Reachable and controllable sets for two-dimensional,linear, discrete-time systems

We consider two-dimensional discrete-time linear systems with constrained controls. We propose a simple polynomial time procedure to give an exact external representation of theN-step reachable set and controllable set. The bounding hyperplanes are explicitly derived in terms of the data of the problem. By using a result in computational geometry, all the calculations are made in polynomial time in contrast to classical methods. The limit case asN is also investigated.     

四唑及其衍生物的理论研究（6）

对7个肼基四唑衍生物进行了HF／6－31G水平的几何构型全优化及MP2／6－31G／／HF／6－31G水平的总能量计算．结果表明，四唑环基本上取平面构型，肼基不与环共面．键长与重叠布居之间不存在平行关系．环上N1和N4原子荷负电多、利于质子化．1H．肼基四唑的HOMO－LUMO能级差（△E）较2H式的大，中性分子的△E教相应的负离子的大．还计算研究了7个标题物的红外光谱并由此求得了它们的热力学性质．     

Changes in the conformational parameters of 1-allylbenzotriazole in a mixed halide π-complex [CuCl0.85Br0.15(C6H4N3CH2=CH2)] under the action of bromine atoms

Single crystals of [CuCl_0.85Br_0.15(C₆H₄N₃CH₂=CH₂)] (I) were obtained by alternating current electrochemical synthesis; their X-ray structural investigation has been carried out (DARCh automatic diffractometer, MoK _α radiation, θ/2θ scanning; 1460 reflections with F ≥ 4σ(F), R = 0.0517). The crystals are monoclinic, their space group is P2₁/c, a = 7.292(3) Å, b = 17.947(8) Å, c = 7.398(4) Å, β = 93.56(4)°, V = 966(1) ų, Z = 4). Complex I is close in structure to the previously investigated compound [CuCl(C₆H₄N₃CH₂=CH₂)] (II). In both structures, the trigonal-pyramidal surroundings of the copper atom include two halide atoms (one is apical), a nitrogen atom, and a C=C group. The Cu₂X₂ dimers are associated into {[Cu₂X₂(C₆H₅N₃CH₂=CH₂)]}_n layers due to the bridging function of the 1-allylbenzotriazole molecule. In spite of the similar coordination polyhedra of the metal atoms and identical bridging function of the ligand molecule in I and II, the differences in the conformation parameters of the allyl group π-coordinated by the copper(I) atom (trans-like in I and cis-like in II) caused by the presence of bromine atoms in the coordination sphere predetermine different structures of the organometallic [Cu₂X₂(C₆H₅N₃CH₂=CH₂)]₄ tetramer subunits in the layers and, as a consequence, formation of different crystal structures. Original Russian Text Copyright ? 2005 by E. A. Goreshnik, B. M. Mykhalichko, and V. N. Davydov __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 46, No. 1, pp. 174–178, January–February, 2005.     

Reaction sites of <Emphasis Type="Italic">N,N′</Emphasis>-substituted <Emphasis Type="Italic">p</Emphasis>-phenylenediamine antioxidants

The geometries of N,N′-diphenylbenzene-1,4-diamine (DPPD), N-phenyl-N′-(1-phenylethyl)benzene-1,4-diamine (SPPD), N-(4-methylpentan-2-yl)-N′-phenylbenzene-1,4-diamine (6PPD), N-propan-2-yl-N′-phenylbenzene-1,4-diamine (IPPD), N-(2-methoxybenzyl)-N′-phenylbenzene-1,4-diamine (MBPPD), and N-phenyl-N′-(2-phenylpropan-2-yl)benzene-1,4-diamine (CPPD) as well as of their dehydrogenation products were optimized by the semiempirical AM1 method. The results support the idea of stable N_B=C_X structures formation during the consecutive dehydrogenation of SPPD, 6PPD, IPPD, and MBPPD antioxidants. The biradicals formed during the second step of dehydrogenation of substituted phenylenediamines might be important for their antioxidant effectiveness. Dedicated to Professor Vladimír Kvasnička, DrSc., in honour of his 65th birthday     

Point Cloud Geometry Compression Based on Multi-Layer Residual Structure

Point cloud data are extensively used in various applications, such as autonomous driving and augmented reality since it can provide both detailed and realistic depictions of 3D scenes or objects. Meanwhile, 3D point clouds generally occupy a large amount of storage space that is a big burden for efficient communication. However, it is difficult to efficiently compress such sparse, disordered, non-uniform and high dimensional data. Therefore, this work proposes a novel deep-learning framework for point cloud geometric compression based on an autoencoder architecture. Specifically, a multi-layer residual module is designed on a sparse convolution-based autoencoders that progressively down-samples the input point clouds and reconstructs the point clouds in a hierarchically way. It effectively constrains the accuracy of the sampling process at the encoder side, which significantly preserves the feature information with a decrease in the data volume. Compared with the state-of-the-art geometry-based point cloud compression (G-PCC) schemes, our approach obtains more than 70–90% BD-Rate gain on an object point cloud dataset and achieves a better point cloud reconstruction quality. Additionally, compared to the state-of-the-art PCGCv2, we achieve an average gain of about 10% in BD-Rate.     

Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry

Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Carlo (MC) simulation of SDEs. Specifically, we develop a new MC SDE method to overcome the challenges in calculating a time-dependent PDF and information geometric diagnostics and to speed up simulations by utilizing GPU computing. Using MC SDE simulations, we reproduce Information Geometric scaling relations found from the Fokker–Planck method for the case of a stochastic process with linear and cubic damping terms. We showcase the advantage of MC SDE simulation over FPE solvers by calculating unequal time joint PDFs. For the linear process with a linear damping force, joint PDF is found to be a Gaussian. In contrast, for the cubic process with a cubic damping force, joint PDF exhibits a bimodal structure, even in a stationary state. This suggests a finite memory time induced by a nonlinear force. Furthermore, several power-law scalings in the characteristics of bimodal PDFs are identified and investigated.     

基于Simulink大功率电子管放大器仿真

选用4616V4型四极电子管,单管输出350 kW,采用两路并行放大链路,设计了一套输出功率350 kW2的大功率电子管功率源系统。基于四极电子管的恒流特性曲线及实验数据,拟合输出功率与阳极电压、输入功率的关系曲线,利用Origin软件拟合函数,建立数学模型,并利用闭环比例-积分(PI)反馈控制,稳定输出电压,通过Simulink仿真探寻最佳工作点,较低的阳极电压以及近饱和的输入功率既能有效增大工作频率,又能满足高功率输出的要求,仿真结果与实际联机调试数据对比,误差低于5%,根据仿真数据得到的结论与13点分析法一致,可以有效指导探寻最佳工作点。     

Integral Operators Between Fock Spaces∗

In this paper, the authors study the integral operator Sφf(z) = Z C φ(z, w)f(w)dλα(w) induced by a kernel function φ(z, ·) ∈ F ∞α between Fock spaces. For 1 ≤ p ≤ ∞, they prove that Sφ : F 1 α → F p α is bounded if and only if sup a∈C kSφkakp,α < ∞, (?) where ka is the normalized reproducing kernel of F 2 α; and, Sφ : F 1 α → F p α is compact if and only if lim |a|→∞ kSφkakp,α = 0. When 1 < q ≤ ∞, it is also proved that the condition (?) is not sufficient for boundedness of Sφ : F q α → F p α . In the particular case φ(z, w) = eαzw?(z ? w) with ? ∈ F 2 α, for 1 ≤ q < p < ∞, they show that Sφ : F p α → F q α is bounded if and only if ? = 0; for 1 < p ≤ q < ∞, they give sufficient conditions for the boundedness or compactness of the operator Sφ : F p α → F q α.     

2,8(4,6)-二取代半瞬烯及其BCO衍生物的Cope重排

运用从头计算量化方法计算了一系列Cope重排的2,8(或4,6)-二取代半瞬烯(1和2), 以及2,8:4,6-四取代半瞬烯(3和4)的过渡态结构、活化能、能量差和核独立化学位移. 在2,8(或4,6)-二取代半瞬烯体系里, π电子基均使得Cope重排向2进行, 这与Hoffmann早年对此的定性预测相反. 它们的过渡态是离域双同芳香性的. 本文重点讨论了π电子基与BCO共同取代的2,8:4,6-四取代半瞬烯体系, 由于BCO的稳定效应和π电子基共轭效应, π电子基均使得结构4具有优先稳定性, 其Cope重排活化能也大大降低甚至消除. 随着卤素主量子数的变化, 它们的取代半瞬烯Cope重排相关参数也有相应的规律性变化.     

Stuffed Tridymite Structures: Synthesis,Structure, Second Harmonic Generation,Optical, and Multiferroic Properties

The stuffed tridymite structure Ba(Zn/Co)_1−xSi_1−xM_2xO₄ (M=Al³⁺ and Fe³⁺) is explored for the possible multiferroic behavior and to develop new inorganic colored materials. The compounds were synthesized by employing conventional solid-state chemistry methods in the temperature range 1100–1175 °C for 24 h. The powder X-ray diffraction (PXRD) and Rietveld refinement studies indicate that the compounds stabilize in the P63 space group (no. 173). The refinement results were also rationalized by employing Raman spectroscopic studies. The compounds were found to be second harmonic generation (SHG) active and show weak ferroelectric behavior. The co-substitution of Co²⁺ and Fe³⁺ in the structure gives rise to a weak ferromagnetic behavior to the compound, BaCo_0.75Si_0.75Fe_0.5O₄, making it a multiferroic material. The optical studies on the prepared compounds exhibited blue color (Co²⁺ in T_d geometry), purple color (Ni²⁺ in T_d geometry), and simultaneous substitution of Co²⁺ and Fe³⁺ gives rise to blue-green color owing to metal-to-metal charge transfer (MMCT) effect.