A NEW FAMILY OF FILTRATION S+5 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s ＋ 5 in the stable homotopy groups of spheres πrS,which is represented by 0 ≠γ^-s＋3hnhm∈Ext^s＋5,A ^t（Zp,Zp）in the Adams spectral sequence,where r=q（p^m＋p^n＋（s＋3）p^2＋（s＋2）p＋（s＋1））-5,t=p^mq＋p^nq＋（s＋3）p^2q＋（s＋2）pq＋（s＋1）q＋s,p≥7,m≥n＋2〉5,0≤s〈p-3,q=2（p-1）.

COMMUTATORS OF BOCHNER-RIESZ OPERATORS FOR A CLASS OF RADIAL FUNCTIONS

In this article, we prove the boundedness of commutators generated by BochnerRiesz operators below the critical index and BMO functions on the class of radial functions in Lp（Rn） with ｜1/p-1/2｜〈（1＋2α）/（2n）.

THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of the product operator C_(φ)D^(m) acting on Bloch-type spaces of slice regular functions.After that,an equivalent estimation for its essential norm is established,which can imply several existing results on holomorphic spaces.

Symmetry and monotonicity of positive solutions to Schr?dinger systems with fractional p-Laplacians

In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-Laplacian{(-△)^(s)_(p)u+au^(p-1)=f(u,v),(-△)^(t)_(p)v+bv(p-1)=g(u,v),where 0<s,t<1 and 2<p<∞.We obtain the radial symmetry in the unit ball or the whole space R^(N)(N≥2),the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g,respectively.

Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES

In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space. The disjoint supercyclic properties of weighted translations on locally compact discrete groups, the di rec t sums of finite classical weighted backward shifts, and the bilateral backward opera tor weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space l^2 (Z) never satisfy the d-Supercyclicity Criterion by a simple proof.

THE FIELD ALGEBRA IN HOPF SPIN MODELS DETERMINED BY A HOPF*-SUBALGEBRA AND ITS SYMMETRIC STRUCTURE

Denote a finite dimensional Hopf C*-algebra by H, and a Hopf *-subalgebra of H by H1. In this paper, we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry. More precisely, we consider the quantum double D(H, H_(1)) as the bicrossed product of the opposite dual Hopˆ of H and H1 with respect to the coadjoint representation, the latter acting on the former and vice versa, and under the non-trivial commutation relations between H1 and Ĥ we define the observable algebra AH1. Then using a comodule action of D(H, H1) on AH1, we obtain the field algebra FH1, which is the crossed product AH1⋊D(H,H_(1)), and show that the observable algebra AH1 is exactly a D(H, H1)-invariant subalgebra of FH1. Furthermore, we prove that there exists a duality between D(H, H1) and AH1, implemented by a*-homomorphism of D(H, H_(1)).

Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth

This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,Du)+■π=f,div u=0,where Du is the symmetric part of the gradient■u.We first establish anε-regularity criterion involving both the excess functional of the symmetric gradient Du and Wolff potentials of the nonhomogeneous term f to guarantee the local vanishing mean oscillation(VMO)-regularity of Du in an open subset Ω_(u) of Ω with full measure.Such anε-regularity criterion leads to a pointwise Wolff potential estimate of Du,which immediately infers that Du is partially C^(0)-regular under appropriate assumptions.Finally,we give a local continuous modulus estimate of Du.

Dynamics of coherence-induced state ordering under Markovian channels

We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels： amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qnbit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α-entropies, while the bit flit channel does change for some special cases.

Construction of Supersaturated Design with Large Number of Factors by the Complementary Design Method

Supersaturated designs （SSDs） have been widely used in factor screening experiments. The present paper aims to prove that the maximal balanced designs are a kind of special optimal SSDs under the E（fNOD） criterion. We also propose a new method, called the complementary design method, for constructing E（fNoD） optimal SSDs. The basic principle of this method is that for any existing E（fNOD） optimal SSD whose E（fNOD） value reaches its lower bound, its complementary design in the corresponding maximal balanced design is also E（fNOD） optimal. This method applies to both symmetrical and asymmetrical （mixed-level） cases. It provides a convenient and efl：icient way to construct many new designs with relatively large numbers of factors. Some newly constructed designs are given as examples.

On Covering Number of Groups with Trivial Fitting Subgroup

Let G be a finite group and S be a subset of Irr(G).If for every prime divisor p of|G|there is a characterχin S such that p dividesχ(1),S is called a covering set of G.The covering number of G,denoted by cn(G),is defined as the minimal number of Card(S),where S is a covering set of G and Card(S)is the cardinality of set S.In this paper,we prove that if G is a finite group with F(G)=1,then the covering number cn(G)≤3.Especially,if PSL2(q)or J1 is not involved in G,then cn(G)≤2.

N-Widths and Average Widths of Besov Classes in Sobolev Spaces

In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.

Integrating of metal-organic framework UiO-66-NH2 and cellulose nanofibers mat for high-performance adsorption of dye rose bengal

UiO-66-NH2 is an efficient material for removing pollutants from wastewater due to its high specific surface area,high porosity and water stability.However,recycling them from wastewater is difficult.In this study,the cellulose nanofibers mat deacetylated from cellulose acetate nanofibers were used to combine with UiO-66-NH_(2)by the method of in-situ growth to remove the toxic dye,rose bengal.Compared to previous work,the prepared composite could not only provide ease of separation of UiO-66-NH_(2)from the water after adsorption but also demonstrate better adsorption capacity(683 mg∙g‒1(T=25°C,pH=3))than that of the simple UiO-66-NH_(2)(309.6 mg∙g^(‒1)(T=25℃,pH=3)).Through the analysis of adsorption kinetics and isotherms,the adsorption for rose bengal is mainly suitable for the pseudo-second-order kinetic model and Freundlich model.Furthermore,the relevant research revealed that the main adsorption mechanism of the composite was electrostatic interaction,hydrogen bonding andπ–πinteraction.Overall,the approach depicts an efficient model for integrating metal-organic frameworks on cellulose nanofibers to improve metal-organic framework recovery performance with potentially broad applications.

Boundary Control Method to Identification of Elastic Modulus of String Equation from Neumann-Dirichlet Map

This paper considers identification for the spatial variable coefficient of a vibrating string with Neumann boundary control from the measured boundary displacement. The reconstruction algorithm consists of two steps: The first step is to recover the spectral data from the measured boundary displacement by showing that the system is spectral controllable; the second step is to reconstruct the coefficient from the recovered spectral data using the boundary control method, for which the required exact controllability is also verified.

Higher Order Fractional Differentiability for the Stationary Stokes System

This paper focuses on the higher order fractional differentiability of weak solution pairs to the following nonlinear stationary Stokes system{div A(x-Du)-■π=divF,inΩdivu=0,inΩ.In terms of the difference quotient method,our first result reveals that if F∈B_(p,q.loc)^(β)(Ω,R^(n))for p=2 and 1≤q≤2n/n-2β,then such extra Besov regularity can transfer to the symmetric gradient Du and its pressureπwith no losses under a suitable fractional differentiability assumption on x■A(x,ξ).Furthermore,when the vector field A(x,Du)is simplified to the full gradient■u,we improve the aforementioned Besov regularity for all integrability exponents p and q by establishing a new Campanato-type decay estimates for(■u,π).

The average errors for Hermite-Fejr interpolation on the Wiener space

For 1≤ p < ∞, firstly we prove that for an arbitrary set of distinct nodes in [-1, 1], it is impossible that the errors of the Hermite-Fejr interpolation approximation in L p -norm are weakly equivalent to the corresponding errors of the best polynomial approximation for all continuous functions on [-1, 1]. Secondly, on the ground of probability theory, we discuss the p-average errors of Hermite-Fejr interpolation sequence based on the extended Chebyshev nodes of the second kind on the Wiener space. By our results we know that for 1≤ p < ∞ and 2≤ q < ∞, the p-average errors of Hermite-Fejr interpolation approximation sequence based on the extended Chebyshev nodes of the second kind are weakly equivalent to the p-average errors of the corresponding best polynomial approximation sequence for L q -norm approximation. In comparison with these results, we discuss the p-average errors of Hermite-Fejr interpolation approximation sequence based on the Chebyshev nodes of the second kind and the p-average errors of the well-known Bernstein polynomial approximation sequence on the Wiener space.

Solvable D_2-Groups

Let G be a finite group, Irra（G） be the set of nonlinear irreducible characters of G and cdl （G） the set of degrees of the characters in Irrl （G）. A group G is said to be a D2-group if │cdl （G）│ = │Irrl（G）│ - 2. In this paper, we give a complete classification of solvable D2-groups.

A Boosting Procedure for Variational-Based Image Restoration

Variational methods are an important class of methods for general image restoration.Boosting technique has been shown capable of improving many image denoising algorithms.This paper discusses a boosting technique for general variation-al image restoration methods.It broadens the applications of boosting techniques to a wide range of image restoration problems,including not only denoising but also deblur-ring and inpainting.In particular,we combine the recent SOS technique with dynamic parameter to variational methods.The dynamic regularization parameter is motivated by Meyer’s analysis on the ROF model.In each iteration of the boosting scheme,the variational model is solved by augmented Lagrangian method.The convergence analy-sis of the boosting process is shown in a special case of total variation image denoising with a“disk”input data.We have implemented our boosting technique for several im-age restoration problems such as denoising,inpainting and deblurring.The numerical results demonstrate promising improvement over standard variational restoration mod-els such as total variation based models and higher order variational model as total generalized variation.

Nearly invariant subspaces for shift semigroups

Let{T(t)}_(t≥0) be a C_(0)-semigroupon an infinite-dimensional separable Hilbert space;a suitable definition of near{T(t)^(*)}_(t≥0) invariance of a subspace is presented in this paper.A series of prototypical examples for minimal nearly{S(t)^(*)}_(t≥0) invariant subspaces for the shift semigroup{S(t)}_(t≥0) on L^(2)(0,∞)are demonstrated,which have close links with near T_(θ)^(*)invariance on Hardy spaces of the unit disk for an inner functionθ.Especially,the corresponding subspaces on Hardy spaces of the right half-plane and the unit disk are related to model spaces.This work further includes a discussion on the structure of the closure of certain subspaces related to model spaces in Hardy spaces.

Hermitian geometry on the resolvent set(Ⅱ)

For an element A in a unital C^(*)-algebra B,the operator-valued 1-formωA(z)=(z-A)^(-1) dz is analytic on the resolvent setρ(A),which plays an important role in the functional calculus of A.This paper defines a class of Hermitian metrics onρ(A)through the coupling of the operator-valued(1,1)-formΩA=-ωA^(*)∧ωA with tracial and vector states.Its main goal is to study the connection between A and the properties of the metric concerning curvature,arc length,completeness and singularity.A particular example is when A is quasi-nilpotent,in which case the metric lives on the punctured complex plane C\{0}.The notion of the power set is defined to gauge the"blow-up"rate of the metric at 0,and examples are given to indicate a likely link with A’s hyper-invariant subspaces.