A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Novel halogenated cyclopentasilylene-2,4-dienes via DFT

In view of immense importance of silylenes and the fact that their properties undergo significant changes on substitution with halogens, here, we have used B3LYP/6-311++G** level of theory to access the effects of 1–4 halogens (X = F, Cl, Br, and I) on four unprecedented sets of cyclopentasilylene-2,4-dienes; with the following formulas: SiC₄H₃X ( 1 _X ), SiC₄H₂X₂ ( 2 _X ), SiC₄HX₃ ( 3 _X ), and SiC₄X₄ ( 4 _X ). In going down from F to I, the singlet (s)-triplet (t) energy gap (ΔE_s-t, a possible indication of stability), and band gap (ΔE_H-L) decrease while nucleophilicity (N), chemical potential (μ), and proton affinity (PA) increase. The overall order of N, μ, and PA for each X is 2 _X > 1 _X > 3 _X > 4 _X . Precedence of 2 _X over 1 _X is attributed to the symmetric cross conjugation in the former. The highest and lowest N are shown by 2 _I and 4 _F . The trend of divalent angle () for each X is 4 _X > 1 _X > 3 _X > 2 _X . The results show that in going from electron withdrawing groups (EWGs) to electron donating groups (EDGs), the ΔE_s-t and ΔE_H-L decrease while N, μ, and PA increase. Also, rather high N of our scrutinized silylenes may suggest new promising ligands in organometallic chemistry.     

Optical Properties of One-dimensional Three-component Photonic Band Gap Structure

1　IntroductionMaterialswithPhotonicBandGaps (PBG’s)havebeenwidelystudiedboththeoreticallyandex perimentallyinthepastfew years[1～ 4] .Theexis tenceofgaps,which prohibitthepropagationofelectromagnetic (EM )wavesinacertainrangeoffrequencies,canhavesignificantimpactsbothinsci enceandtechnology .Manypracticalapplicationsofthesestructureshavebeensuggestedanddemon strated ,suchasPhotonicCrystal (PC)microcavi ties[5] ,infraredPC[6] ,PClens[7] ,suppressingspontaneousemission ,manipulatinglight…     

低插损窄带型10.7MHz压电陶瓷滤波器的研制

介绍了低插损窄带型10.7 MHz压电陶瓷滤波器的一种设计制作方法。结合压电陶瓷能陷模理论,通过对滤波器分割电极设计和制造工艺控制技术的研究,强调了工艺控制的重要性。产品达到日本村田同类产品水平,对国产化窄带型10.7 MHz压电陶瓷滤波器的研发和生产具有十分重要的意义。认为选用高Qm值压电陶瓷材料、分割电极和耦合电容的设计、焊接和点蜡工艺的控制等是研制低插损窄带型10.7 MHz压电陶瓷滤波器的重点。     

A New Comb Circular Polarizer Suitable for Millimeter‐Band Application

This letter presents a new polarizer which has a simple comb structure inside a circular waveguide. The electrical performance of the proposed comb polarizer is optimized by a circular waveguide radius and by the physical parameters of the comb plates. This polarizer is suitable for providing good performance in millimeter‐band application because of its simple structure and low fabrication cost. In our experiments the dual‐band comb polarizer designed in band 1(K) and band 2(Ka) showed good electrical performance without any tuning elements.     

基于EPF10K30的ISA接口设计

随着计算机技术日新月异的发展。计算机控制已经深入到了各个领域，特别是在工业控制领域，计算机通过ISA总线与接口电路进行通信，然后由接口电路去控制被控设备，从而完成预期的控制工作．     

IEEE 802.11g性能分析及应用

全面介绍IEEE802.11g标准的无线局域网,详细讲述IEEE802.11g草案标准的概念、产生背景、特点、构件及其体系结构和发展前景,探讨实现IEEE802.11gWLAN所需的关键技术及其双频多模应用方式,同时分析IEEE802.11g标准的网络性能。     

反铁磁晶体的红外频率特性

研究了红外频段非线性s偏振表面波在反铁磁晶体和电介质交界面上的频率特性，求出了非线性色散方程，揭示了非线性s偏振表面波存在一个临界频率，低于这个频率，非线性s偏振表面波的频率范围，发现功率不再是决定导波频率范围的唯一因素，两种材料的介电常数比在这里起了至关重要的作用。