Quantum control based on three forms of Lyapunov functions

This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.

THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED PERTURBATIONS

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

CONVEXITY OF THE FREE BOUNDARY FOR AN AXISYMMETRIC INCOMPRESSIBLE IMPINGING JET

This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THERMOMECHANICAL CUCKER-SMALE-STOKES EQUATIONS IN THE WHOLE DOMAIN

We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.

Oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions via Prufer transformation

A class of Sturm-Liouville problems with discontinuity is studied in this paper.The oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions are obtained.The main method used in this paper is based on Prufer transformation,which is different from the classical ones.Moreover,we give two examples to verify our main results.

Identification of an immune-related gene signature for predicting prognosis and immunotherapy efficacy in liver cancer via cell-cell communication

BACKGROUND Liver cancer is one of the deadliest malignant tumors worldwide.Immunotherapy has provided hope to patients with advanced liver cancer,but only a small fraction of patients benefit from this treatment due to individual differences.Identifying immune-related gene signatures in liver cancer patients not only aids physicians in cancer diagnosis but also offers personalized treatment strategies,thereby improving patient survival rates.Although several methods have been developed to predict the prognosis and immunotherapeutic efficacy in patients with liver cancer,the impact of cell-cell interactions in the tumor microenvir-onment has not been adequately considered.AIM To identify immune-related gene signals for predicting liver cancer prognosis and immunotherapy efficacy.METHODS Cell grouping and cell-cell communication analysis were performed on single-cell RNA-sequencing data to identify highly active cell groups in immune-related pathways.Highly active immune cells were identified by intersecting the highly active cell groups with B cells and T cells.The significantly differentially expressed genes between highly active immune cells and other cells were subsequently selected as features,and a least absolute shrinkage and selection operator(LASSO)regression model was constructed to screen for diagnostic-related features.Fourteen genes that were selected more than 5 times in 10 LASSO regression experiments were included in a multivariable Cox regression model.Finally,3 genes(stathmin 1,cofilin 1,and C-C chemokine ligand 5)significantly associated with survival were identified and used to construct an immune-related gene signature.RESULTS The immune-related gene signature composed of stathmin 1,cofilin 1,and C-C chemokine ligand 5 was identified through cell-cell communication.The effectiveness of the identified gene signature was validated based on experi-mental results of predictive immunotherapy response,tumor mutation burden analysis,immune cell infiltration analysis,survival analysis,and expression analysis.CONCLUSION The findings suggest that the identified gene signature may contribute to a deeper understanding of the activity patterns of immune cells in the liver tumor microenvironment,providing insights for personalized treatment strategies.

Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes

This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.

SOME NEW IDENTITIES OF ROGERS-RAMANUJAN TYPE

In this paper,we establish two transformation formulas for nonterminating basic hypergeometric series by using Carlitz's inversions formulas and Jackson s transformation formula.In terms of application,by specializing certain parameters in the two transformations,four Rogers-Ramanujan type identities associated with moduli 20 are obtained.

Satellite observations of coastal upwelling in the northern Arafura Sea

Coastal upwelling is significant for marine ecosystems by lifting nutrient-rich deep waters into the euphotic zone,thereby increasing primary and secondary productivity.The satellite observations show that the northern Arafura Sea(NAS),especially in the coastal region,features high chlorophyll-a(chl-a)concentrations,implying a strong coastal upwelling.However,coastal upwelling in the NAS has not received much attention.Based on a semi-automatic image processing technology,the seasonal and interannual variability of coastal upwelling in the NAS are investigated in this study using satellite-observed sea surface temperature(SST)and wind data.The results suggest that there are seasonal coastal upwelling events in the NAS modulated by upwelling-favorable southeast monsoon(SEM).The annual mean days,mean area,and annual mean intensity of coastal upwelling events during the SEM season are 92 days,6514 km^(2),and-5.31×10^(5),respectively,while the corresponding values during the northwest monsoon(NWM)season are 32 days,5569 km^(2),and-1.41×10^(5).It is also found that the SEM coastal upwelling in the NAS displays prominent interannual variability.The strong upwelling events are found in 2010,2013,2016,and 2017 when the southeast monsoon winds were weaker.Further analysis suggests that at the interannual scale,the upwelling index(UI)averaged in the SEM season is negatively correlated with that of three upwelling indicators.This can be attributed to the limitation of onshore geostrophic flow which is evidenced by the negative correlation between the UI and the alongshore difference in sea surface height.This study highlights the important role of the southeast monsoon in the temporal variability of coastal upwelling in the NAS.

Necessary and Sufficient Conditions for Oscillations of the Generalized Liénard Systems

In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.

Teaching Reform of “Probability Theory and Mathematical Statistics” Under the Background of New Engineering

Probability theory and mathematical statistics are fundamental courses for various majors in science and engineering.In response to the current teaching situation,we should integrate theory with practice,implement teaching reform,and carry out teaching innovation.The article carries out blended teaching with deep integration of online and offline modes and within and outside of class,constructing innovative measures of“four integrations and four reshaping.”The article conducts diversified evaluations to stimulate learning motivation and help achieve talent cultivation goals.Through the close integration of probability theory and mathematical statistics course teaching with professional education and practical application,the“three-in-one”teaching goal of value shaping,ability cultivation,and knowledge exploration is achieved.The fundamental task of“cultivating morality and talents”is implemented.

Research Progress on the Preparation of Inorganic/Natural Materials Composite Microspheres

Microspheres are a new type of drug carrier with great potential for development and application.Natural polymers have good biocompatibility,biodegradability,and are easily dispersed in living organisms,making them suitable for preparing microspheres.Inorganic materials(mainly inorganic minerals)have excellent mechanical properties and are inexpensive and easy to obtain.Through the coupling and hybridization of natural polymers and inorganic materials,they can complement each other's advantages and synergistically enhance efficiency,resulting in many excellent physical and chemical properties.Inorganic materials/natural polymer composite microspheres can be prepared by modifying natural polymers with inorganic materials through various methods such as emulsification crosslinking,solution mixing,in-situ synthesis,extrusion,etc.The application of inorganic materials/natural polymer composite microspheres in drug delivery systems has significant sustained-release effects,is safe and non-toxic,and the cost of carrier materials is relatively low,which has certain significance for the development of new drug carriers.This article reviews the recent research on the preparation,drug loading and release properties of inorganic material/natural polymer composite microspheres,analyzes the advantages and disadvantages of commonly used preparation methods,and looks forward to the development direction of composite microspheres.

Diversity of Rogue Wave Solutions to the (1+1)-Dimensional Boussinesq Equation

A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 but also has a relationship with the other parameters c0, α, β.

On the Equality of Weighted BajratarevićMeans to Quasi-Arithmetic Means

In this paper, we considered the equality problem of weighted Bajraktarević means with weighted quasi-arithmetic means. Using the method of substituting for functions, we first transform the equality problem into solving an equivalent functional equation. We obtain the necessary and sufficient conditions for the equality equation.

Discussion on the Complex Structure of Nilpotent Lie Groups Gk

Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.

Distributional Chaoticity of the Minimal Subshift of Shift Operators

This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution.

Dynamics of Plate Equations with Memory Driven by Multiplicative Noise on Bounded Domains

This article examines the dynamics for stochastic plate equations with linear memory in the case of bounded domain. We investigate the existence of solutions and bounded absorbing set by using the uniform pullback attractors on the tails estimates, and the asymptotic compactness of the random dynamical system is proved by decomposition method, and then we obtain the existence of a random attractor.

Enabling structural and interfacial stability of 5 V spinel LiNi0.5Mn1.5O4 cathode by a coherent interface

Spinel LiNi_(0.5)Mn_(1.5)O_(4)(LNMO),a 5 V class high voltage cathode,has been regarded as an attractive candidate to further improve the energy density of lithium-ion battery.The issue simultaneously enabling side stability and maintaining high interfacial kinetics,however,has not yet been resolved.Herein,we design a coherent Li_(1.3)A_(l0.3)Ti_(1.7)(PO)_(4)(LATP)layer that is crystally connected to the spinel LNMO host lattices,which offers fast lithium ions transportation as well as enhances the mechanical stability that prevents the particle fracture.Furthermore,the inactive Li_(3)BO_(3)(LBO)coating layer inhibits the corrosion of transition metals and continuous side reactions.Consequently,the coherent-engineered LNMO-LATPLBO cathode material exhibits superior electrochemical cycling stability in a window of 3.0–5.0 V,for example a high-capacity retention that is 89.7%after 500 cycles at 200 m A g-1obtained and enhanced rate performance(85.1 m A h g^(-1)at 800 m A g^(-1))when tested with a LiPF6-based carbonate electrolyte.Our work presents a new approach of engineering 5 V class spinel oxide cathode that combines interfacial coherent crystal lattice design and surface coating.

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

A large member of lump chain solutions of the(2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili(BKP)equation are constructed by means of theτ-function in the form of Grammian.The lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and velocities.An analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump chains.The degenerate structures of parallel,superimposed,and molecular lump chains are presented.The interaction solutions between lump chains and kink-solitons are investigated,where the kink-solitons lie on the boundaries of dominant region determined by the constant term in theτ-function.Furthermore,the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are investigated.The analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.

Novel Analysis of Two Kinds Hybrid Models in Ferro Martial Inserting Variable Lorentz Force Past a Heated Disk:An Implementation of Finite Element Method

In this article,the rheology of Ferro-fluid over an axisymmetric heated disc with a variable magnetic field by considering the dispersion of hybrid nanoparticles is considered.The flow is assumed to be produced by the stretching of a rotating heated disc.The contribution of variable thermophysical properties is taken to explore themomentum,mass and thermal transportation.The concept of boundary layermechanismis engaged to reduce the complex problem into a simpler one in the form of coupled partial differential equations system.The complex coupled PDEs are converted into highly nonlinear coupled ordinary differential equations system(ODEs)and the resulting nonlinear flow problem is handled numerically.The solution is obtained via finite element procedure(FEP)and convergence is established by conducting the grid-independent survey.The solution of converted dimensionless problem containing fluid velocity,temperature and concentration field is plotted against numerous involved emerging parameters and their impact is noted.From the obtained solution,it is monitored that higher values of magnetic parameter retard the fluid flow and escalating values of Eckert number results in to enhance temperature profile.Ferro-fluid flow and heat energy for the case of the Yamada Ota hybrid model are higher than for the case of the Hamilton Crosser hybrid model.Developing a model is applicable to the printing process,electronic devices,temperature measurements,engineering process and food-making process.The amount of mass species is reduced vs.incline impacts of chemical reaction and Schmidt parameter.