An upper gradient approach to weakly differentiable cochains

The aim of the present paper is to define a notion of weakly differentiable cochain in the generality of metric measure spaces and to study basic properties of such cochains. Our cochains are (sub)additive functionals on a subspace of chains, and a suitable notion of chains in metric spaces is given by Ambrosio–Kirchheim?s theory of metric currents. The notion of weak differentiability we introduce is in analogy with Heinonen–Koskela?s concept of upper gradients of functions. In one of the main results of our paper, we prove continuity estimates for cochains with p-integrable upper gradient in n-dimensional Lie groups endowed with a left-invariant Finsler metric. Our result generalizes the well-known Morrey–Sobolev inequality for Sobolev functions. Finally, we prove several results relating capacity and modulus to Hausdorff dimension.     

On the Construction of Finite Oscillator Dictionary

A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani, and Sochen in [3 Gurevich , S. , Hadani , R. , Sochen , N. (2008). The finite harmonic oscillator and its applications to sequences, communication and radar. IEEE Trans. Inform. Theory 54(9):4239–4253.[Crossref], [Web of Science ®] , [Google Scholar]]. In this paper, closed formulae of the finite split oscillator dictionary 𝔖 ^s are revisited by a simple proof, the structure of nonsplit tori of the group SL(2, 𝔽 _p ) is studied, and an explicit algorithm for computing the finite nonsplit oscillator dictionary 𝔖 ^ns is described.     

线性等式约束下线性模型中BLU估计的稳健性

研究了线性等式约束下线性模型中BLU估计关于协方差的稳健性,得到了在协方差发生变化时,条件可估函数c′β的条件BLU估计具有稳健性的充要条件.     

循环多胞形$C^{3}(6)$的对偶和单形乘积上的小覆盖

计算了循环多胞形$C^{3}(6)$的对偶和单形乘积上(可定向)小覆盖的等变同胚类的个数     

变量核的Marcinkiewicz积分的加权有界性

对Marcinkiewicz积分算子的有界性问题进行研究.应用Morrey-Herz空间的分解特征和算子在Lρ上的有界性结果,得到变量核的Marcinkiewicz积分算子在Morrey-Herz空间上的加权有界性.     

A Large Deviation Principle of Retarded Ornstein-Uhlenbeck Processes Driven by Lévy Noise

In this article, we develop a large deviation principle (LDP) for a class of retarded Ornstein-Uhlenbeck processes driven by Lévy processes. We first present a LDP result for time delay systems driven by cylindrical Wiener processes based on the large deviations of Gaussian processes. By using a contraction technique and passing on a finite-dimensional approximation, an LDP is obtained for stochastic time delay evolution equations driven by additive Lévy noise, whose solutions are generally not Lévy processes any more.     

Penetrating view of nano-structures in Aleochara verna spermatheca and flagellum by hard X-ray microscopy

A penetrating view of the three-dimensional nanostructure of female spermatheca and male flagellum in the species Aleochara verna is obtained with 100-nm resolution using a hard X-ray microscope, which provides a fast noninvasive imaging technology for insect morphology. Through introducing Zernike phase contrast and heavy metal staining, images taken at 8 keV displayed sufficient contrast for observing nanoscale fine structures, such as the spermatheca cochleate duct and the subapex of the flagellum, which have some implications for the study of the sperm transfer process and genital evolution in insects. This work shows that both the spatial resolution and the contrast characteristic of hard X-ray microscopy are quite promising for insect morphology studies and, particularly, provide an attractive alternative to the destructive techniques used for investigating internal soft tissues.     

Metal insulator transition characteristics of macro-size single domain VO2 crystals

The metal insulator transition (MIT) characteristics of macro-size single-domain VO₂ crystal were investigated. At the MIT, the VO₂ crystal exhibited a rectangular shape hysteresis curve, a large change in resistance between the insulating and the metallic phases, in the order of ～10⁵, and a small transition width (i.e. temperature difference before and after MIT) as small as 10^?3°C. These MIT characteristics of the VO₂ crystals are discussed in terms of phase boundary motion and the possibility of controlling the speed of the phase boundary, with change in size of crystal, is suggested.