Buckling and Multiple Equilibrium States ofViscoelastic Rectangular Plates

On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonlinear integro partial differential equations is first presented by means of a structural function introduced in this paper. Then, by using the Galerkin technique in spatial field and a backward difference scheme in temporal field, the set of nonlinear integro partial differential equations reduces to a system of nonlinear algebraic equations. After solving the algebraic equations, the buckling behavior and multiple equilibrium states can be obtained.

Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)concepts.Under accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive.An economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s risks.Numerical results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are discussed.Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions.The AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling plans.Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

Multiple valence states of Fe boosting SERS activity of Fe_(3)O_(4) nanoparticles and enabling effective SERS-MRI bimodal cancer imaging

Developing novel nanoparticle-based bioprobes utilized in clinical settings with imaging resolutions ranging from cell to tissue levels is a major challenge for tumor diagnosis and treatment.Herein,an optimized strategy for designing a Fe_(3)O_(4)-based bioprobe for dual-modal cancer imaging based on surface-enhanced Raman scattering(SERS)and magnetic resonance imaging(MRI)is introduced.Excellent SERS activity of ultrasmall Fe_(3)O_(4) nanoparticles(NPs)was discovered,and a 5×10^(-9)M limit of detection for crystal violet molecules was successfully obtained.The high-efficiency interfacial photon-induced charge transfer in Fe_(3)O_(4) NPs was promoted by multiple electronic energy levels ascribed to the multiple valence states of Fe,which was observed using ultraviolet-visible diffuse reflectance spectroscopy.Density functional theory calculations were utilized to reveal that the narrow band gap and high electron density of states of ultrasmall Fe_(3)O_(4) NPs significantly boosted the vibronic coupling resonances in the SERS system upon illumination.The subtypes of cancer cells were accurately recognized via high-resolution SERS imaging in vitro using the prepared Feg Og-based bioprobe with high sensitivity and good specificity.Notably,Fe_(3)O_(4)-based bioprobes simultaneously exhibited T,-weighted MRI contrast enhancement with an active targeting capability for tumors in vivo.To the best of our knowledge,this is the first report on the use of pure semiconductor-based SERS-MRI dual-modal nanoprobes in tumor imaging in vivo and in vitro,which has been previously realized only using semiconductor-metal complex materials.The non-metallic materials with SERS-MRI dual-modal imaging established in this report are a promising cancer diagnostic platform,which not only showed excellent performance in early tumor diagnosis but also possesses great potential for image-guided tumor treatment.

A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull distribution.We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot acceptance.The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve values.In addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan.The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.

Multiple steady state phenomenon in martensitic transformation

Based on the basic facts that the martensitic transformation is a physical phenomenon which occurs in non equilibrium conditions and there exists the feedback mechanism in the martensitic transformation, the dynamical processes of the isothermal and athermal martensitic transformations were analyzed by using nonlinear theory and a bifurcation theory model was established. It is shown that a multiple steady state phenomenon can take place as austenite is cooled, and the transitions of the steady state temperature between the branches of stable steady states can be considered the transformation from austenite to martensite. This model can estimate the starting temperature of the martensitic transformation and explain some experimental features of the martensitic transformation such as the effects of cooling rate, fluctuation and austenitic grain size on the martensitic transformation. [

THE ACTIVATION METHOD FOR DISCRETIZED CONSERVATIVE NONLINEAR STABILITY PROBLEMS WITH MULTIPLE PARAMETER AND STATE VARIABLES

For nonlinear stability problems of discretized conservative systems with multiple parameter variables and multiple state variables, the activation method is put forward, by which activated potential functions and activated equilibrium equations are derived. The activation method is the improvement and enhancement of Liapunov-Schmidt method in elastic stability theory. It is more generalized and more normalized than conventional perturbation methods. The activated potential functions may be transformed into normalized catastrophe potential functions. The activated equilibrium equations may be treated as bifurcation equations. The researches in this paper will motivate the combination of elastic stability theory with catastrophe theory and bifurcation theory

Realization of one-dimensional 2^(n)-root topological states in photonic lattices

Square-root topological insulators recently discovered are intriguing topological phases.They possess topological properties inherited from the squared Hamiltonian and exhibit double-band structures.The mechanism of the square root was generalized to 2^(n)-root topological insulators,giving rise to more band gaps.In this study,we describe the experimental realization of onedimensional 2^(n)-root topological insulators in photonic waveguide arrays using the archetypical Su-Schrieffer-Heeger(SSH)model.Topological edge states with tunable numbers are clearly observed under visible light.In particular,we visualized the dynamic evolutions of the light propagation by varying the sample lengths,which further proved the localization and multiple numbers of edge states in 2^(n)-root topological systems.The experiment,which involves constructing 2^(n)-root topological photonic lattices in various geometric arrangements,provides a stable platform for studying topological states that exhibit a remarkable degree of flexibility and control.

The Bifurcation Behavior of CO Coupling Reactor

The bifurcation behavior of the CO coupling reactor was examined based on the one-dimensional pseudo homogeneous axial dispersion dynamic model. The method of finite difference was used for solving the boundary value problem; the continuation technique and the direct method were applied to determine the bifurcation diagram. The effects of dimensionless adiabatic temperature rise, Damkohler number, activation energy, heat transfer coefficient and feed ratio on the bifurcation behavior were investigated. It was shown that there existed static bifurcation and the oscillations did not occur in the reactor. The result also revealed that the reactor exhibited at most 1-3-1 multiplicity patterns within the range of practical possible parameters and the measures, such as weakening the axial dispersion of reactor, enhancing heat transfer, decreasing the concentration of ethyl nitrite, were efficient for avoiding the possible risk of multiple steady states.

A Quantum Secret Sharing Scheme Using Orbital Angular Momentum onto Multiple Spin States Based on Fibonacci Compression Encoding

Since the use of a quantum channel is very expensive for transmitting large messages, it is vital to develop an effective quantum compression encoding scheme that is easy to implement. Given that, with the single-photon spin-orbit entanglement, we propose a quantum secret sharing scheme using orbital angular momentum onto multiple spin states based on Fibonacci compression encoding. In our proposed scheme, we can represent the frequency of any secret message which is typically collection of bits encodings of text or integers as a bitstring using the base Fibonacci sequence, which is encoded multiple spin states for secret shares transmitted to participants. We demonstrate that Fibonacci compression encoding carries excellent properties that enable us to achieve more robust quantum secret sharing schemes with fewer number of photons.

Development of a bifurcation analysis approach based on gPROMS platform

A bifurcation analysis approach is developed based on the process simulator gPROMS platform, which can automatically trace a solution path, detect and pass the bifurcation points and check the stability of solutions. The arclength continuation algorithm is incorporated as a process entity in gPROMS to overcome the limit of turning points and get multiple solutions with respect to a user-defined parameter. The bifurcation points are detected through a bifurcation test function τ which is written in C ++ routine as a foreign object connected with gPROMS through Foreign Process Interface. The stability analysis is realized by evaluating eigenvalues of the Jacobian matrix of each steady state solution. Two reference cases of an adiabatic CSTR and a homogenous azeotropic distillation from literature are studied, which successfully validate the reliability of the proposed approach. Besides the multiple steady states and Hopf bifurcation points, a more complex homoclinic bifurcation behavior is found for the distillation case compared to literature.

A Mathematical Model of the Photosynthetic Carbon Metabolism Has Multiple Steady States Under the Same Parameter Conditions

This paper analyzes a mathematical model of the photosynthetic carbon metabolism, which incorporates not only the Calvin-Benson cycle, but also another two important metabolic pathways： starch synthesis and photorespiratory pathway. Theoretically, the paper shows the existence of steady states, stability and instability of the steady states, the effects of CO2 concentration on steady states. Especially, a critical point is found, the system has only one steady state with C02 concentration in the left neighborhood of the critical point, but has two with C02 concentration in the right neighborhood. In addition, the paper also explores the influence of C02 concentration on the efficiency of photosynthesis. These theoretical results not only provide insight to the kinetic behaviors of the photosynthetic carbon metabolism, but also can be used to help improving the efficiency of photosynthesis in plants.

On the Bifurcations and Multiple Endemic States of a Single Strain HIV Model Dedicated to Professor Toshikazu Sunada on the Occasion of his 60th Birthday

The dynamics of a single strain HIV model is studied. The basic reproduction number R0 used as a bifurcation parameter shows that the system undergoes transcritical and saddle-node bifurcations. The usual threshold unit value of R0 does not completely determine the eradication of the disease in an HIV infected person. In particular, a sub-threshold value Rc is established which determines the system＇s number of endemic states： multiple if Rc 〈 Ro 〈 1, only one if Rc=Ro = 1, and none if R0 〈 Rc 〈 1.

An Improved Cass-Koopmans Model with Endogenous Fertility under the CES Production Technology

Under the CES production technology, an improved Cass Coopmans model with solvable endogenous fertility is given. We prove that there are multiple growth paths and multiple steady states when CES 0<σ<1 and the technology level is high enough; the growth path and the steady state is unique when σ>1 and the ratio of capital is smaller than a constant. So, the dynamic system which describes the model undergoes a bifurcation when σ=1 . We discuss the economic sense of the main results we give.

Multiple Multi-Qubit Quantum States Sharing

A multiple multi-qubit quantum states sharing scheme is proposed,in which the dealer can share multiple multi-qubit quantum states among the participants through only one distribution and one recovery.The dealer encodes the secret quantum states into a special entangled state,and then distributes the particles of the entangled state to the participants.The participants perform the single-particle measurements on their particles,and can cooperate to recover the multiple multi-qubit quantum states.Compared to the existing schemes,our scheme is more efficient and more flexible in practice.

Full-temperature covered switching material with triple optic-dielectric states in a lead-free hybrid perovskite

Optic-electric responsive materials have attracted much attention for their applications in temperaturesensing,actuators,and memory switches.However,it is a challenge to integrate various functions to form multifunctional responsive materials.As molecule-based hybrid materials usually consist of organic and inorganic components,the introduction of multiple functions can be achieved through structural construction.Thus far,even though fulltemperature cover is required for device applications,fulltemperature covered multi-switchable hybrid materials have rarely been successfully synthesized.Herein,the dynamic[(CH3)3NOH]+cation and luminous center Mn(II)were introduced to form a hybrid material[(CH3)3NOH][Mn Cl3],showing multiple temperature-responsive behaviors.Upon temperature change,it exhibits multi-state dielectric switching response and intensity or peak shift response of luminous in full-temperature range(low,room,and high temperatures).These responsive behaviors are triggered by the motion or reorientation of[(CH3)3NOH]+cations and inorganic framework.Overall,the switchable photoelectric material has potential applications in multiple encrypted storage and sensor devices.

Optimal LQG control for discrete time-varying system with multiplicative noise and multiple state delays

This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in virtue of Pontryagin’s maximum principle,we solve the forward and backward stochastic difference equations(FBSDEs)and show the relationship between the state and the costate.Second,based on the solution to the FBSDEs and the coupled difference Riccati equations,the necessary and sufficient condition for the optimal problem is obtained.Meanwhile,an explicit analytical expression is given for the optimal LQG controller.Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.

Robustly stable intermediate memory states in HfO_(2)-based ferroelectric field-effect transistors

Multilevel ferroelectric field-effect transistors(FeFETs)integrated with HfO_(2)-based ferroelectric thin films demonstrate tremendous potential in high-speed massive data storage and neuromorphic computing applications.However,few works have focused on the stability of the multiple memory states in the HfO_(2)-based FeFETs.Here we firstly report the write/read disturb effects on the multiple memory states in the Hf_(0.5)Zr_(0.5)O_(2)(HZO)-based FeFETs.The multiple memory states in HZO-based FeFETs do not show obvious degradation with the write and read disturb cycles.Moreover,the retention characteristics of the intermediate memory states in HZO-based FeFETs with unsaturated ferroelectric polarizations are better than that of the memory state with saturated ferroelectric polarization.Through the deep analysis of the operation principle of in HZO-based FeFETs,we speculate that the better retention properties of intermediate memory states are determined by the less ferroelectric polarization degradation and the weaker ferroelectric polarization shielding.The experimental and theoretical evidences confirm that the long-term stability of the intermediate memory states in HZO-based FeFETs are as robust as that of the saturated memory state,laying a solid foundation for their practical applications.

Convergence of community composition during secondary succession on Zokor rodent mounds on the Tibetan Plateau

Aims The community succession theory is much debated in ecology.We studied succession on Zokor rodent mounds on the Tibetan Plateau to address several fundamental questions,among them:(i)During secondary succession,does the community composition converge towards one community state or multiple states depending on the initial colonization?(ii)Do mound communities located in different background communities exhibit different assembly trajectories?Methods In a sub-alpine meadow,we investigated a total of 80 mound com-munities at several successional stages in three different background communities resulting from different management histories and compared their changes in species composition.The distribution of plant communities over time was analyzed with quantitative clas-sification and ordination methods.The co-occurrence patterns of species were evaluated at each successional stage,and the degree of convergence/divergence among communities was obtained by calculating two beta-diversity indices.Important Findings During secondary succession,species richness of mound com-munities changed over time,and this change was dependent on the background community.Five life-form groups exhibited different dynamic patterns in species richness and plant cover.Community composition and the degree of species co-occur-rence between communities increased over time since disturb-ance.There was much variation in species composition at earlier stages of succession,but communities on older mounds became more similar to each other and to their surrounding vegetation over the course of secondary succession.Post-disturbance suc-cession of Zokor mound communities transitioned from‘multiple alternative states’to‘background-based deterministic commu-nity assembly’over time.Tradeoffs between competition and colonization,as well as the characteristics of different life-forms and mass effects within a limited species pool are the mecha-nisms responsible for convergence of mound communities.

Simultaneous H_2/H_∞ Stabilization for Chemical Reaction Systems Based on Orthogonal Complement Space

This paper presents a simultaneous H2/H∞ stabilization problem for the chemical reaction systems which can be modeled as a finite collection of subsystems. A single dynamic output feedback controller which simultaneously stabilizes the multiple subsystems and captures the mixed H2/H∞ control performance is designed. To ensure that the stability condition, the H2 characterization and the H∞ characterization can be enforced within a unified matrix inequality framework, a novel technique based on orthogonal complement space is developed. Within such a framework, the controller gain is parameterized by the introduction of a common free positive definite matrix, which is independent of the multiple Lyapunov matrices. An iterative linear matrix inequality （ILMI） algorithm using Matlab Yalmip toolbox is established to deal with the proposed framework. Simulation results of a typical chemical reaction system are exploited to show the validity of the proposed methodology.

MOS Capacitance-Voltage Characteristics:Ⅳ.Trapping Capacitance from 3-Charge-State Impurities

Metal-Oxide-Semiconductor Capacitance-Voltage （MOSCV） characteristics containing giant carrier trapping capacitances from 3-charge-state or 2-energy-level impurities are presented for not-doped, n-doped, p- doped and compensated silicon containing the double-donor sulfur and iron, the double-acceptor zinc, and the amphoteric or one-donor and one-acceptor gold and silver impurities. These impurities provide giant trapping ca- pacitances at trapping energies from 200 to 800 meV （50 to 200 THz and 6 to 1.5 μm）, which suggest potential sub-millimeter, far-infrared and spin electronics applications.