Generalized estimating equations method as a powerful method for estimating parameters, is wildly used in many fields, such as biostatistics, econometrics and medical insurance, and so on. For longitudinal data, We should take account into within-subject correlation structure in order to improve efficiency of a estimator. It is often useful to suppose that there is a parametric assumption within-subject correlation in longitudinal data analysis. But unreasonable assumptions made on within-subject correlation structure can result in inefficient estimation for parameters or even result in misspecification. For the generalized estimating equations with longitudinal data, we propose the extended GMM methods and extended EL methods and construct the large sample properties for our estimators. One of the proposed EL methods which is called block empirical likelihood is robust because of avoiding any assumptions on withinsubject correlation structure. We also provide two simulation examples to illustrate the finite properties for our estimators.  

We study a nonlinear Schrödinger equation modeling light waves propagating in a photorefractive crystal. We first construct the global weak attractor for this system. And then by exact analysis of the energy equation, we show that the global weak attractor is actually the global strong attractor. Further, we give the upper bound of the fractal and Hausdorff dimensions of the global attractor.  

In this paper, various subfamilies H_k(R_I(m,n))of holomorphic mappings defined in the first classical domain R_I(m,n)are introduced. When k tends to +∞, this family reduces to the class of locally biholomorphic mappings on R_I(m,n). We establish the Bonk distortion theorems for H_k(R_I(m,n)). In particular, when k = 1 and k → +∞, the theorems reduce to that of Fitzgerald and Gong, respectively. When m = n = 1, this distortion theorem coincides with Liu and Minda as the unit disk case. As applications of the Bonk distortion theorems, various estimates of Bloch constants for these subfamilies of holomorphic mappings on R_I(m,n)are obtained. We not only give all Bloch estimates of holomorphic mappings between 1 < k < +∞ defined in R_I(m,n), but also extend our early Bloch constant estimates of the unit ball to the classical domain of the first type R_I(m,n).  

In this paper, let C be a class of right R-modules closed under isomorphisms and direct summands. The relations between left(right)C-dimensions and left exact functors are considered for an(injectively)coresolving class C or a(projectively)resolving class C. In view of those, there are some applications.  

In this paper, firstly some existence results for unbounded connected component of solutions set of some nonlinear operator equations with parameter be obtained by using the global bifurcation theories, and then some existence results for positive solutions of a non-positone operator equation be obtained by using the positive connected property of the operator. The main results can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinear terms are positone.  

A domain R is called ω-coherent if every finite type ideal is of finitely presented type. In this paper we show that ω-coherent domains are υ-coherent and if(RDTF,M)is a Milnor square, then for the case that F is the quotient field of D, R is ω-coherent if and only if D and T are ω-coherent and T_M is a valuation domain; and for the case that F is not the quotient field of D, R is ω-coherent if and only if D is a field, [F:D] < ∞, M is a finite type ideal of R, T is ω-coherent and R_M is coherent.  

We study the existence of solutions for the fully nonlinear elliptic system 

where Ω⊂R_n, n ≥ 2 is a smooth bounded domain, -M_λ,∧⁺ is the Pucci operator with parameters 0 < λ ≤ Λ. Firstly, we show that the system has a bounded nonnegative solution if F_i, i=1,2 are uniformly bounded functions. Secondly, we prove that the system has a maximal nonnegative solution and a minimal nonnegative solution by using the method of super-subsolution combining with a fixed point theorem of increasing operator if {f₁,f₂}is quasi-increasing and the system has a supersolution and a subsolution. If {f₁,f₂} is either quasi-decreasing or blended quasi-monotony, the existence of a non-negative solution is presented by the Schauder fixed point theorem. For some particular type of F_i, the existence of positive solutions for the system is also obtained. We finally give some examples as application.  

A Hilbert space operator T ∈ B(H)may be said to be “consistent in invertibility” provided that for each S ∈ B(H), TS and ST are either both or neither invertible. The induced spectrum contributes the stability of generalized property(ω), for a bounded operator T acting on a Hilbert space, under perturbations by finite rank operators, by nilpotent operators and quisi-nilpotent operators commuting with T. The stability of generalized property(ω)of the operators which are the products of finitely normal operators are considered.  

We discuss the existence of positive almost periodic solutions for some neutral integral equation, by constructing a new fixed point theorem in the cone. Some new results are obtained.  

Gross, Klein and Rieper(1993)obtained the genus distri- butions of necklaces. Chen, Liu and Wang(2006), and Yang, Liu(2007), calculated total embedding distributions of necklaces, they obtained recurrence relations and ex- plicit formula, respectively. In this paper, we get a simpler explicit formula for the total embedding distributions of necklaces.  

This paper applies the concept of fuzzy soft sets to polygroup theory. The notions of(∈γ, ∈γ∨qδ)-fuzzy soft polygroups and normal(∈γ, ∈γ∨qδ)-fuzzy soft polygroups over a polygroup are introduced and their basic properties are investigated.  

We consider the dual risk model with interest and a constant dividend barrier. First, the integral-differential equation satisfied by the expected discounted dividend payments is given, and the closed form for the expected discounted dividend payments is provided in the case where profits follow an exponential distribution. Second, the integral-differential equation satisfied by the moments of the discounted dividend payments is given, and the closed form for the moments of the discounted dividend payments is also obtained in the case where profits follow an exponential distribution. Finally, we provide the numerical results for the expected discounted dividend payments in the case of exponential distribution.  

By using a Type-function of the infinite order, the growth and the distribution of values of the Laplace-Stieltjes transforms convergent in the right half-plane are investigated. Some results similar to the Dirichlet series are obtained.  

We study the existence of monotone positive solutions for the semipositone right focal boundary value problems 
 
where λ > 0 is a parameter, n ≥ 3, 1 < k ≤ n-1 is fixed, f may change sign for 0 < t < 1 and we allow f is both semipositone and lower unbounded. Without making any monotone type assumption, the existence results of at least one and two monotone positive solutions are obtained by means of the fixed point theorems in cones.  

Let {X_i}_i=1^∞ be i.i.d random sequence with common distribution F(x)which belongs to one of the domains of attraction of D(G_γ),(γ∈R). The large quantile of F(x)is estimated under some conditions as the smoothing parameter is fixed, and the asymptotic distribution is obtained. And lead to asymptotic confidence interval.  

We will apply analytic methods to give the variational formula of the optimal constants in the L^p-Poincaré inequalities on the half line with finite measure and Dirichlet boundary condition. Moreover, by using iterating methods and the variational formula, we can get the explicit estimation of the optimal constants.  

We discuss the boundedness of Fatou components of transcendental entire function with certain gaps. We prove that every component of its Fatou set is bounded.  

Mazur conjectured that the normalizer property holds for finite groups with abelian Sylow 2-subgroups. Let G be a finite group and let N be a normal subgroup of G such that Z(G/N)has only trivial units. In this paper, a connection is established between the automorphisms of G induced by units in Z(G/N)and Coleman automorphisms of N. Based on this connection, we confirm that if G is a finite group with abelian Sylow 2-subgroups and Z(G/F*(G))has only trivial units then Mazur's conjecture holds for G.  

The pooling design has many application in practice. A mathematical model of pooling design is a dz-disjunct matrix. In this paper, we construct a kind of new dz-disjunct matrices with the subspaces of the unitary space. In order to discuss the correction capability of the design, we study the following arrangement problem on the subspace of the unitary space. For a given subspace C of type (m, s) in unitary space Fq2(n) and an integer d, we find d subspaces of type (m?1, s?1), H1, H2,…Hd of C that maximize the number of the subspaces of type (r, s?4) contained in H1∪H2∪…∪Hd. Then we give the tighter bound of z which is a reflection of correction capability on dz-disjunct matrix by the preceding result.

In this paper, for weighted approximation in L_p-norm, we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Lagrange interpolation sequence which based on the extended Chebyshev nodes of the second kind on the 1-fold integrated Wiener space. These results show that the average errors of both function approximation and derivative approximation by above mentioned Lagrange interpolation sequence are weakly equivalent to the average errors of the corresponding best polynomial approximation sequence for approximation in L_p-norm. In the sense of Information-Based Complexity, if permissible information functionals consist of standard information, then the average errors of both function approximation and derivative approximation by above mentioned interpolation sequence are weakly equivalent to the corresponding sequences of minimal average radii of nonadaptive information.

Without the periodity and symmetricity, we present new results on the existence of infinitely solutions for some nonlinear superlinear Schrödinger equation in the entire space without Ambrosetti-Rabinowitz growth condition. Also, we get the existence of infinitely many large energy solutions for some superlinear Schrödinger- Maxwell equations.

Some questions of Weighted composition operators T_ψ,φ from F(p,q,s) space to β_μ space in the unit ball are studied. By the methods of functional analysis and several complex variables, the necessary and sufficient conditions are given for Weighted composition operators T_ψ,φF(p,q,s) space to β_μ space in the unit ball.

In the present paper we will study the relations between spectra and tilings in two special cases. We first estimate and compare the Lebesgue measure of sets in the spectra-tilings relations. This includes a generalization of several results when the density method fails to apply, and the comparison of Lebesgue measure of sets among the orthogonal pairs, packing pairs and covering pairs. We then clarify some spectratilings relations between the translative pairs (D,Λ+Γ) and (D+Λ,Γ). The research here is based on the fundamental properties of spectra and tilings, and is closely related to the dual Fuglede conjecture.

We analyzed the properties of the ergodic matrix over finite field, And deduced the theorem on the number of the ergodic matrices over finite fields. We also comprehensively analyzes the rank and cardinal number of the two-side exponentiation set about the given matrix M and the ergodic matrix pair (A,B). And given the related theorems about the structure and cardinal number of the set. The results have the important theoretical significance for constructing the public key cryptography based on the ergodic matrices.

We first present a kind of new definition of fractional difference, fractional summation, and fractional equations, give methods for explicitly solving fractional difference equations of order (2, q) by use of the method of undetermined coefficients.

Determining the preimage distribution of a perfect nonlinear function, is very useful for both the existence of perfect nonlinear functions and the construction of some linear codes based on perfect nonlinear functions. This is a well-known open problem. In this paper, for the equation of the preimage distribution of a perfect nonlinear function, we determine its all integer solutions when m = 5 and m = 6.

We give the concepts of two classes of operators which are closely related to the invariant subspaces, namely (NCI) operators and (NFI) operators. We consider the properties of these two classes of operators, such as the existence, the similar invariance and the relations between the strongly irreducible operators and them. We also consider the problem whether every operator with spectrum {0} is a small and compact perturbation of an (NFI) operator on a separable Banach space.

In this paper, under the existence and uniqueness of the solution of stochastic 2-D Navier-Stokes equation, we prove Freidlin-Wentzell’s large deviation principle for 2-D Stochastic Navier-Stokes Equation driven by multiplicative noise with Poisson jumps by using weak convergence approach.

We use the elementary method and the properties of the floor function to study the infinite sums derived from the reciprocals of the cubic of the Fibonacci numbers, and give a new and interesting identity involving the reciprocals of this sums.

We investigate the exponent of convergence of zeros of solutions for some higher order homogeneous linear differential equation. When A₀ is an entire function that its taylor expansion is a gap power series and A₀ is the dominant coefficient, we proved that any two linearly independent solutions f1 and f2 of equation
f^(k)+A_k-2f^(k-2)+…+A₁f′+A₀f=0
satisfy max{λ(f₁),λ(f₂)}=∞, where λ(f) denotes the exponent of convergence of zeros of meromorphic function f.

For the Laplace-Stieltjes transforms of τ (2 < τ < +∞) order in the right half plane, given some conditions, then there exists a Borel point dealing with small functions about type function in the imaginary axis. For the Laplace-Stieltjes transforms of infinite order in the right half plane, given some conditions, then there exists a infinite order Borel point dealing with small functions in the imaginary axis.

Let N be a nest on a Banach space X, and D be a weakly closed Jordan module of AlgN. Suppose that for every N ∈ N, either dim(N/N_-)≠1 or N is topologically complementary. Then D must be an associative module of AlgN.

We will obtain some weighted strong type and weak type estimates of Bochner-Riesz operators T_R^(n-1)/2 on the weighted Morrey spaces L^p,k(w) for 1 ≤ p < ∞ and 0 < κ < 1. We will also prove that the commutator formed by a BMO(Rⁿ) function b(x) and T_R^δ (δ ≥ (n ? 1)/2) is a bounded operator on the weighted Morrey spaces L^p,k(w) for 1 < p < ∞ and 0 < κ < 1.

A sufficient and necessary condition that an ordered vectors-set is a pseudosymmetric point set in Eⁿ is explored. Based on this condition, several equivalent ways of characterizing regular simplices are obtained. A relationship between a pseudosymmetric point set and a regular simplex is given, i.e., let I_m={A₁,A₂,…,A_n+1}be a point set in Eⁿ, then I_m is an n-pseudo-symmetric point set if and only if the simplex with vertex set I_m is regular.

Let β be a nest on a Hilbert space of dimension greater than 1, algβ be the associated nest algebra, and k be a non-zero rational number. In this paper, We prove that a k-Jordan derivable map δ on algβ, δ(k(ab+ba)) = k[δ(a)b+aδ(b)+δ(b)a+bδ(a)] for all a, b ∈ algβ, is an additive derivation on algβ. In particular, it is an inner derivation when H is infinite dimensional. Related results concerning k-Jordan triple derivable maps are given.

Sampling theorem plays a key role in digital signal communication and image processing since a continuous signal is usually recovered and processed by using its discrete samples. In this paper, we shall study the extension of sampling theorem related to generalized interpolating refinable function vectors introduced in Han Bin [J. Comput. Appl. Math., 2009, 227: 254-270]. Precisely, for an existing generalized interpolating d-refinable function vector ø=(ø₁,…,ø_r)^T, i.e.øl(m/r + k)= δ_kδ_l-1-m,Ⅴk∈Z,m=0,1,…,r-1,l=1,…,r.we construct a set of functions{ø_r+1,...,ø_dr} such that ø^#=(ø^T,ø_r+1,…,ø_dr)^T is also a continuous d-refinable function vector and satisfies øl(m/dr+k)=δ_kδ_θd,r(l)-m, Ⅴk|∈Z,m=0,1,…,dr-1,l=r+1,…,dr,with θd,r(l)=l-r+R_l-1-r,d-1,R_l-1-r,d-1=[l-1-r/d-1].The multiwavelet sampling theorem associated with ø^# is established. Obviously, the sampling theorem in the multiwavelet subspaces of ø is extended. Moreover, we estimate the truncated error of the sampling theorem, which is desirable for application.

Let Ω ∈ L^q(S^n?1) with 1 < q ≤ ∞ be homogeneous of degree zero and has mean value zero on S^n?1. In this paper, we will study the boundedness of homogeneous singular integrals and Marcinkiewicz integrals with rough kernel on the weighted Morrey spaces L^p,κ(w) for q’ ≤ p < ∞ (or q’ < p < ∞) and 0 < κ < 1. We will also prove that the commutator operators formed by a BMO(Rⁿ) function b(x) and these rough operators are bounded on the weighted Morrey spaces L^p,κ(w) for q’ < p < ∞ and 0 < κ < 1.

In this paper, the notion of not-finitely graded centerless super-Virasoro algebras is introduced, and a class of modules of the intermediate series over the notfinitely graded centerless super-Virasoro algebras is determined.

Rotation symmetric Boolean functions have important applications in Cryptology. In this paper, we study the fast evaluation of a special type of rotation symmetric Boolean function and the recurrence relation about its Hamming weight. Then, we factor the function into several sub-functions. Finally, we prove that the nonlinearity of the function is the same as its Hamming weight with the recurrence relations about Fourier-transform values of these sub-functions. The conclusions and the methods used to deal with exponential sums in this paper may be applied for the further research on a conjecture of Cusick.

Based on the minimal projective bimodule resolution given by Snashall and Taillefer, we explicitly calculate the dimension of each Hochschild homology group of a class of self-injective Koszul special biserial algebras Λ_N in terms of combinatorics, and thus show intuitively that the Han’s conjecture holds true for Λ_N by means of calculation.