Abstract:
We characterize the boundedness and compactness of the weighted composition operator on the Zygmund space ={∈()∶sup∈(1？||2)|()|<∞} and the little Zygmund space 0.

Abstract:
A tensor $\mathcal T\in \mathbb T(\mathbb C^n,m+1)$, the space of tensors of order $m+1$ and dimension $n$ with complex entries, has $nm^{n-1}$ eigenvalues (counted with algebraic multiplicities). The inverse eigenvalue problem for tensors is a generalization of that for matrices. Namely, given a multiset $S\in \mathbb C^{nm^{n-1}}/\mathfrak{S}(nm^{n-1})$ of total multiplicity $nm^{n-1}$, is there a tensor in $\mathbb T(\mathbb C^n,m+1)$ such that the multiset of eigenvalues of $\mathcal{T}$ is exact $S$? The solvability of the inverse eigenvalue problem for tensors is studied in this paper. With tools from algebraic geometry, it is proved that the necessary and sufficient condition for this inverse problem to be generically solvable is $m=1,\ \text{or }n=2,\ \text{or }(n,m)=(3,2),\ (4,2),\ (3,3)$.

Abstract:
All the 62 monomial elements in the canonical basis B of the quantized enveloping algebra for type $A_4$ have been determined in [2]. According to Lusztig's idea [7], the elements in the canonical basis B consist of monomials and linear combinations of monomials (for convenience, we call them polynomials). In this note, we compute all the 144 polynomial elements in one variable in the canonical basis B of the quantized enveloping algebra for type $A_4$ based on our joint note [2]. We conjecture that there are other polynomial elements in two or three variables in the canonical basis B, which include independent variables and dependent variables. Moreover, it is conjectured that there are no polynomial elements in the canonical basis B with four or more variables

Abstract:
We study in this article multiplicities of eigenvalues of tensors. There are two natural multiplicities associated to an eigenvalue $\lambda$ of a tensor: algebraic multiplicity $\operatorname{am}(\lambda)$ and geometric multiplicity $\operatorname{gm}(\lambda)$. The former is the multiplicity of the eigenvalue as a root of the characteristic polynomial, and the latter is the dimension of the eigenvariety (i.e., the set of eigenvectors) corresponding to the eigenvalue. We show that the algebraic multiplicity could change along the orbit of tensors by the orthogonal linear group action, while the geometric multiplicity of the zero eigenvalue is invariant under this action, which is the main difficulty to study their relationships. However, we show that for a generic tensor, every eigenvalue has a unique (up to scaling) eigenvector, and both the algebraic multiplicity and geometric multiplicity are one. In general, we suggest for an $m$-th order $n$-dimensional tensor the relationship \[ \operatorname{am}(\lambda)\geq \operatorname{gm}(\lambda)(m-1)^{\operatorname{gm}(\lambda)-1}. \] We show that it is true for serveral cases, especially when the eigenvariety contains a linear subspace of dimension $\operatorname{gm}(\lambda)$ in coordinate form. As both multiplicities are invariants under the orthogonal linear group action in the matrix counterpart, this generalizes the classical result for a matrix: the algebraic mutliplicity is not smaller than the geometric multiplicity.

Abstract:
In this paper, an aggregate game approach is proposed for the modeling and analysis of energy consumption control in smart grid. Since the electricity user's cost function depends on the aggregate load, which is unknown to the end users, an aggregate load estimator is employed to estimate it. Based on the communication among the users about their estimations on the aggregate load, Nash equilibrium seeking strategies are proposed for the electricity users. By using singular perturbation analysis and Lyapunov stability analysis, a local convergence result to the Nash equilibrium is presented for the energy consumption game that may have multiple Nash equilibria. For the energy consumption game with a unique Nash equilibrium, it is shown that the players' strategies converge to the Nash equilibrium non-locally. More specially, if the unique Nash equilibrium is an inner Nash equilibrium, then the convergence rate can be quantified. Energy consumption game with stubborn players is also investigated. Convergence to the best response strategies for the rational players is ensured. Numerical examples are provided to verify the effectiveness of the proposed methods.

Abstract:
A CPW-fed ultra-wideband antenna was designed. The antenna was etched on a single-layer copper-cladding substrate, of which the material was FR4 with relative permittivity of 4.4, and the magnitude was 40.0 mm × 50.0 mm × 1.6 mm. The parameters of the antenna are simulated and optimized with HFSS. This paper proposes a new trapezoidal CPW-fed UWB antenna that the bandwidth (return loss ≤ ?10 dB) covers 2.7 - 9.3 GHz range, which means a relative bandwidth of 110% with good radiation patterns and gain. Simulated and measured results for return loss, radiation pattern and gain were presented. A good agreement has been obtained between the simulation and experiment and the proposed antenna meets the requirements of the ultra-wideband antenna.

A solid superacid catalyst Pt-SO_{4}^{2-}/ZrO_{2}-A1_{2}O_{3} for n-pentane isomerization, was prepared by incipient-wetness impregnation. Preparetion
conditions, namely, calcination temperature, concentration of sulfuric acid
solution used in impregnation and Al_{2}O_{3 }concentration,
were varied to investigate the effects on catalytic performance of Pt-SO_{4}^{2-}/ZrO_{2}-A1_{2}O_{3}.
The results showed that the PtSZA catalyst exhibited excellent catalytic
performance for n-pentane isomerization. Under optimized preparation conditions
of calcination temperature of 650°C, reaction time for 3 h, concentration of
sulfuric acid solution for 0.5 mol/L, 30% of Al_{2}O_{3} concentration and 0.3% of Pt concentration, the n-pentane conversion and
isopentane selectivity of Pt-SO_{4}^{2-}/ZrO_{2}-A1_{2}O_{
}

For enhancing the activity of Ni/TiO_{2}-SAPO-11 catalyst,
SAPO-11, the precursor was prepared by hydrothermal crystallization, and TiO_{2}-SAPO-11
complex carrier was prepared by sol-gel method, then Ni/TiO_{2}-SAPO-11
was produced by the final product. The catalytic performance of Ni/TiO_{2}-SAPO-11
was studied in n-heptane isomerization, and the impact of catalyst preparation conditions
on n-heptane isomerization was discussed in detail. The results showed that,
with 20% of TiO_{2} composition, 2% of Ni capacity percentage and calcined
temperature at 500°C, conversion of n-heptane and isomerization selectivity was
up to 40.94% and 88.97% respectively.

Abstract:
MPEG is undertaking a new initiative to standardize content description of audio and video data/documents. When it is finalized in 2001, MPEG-7 is expected to provide standardized description schemes for concise and unambiguous content description of data/documents of complex media types. Meanwhile, other meta-data or description schemes, such as Dublin Core, XML, etc., are becoming popular in different application domains. In this paper, we propose the Multimedia Description Framework (MDF), which is designated to accommodate multiple description (meta-data) schemes, both MPEG-7 and non-MPEG-7, into integrated architecture. We will use examples to show how MDF description makes use of combined strength of different description schemes to enhance its expression power and flexibility. We conclude the paper with discussion of using MDF description of a movie video to search/retrieve required scene clips from the movie, on the MDF prototype system we have implemented.

Abstract:
According to the situation of sales logistics transportation management in an iron and steel enterprise and the possible logistics risks, the architecture of mobile electronic delivery platform for iron and steel sales logistics based on 3G netbook is proposed. The delivery process based on 3G netbook is analyzed. The three-tier C/S-based platform framework is also proposed, including database server, application server and clients. The function design of the platform is given. Finally, the key technologies of the platform are discussed.