In the present paper, we make use of codes with good parameters and algebraic curves over finite fields with many rational points to construct dense packings of superballs. It turns out that our packing density is quite reasonable. In particular, we improve some values for the best-known lower bounds on packing density.

The author constructs a class of indecomposable non-degenerate solvable Lie Algebras corresponding to a Cartan matrix A over the field of complex numbers and we determine all their derivations.

The authors consider the well-posedness in energy space of the critical non-linear system of wave equations with Hamiltonian structure  where there exists a function F(λ, μ) such that ∂F(λ, μ)/∂λ=F₁(λ, μ)/∂μ=F₂(λ, μ). By showing that the energy and dilation identities hold for weak solution under some assumptions on the non-linearities, we prove the global well-posedness in energy space by a similar argument to that for global regularity as shown in "Shatah and Struwe's paper, Ann. of Math. 138, 503-518 (1993)".

We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem
y''''= λa(x)f(y),0 < x < 1,
y(0)=y(1)=y''(0)=y''(1)=0,
where λ is a positive parameter, a ∈ C([0, 1], (0, ∞)), f ∈ C (R, R) satisfies f(u)u > 0 for all u ≠ 0. We give conditions on the ratio f(s)/s, at infinity and zero, that guarantee the existence of nodal solutions. The proof of our main results is based upon bifurcation techniques.

We prove the superlinear convergence of a nonmonotone BFGS algorithm on convex objective functions under suitable conditions.

This paper is concerned with a conjecture formulated by Coates et al in [4] which describes the relation between the integrality of the characteristic elements and their evaluations in the noncommutative Iwasawa theory. We give an almost equivalent description of the conjecture and prove a certain part of it.

Let {X,X1,X2,…} be a strictly stationary φ-mixing sequence which satisfies EX=0, EX2(log2 |X|)2 < ∞ and φ(n)=O(1/(log n)T) for some T > 2. Let Sn=Σk=1n Xk and an=O(√n/(log2n)γ) for some γ > 1/2. We prove that

The results of Gut and Sp?taru (2000) are special cases of ours.

We study the minimizers of the Ginzburg-Landau model for variable thickness, superconducting, thin films with high κ, placed in an applied magnetic field h_ex, when h_ex is of the order of the "first critical field", i.e. of the order of |ln ε|. We obtain the asymptotic estimates of minimal energy and describe the possible locations of the vortices.

We prove that (E.A) property buys the required containment of range of one mapping into the range of other in common fixed point considerations up to a pair of mappings. While proving our results, we utilize the idea of implicit functions due to Popa, keeping in view their unifying power.

A recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas (Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22, (2), 161-168 (1998)), combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first-and second-order functional semi linear and neutral damped differential equations in Fréchet space.

The authors study evolution hemivariational inequalities of semilinear type containing a hysteresis operator. For such problems we establish an existence result by reducing the order of the equation and then by the use of the time-discretization procedure.

We consider the asymptotic probability distribution of the size of a reversible random coagulation-fragmentation process in the thermodynamic limit. We prove that the distributions of small, medium and the largest clusters converge to Gaussian, Poisson and 0-1 distributions in the supercritical stage (post-gelation), respectively. We show also that the mutually dependent distributions of clusters will become independent after the occurrence of a gelation transition. Furthermore, it is proved that all the number distributions of clusters are mutually independent at the critical stage (gelation), but the distributions of medium and the largest clusters are mutually dependent with positive correlation coefficient in the supercritical stage. When the fragmentation strength goes to zero, there will exist only two types of clusters in the process, one type consists of the smallest clusters, the other is the largest one which has a size nearly equal to the volume (total number of units).

Let G be a mixed graph which is obtained from an undirected graph by orienting some of its edges. The eigenvalues and eigenvectors of G are, respectively, defined to be those of the Laplacian matrix L(G) of G. As L(G) is positive semidefinite, the singularity of L(G) is determined by its least eigenvalue λ₁(G).This paper introduces a new parameter edge singularity εs(G) that reflects the singularity of L(G), which is the minimum number of edges of G whose deletion yields that all the components of the resulting graph are singular. We give some inequalities between εs(G) and λ₁(G) (and other parameters) of G. In the case of εs(G)=1, we obtain a property on the structure of the eigenvectors of G corresponding to λ₁(G), which is similar to the property of Fiedler vectors of a simple graph given by Fiedler.

The distributional dimension of fractal sets in Rⁿ has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spaces and the F-type spaces on local fields, then we give the definition of the distributional dimension dim_D in local fields and study the relations between distributional dimension and Hausdorff dimension. Moreover, the analysis expression of the Hausdorff dimension is given. Lastly, we define the Fourier dimension in local fields, and obtain the relations among all the three dimensions.

Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive 2-soluble n-Lie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.

This paper is devoted to studying the growth problem, the zeros and fixed points distribution of the solutions of linear differential equations f''+e^-zf'+Q(z)f=F(z), where Q(z) ≡ h(z)e^cz and c ∈ R.

This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces.In this framework,the Leray-Schauder,Browder-Petryshyn,and Amann-Weiss degree theories are considered,and several existence results are obtained.The non-Archimedean case is also discussed.

In this paper,we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζ_q(s₁,...,s_d) when the arguments are all positive integers or all non-positive integers.This generalizes the work of Guo and Zhang (Renormalization of Multiple Zeta Values,arxiv:math/0606076v3).We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζ_q(s₁,...,s_d) (i.e.,s₁≤1).Moreover,when q↑1 our renormalizations agree with those of Guo and Zhang.

This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation.The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients.It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence.Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.

In this paper,we prove the persistence of hyperbolic lower dimensional invariant tori for Gevrey-smooth perturbations of partially integrable Hamiltonian systems under Rüssmann's nondegeneracy condition by an improved KAM iteration,and the persisting invariant tori are Gevrey smooth,with the same Gevrey index as the Hamiltonian.

Problems of the simultaneous optimal estimates and the optimal tests in general mixed models are considered.A necessary and sufficient condition is presented for the least squares estimate of the fixed effects and the analysis of variance (Hendreson Ⅲ's) estimate of variance components being uniformly minimum variance unbiased estimates simultaneously.This result can be applied to the problems of finding uniformly optimal unbiased tests and uniformly most accurate unbiased confidential interval on parameters of interest,and for finding equivalences of several common estimates of variance components.

We characterise bijections on the space of hermitian matrices preserving the invertibility of differences of matrix pairs in both directions.

We show the close connection between apparently different Galois theories for comodules introduced recently in [J.Gómez-Torrecillas and J.Vercruysse,Comatrix corings and Galois Comodules over firm rings,Algebr.Represent.Theory,10 (2007),271-306] and [Wisbauer,On Galois comodules,Comm.Algebra 34 (2006),2683-2711].Furthermore we study equivalences between categories of comodules over a coring and modules over a firm ring.We show that these equivalences are related to Galois theory for comodules.

In this paper we discuss the K-groups of Wiener algebra .For the 1-shift space X_GM2,we obtain a characterization of Fredholm operators on X_GM2ⁿ for all n∈N.We also calculate the K-groups of operator algebra on the 1-shift space X_GM2.

In the present paper we describe a specialization of prinjective Ringel-Hall algebra to 1,for prinjective modules over incidence algebras of posets of finite prinjective type,by generators and relations.This gives us a generalisation of Serre relations for semisimple Lie algebras.Connections of prinjective Ringel-Hall algebras with classical Lie algebras are also discussed.

In this paper we discuss the Einstein-Kähler metric on the third Cartan-Hartogs domain Y_Ⅲ(n,q;K).Firstly we get the complete Einstein-Kähler metric with explicit form on Y_Ⅲ(n,q;K) in the case of K=q/2+1/q-1.Secondly we obtain the holomorphic sectional curvature under this metric and get the sharp estimate for this holomorphic curvature.Finally we prove that the complete Einstein-Kähler metric is equivalent to the Bergman metric on Y_Ⅲ(n,q;K) in case of K=q/2+1/q-1.

This paper deals with asymptotic behavior of solutions to a parabolic system,where two heat equations with inner absorptions are multi-coupled via inner sources and boundary flux.We determine four kinds of simultaneous blow-up rates under different dominations of nonlinearities in the model.Two characteristic algebraic systems associated with the problem are introduced to get very simple descriptions for the four simultaneous blow-up rates as well as the known critical exponents,respectively.It is observed that the blow-up rates are independent of the nonlinear inner absorptions.

In this paper,we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space,which will play a key role in studying g-frames and g-Riesz bases etc.Using the pre-frame operator Q,we give some necessary and sufficient conditions for a g-Bessel sequence,a g-frame,and a g-Riesz basis in a complex Hilbert space,which have properties similar to those of the Bessel sequence,frame,and Riesz basis respectively.We also obtain the relation between a g-frame and a g-Riesz basis,and the relation of bounds between a g-frame and a g-Riesz basis.Lastly,we consider the stability of a g-frame or a g-Riesz basis for a Hilbert space under perturbation.

In this paper,using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space.For f(z)=zⁿg(z)(n≥1),g(z)=b₀+b₁z^p1+b₂z^p2+…,b_k≠0(k=0,1,2,…),our main result is (M_f)=(M_zⁿ)∩ (M_g)=(M_z^s),where s=g.c.d.(n,p1,p2,...).In the last section,we study the relation between strongly irreducible curve and the winding number W(f,f(α)),α∈D.

In this paper,we prove the following theorem:Let p be a prime number,P a Sylow psubgroup of a group G and π=π(G)\{p}.If P is seminormal in G,then the following statements hold:1) G is a p-soluble group and P'≤O_p(G); 2) l_p(G)≤2 and l_π(G)≤2; 3) if a π-Hall subgroup of G is q-supersoluble for some q∈π,then G is q-supersoluble.

The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains.We first give the representation of solutions of the Tricomi problem for the equations,and then prove the uniqueness and existence of solutions for the problem by a new method,i.e.the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.

We prove the boundedness of the maximal operator U_Γ in the spaces L^p(·)(Γ,ρ) with variable exponent p(t) and power weight ρ on an arbitrary Carleson curve under the assumption that p(t) satisfies the log-condition on Γ.

We prove also weighted Sobolev type L^p(·)(Γ,ρ)→L^q(·)(Γ,ρ)-theorem for potential operators on Carleson curves.

A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups.In the previous paper,we determined the partial order in the knot table.In this paper,we prove that 3₁ and 4₁ are minimal elements.Further,we study which surjection a pair of a periodic knot and its quotient knot induces,and which surjection a degree one map can induce.

This paper is contributed to the combinatorial properties of the periodic kneading words of antisymmetric cubic maps defined on a interval.The least words of given lengths,the adjacency relations on the words of given lengths and the parity-alternative property in some sets of such words are established.

Let R be a ring with a subset S.A mapping of R into itself is called strong commutativity-preserving (scp) on S,if [f(x),f(y)]=[x,y] for all x,y∈S.The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring,respectively.The semiprime case is also considered.

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This paper introduces a notion of linear perturbed Palais-Smale condition for real-valued functions on Banach spaces.In terms of strongly exposed points,it presents a characterization which guarantees linear perturbed Palais-Smale condition holds for lower semicontinuous functions with bounded effective domains defined on a Banach space with the Radon-Nikodým property; and gives an example showing that linear perturbed P-S condition is strictly weaker than the P-S condition.

Laguerre geometry of surfaces in R³ is given in the book of Blaschke,and has been studied by Musso and Nicolodi,Palmer,Li and Wang and other authors.In this paper we study Laguerre minimal surface in 3-dimensional Euclidean space R³.We show that any Laguerre minimal surface in R³ can be constructed by using at most two holomorphic functions.We show also that any Laguerre minimal surface in R³ with constant Laguerre curvature is Laguerre equivalent to a surface with vanishing mean curvature in the 3-dimensional degenerate space R₀³.

Under some mild conditions,we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field.If the so-called optimal bandwidth h_n =O(|n|^-1/5),n∈Z^d,is chosen,then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O(|n|^-4/5 log |n|).Moreover,we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.

In this paper,we find two integers k₀,m of 159 decimal digits such that if k≡k₀ (mod m),then none of five consecutive odd numbers k,k-2,k-4,k-6 and k-8 can be expressed in the form 2ⁿ±p^α,where p is a prime and n,α are nonnegative integers.