Littlewood-Paley and Lusin functions on nilpotent Lie groups

In this paper, we define the Littlewood-Paley and Lusin functions associated to the sub-Laplacian operator on nilpotent Lie groups. Then we prove the Lp (1<p<∞) boundedness of Littlewood-Paley and Lusin functions.     

Quaternion-valued admissible wavelets and orthogonal decomposition of L 2(IG(2), ℍ)

A series of admissible wavelets is fixed, which forms an orthonormal basis for the Hilbert space of all the quaternion-valued admissible wavelets. It turns out that their corresponding admissible wavelet transforms give an orthogonal decomposition of L ²(IG(2), ℍ).      

Windowed-Kontorovich-Lebedev transforms

The aim of this paper is to study the boundedness of the windowed-Kontorovich-Lebedev transforms. For this purpose, we first define the translation associated to the Kontorovich-Lebedev transform and a generalized convolution product, then obtain some harmonic analysis results. We present a sufficient and necessary condition for the boundedness of the windowed-Kontorovich-Lebedev transform. Finally, we define the corresponding Weyl operator, and study the boundedness and compactedness of the Weyl operator with symbols in L ^q (q ∈ [1, 2]) acting on L ^p .     

Characterization of Clifford-valued Hardy spaces and compensated compactness

In this paper, the general Clifford -valued Hardy spaces and conjugate Hardy spaces are characterized. In particular, each function in -valued Hardy space can be determined by half of its function components through Riesz transform, and the explicit determining formulas are given. The products of two functions in the Hardy space give six kinds of compensated quantities, which correspond to six paracommutators, and their boundedness, compactness and Schatten-von Neumann properties are given.

     

Quaternion-valued admissible wavelets and orthogonal decomposition of L2(IG(2),(H))

A series of admissible wavelets is ?xed, which forms an orthonormal basis for the Hilbert space of all the quaternion-valued admissible wavelets. It turns out that their corresponding admissible wavelet transforms give an orthogonal decomposition of L²(IG(2),H).     

体相掺钇、铝的α-Ni(OH)2的固相合成和高温电化性能

固相法合成含不同Y3 的铝基α-Ni(OH)2,样品的组成、晶相结构、表面形态等用XRD,SEM,FT-IR,AAS和CT等表征.用此材料组装成氢镍模拟电池.在不同温度下做了恒流充放电研究.结果表明,在30℃时Y3 使铝基α-Ni(OH)2电极材料的放电比容量稍有下降.而60℃时,在各实验倍率充放电情况下以掺Y(OH)3摩尔含量1.2%为合适比例,它比不掺钇的铝基α-Ni(OH)2放电比容量要高出17%～29%.高温放电电位也有所改善.对电极材料的高温性能改善的机制也做了探讨.     

Synthesis and bio-applications of targeted magnetic-fluorescent composite nanoparticles

Magnetic-fluorescent nanoparticles have a tremendous potential in biology. As the benefits of these materials gained recognition, increasing attention has been given to the conjugation of magnetic-fluorescent nanoparticles with targeting ligands. The magnetic and fluorescent properties of nanoparticles offer several functionalities, including imaging, separation, and visualization, while the presence of a targeting ligand allows for selective cell and tissue targeting. In this review, methods for the synthesis of targeted magnetic-fluorescent nanoparticles are explored, and recent applications of these nanocomposites to the detection and separation of biomolecules, fluorescent and magnetic resonance imaging, and cancer diagnosis and treatment will be summarized. As these materials are further optimized, targeted magnetic-fluorescent nanoparticles hold great promise for the diagnosis and treatment of some diseases.     

Clifford Algebra-Valued Wavelet Transform on Multivector Fields

This paper presents a construction of the n = 2 (mod 4) Clifford algebra Cl _n,0-valued admissible wavelet transform using the admissible similitude group SIM(n), a subgroup of the affine group of \mathbbRⁿ{\mathbb{R}^{n}} . We express the admissibility condition in terms of the Cl _n,0 Clifford Fourier transform (CFT). We show that its fundamental properties such as inner product, norm relation, and inversion formula can be established whenever the Clifford admissible wavelet satisfies a particular admissibility condition. As an application we derive a Heisenberg type uncertainty principle for the Clifford algebra Cl _n,0-valued admissible wavelet transform. Finally, we provide some basic examples of these extended wavelets such as Clifford Morlet wavelets and Clifford Hermite wavelets.     

Variable Hardy Spaces on the Heisenberg Group

We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.