Planar System-Masses in an Equilateral Triangle:Numerical Study within Fractional Calculus

In this work,a system of three masses on the vertices of equilateral triangle is investigated.This system is known in the literature as a planar system.We first give a description to the system by constructing its classical Lagrangian.Secondly,the classical Euler-Lagrange equations(i.e.,the classical equations of motion)are derived.Thirdly,we fractionalize the classical Lagrangian of the system,and as a result,we obtain the fractional Euler-Lagrange equations.As the final step,we give the numerical simulations of the fractional model,a new model which is based on Caputo fractional derivative.

EXISTENCE OF PERIODIC SOLUTIONS OF PLANAR SYSTEMS WITH FOUR DELAYS

The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.

Switching Tracking Control for Planar Systems with Transient Performance Constraints

这份报纸学习与被 overshoot 和安定时间决定的一些给定的短暂性能限制为平面系统的一个类追踪问题的输出。与产量限制(SSOFTOC ) 追踪的交换静态的产量反馈的问题第一次被建议并且解决。静态的输出反馈控制器和一条所谓的圆锥形的切换法律在没有违背短暂性能限制，靠近环的交换系统的输出能 asymptotically 在哪个下面追踪步信号下面被设计。而且，最佳的加权的短暂表演被解决一个非线性的编程问题获得。最后，到飞机扇涡轮引擎的一个数字例子和应用被给说明有效性和建议方法的适用性。

Planar Systems嵌入型公众多媒体查询系统显示器

Planar Systems推出LB1500R和LB1503R公众多媒体查询系统显示器，可给公众多媒体查询系统（kiosk）的集成商和OEM提供明亮的引人注目的显示器。该产品亮度为550cd／m^2，增强了可见度从而适应更多的人。在零售店或酒店中，15″ LB15系列为流视频广告的集成复合视频提供选择，并且为零售店、停车场和办公大厅支持来自安全摄像机的实时监控资料。所有型号产品都能够集成到交互式POP kiosk、

PERIODIC SOLUTIONS OF PLANAR SYSTEMS WITH FOUR DELAYS

We obtain sufficient conditions for the existence of non-constant periodic solutions of the following planar system with four delays Our approach is based on the continuation theorem of the coincidence degree, and the a-priori estimate of periodic solutions.

PERIODIC SOLUTIONS OF PLANAR SYSTEM WITH SIX DELAYS

In this paper we obtain some sufficient conditions for the existence of non-constant periodic solutions of the following planar system with six delaysOur approach is based on the continuation theorem of the coincidence degree.

A reusable planar triggered spark-gap switch batched-fabricated with PCB technology for medium- and low-voltage pulse power systems

Triggered spark-gap switch is a popular discharge switch for pulse power systems.Previous studies have focused on planarizing this switch using thin film techniques in order to meet the requirements of compact size in the systems.Such switches are one-shot due to electrodes being too thin to sufficiently resist spark-erosion.Additionally,these switches did not employ any structures in securing internal gas composition,resulting in inconsistent performance under harsh atmospheres.In this work,a novel planar triggered spark-gap switch(PTS)with a hermetically sealed cavity was batched-prepared with printed circuit board(PCB)technology,to achieve reusability with low cost.The proposed PTS was inspected by micro-computed tomography to ensure PCB techniques meet the requirements of machining precision.The results from electrical experiments demonstrated that PCB PTS were consistent and reusable with lifespan over 20 times.The calculated switch voltage and circuit current were consistent with those derived from real-world measurements.Finally,PCB PTS was used to introduce hexanitrostilbene(HNS)pellets in a pulse power system to verify its performance.

DESIGN OF CONTROL INVARIANT SETS OF PLANAR SYSTEMS

Control invariant sets play a key role in model predictive control.Using Lyapunov function,a technique is proposed to design control invariant sets of planar systems in a precise form.First,itis designed for a linear system in Brunovsky canonical form.Then,the result is extended to generallinear systems.Finally,the nonlinear control systems are considered,and some sufficient conditionsand design techniques are also obtained.Numerical examples are presented to illustrate the proposeddesign methods.

Crossing Limit Cycles of Planar Piecewise Hamiltonian Systems with Linear Centers Separated by Two Parallel Straight Lines

In this paper, we have studied several classes of planar piecewise Hamiltonian systems with three zones separated by two parallel straight lines. Firstly, we give the maximal number of limit cycles in these classes of systems with a center in two zones and without equilibrium points in the other zone (or with a center in one zone and without equilibrium points in the other zones). In addition, we also give examples to illustrate that it can reach the maximal number.

Electrically tunable planar liquid-crystal singlets for simultaneous spectrometry and imaging

Conventional hyperspectral cameras cascade lenses and spectrometers to acquire the spectral datacube,which forms the fundamental framework for hyperspectral imaging.However,this cascading framework involves tradeoffs among spectral and imaging performances when the system is driven toward miniaturization.Here,we propose a spectral singlet lens that unifies optical imaging and computational spectrometry functions,enabling the creation of minimalist,miniaturized and high-performance hyperspectral cameras.As a paradigm,we capitalize on planar liquid crystal optics to implement the proposed framework,with each liquid-crystal unit cell acting as both phase modulator and electrically tunable spectral filter.Experiments with various targets show that the resulting millimeter-scale hyperspectral camera exhibits both high spectral fidelity(>95%)and high spatial resolutions(~1.7 times the diffraction limit).The proposed“two-in-one”framework can resolve the conflicts between spectral and imaging resolutions,which paves a practical pathway for advancing hyperspectral imaging systems toward miniaturization and portable applications.

Compact magneto-optical traps using planar optics

Magneto-optical traps (MOTs) composed of magnetic fields and light fields have been widely utilized to cool andconfine microscopic particles. Practical technology applications require miniaturized MOTs. The advancement of planaroptics has promoted the development of compact MOTs. In this article, we review the development of compact MOTs basedon planar optics. First, we introduce the standardMOTs. We then introduce the gratingMOTs with micron structures, whichhave been used to build cold atomic clocks, cold atomic interferometers, and ultra-cold sources. Further, we introducethe integrated MOTs based on nano-scale metasurfaces. These new compact MOTs greatly reduce volume and powerconsumption, and provide new opportunities for fundamental research and practical applications.

Asymptotic analysis on bright solitons and breather solutions of a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide

We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on Lax pair obtained by us,we derive the infinitely-many conservation laws.We give the bright one-,two-,and N-soliton solutions,and the first-,second-,and Nth-order breather solutions based on the N-fold DT.We conclude that the velocities of the bright solitons are influenced by the distributed gain function,g(z),and variable coefficients in equation,h1(z),p1(z),r1(z),and s1(z)via the asymptotic analysis,where z represents the propagation variable or spatial coordinate.We also graphically observe that:the velocities of the first-and second-order breathers will be affected by h1(z),p1(z),r1(z),and s1(z),and the background wave depends on g(z).

Planar Hall Effect in the Charge-Density-Wave Bi_(2)Rh_(3)Se_(2)

We systematically investigate in-plane transport properties of ternary chalcogenideBi_(2)Rh_(3)Se_(2).Upon rotating the magnetic field within the plane of the sample, one can distinctly detect the presence of both planar Hall resistance and anisotropic longitudinal resistance, and the phenomena appeared are precisely described by the theoretical formulation of the planar Hall effect (PHE). In addition, anisotropic orbital magnetoresistance rather than topologically nontrivial chiral anomalies dominates the PHE in Bi_(2)Rh_(3)Se_(2). The finding not only provides another platform for understanding the mechanism of PHE, but could also be beneficial for future planar Hall sensors based on two-dimensional materials.

High-performance GaSb planar PN junction detector

This paper examines GaSb short-wavelength infrared detectors employing planar PN junctions. The fabrication was based on the Zn diffusion process and the diffusion temperature was optimized. Characterization revealed a 50% cut-off wavelength of 1.73 μm, a maximum detectivity of 8.73 × 10^(10) cm·Hz^(1/2)/W, and a minimum dark current density of 1.02 × 10^(-5) A/cm^(2).Additionally, a maximum quantum efficiency of 60.3% was achieved. Subsequent optimization of fabrication enabled the realization of a 320 × 256 focal plane array that exhibited satisfactory imaging results. Remarkably, the GaSb planar detectors demonstrated potential in low-cost short wavelength infrared imaging, without requiring material epitaxy or deposition.

An approach for determination of lateral limit angle in kinematic planar sliding analysis for rock slopes

Planar sliding is one of the frequently observed types of failure in rock slopes.Kinematic analysis is a classic and widely used method to examine the potential failure modes in rock masses.The accuracy of planar sliding kinematic analysis is significantly influenced by the value assigned to the lateral limit angleγlim.However,the assignment ofγlim is currently used generally based on an empirical criterion.This study aims to propose an approach for determining the value ofγlim in deterministic and probabilistic kinematic planar sliding analysis.A new perspective is presented to reveal thatγlim essentially influences the probability of forming a potential planar sliding block.The procedure to calculate this probability is introduced using the block theory method.It is found that the probability is correlated with the number of discontinuity sets presented in rock masses.Thus,different values ofγlim for rock masses with different sets of discontinuities are recommended in both probabilistic and deterministic planar sliding kinematic analyses;whereas a fixed value ofγlim is commonly assigned to different types of rock masses in traditional method.Finally,an engineering case was used to compare the proposed and traditional kinematic analysis methods.The error rates of the traditional method vary from 45%to 119%,while that of the proposed method ranges between 1%and 17%.Therefore,it is likely that the proposed method is superior to the traditional one.

Design,fabrication and performance test of an integrated exploding foil initiator system OA

The integration method of exploding foil initiator system(EFIs) used to be researched to broaden its application range in military and aerospace in the last few decades.In order to lower the firing voltage below 1 kV,an integrated EFIs with enhanced energy efficiency was designed.Corresponding exploding foil initiator chips were fabricated in batch via micro electromechanical systems technology by integrating a unified foil,a flyer layer and a barrel on a glass substrate successively,meanwhile its package of the whole system was proposed at a volume of 2.194 cm^(3).The structural parameters were determined by predicted performance including flyer velocity,impact behavior and conduction property via the proposed theoretical models and the static electric field simulation.As expect,this integrated EFIs exhibited excellent functions,which could accelerate the flyer to a terminal velocity over 4 km/s and preeminently initiate HNS-IV pellet at a circuit of 0.24 μF/0.9 kV.Furthermore,the theoretical design,fabrication and performance test have been all included to validate the feasibility of this integrated EFIs that was beneficial for its commercial development in the future.

Angular and planar transport properties of antiferromagnetic V_(5)S_(8)

Systemically angular and planar transport investigations are performed in layered antiferromagnetic(AF)V_(5)S_(8).In this AF system,obvious anomalous Hall effect(AHE)is observed with a large Hall angle of 0.1 compared to that in ferromagnetic(FM)system.It can persist to the temperatures above AF transition and exhibit strong angular field dependence.The phase diagram reveals various magnetic states by rotating the applied field.By analyzing the anisotropic transport behavior,magnon contributions are revealed and exhibit obvious angular dependence with a spin-flop vanishing line.The observed prominent planar Hall effect and anisotropic magnetoresisitivity exhibit two-fold systematical angular dependent oscillations.These behaviors are attributed to the scattering from spin–orbital coupling instead of nontrivial topological origin.Our results reveal anisotropic interactions of magnetism and electron in V5S8,suggesting potential opportunities for the AF spintronic sensor and devices.

Nonlinear dynamic modeling of planar moving Timoshenko beam considering non-rigid non-elastic axial effects

Due to the importance of vibration effects on the functional accuracy of mechanical systems,this research aims to develop a precise model of a nonlinearly vibrating single-link mobile flexible manipulator.The manipulator consists of an elastic arm,a rotary motor,and a rigid carrier,and undergoes general in-plane rigid body motion along with elastic transverse deformation.To accurately model the elastic behavior,Timoshenko’s beam theory is used to describe the flexible arm,which accounts for rotary inertia and shear deformation effects.By applying Newton’s second law,the nonlinear governing equations of motion for the manipulator are derived as a coupled system of ordinary differential equations(ODEs)and partial differential equations(PDEs).Then,the assumed mode method(AMM)is used to solve this nonlinear system of governing equations with appropriate shape functions.The assumed modes can be obtained after solving the characteristic equation of a Timoshenko beam with clamped boundary conditions at one end and an attached mass/inertia at the other.In addition,the effect of the transverse vibration of the inextensible arm on its axial behavior is investigated.Despite the axial rigidity,the effect makes the rigid body dynamics invalid for the axial behavior of the arm.Finally,numerical simulations are conducted to evaluate the performance of the developed model,and the results are compared with those obtained by the finite element approach.The comparison confirms the validity of the proposed dynamic model for the system.According to the mentioned features,this model can be reliable for investigating the system’s vibrational behavior and implementing vibration control algorithms.

On the (Δ + 2)-Total-Colorability of Planar Graphs with 7-Cycles Containing at Most Two Chords

The Total Coloring Conjecture (TCC) proposes that every simple graph G is (Δ + 2)-totally-colorable, where Δ is the maximum degree of G. For planar graph, TCC is open only in case Δ = 6. In this paper, we prove that TCC holds for planar graph with Δ = 6 and every 7-cycle contains at most two chords.

HEVC帧内预测Planar和DC模式的VLSI架构设计与实现

在研究新一代高性能视频编码标准(HEVC)帧内预测中planar和DC模式预测算法的基础上,分别设计了高效VLSI架构,通过状态机的自适应控制和模块的复用来实现速度的提高和面积的减少。针对planar模式,设计了一种基于状态机自适应控制的寄存器累加架构;针对DC模式,设计了一种基于算法的分割处理架构。实验结果表明,所设计的架构在TSMC180 nm的工艺下最高频率为350 MHz,面积合计为68.1 kgate,能够实现对4∶2∶0格式7 680×4 320@30 f/s视频序列的实时编码,最高工作频率可以达到23.4 MHz。