F\left( u \right),$$ on compact Riemannian manifolds M n , where F ∈ C 2(0,∞), F′ > 0 and f is a C 2-smooth function defined on M n . As application, the Harnack differential inequalities for fast diffusion type equation and porous media type equation are derived. On the other hand, we derive a local Hamilton type gradient estimate for positive solutions of the degenerate parabolic equation on complete Riemannian manifolds. As application, related local Hamilton type gradient estimate and Harnack inequality for fast dfiffusion type equation are established. Our results generalize some known results. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-6260-2 Issue No:Vol. 33, No. 5 (2017)

Authors:Jing Chen; Xian Wen Zhang; Ran Gao Pages: 635 - 656 Abstract: Abstract We investigate the Cauchy problem for the Vlasov–Poisson system with radiation damping. By virtue of energy estimate and a refined velocity average lemma, we establish the global existence of nonnegative weak solution and asymptotic behavior under the condition that initial data have finite mass and energy. Furthermore, by building a Gronwall inequality about the distance between the Lagrangian flows associated to the weak solutions, we can prove the uniqueness of weak solution when the initial data have a higher order velocity moment. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-6310-9 Issue No:Vol. 33, No. 5 (2017)

Authors:Qing Lin Lu Pages: 657 - 667 Abstract: Abstract In this paper, we study the class S of skew Motzkin paths, i.e., of those lattice paths that are in the first quadrat, which begin at the origin, end on the x-axis, consist of up steps U = (1, 1), down steps D = (1,−1), horizontal steps H = (1, 0), and left steps L = (−1,−1), and such that up steps never overlap with left steps. Let S n be the set of all skew Motzkin paths of length n and let s n = S n . Firstly we derive a counting formula, a recurrence and a convolution formula for sequence {s n } n ≥0. Then we present several involutions on S n and consider the number of their fixed points. Finally we consider the enumeration of some statistics on S n . PubDate: 2017-05-01 DOI: 10.1007/s10114-016-5292-y Issue No:Vol. 33, No. 5 (2017)

Authors:Qing Hou Zeng; Jian Feng Hou; Jin Deng; Xia Lei Pages: 668 - 680 Abstract: Abstract Let G = (V,E) be a graph with m edges. For reals p ∈ [0, 1] and q = 1− p, let m p(G) be the minimum of qe(V 1) +pe(V 2) over partitions V = V 1 ∪ V 2, where e(V i) denotes the number of edges spanned by V i. We show that if m p(G) = pqm−δ, then there exists a bipartition V 1, V 2 of G such that \(e{V_1} \leqslant {p^2}m - \delta + p\sqrt {m/2} + o\left( {\sqrt m } \right)\) and \(e{V_2} \leqslant {q^2}m - \delta + q\sqrt {m/2} + o\left( {\sqrt m } \right)\) for δ = o(m2/3). This is sharp for complete graphs up to the error term \(o\left( {\sqrt m } \right)\) . For an integer k ≥ 2, let f k(G) denote the maximum number of edges in a k-partite subgraph of G. We prove that if f k(G) = (1 − 1/k)m + α, then G admits a k-partition such that each vertex class spans at most m/k 2 − Ω(m/k 7.5) edges for α = Ω(m/k 6). Both of the above improve the results of Bollobás and Scott. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-6043-9 Issue No:Vol. 33, No. 5 (2017)

Authors:Qing Jin Cheng; Yun Bai Dong Pages: 681 - 690 Abstract: Abstract Assume that the unit spheres of Banach spaces X and Y are uniformly homeomorphic. Then we prove that all unit spheres of the Lebesgue–Bochner function spaces L p (μ,X) and L q (μ, Y) are mutually uniformly homeomorphic where 1 ≤ p, q < ∞. As its application, we show that if a Banach space X has Property H introduced by Kasparov and Yu, then the space L p (μ,X), 1 ≤ p < ∞, also has Property H. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-6245-1 Issue No:Vol. 33, No. 5 (2017)

Authors:Xiang Rong Zhu Pages: 691 - 704 Abstract: Abstract Let Ω be a bounded domain in ℝ n with smooth boundary. Here we consider the following Jacobian-determinant equation $$\left\{ {\begin{array}{*{20}{c}} {\det \nabla u\left( x \right) = f\left( x \right),}&{x \in \Omega ;} \\ {u\left( x \right) = x,}&{x \in \partial \Omega ,} \end{array}} \right.$$ where f is a function on Ω with minΩ f = δ > 0 and ∫Ω f(x)dx = Ω . We prove that if \(f \in B_{p1}^{\frac{n}{p}}\left( \Omega \right)\) for some p ∈ (n,∞), then there exists a solution \(u \in B_{p1}^{\frac{n}{p} + 1}\left( \Omega \right) \subset {C^1}\left( \Omega \right)\) to this equation. On the other hand, we give a simple example such that u ∈ C 0 1(ℝ2,ℝ2) while det∇u does not lie in \(B_{p1}^{\frac{2}{p}}\left( {{\mathbb{R}^{}}} \right)\) for any p < ∞. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-5749-z Issue No:Vol. 33, No. 5 (2017)

Authors:Jian Min Chen; Jin Jing Chen; Ya Nan Lin Pages: 705 - 724 Abstract: Abstract In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can characterize the category of coherent sheaves. Moreover, we describe the relationship between Prüfer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prüfer sheaves. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-5063-9 Issue No:Vol. 33, No. 5 (2017)

Authors:He Guo Liu; Yu Lei Wang Pages: 725 - 730 Abstract: Abstract A finite p-group P is called resistant if, for any finite group G having P as a Sylow p-group, the normalizer N G (P) controls p-fusion in G. Let P be a central extension as $$1 \to {\mathbb{Z}_{{p^m}}} \to P \to {\mathbb{Z}_p} \times \cdots {\mathbb{Z}_p} \to 1,$$ and P′ ≤ p, m ≥ 2. The purpose of this paper is to prove that P is resistant. PubDate: 2017-05-01 DOI: 10.1007/s10114-016-4016-7 Issue No:Vol. 33, No. 5 (2017)

Authors:Ke Feng Liu; Yong Wang Pages: 455 - 469 Abstract: Abstract By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on (4r − 1)-dimensional manifolds with no assumption that the 3rd de-Rham cohomology of manifolds vanishes. These anomaly cancellation formulas generalize our previous anomaly cancellation formulas on (4r − 1)-dimensional manifolds. We also generalize our previous anomaly cancellation formulas on (4r − 1)-dimensional manifolds and the Han–Yu rigidity theorem to the (a, b) case. PubDate: 2017-04-01 DOI: 10.1007/s10114-016-5714-x Issue No:Vol. 33, No. 4 (2017)

Authors:Yi Jie Lin; Jian Zhou Pages: 470 - 494 Abstract: Abstract We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived. PubDate: 2017-04-01 DOI: 10.1007/s10114-016-6155-2 Issue No:Vol. 33, No. 4 (2017)

Authors:Lin Chen; Fang Yan Lu Pages: 495 - 500 Abstract: Abstract Let Alg ℒ be a J -subspace lattice algebra on a Banach space X and M be an operator in Alg ℒ. We prove that if δ: Alg ℒ → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B) for all A,B ∈ Alg ℒ with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras. PubDate: 2017-04-01 DOI: 10.1007/s10114-016-6235-3 Issue No:Vol. 33, No. 4 (2017)

Authors:Wei Hua He; Hao Li; Yan Dong Bai; Qiang Sun Pages: 501 - 508 Abstract: Abstract A linear directed forest is a directed graph in which every component is a directed path. The linear arboricity la(D) of a digraph D is the minimum number of linear directed forests in D whose union covers all arcs of D. For every d-regular digraph D, Nakayama and Péroche conjecture that la(D) = d + 1. In this paper, we consider the linear arboricity for complete symmetric digraphs, regular digraphs with high directed girth and random regular digraphs and we improve some well-known results. Moreover, we propose a more precise conjecture about the linear arboricity for regular digraphs. PubDate: 2017-04-01 DOI: 10.1007/s10114-016-5071-9 Issue No:Vol. 33, No. 4 (2017)

Authors:Ye Chen; Xiang Qun Yang; Ying Qiu Li; Xiao Wen Zhou Pages: 509 - 525 Abstract: Abstract For a < r < b, the approach of Li and Zhou (2014) is adopted to find joint Laplace transforms of occupation times over intervals (a, r) and (r, b) for a time homogeneous diffusion process before it first exits from either a or b. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively. PubDate: 2017-04-01 DOI: 10.1007/s10114-016-5184-1 Issue No:Vol. 33, No. 4 (2017)

Authors:Cheng Jun Hou Pages: 526 - 544 Abstract: Abstract We introduce the notion of property (RD) for a locally compact, Hausdorff and r-discrete groupoid G, and show that the set S 2 l (G) of rapidly decreasing functions on G with respect to a continuous length function l is a dense spectral invariant and Fréchet *-subalgebra of the reduced groupoid C*-algebra C r * (G) of G when G has property (RD) with respect to l, so the K-theories of both algebras are isomorphic under inclusion. Each normalized cocycle c on G, together with an invariant probability measure on the unit space G 0 of G, gives rise to a canonical map τ c on the algebra C c (G) of complex continuous functions with compact support on G. We show that the map τ c can be extended continuously to S 2 l (G) and plays the same role as an n-trace on C r * (G) when G has property (RD) and c is of polynomial growth with respect to l, so the Connes’ fundament paring between the K-theory and the cyclic cohomology gives us the K-theory invariants on C r * (G). PubDate: 2017-04-01 DOI: 10.1007/s10114-016-6264-y Issue No:Vol. 33, No. 4 (2017)

Authors:Zhi Tao Yang; Yu Feng Lu; Qing Jin Cheng Pages: 545 - 553 Abstract: Abstract We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that the closed convex hull co̅C of C is super weakly compact. We also show that a Banach space X is super weakly compactly generated iff the dual unit ball B X* of X* in its weak star topology is affinely homeomorphic to a super weakly compactly convex subset of a Banach space. PubDate: 2017-04-01 DOI: 10.1007/s10114-017-6354-5 Issue No:Vol. 33, No. 4 (2017)

Authors:Qing Hua Xu; Fang Fang; Tai Shun Liu Pages: 554 - 564 Abstract: Abstract Let S α * be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szegö inequality for the class S α * , and then we generalize this result to the unit ball in a complex Banach space or on the unit polydisk in C n . PubDate: 2017-04-01 DOI: 10.1007/s10114-016-5762-2 Issue No:Vol. 33, No. 4 (2017)

Authors:Tao Xu; He Guo Liu Pages: 565 - 570 Abstract: Abstract Let G be a polycyclic group and α a regular automorphism of order four of G. If the map φ: G → G defined by g φ = [g,α] is surjective, then the second derived group of G is contained in the centre of G. Abandoning the condition on surjectivity, we prove that C G (α 2) and G/[G, α 2] are both abelian-by-finite. PubDate: 2017-04-01 DOI: 10.1007/s10114-016-4660-y Issue No:Vol. 33, No. 4 (2017)

Authors:Zhao Lin Jiang; Yun Cheng Qiao; Shu Dong Wang Pages: 571 - 590 Abstract: Abstract In this paper, three new circulant operator matrices, scaled circulant operator matrices, diag-circulant operator matrices and retrocirculant operator matrices, are given respectively. Several norm equalities and inequalities for these operator matrices are proved. We show the special cases for norm equalities and inequalities, such as the usual operator norm and the Schatten p-norm. Pinching type inequality is also given for weakly unitarily invariant norms. These results are closely related to the nice structure of these special operator matrices. Furthermore, some special cases and specific examples are also considered. PubDate: 2017-04-01 DOI: 10.1007/s10114-016-5607-z Issue No:Vol. 33, No. 4 (2017)