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 tea...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.展开更多
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 st...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.展开更多
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...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.展开更多
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 combin...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−.展开更多
This paper is devoted to studying the El Nin o 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 so...This paper is devoted to studying the El Nin o 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.展开更多
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 ta...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. .展开更多
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,provi...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.展开更多
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 par...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.展开更多
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 solv...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.展开更多
Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other p...Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.展开更多
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 tempe...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.展开更多
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-cal...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 dur-ing 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 solidi-fication 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%.展开更多
<正> In this short note,a new projective equation(φ′=σφ+φ~2)is used to obtain the variable separationsolutions with two arbitrary functions of the(2+1)-dimensional Boiti-Leon-Manna-Pempinelli system(BLMP).B...<正> In this short note,a new projective equation(φ′=σφ+φ~2)is used to obtain the variable separationsolutions with two arbitrary functions of the(2+1)-dimensional Boiti-Leon-Manna-Pempinelli system(BLMP).Basedon the derived solitary wave solution and by selecting appropriate functions,some novel localized excitations such asmulti dromion-solitoffs and fractal-solitons are investigated.展开更多
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 nece...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.展开更多
Based on a 4 x 4 matrix spectral problem, an AKNS soliton hierarchy with six potentials is generated. Associated with this spectral problem, a kind of Riemann-Hilbert problems is formulated for a six-component system ...Based on a 4 x 4 matrix spectral problem, an AKNS soliton hierarchy with six potentials is generated. Associated with this spectral problem, a kind of Riemann-Hilbert problems is formulated for a six-component system of mKdV equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled mKdV equations are computed, through a reduced Riemann-Hilbert problem where an identity jump matrix is taken.展开更多
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-...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.展开更多
By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters ...By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.展开更多
The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current(AC) and direct-current(DC) elect...The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current(AC) and direct-current(DC) electric field E app = E 0(1 + sin ωt).The dielectric profile of the cylindrical inclusions is modeled by function ε i(r) = C k r k(r ≤ a),where r is the radius of the cylindrical inclusion,and C k,k,a are parameters.In the dilute limit,the local potentials and the effective nonlinear responses at all harmonics are derived.Meanwhile,the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field.It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field.Moreover,the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable,and the maximum of the electric field inside the cylinder is at its center.展开更多
文摘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.
基金supported by the Natural Science Foundation of Jiangsu Province(BK20200800)the National Natural Science Foundation of China(22209075,51902165,12004145)+1 种基金the Natural Science Foundation of Jiangxi Province(20212BAB214032,20192ACBL20048)the Key Science and Technology Plan Project of Ji’an City(20211-015311)。
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11904036 and 12175081)Fundamental Research Funds for the Central Universities(Grant No.CCNU22QNOO4)。
文摘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.
基金The National Key Research and Development Program of China under contract No.2022YFE0140500the National Natural Science Foundation of China under contract Nos 41821004 and 42130406+2 种基金the National Natural Science Foundation of China-Shandong Joint Fund under contract No.U1906215the Open Fund of Key Laboratory of Ocean Circulation and Waves,Chinese Academy of Sciences under contract No.KLOCW2003the Project of Doctoral Found of Qingdao University of Science and Technology under contract No.210010022746.
文摘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−.
基金supported by the National Natural Science Foundation of China (Grant No. 40676016)the Natural Science Foundation of Jiangsu Province of China (Grant Nos. BK2009105 and BK2008119)+2 种基金the Natural Science Foundation of Jiangsu Education Committee, China (Grant Nos. 09kjd110001 and 08kjb110011)Key Natural Science Foundation by the Bureau of Education of Anhui Province of China (Grant No. KJ2008A05ZC)Jiangsu Teachers University of Technology Foundation (Grant No. KYY08033)
文摘This paper is devoted to studying the El Nin o 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.
文摘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. .
基金supported in part by the National Natural Science Foundation of China(12101088)the Natural Science Foundation of Sichuan Province(2022NSFSC1858)。
文摘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.
基金supported by the National Key R&D Program of China(Grant No.2023YFA1606703)the National Natural Science Foundation of China(Grant No.12075288)the Youth Innovation Promotion Association CAS.
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grand Nos.11147158 and 11264020)the Natural Science Foundation of Jiangxi Province,China(Grand No.2010GQW0031)the Scientific Research Program of the Education Bureau of Jiangxi Province,China(Grand No.GJJ12483)
文摘Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.
基金Supported by the National Natural Science Foundation of China under Grant No 11574253the Scientific and Technological Research Program of Chongqing Municipal Education Commission under Grant Nos KJ1601111 and KJ1601118the Basic and Frontier Research Projects of Chongqing under Grant No cstc2015jcyjA40054
文摘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.
文摘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 dur-ing 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 solidi-fication 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%.
基金Supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106 and Y606128the Scientific Research Fund of Zhejiang Provincial Education Department of China under Grant No.20070568the Natural Science Foundation of Zhejiang Lishui University under Grant Nos.KZ08001 and KZ09005
文摘<正> In this short note,a new projective equation(φ′=σφ+φ~2)is used to obtain the variable separationsolutions with two arbitrary functions of the(2+1)-dimensional Boiti-Leon-Manna-Pempinelli system(BLMP).Basedon the derived solitary wave solution and by selecting appropriate functions,some novel localized excitations such asmulti dromion-solitoffs and fractal-solitons are investigated.
基金Supported by the National Natural Science Foundation of China(10972151,11272227)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province(CXZZ11_0949)the Innovation Program for Postgraduate of Suzhou University of Science and Technology(SKCX11S_050)
文摘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.
基金supported in part by NSFC(11371326,11301331,and 11371086)NSF under the grant DMS-1664561+2 种基金the 111 project of China(B16002)the China state administration of foreign experts affairs system under the affiliation of North China Electric Power University,Natural Science Fund for Colleges and Universities of Jiangsu Province under the grant 17KJB110020the Distinguished Professorships by Shanghai University of Electric Power,China and North-West University,South Africa
文摘Based on a 4 x 4 matrix spectral problem, an AKNS soliton hierarchy with six potentials is generated. Associated with this spectral problem, a kind of Riemann-Hilbert problems is formulated for a six-component system of mKdV equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled mKdV equations are computed, through a reduced Riemann-Hilbert problem where an identity jump matrix is taken.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11774088 and 11474090)。
文摘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.
文摘By constructing two suitable generalized Lyapunov functions,we derived a generalized ellipsoidal estimate of the globally attractive set and positively invariant set of the unified chaotic system with the parameters α=1/29 and 1/29<α<2/29,respectively,which extends some related results of Li,et al. [Li DM,Lu JA,Wu XQ,Chen GR,Estimating the global basin of attraction and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Applications,2006,323(2): 844-853]. The theoretical results obtained in this paper will find wide application in chaos control and synchronization.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.40876094 and JQ10974106)the National High Technology Research and Development Program of China(Grant Nos.2009AA09Z102 and 2008AA09A403)+1 种基金the Excellent Youth Fundation of Shandong Scientific Committee,China(Grant No.JQ201018)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2009AZ002)
文摘The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current(AC) and direct-current(DC) electric field E app = E 0(1 + sin ωt).The dielectric profile of the cylindrical inclusions is modeled by function ε i(r) = C k r k(r ≤ a),where r is the radius of the cylindrical inclusion,and C k,k,a are parameters.In the dilute limit,the local potentials and the effective nonlinear responses at all harmonics are derived.Meanwhile,the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field.It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field.Moreover,the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable,and the maximum of the electric field inside the cylinder is at its center.
