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.

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.

The combined effects of North Atlantic Oscillation and Western Pacific teleconnection on winter temperature in Eastern Asia during 1980−2021

As important atmospheric circulation patterns in Northern Hemisphere(NH),the North Atlantic Oscillation(NAO)and the Western Pacific teleconnection(WP)affect the winter climate in Eurasia.In order to explore the combined effects of NAO and WP on East Asian(EA)temperature,the NAO and WP indices are divided into four phases from 1980−2021:the positive NAO and WP phase(NAO+/WP+),the negative NAO and WP phase(NAO−/WP−),the positive NAO and negative WP phase(NAO+/WP−),the negative NAO and positive WP phase(NAO−/WP+).In the phase of NAO+/WP+,the low geopotential height(GH)stays in north of EA at 50°−80°N;the surface air temperature anomaly(SATA)is 0.8−1℃lower than Southern Asian.In the phase of NAO−/WP−,the center of high temperature and GH locate in the northeast of EA;the cold air spreads to Southern Asia,causing the SATA decreases 1−1.5℃.In the phase of NAO+/WP−,the high GH belt is formed at 55°−80°N.Meanwhile,the center of high SATA locates in the north of Asia that increases 0.8−1.1℃.The cold airflow causes temperature dropping 0.5−1℃in the south of EA.The SATA improves 0.5−1.5℃in south of EA in the phase of NAO−/WP+.The belt of high GH is formed at 25°−50°N,and blocks the cold air which from Siberia.The NAO and WP generate two warped plate pressure structures in NH,and affect the temperature by different pressure configurations.NAO and WP form different GH,and GH acts to block and push airflow by affecting the air pressure,then causes the temperature to be different from the north and south of EA.Finally,the multiple linear regression result shows that NAO and WP are weakened by each other such as the phase of NAO+/WP+and NAO−/WP−.

Exploring unbinding mechanism of drugs from SERT via molecular dynamics simulation and its implication in antidepressants

The human serotonin transporter(SERT)terminates neurotransmission by removing serotonin from the synaptic cleft,which is an essential process that plays an important role in depression.In addition to natural substrate serotonin,SERT is also the target of the abused drug cocaine and,clinically used antidepressants,escitalopram,and paroxetine.To date,few studies have attempted to investigate the unbinding mechanism underlying the orthosteric and allosteric modulation of SERT.In this article,the conserved property of the orthosteric and allosteric sites(S1 and S2)of SERT was revealed by combining the high resolutions of x-ray crystal structures and molecular dynamics(MD)simulations.The residues Tyr95 and Ser438 located within the S1 site,and Arg104 located within the S2 site in SERT illustrate conserved interactions(hydrogen bonds and hydrophobic interactions),as responses to selective serotonin reuptake inhibitors.Van der Waals interactions were keys to designing effective drugs inhibiting SERT and further,electrostatic interactions highlighted escitalopram as a potent antidepressant.We found that cocaine,escitalopram,and paroxetine,whether the S1 site or the S2 site,were more competitive.According to this potential of mean force(PMF)simulations,the new insights reveal the principles of competitive inhibitors that lengths of trails from central SERT to an opening were~18A for serotonin and~22 A for the above-mentioned three drugs.Furthermore,the distance between the natural substrate serotonin and cocaine(or escitalopram)at the allosteric site was~3A.Thus,it can be inferred that the potent antidepressants tended to bind at deeper positions of the S1 or the S2 site of SERT in comparison to the substrate.Continuing exploring the processes of unbinding four ligands against the two target pockets of SERT,this study observed a broad pathway in which serotonin,cocaine,escitalopram(at the S1 site),and paroxetine all were pulled out to an opening between MT1b and MT6a,which may be helpful to understand the dissociation mechanism of antidepressants.

Cyclic Solution and Optimal Approximation of the Quaternion Stein Equation

In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .

Existence and asymptotic estimates of periodic solutions of El Nio mechanism of atmospheric physics

This paper is devoted to studying the El Nino mechanism of atmospheric physics. The existence and asymptotic estimates of periodic solutions for its model are obtained by employing the technique of upper and lower solution, and using the continuation theorem of coincidence degree theory.

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.

STABILITY OF THE RAREFACTION WAVE IN THE SINGULAR LIMIT OF A SHARP INTERFACE PROBLEM FOR THE COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM

This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy but possibly large oscillations of rarefaction wave solutions near phase separation,and where the strength of the initial phase field could be arbitrarily large,we prove that the solution of the Cauchy problem exists for all time,and converges to the centered rarefaction wave solution of the corresponding standard two-phase Euler equation as the viscosity and the thickness of the interface tend to zero.The proof is mainly based on a scaling argument and a basic energy method.

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.

Memristive feature and mechanism induced by laser-doping in defect-free 2D semiconductor materials

Memristors as non-volatile memory devices have gained numerous attentions owing to their advantages in storage,in-memory computing, synaptic applications, etc. In recent years, two-dimensional(2D) materials with moderate defects have been discovered to exist memristive feature. However, it is very difficult to obtain moderate defect degree in 2D materials, and studied on modulation means and mechanism becomes urgent and essential. In this work, we realized memristive feature with a bipolar switching and a configurable on/off ratio in a two-terminal MoS_(2) device(on/off ratio ~100), for the first time, from absent to present using laser-modulation to few-layer defect-free MoS_(2)(about 10 layers), and its retention time in both high resistance state and low resistance state can reach 2×10^(4) s. The mechanism of the laser-induced memristive feature has been cleared by dynamic Monte Carlo simulations and first-principles calculations. Furthermore, we verified the universality of the laser-modulation by investigating other 2D materials of TMDs. Our work will open a route to modulate and optimize the performance of 2D semiconductor memristive devices.

e^(+)e^(-)→Λ_(c)+Λ_(c)^(- ) Cross Sections and the Λ_(c)^(+) Electromagnetic Form Factors within the Extended Vector Meson Dominance Model

Within the extended vector meson dominance model,we investigate the𝑒e^(+)e^(-)→Λ_(c)+Λ_(c)^(- ) reaction and the electromagnetic form factors of the charmed baryon𝛬 Λ_(c)^(+)𝑐.The model parameters are determined by fitting them to the cross sections of the process𝑒e^(+)e^(-)→Λ_(c)+Λ_(c)^(- ) and the magnetic form factor|G_(M)|of Λ_(c)^(+) .By considering four charmonium-like states,called𝜓(4500),𝜓(4660),𝜓(4790),and𝜓(4900),we can well describe the current data on the𝑒e^(+)e^(-)→Λ_(c)+Λ_(c)^(- ) reaction from the reaction threshold up to 4.96 GeV.In addition to the total cross sections and|𝐺M|,the ratio|G_(E)/G_(M)|and the effective form factor|Geff|for Λ_(c)^(+) 𝑐are also calculated,and found that these calculations are consistent with the experimental data.Within the fitted model parameters,we have also estimated the charge radius of the charmed Λ_(c)^(+) baryon.

Probing the Gamma-Ray Emission Region of Five TeV Flat Spectrum Radio Quasars

The location ofγ-ray emission of blazars remains a contested topic,inspiring the development of numerous investigative techniques to address this issue.In this work,we analyzed Fermiγ-ray light curves in the GeV and MeV bands,employing the discrete cross-correlation function method to discern time lags between the two bands.For 4C+21.35,Ton 599,B21420+32,and PKS 1510-089,we identified a time lag spanning several days,while for PKS 1441+25,the time lag was not statistically found.The results imply that the soft photons necessary for inverse Compton scattering predominantly originate from the dusty torus in the first four sources,whereas for PKS1441+25,they seem to be sourced mainly from the broad-line region.Further analysis of the opacity(τγγ)and the GeV spectra study supports the conclusion that the location of the dissipation region must be beyond the BLR to avoid significant absorption.Notably,for PKS 1441+25,the emission region is also posited to lie outside yet proximate to the BLR.The parameters of describing the emission region were obtained by fitting broadband spectral energy distribution with contemporaneous observation data.Our findings suggest that for the five TeV FSRQs,during Te V flaring events,the jet appears to maintain an equilibrium between the energy density of the magnetic field and that of the particles for all investigated sources,with the exceptions of 4C+21.35 and PKS1441+25.In terms of the overall jet power,particle energy is the dominant contributor,and the observed blazar radiation cannot be solely attributed to the magnetic field,except in the case of 4C+21.35.Consequently,magnetic reconnection is unlikely to be the primary mechanism behind particle acceleration in these systems.

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.

Temperature-Dependent Debye Temperature and Specific Capacity of Graphene

The shot-range interaction and the atomic anharmonic vibration are both considered, and then the analytic functions of the Debye temperature, the specific capacity and the thermal conductivity of graphene with the temperature are obtained. The influence of anharmonic vibration on these thermal physical properties is also investigated. Some theoretical results are given. If only the harmonic approximation is considered, the Debye temperature of the graphene is unrelated to the temperature. If the anharmonic terms are considered, it increases slowly with the increasing temperature. The molar heat capacity of the graphene increases nonlinearly with the increasing temperature. The mean free path of phonons and the thermal conductivity of the graphene decrease nonlinearly with the increasing temperature. The relative changes of the Debye temperature, the specific heat capacity and the thermal conductivity caused by the anharmonic terms increase with the increasing temperature. The anharmonic effect of atomic vibration becomes more significant under higher temperature.

BLOW-UP AND GLOBAL EXISTENCE FOR A COUPLED SYSTEM OF DEGENERATE PARABOLIC EQUATIONS IN A BOUNDED DOMAIN

This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l ＋ u^p1v^q1 and vt = △v ^m ＋ u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - （l -p1）（m- q2）, the initial data, and the domain Ω.

Microsegregation and Rayleigh number variation during the solidification of superalloy Inconel 718

The microstructure and composition of the residual liquid at different temperatures were investigated by scanning electron microscopy （SEM） and energy dispersive X-ray spectrometer （EDX） associated with the Thermo-calc software calculation of the equilibrium phase diagrams of Inconel 718 and segregated liquid. The liquid density difference and Rayleigh number variation during solidification were estimated as well. It is found that the heavy segregation of Nb in liquid prompts the precipitation of δ and Laves phase directly from liquid and the resultant quenched liquid microstructure consists of pro-eutectic γ＋eutectic,or complete eutectic according to the content of Nb from low to high. The liquid density increases with decreasing temperature during the solidification of Inconel 718 and the liquid density difference is positive. The largest relative Rayleigh number occurs at 1320°C when the liquid fraction is about 40vol%.

Effect of cooling rate on the phase transformation and stability of the mushy zone during the solidification of Waspaloy

Scanning electron microscopy（SEM） and energy dispersive X-ray analysis（EDAX） were used to study the microstructure,microsegregation, and fluid flow tendency of the superalloy Waspaloy in the mushy zone,which had been solidified at different cooling rates. The investigation was accompanied with the calculation of Rayleigh numbers.It is found that Ti is the main segregating element and the content of Ti is the highest in the final liquid at the cooling rates of 3-6℃/min.The eta phase（η） precipitate presented in the residual liquid at the cooling rates higher than 6℃/min is responsible for the fluctuations in the curves of Ti content.The dendrite arm spacing is found to markedly decrease with the increase of cooling rate.The maximum relative Rayleigh number occurs at 10-20℃below the liquidus temperature at a cooling rate of 1℃/min,where the mushy zone is most unstable and fluid flow is most prone to occur.

Identification of denatured and normal biological tissues based on compressed sensing and refined composite multi-scale fuzzy entropy during high intensity focused ultrasound treatment

In high intensity focused ultrasound(HIFU)treatment,it is crucial to accurately identify denatured and normal biological tissues.In this paper,a novel method based on compressed sensing(CS)and refined composite multi-scale fuzzy entropy(RCMFE)is proposed.First,CS is used to denoise the HIFU echo signals.Then the multi-scale fuzzy entropy(MFE)and RCMFE of the denoised HIFU echo signals are calculated.This study analyzed 90 cases of HIFU echo signals,including 45 cases in normal status and 45 cases in denatured status,and the results show that although both MFE and RCMFE can be used to identify denatured tissues,the intra-class distance of RCMFE on each scale factor is smaller than MFE,and the inter-class distance is larger than MFE.Compared with MFE,RCMFE can calculate the complexity of the signal more accurately and improve the stability,compactness,and separability.When RCMFE is selected as the characteristic parameter,the RCMFE difference between denatured and normal biological tissues is more evident than that of MFE,which helps doctors evaluate the treatment effect more accurately.When the scale factor is selected as 16,the best distinguishing effect can be obtained.

Fractional Pfaff-Birkhoff Principle and Birkhoff′s Equations in Terms of Riesz Fractional Derivatives

The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system.Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations.The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics.Here,the fractional Pfaff-Birkhoff variational problem is presented and studied.The definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly given.Secondly,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively.Finally,an example is given to illustrate the application of the results.