In this paper, we discuss the moving-average process , where {α _i ;-∞ < i < ∞} is a doubly infinite sequence of identically distributed φ-mixing or negatively associated random variables with mean zeros and finite variances, {α _i ;-∞ < i < ∞} is an absolutely summable sequence of real numbers. Set . Suppose that . We prove that for any ,

, and if ,

where is a Gamma function and μ^(2δ+2) stands for the (2δ + 2)-th absolute moment of the standard normal distribution.

We continue the work initiated in [1] (Second order nonlinear evolution inclusions I: Existence and relaxation results. Acta Mathematics Science, English Series, 21(5), 977-966 (2005)) and study the structural properties of the solution set of second order evolution inclusions which are defined in the analytic framework of the evolution triple. For the convex problem we show that the solution set is compact R _δ , while for the nonconvex problem we show that it is path connected. Also we show that the solution set is closed only if the multivalued nonlinearity is convex valued. Finally we illustrate the results by considering a nonlinear hyperbolic problem with discontinuities.

In this part II the fundamental inequality of the third order general regular variation is proved and the second order Edgeworth expansion of the distribution of the extreme values is discussed.

In this paper, the authors study the boundedness properties of generated by the function b ∈ Lip _β (?ⁿ)(0 < β ≤ 1/m) and the Marcinkiewicz integrals operator μ _Ω . The boundednesses are established on the Hardy type spaces and the Herz–Hardy type spaces .

This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion Spin ^c structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are obtained.

In this paper, we first define a doubly transitive resolvable idempotent quasigroup (DTRIQ), and show that a DTRIQ of order v exists if and only if v ≡ 0 (mod 3) and v ? 2 (mod 4). Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang (J. Combin. Designs, 4 (1996), 301–321). As an application, we obtain an LRDTS(4 · 3 ⁿ ) for any integer n ≥ 1, which provides an infinite family of even orders.

 Kernel theorems are established for Banach space–valued multilinear mappings. A moment characterization theorem for Banach space–valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space–valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space–valued generalized functionals.

Let A be a matrix with the absolute values of all eigenvalues strictly larger than one, and let Z ₀ be a subset of Z such than n∈Z ₀ implies n + 1 ∈Z ₀. Denote the space of all compactly supported distributions by D′, and the usual convolution between two compactly supported distributions f and g by f*g. For any bounded sequence G _n and H _n , n∈Z ₀, in D′, define the corresponding nonstationary nonhomogeneous refinement equation

((*))

where Φ _n , n∈Z ₀, is in a bounded set of D′. The nonstationary nonhomogeneous refinement equation (*) arises in the construction of wavelets on bounded domain, multiwavelets, and of biorthogonal wavelets on nonuniform meshes. In this paper, we study the existence problem of compactly supported distributional solutions Φ _n , n∈Z ₀, of the equation (*). In fact, we reduce the existence problem to finding a bounded solution of the linear equations

where the matrices S _n and the vectors , n∈Z ₀, can be constructed explicitly from H _n and G _n respectively. The results above are still new even for stationary nonhomogeneous refinement equations.

We derive some quadratic recursion relations for some Hodge integrals by virtual localization and obtain many closed formulas. We apply our formulas to the local geometry of toric Fano surfaces in a Calabi-Yau threefold and compute some of the numbers in Gopakumar-Vafa's formula for all g in this case.

 By using vector Riccati transformation and averaging technique, some oscillation criteria for the quasilinear elliptic di.erential equation of second order,

are obtained. These theorems extend and include earlier results for the semilinear elliptic equation and PDE with p-Laplacian.

We obtain formulae and estimates for character sums of the type where p ^m is a prime power with m ≥ 2, χ is a multiplicative character (mod p ^m ), and f=f ₁/f ₂ is a rational function over ?. In particular, if p is odd, d=deg(f ₁)+deg(f ₂) and d* = max(deg(f ₁), deg(f ₂)) then we obtain for any non-constant f (mod p) and primitive character χ. For p = 2 an extra factor of is needed.

Rips conjectured that a non-clementary word hyperbolic group is cohopfian if and only if it is freely indecomposable. The results and examples in this paper show that cohopficity phenomenon in the case of word hyperbolic group with torsion is much more complicated than the conjecture. In particular, the cohopficity of such groups is not determined by the numbers of their ends and the cohopficity is not preserved by finite index subgroups. Our results and examples arise from Kleinian groups. Orbifold structures and orbifold maps are the new tools in our discussions.

 The notion of the xst-rings was introduced by García and Marín [5] in 1999. In this paper, we consider Morita context, Morita-like equivalence and the exchange property for the xst-rings. The results of the first Morita theorem are generalized to the xst-rings. So we obtain an important Morita-like equivalence of the xst-rings, from which, as an immediate consequence, we deduce the main result of Xu-Shum-Turner [4] and the standard Morita equivalence, A ∼ M _n (A), for a unital ring A. Moreover, we describe the properties of those well-known intermediate matrix rings, and show that the exchange property of a unital ring A coincides with the one for any M _n (A) as well as any intermediate matrix ring sitting between FM _Γ(A) and FC _Γ(A), which is an extension of a well-known result obtained by Nicholson [7].

Two boundary value problems are investigated for an over–determined elliptic system with several complex variables in polydisc. Necessary and sufficient conditions for the existence of finitely many linearly independent solutions and finitely many solvability conditions are derived. Moreover, the boundary value problem for any number of complex variables is treated in a unified way and the essential difference between the case of one complex variable and that of several complex variables is revealed.

The paper explores the connection of Graph-Lagrangians and its maximum cliques for 3-uniform hypergraphs. Motzkin and Straus showed that the Graph-Lagrangian of a graph is the Graph-Lagrangian of its maximum cliques. This connection provided a new proof of Turán classical result on the Turán density of complete graphs. Since then, Graph-Lagrangian has become a useful tool in extremal problems for hypergraphs. Peng and Zhao attempted to explore the relationship between the Graph-Lagrangian of a hypergraph and the order of its maximum cliques for hypergraphs when the number of edges is in certain range. They showed that if G is a 3-uniform graph with m edges containing a clique of order t-1, then λ(G) = λ([t-1]⁽³⁾) provided (₃ ^t-1) ≤ m ≤ (₃ ^t-1) + (₂ ^t-2). They also conjectured: If G is an r-uniform graph with m edges not containing a clique of order t-1, then λ(G) < λ([t-1]^(r)) provided (_r ^t-1) ≤ m ≤ (_r ^t-1) + (_r-1 ^t-2). It has been shown that to verify this conjecture for 3-uniform graphs, it is sufficient to verify the conjecture for left-compressed 3-uniform graphs with m = (₃ ^t-1) +(₂ ^t-2). Regarding this conjecture, we show: If G is a left-compressed 3-uniform graph on the vertex set [t] with m edges and |[t-1]⁽³⁾\E(G)| = p, then λ(G) < λ([t-1]⁽³⁾) provided m = (³ _t-1) + (² _t-2) and t ≥ 17p/2 + 11.

We consider the Cauchy-Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg flat domain. The coefficients supposed to be only measurable in one of the space variables and small BMO with respect to the others. We obtain Calder′on-Zygmund type estimate for the gradient of the solution in generalized weighted Morrey spaces with Muckenhoupt weight.

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.