A Study on the Transmission Dynamics of the Omicron Variant of COVID-19 Using Nonlinear Mathematical Models

This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.

On the stability of two-step predictive controller based on state observer

For input saturated Hammerstein systems, the two-step predictive control strategy is adopted. The first step calculates the desired intermediate variable applying unconstrained linear modal and predictive control. The second step obtains the real-time control action by solving algebraic equation and desaturation. The case of immeasurable state is considered where the observer gain matrix is solved by Sylvester equation. The sufficient closed-loop stability condition is given and the designing and tuning algorithm for the domain of attraction is proposed. The theoretical results are validated by an example.

The Existence and Stability of Nontrivial Steady-State for a Delay Competition-Diffusion Model

This paper investigates the competition diffusion model with delay. The existence and stability of nontrivial steady state are studied.

On the evolution of terrestrial planets:Bi-stability,stochastic effects,and the non-uniqueness of tectonic states

The Earth is the only body in the solar system for which significant observational constraints are accessible to such a degree that they can be used to discriminate between competing models of Earth's tectonic evolution.It is a natural tendency to use observations of the Earth to inform more general models of planetary evolution.However,our understating of Earth's evolution is far from complete.In recent years,there has been growing geodynamic and geochemical evidence that suggests that plate tectonics may not have operated on the early Earth,with both the timing of its onset and the length of its activity far from certain.Recently,the potential of tectonic bi-stability(multiple stable,energetically allowed solutions)has been shown to be dynamically viable,both from analytical analysis and through numeric experiments in two and three dimensions.This indicates that multiple tectonic modes may operate on a single planetary body at different times within its temporal evolution.It also allows for the potential that feedback mechanisms between the internal dynamics and surface processes(e.g.,surface temperature changes driven by long term climate evolution),acting at different thermal evolution times,can cause terrestrial worlds to alternate between multiple tectonic states over giga-year timescales.The implication within this framework is that terrestrial planets have the potential to migrate through tectonic regimes at similar‘thermal evolution times'(e.g.,points were they have a similar bulk mantle temperature and energies),but at very different'temporal times'(time since planetary formation).It can be further shown that identical planets at similar stages of their evolution may exhibit different tectonic regimes due to random variations.Here,we will discuss constraints on the tectonic evolution of the Earth and present a novel framework of planetary evolution that moves toward probabilistic arguments based on general physical principals,as opposed to particular rheologies,and incorporates the potential of tectonic regime transitions and multiple tectonics states being viable at equivalent physical and chemical conditions.

The Analysis of Global Input-to-state Stability for Piecewise Affine Systems with Time-delay

In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.

Long-term Stability and Oceanic Mean State Simulated by the Coupled Model FGOALS-s2

We describe the long-term stability and mean climatology of oceanic circulations simulated by version 2 of the Flexible Global Ocean-Atmosphere-Land System model （FGOALS-s2）. Driven by pre-industrial forcing, the integration of FGOALS-s2 was found to have remained stable, with no obvious climate drift over 600 model years. The linear trends of sea SST and sea surface salinity （SSS） were -0.04℃ （100 yr）-1 and 0.01 psu （100 yr）-1, respectively. The simulations of oceanic temperatures, wind-driven circulation and thermohaline circulation in FGOALS-s2 were found to be comparable with observations, and have been substantially improved over previous FGOALS-s versions （1.0 and 1.1）. However, significant SST biases （exceeding 3℃） were found around strong western boundary currents, in the East China Sea, the Sea of Japan and the Barents Sea. Along the eastern coasts in the Pacific and Atlantic Ocean, a warm bias （〉3℃） was mainly due to overestimation of net surface shortwave radiation and weak oceanic upwelling. The difference of SST biases in the North Atlantic and Pacific was partly due to the errors of meridional heat transport. For SSS, biases exceeding 1.5 psu were located in the Arctic Ocean and around the Gulf Stream. In the tropics, freshwater biases dominated and were mainly caused by the excess of precipitation. Regarding the vertical dimension, the maximal biases of temperature and salinity were located north of 65°N at depths of greater than 600 m, and their values exceeded 4℃ and 2 psu, respectively.

Study about thermal runaway behavior of high specific energy density Li-ion batteries in a low state of charge

Lithium-ion batteries are widely used in electric vehicles and electronics, and their thermal safety receives widespread attention from consumers. In our study, thermal runaway testing was conducted on the thermal stability of commercial lithium-ion batteries, and the internal structure of the battery was analyzed with an in-depth focus on the key factors of the thermal runaway. Through the study of the structure and thermal stability of the cathode, anode, and separator, the results showed that the phase transition reaction of the separator was the key factor affecting the thermal runaway of the battery for the condition of a low state of charge.

Solid state synthesis of nano-mineral particles

Many researchers in academia and industries are interested in reducing particle sizes from few submicrometers to nano-meter levels.These nano-particles find application in several areas including ceramics,paints,cosmetics,microelectronics,sensors,textiles and biomedical,etc.This article reviews the present state of the art for solid state synthesis of mineral nano-particles by wet milling,including their operating variables such as ball size,solid mass fraction and suspension stability.This article concludes and recommends with a critical discussion of nano-particles synthesis and a few common strategies to overcome stability issues.

THE THEOREM OF THE STABILITY OF LINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION AND ITS APPLICATION IN THE STABILITY ANALYSIS OF ROBOT

The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of[1] and [2], and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov ami the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper. Besides, the analysis of the dynamic stabilitv of robot has been presented by applying the theorem in this paper, which is closer to reality

First-principles Study on the Electronic Structure and Stability of Mo_(2-x)Cr_xC

This paper deals with the electronic structure and stability of a series of carbides Mo2-xCrxC based on the pseudopotential plane-waves approach of density functional theory and using the generalized gradient approximation(GGA) for the exchange and correlation potential.The calculation results of formation energies demonstrate that the structure Mo2-xCrxC in range of 0≤x≤1.75 is stable under ambient conditions.The formation energies/stabilities of the structures Mo2-xCrxC increase /reduce with enhancing the content of Cr in the structure.Calculated density of state(DOS) show that an increase in the content of Cr dissolving in Mo2-xCrxC crystal cell can lead to the crystal cell volume slightly to shrinkage,TDOS to be elevated at the Fermi level and the peak value of DOS to decrease at the lower energy region from-13.78 to-10.16 eV.Mulliken population analysis explains that the Mo2-xCrxC phase possess the metallic,covalent and ionic bonds.

THE THEOREM OF THE STABILITY OF NONLINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION—LIAPUNOV’S INDIRECT METHOD

In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.

Quantum Chemical Study on the Structural Characteristics and Stability of AlS_n~± Clusters

The geometric configurations and electronic structures of AlSn ±（n = 1~10） clusters were studied by the B3LYP（DFT） method at the 6-311G＊＊ level. The changing rules of the ground state structure features, charge transfer and bonding characteristics of the aluminum-sulfur doped clusters were discussed in detail. The ground states of AlSn ±（n 〉 2） are all AlcoreSshell planar or solid double ring structures formed by inserting one Al atom to the Sm and Sn-m（m

Stability Analysis of a Neurocontroller with Kalman Estimator for the Inverted Pendulum Case

In this paper, a practical analysis of stability by simulation for the effect of incorporating a Kalman estimator in the control loop of the inverted pendulum with a neurocontroller is presented. The neurocontroller is calculated by approximate optimal control, without considering the Kalman estimator in the loop following the Theorem of the separation. The results are compared with a time-varying linear controller, which in noiseless conditions in the state or in the measurement has an acceptable performance, but when it is under noise conditions its operation closes into a state space range more limited than the one proposed here.

THEORETICAL STUDY ON THE EXCITED STATES AND STABILITIES OF B_3, B_3^- AND B_3^+

The geometries and vibrational frequencies of the ground and low-lying excited states for B_3, B_3^- and B_3^+ are determined with the energy gradient method using the polarized double-zeta(6-31G*) basis set. The stabilities for the states of B_3,B_3^- and B_3^+ have been investigated based on the vibrational analysis. The correlation energy obtained for each state is considered with the configuration interaction (CISD+Q) technique. B_3 and B_3^+ have stable equilateral triangle geometry, while B_3^- has stable equilateral triangle, isosceles triangle and linear geometries. The Jahn-Teller distortion for a ~3E' state of B_3^- in D_(3h) symmetry is also discussed.

Solution of the HJI equations for nonlinear H_∞ control design by state-dependent Riccati equations approach

The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.

Attaining the Steady State of the Nitriding Potential after a Change of NH_3 Atmosphere Flow Rate during the Gas Nitriding Process

In single and multi-stage nitriding processes, each stage is characterized by the following parameters: temperature and time, type and composition of incoming atmosphere, as well as the set value of the nitriding potential. In the case of an atmosphere composed of raw ammonia and dissociated ammonia (NH3 - NH3cKss), the set value of the nitriding potential can be achieved by a change of the incoming atmosphere make-up, while in the case of atmospheres comprising NH3 and NH} -N2 - by a change of the atmosphere flow rate. The time needed to reach a stabilized state, after the initiation of a change in the atmosphere gas mix can be assessed relatively easily. The problem is much more complex if we want to predict the time of reaching a new stabilized state following a change in atmosphere flow rate. The time of reaching stabilized state is, in this case, a complex function of the flow rate of the atmosphere which forces the potential change, and of temperature. This problem, in the case of the NH3 type atmosphere, is the subject of investigation in this work. Factors are discussed, affecting the rate at which stabilized state is reached by the system after the introduction of a disturbance, necessary to attain the required nitriding potential.

A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM

One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.

The Effect of State-Dependent Control for an SIRS Epidemic Model with Varying Total Population

Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.