The Kolmogorov–Riesz compactness theorem

We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.     

Si／SiNx／SiO2多层膜的光致发光

采用射频磁控溅射法,制备了具有强光致可见发光的纳米Si/SiNx/SiO2多层膜,利用傅立叶红外吸收(FTIR)谱,光致发光(PL)谱对其进行了研究。用260nm光激发得到的PL谱中观察到高强度的392nm(3.2eV)和670nm(1.9eV)光致发光峰,分析认为它们分别来自于缺陷态≡Si-到价带顶和从导带底到缺陷态≡Si-的辐射跃迁而产生的光致激发辐射复合发光。PL谱中只有370nm(3.4eV)处发光峰的峰位会受退火温度的影响,结合FTIR谱认为370nm发光与低价氧化物—SiOx(x<2.0)结合体有密不可分的关系。当SiO2层的厚度增大时,发光强度有所增强,800℃退火后出现最强发光,认为具有较大SiO2层厚度的Si/SiNx/SiO2结构多层膜更有利于退火后形成Si—N网络,能够得到更高效的光致发光。用量子限制-发光中心(QCLC)模型解释了可能的发光机制,并建立了发光的能隙态(EGS)模型。     

Effect of an aliphatic spacer group on the adsorption mechanism on the colloidal silver surface of L‐proline phosphonodipeptides

A comparative study of molecular structures of five L ‐proline (L ‐Pro) phosphonodipeptides: L ‐Pro‐NH‐C(Me,Me)‐PO₃H₂ (P1), L ‐Pro‐NH‐C(Me,iPr)‐PO₃H₂ (P2), L ‐Pro‐L ‐NH‐CH(iBu)‐PO₃H₂ (P3), L ‐Pro‐L ‐NH‐CH(PA)‐PO₃H₂ (P4) and L ‐Pro‐L ‐NH‐CH(BA)‐PO₃H₂ (P5) has been carried out using Raman and absorption infrared techniques of molecular spectroscopy. The interpretation of the obtained spectra has been supported by density functional theory calculations (DFT) at the B3LYP; 6–31 + + G** level using Gaussian 2003 software. The surface‐enhanced Raman scattering (SERS) on Ag‐sol in aqueous solutions of these phosphonopeptides has also been investigated. The surface geometry of these molecules on a silver colloidal surface has been determined by observing the position and relative intensity changes of the Pro ring, amide, phosphonate and so‐called spacer (−R) groups vibrations of the enhanced bands in their SERS spectra. Results show that P4 and P5 adsorb onto the silver as anionic molecules mainly via the amide bond (∼1630, ∼1533, ∼1248, ∼800 and ∼565 cm⁻¹), Pro ring (∼956, ∼907 and ∼876 cm⁻¹) and carboxylate group (∼1395 and ∼909 cm⁻¹). Coadsorption of the imine nitrogen atom and PO group with the silver surface, possibly by formation of a weaker interaction with the metal, is also suggested by the enhancement of the bands at 1158 and 1248 cm⁻¹. P1, P2 and P3 show two orientations of their main chain on the silver surface resulting from different interactions of the  C CH₃,  NH and  CONH fragments with this surface. Bonding to the Ag surface occurs mainly through the imino atom (1166 cm⁻¹) for P2, while for P1 and P3 it occurs via the methyl group(s) (1194–1208 cm⁻¹). The amide group functionality (CONH) is practically not involved in the adsorption process for P1 and P2, whereas the C_s P bonds do assist in the adsorption. Copyright © 2008 John Wiley & Sons, Ltd.     

Wavelet-modified maximum average correlation height filter for out-of-plane rotation invariance

In this paper, we implement a wavelet-modified maximum average correlation height (WaveMACH) filter for recognition of 0-360° out-of-plane rotated targets employing hybrid digital-optical correlator architecture. A chirp function is used with the synthesized WaveMACH filter, which focuses the correlation signals in three different planes, thereby providing the choice of recording a single correlation peak at a particular plane. Signal-to-noise ratio and peak-to-sidelobe ratio have been calculated as metrics of goodness of the proposed WaveMACH filter.     

Free-space Fresnel diffraction for the approximation of fractional Fourier transform

Fractional Fourier transformation of an object can be approximated by the object's free-space Fresnel diffraction pattern under some restricted conditions and plane wave illumination according to Hua's method. A better approximation is achieved under least-squared conditions developed in this paper. Simulation results verify that our theoretical development works for any fractional order a compared with the previous approach.     

An efficient algorithm for Bermudan barrier option pricing

An efficient option pricing method based on Fourier-cosine expansions was presented by Fang and Oosterlee for European options in 2008,and later,this method was also used by them to price early-exercis...     

The expected discounted penalty function under a renewal risk model with stochastic income

In this paper, we consider a renewal risk model with stochastic premiums income. We assume that the premium number process and the claim number process are a Poisson process and a generalized Erlang (n) processes, respectively. When the individual stochastic premium sizes are exponentially distributed, the Laplace transform and a defective renewal equation for the Gerber-Shiu discounted penalty function are obtained. Furthermore, the discounted joint distribution of the surplus just before ruin and the deficit at ruin is given. When the claim size distributions belong to the rational family, the explicit expression of the Gerber-Shiu discounted penalty function is derived. Finally, a specific example is provided.     

电子稳像技术中的坐标变换及像偏移函数分析

为了进行图像偏移的数字补偿 ,需要分析图像的偏移函数 ,要对定坐标系O0 X0 Y0 Z0 ,CCD摄像机载体坐标系O1X1Y1Z1和像空间坐标系O2 X2 Y2 Z2 进行坐标变换 ,从而得出图像偏移与载体运动速度的关系 ,为数字电子稳像奠定基础。     

Toeplitz quantization on Fock space

For Toeplitz operators $T_f^{(t)}$ acting on the weighted Fock space $H_t^2$, we consider the semi-commutator $T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}$, where $t>0$ is a certain weight parameter that may be interpreted as Planck's constant ? in Rieffel's deformation quantization. In particular, we are interested in the semi-classical limit

($?$)$\underset{t\to 0}{\lim }?{6T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}6}_t.$

It is well-known that ${6T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}6}_t$ tends to 0 under certain smoothness assumptions imposed on f and g. This result was recently extended to $f,g\in \mathrm{BUC}({\mathbb{C}}^n)$ by Bauer and Coburn. We now further generalize (?) to (not necessarily bounded) uniformly continuous functions and symbols in the algebra $\mathrm{VMO}\cap L^{\infty }$ of bounded functions having vanishing mean oscillation on ${\mathbb{C}}^n$. Our approach is based on the algebraic identity $T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}=?{(H_{\overline{f}}^{(t)})}^{?}{H}_g^{(t)}$, where $H_g^{(t)}$ denotes the Hankel operator corresponding to the symbol g, and norm estimates in terms of the (weighted) heat transform. As a consequence, only f (or likewise only g) has to be contained in one of the above classes for (?) to vanish. For g we only have to impose ${\lim \sup }_{t\to 0}{6H_g^{(t)}6}_t<\infty$, e.g. $g\in L^{\infty }({\mathbb{C}}^n)$. We prove that the set of all symbols $f\in L^{\infty }({\mathbb{C}}^n)$ with the property that ${\lim }_{t\to 0}?{6T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}6}_t={\lim }_{t\to 0}?{6T_g^{(t)}{T}_f^{(t)}?T_{gf}^{(t)}6}_t=0$ for all $g\in L^{\infty }({\mathbb{C}}^n)$ coincides with $\mathrm{VMO}\cap L^{\infty }$. Additionally, we show that $\underset{t\to 0}{\lim }?{6T_f^{(t)}6}_t={6f6}_{\infty }$ holds for all $f\in L^{\infty }({\mathbb{C}}^n)$. Finally, we present new examples, including bounded smooth functions, where (?) does not vanish.     

A generalization of inverse distance weighting and an equivalence relationship to noise-free Gaussian process interpolation via Riesz representation theorem

In this paper, we show the relationship between two seemingly unrelated approximation techniques. On the one hand, a certain class of Gaussian process-based interpolation methods, and on the other hand inverse distance weighting, which has been developed in the context of spatial analysis where there is often a need for interpolating from irregularly spaced data to produce a continuous surface. We develop a generalization of inverse distance weighting and show that it is equivalent to the approximation provided by the class of Gaussian process-based interpolation methods. The equivalence is established via an elegant application of Riesz representation theorem concerning the dual of a Hilbert space. It is thus demonstrated how a classical theorem in linear algebra connects two disparate domains.