In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of nor...In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).展开更多
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality...In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.展开更多
The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the ...The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.展开更多
This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz...This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.展开更多
The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic def...The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic deformation study to determine the deformation pattern and reduce future earthquakes’ impact.Interferometric Synthetic Aperture Radar(In SAR) data were processed using Li CSBAS to get the time series. The time series data were fitted to exponential and logarithmic functions to determine the mechanism of postseismic deformation. The exponential model identified the influence of the viscoelastic mechanism, and the logarithm identified the afterslip mechanism. The Palu earthquake was fitted to logarithmic and exponential, but the logarithmic was more significant than an exponential function.Afterslip mechanism predominates, and viscoelastic mechanisms play a minor role in this postseismic deformation.展开更多
For anyα∈R,the logarithmic Bloch space BLαconsists of those functions f which are analytic in the unit disk D with.■In this paper,we characterize the closure of the analytic functions of bounded mean oscillation B...For anyα∈R,the logarithmic Bloch space BLαconsists of those functions f which are analytic in the unit disk D with.■In this paper,we characterize the closure of the analytic functions of bounded mean oscillation BMOA in the logarithmic Bloch space BLαfor allα∈R.展开更多
Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning thi...Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.展开更多
The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distributi...The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distribution to price European options is that a fat tail can lead to a deviation in one integral required for option pricing. We use a distribution called logarithmic truncated t-distribution to price European options. A risk neutral valuation method was used to obtain a European option pricing model with logarithmic truncated t-distribution.展开更多
稻谷籽粒内部水分扩散的快慢决定了干燥速率。本文基于Logarithmic方程,建立稻谷水分传递动力学模型,并分析热风温度(40、50、60、70℃)和风速(0.3、0.4、0.5 m/s)对稻谷(湿基水分含量23.4%)有效水分扩散系数和扩散活化能的影响。结果表...稻谷籽粒内部水分扩散的快慢决定了干燥速率。本文基于Logarithmic方程,建立稻谷水分传递动力学模型,并分析热风温度(40、50、60、70℃)和风速(0.3、0.4、0.5 m/s)对稻谷(湿基水分含量23.4%)有效水分扩散系数和扩散活化能的影响。结果表明:随着干燥温度和风速的上升,稻谷干燥速率提高,同时对应的有效水分扩散系数越大,分别为5.123×10-12~2.141×10-11m^2/s;扩散活化能从32.94 k J/mol增加至36.30 k J/mol;对比常用的5种谷物干燥模型发现,Logarithmic模型对稻谷薄层干燥的拟合度较好,R2>0.997,RMSE<2.810×10^(-3),同时该模型模拟得出的有效水分扩散系数与实际差值均低于3.8×10^(-13)m^2/s,扩散活化能均低于2.53 k J/mol,与实际值基本吻合。展开更多
A complete mathematical model for logarithmic spiral type sprag one-way clutch design and analysis is given.It assumes that the motion of all clutch components can be expressed by a model of epicyclic gearing.It takes...A complete mathematical model for logarithmic spiral type sprag one-way clutch design and analysis is given.It assumes that the motion of all clutch components can be expressed by a model of epicyclic gearing.It takes advantage of Hunt-Crossley contact impact theory to calculate the contact forces between sprags and races,and it can be used for optimization of design and comparison with other types of sprag clutches.A good deal of analysis shows that the parameters of the steady windup angle,the steady contact force,the natural frequency and natural cycle of clutch have nothing to do with the initial velocity of outer race,while the parameters of the maximum transient windup angle,the maximum transient impact force and the steady engagement time increase linearly in the mode of engaging operation of clutch.It is also shown that the strut angle has great influence on the dynamic engagement performance of clutch.The parameters of the steady windup angle,the maximum transient windup angle,the steady engaging time,the steady contact force,the maximum transient impact force and the natural cycle of clutch decrease linearly nearly with the inner strut angle,while the natural frequency of the system increases linearly with the inner strut angle.展开更多
In this study, a modified logarithmic spiral method is proposed to determine the passive earth pressure and failure surface of cohesionless sloping backfill, with presence of wallesoil interface friction. The proposed...In this study, a modified logarithmic spiral method is proposed to determine the passive earth pressure and failure surface of cohesionless sloping backfill, with presence of wallesoil interface friction. The proposed method is based on a limit equilibrium analysis wherein the assumed profile of the backfill failure surface is a composite of logarithmic spiral and its tangent. If the wallesoil interface is smooth, a straight line does not need to be assumed for the failure surface. The geometry of the failure surface is determined using the Mohr circle analysis of the soil. The resultant passive earth thrust is computed considering equilibrium of moments. The passive earth pressure coefficients are calculated with varied values of soil internal friction angle and cohesion, wall friction angle and inclination angle, and sloping backfill angle. This method is verified with the finite element method(FEM) by comparing the horizontal passive earth pressure and failure surface. The results agree well with other solutions, particularly with those obtained by the FEM. The implementation of the present method is efficient. The logarithmic spiral theory is rigorous and self-explanatory for the geotechnical engineer.展开更多
AIM:To compare the results of visual acuity(VA)measured by Early Treatment Diabetic Retinopathy Study(ETDRS)chart,5 m Standard Logarithm Visual Acuity(5 SL)chart,and 2.5 m Standard Logarithm Visual Acuity(2.5 SL)chart...AIM:To compare the results of visual acuity(VA)measured by Early Treatment Diabetic Retinopathy Study(ETDRS)chart,5 m Standard Logarithm Visual Acuity(5 SL)chart,and 2.5 m Standard Logarithm Visual Acuity(2.5 SL)chart in outpatients of age 12-80 y.METHODS:Each patient(totally 2000 outpatients)had both eyes tested with ETDRS chart at 4 m,5 SL chart at 5 m,and 2.5 SL chart at 2.5 m in random order.The VA values of outpatients were categorized by ages.VA values were expressed by log MAR recording method.RESULTS:The mean VA results of ETDRS charts,5 SL,and 2.5 SL chart were 0.52±0.28,0.50±0.30,and 0.46±0.28 log MAR,respectively.There was a statistically significant difference in the three eye charts in the whole group(P<0.001).For all subjects,the correlation of VA tested with three charts was statistically significant(Spearman correlation coefficient=0.944,0.937,0.946,all P<0.001).Bland–Altman analysis shows the 95%limits of agreement between the 5 SL and 2.5 SL chart were-0.182 to 0.210,-0.139 to 0.251,and-0.151 to 0.235 log MAR,respectively.CONCLUSION:The agreement between the three eye charts is not high.The VA measured by 5 SL chart is slightly better than that by ETDRS chart and 5 SL chart would be a suitable alternative when ETDRS chart are not available in the clinical situation.The VA measured by 2.5 SL chart is about 0.5 line better than VA tested with ETDRS chart,which may overestimate VA.展开更多
An account of numerical solutions to the isothermal and flooded elastohydrodynamic lubrication(EHL)of a logarithmic profile roller,which is rolling over a flat plane,is given The analysis takes account of sideways flo...An account of numerical solutions to the isothermal and flooded elastohydrodynamic lubrication(EHL)of a logarithmic profile roller,which is rolling over a flat plane,is given The analysis takes account of sideways flow of lubricant in the inlet region of the contact When the results are presented in suitable non dimensional groups,it is shown that more uniformly pressure and shape of the film distributing in axial direction is taken place under light loading As the increase of the load,the end closure is displayed and the oil pressure rises sharply at the ends The seal action formed by the end closure makes the film thickness a little And the minimum film thickness is transferred from the central to the ends and the value is reduced rapidly As the increase of the speed,the end closure becomes much serious The optimum crowning value obtained in EHL state is larger than the design value obtained in elastostatic contact state for the same working conditions In order to verify the correctness of theory,optical interferometry is applied to measure the oil film thickness between a logarithmic profiled roller and a glass plate under pure rolling conditions It is found the agreement between numerical solutions and experiments is very good.展开更多
Form milling cutter is built-for-purpose cutter which process the form surface, for example, usually process male and female circular arc face and form trench and so on. From the traditional concept, form milling cutt...Form milling cutter is built-for-purpose cutter which process the form surface, for example, usually process male and female circular arc face and form trench and so on. From the traditional concept, form milling cutter is divided into pointed tooth and relieving follow its structure. Relieving shaped cutter is more convenient than pointed tooth milling cutter, because only its rake face is needed to grind after it turn into blunting, so the current books which are used in college almost select relieving shaped cutter in order to introduce how to design the form milling cutter.The curve of the back of tooth of relieving cutter is the transversal which is formed by the rear face of tooth in the end cut plane of the milling cutter. In the past, because of the limit of the manufacturing technology, the curve of the back of tooth is often selected Archimedes’ curve, in order that the shovel-nose tool acquire the uniform motion when the cutter shovel the back, in other word, the rear face of the milling cutter rotate its axis by the new cutting lip, in the same time, it move uniformly to the axis in order to form the surface. Although this curve of the back of tooth meet the fixedness of the form of blade around grinding the cutter, the rear angle of the dot of the cutting lip don’t keep fixedness. With the development of the modern manufacturing technology, the unmanageable problem of many complex curves is already easily solved. So it is need to study the optimum profile of the curve of the back of tooth in theory, and study the design theory of the relieving shaped cutter under the condition of new manufacture, in order to ensure that the rear angle of the dot of the cutting lip keep fixedness after the relieving shaped cutter is grinded. The paper derive the curve profile of tooth of the form cutter and the modifier calculation formula of the profile of the cutter edge from the definition of the rear angle of the cutter, which establish the foundation for the precision design and manufacture of other form cutter.展开更多
We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a ...We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a positive constant.By using a variational method and the critical point theory for a nonsmooth functional,we obtain the existence of two positive solutions.This result generalizes and improves upon recent results in the literature.展开更多
We investigate a time-independent many-boson system,whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit.Out of these quasi-degenerate ground states we construct a quant...We investigate a time-independent many-boson system,whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit.Out of these quasi-degenerate ground states we construct a quantum state that evolves in time with a period that is logarithmically proportional to the number of particles,that is,T~log N.This boson system in such a state is a quantum time crystal as it approaches the ground state in the thermodynamic limit.The logarithmic dependence of its period on the total particle number N makes it observable experimentally even for systems with very large number of particles.Possible experimental proposals are discussed.展开更多
文摘In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).
基金Supported by the NSFC(11771087,12171091 and 11831005)。
文摘In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.
基金Supported by the National Natural Science Foundation of China(11501342,12001344)。
文摘The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.
文摘This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.
基金partially supported by UGM’s Social Fund in the scheme of the RTA Project 2022
文摘The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic deformation study to determine the deformation pattern and reduce future earthquakes’ impact.Interferometric Synthetic Aperture Radar(In SAR) data were processed using Li CSBAS to get the time series. The time series data were fitted to exponential and logarithmic functions to determine the mechanism of postseismic deformation. The exponential model identified the influence of the viscoelastic mechanism, and the logarithm identified the afterslip mechanism. The Palu earthquake was fitted to logarithmic and exponential, but the logarithmic was more significant than an exponential function.Afterslip mechanism predominates, and viscoelastic mechanisms play a minor role in this postseismic deformation.
基金supported by the National Natural Science Foundation of China(11671357,11801508)。
文摘For anyα∈R,the logarithmic Bloch space BLαconsists of those functions f which are analytic in the unit disk D with.■In this paper,we characterize the closure of the analytic functions of bounded mean oscillation BMOA in the logarithmic Bloch space BLαfor allα∈R.
基金supported in part by the National Natural Science Foundation of China under Grants No.62027803,No.61601096,No.61971111,and No.61801089in part by the Science and Technology Program under Grants No.8091C24,No.2021JCJQJJ0949,and No.2022JCJQJJ0784in part by the Industrial Technology Development Program under Grant No.2020110C041.
文摘Kernel adaptive filters(KAFs)have sparked substantial attraction for online non-linear learning applications.It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion.Concerning this,the logarithmic hyperbolic cosine(lncosh)criterion with better robustness and convergence has drawn attention in recent studies.However,existing lncosh loss-based KAFs use the stochastic gradient descent(SGD)for optimization,which lack a trade-off between the convergence speed and accuracy.But recursion-based KAFs can provide more effective filtering performance.Therefore,a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article.Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness,accuracy performance,and computational cost.
文摘The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distribution to price European options is that a fat tail can lead to a deviation in one integral required for option pricing. We use a distribution called logarithmic truncated t-distribution to price European options. A risk neutral valuation method was used to obtain a European option pricing model with logarithmic truncated t-distribution.
文摘稻谷籽粒内部水分扩散的快慢决定了干燥速率。本文基于Logarithmic方程,建立稻谷水分传递动力学模型,并分析热风温度(40、50、60、70℃)和风速(0.3、0.4、0.5 m/s)对稻谷(湿基水分含量23.4%)有效水分扩散系数和扩散活化能的影响。结果表明:随着干燥温度和风速的上升,稻谷干燥速率提高,同时对应的有效水分扩散系数越大,分别为5.123×10-12~2.141×10-11m^2/s;扩散活化能从32.94 k J/mol增加至36.30 k J/mol;对比常用的5种谷物干燥模型发现,Logarithmic模型对稻谷薄层干燥的拟合度较好,R2>0.997,RMSE<2.810×10^(-3),同时该模型模拟得出的有效水分扩散系数与实际差值均低于3.8×10^(-13)m^2/s,扩散活化能均低于2.53 k J/mol,与实际值基本吻合。
基金Project(2011CB706800)supported by the National Basic Research Program of China
文摘A complete mathematical model for logarithmic spiral type sprag one-way clutch design and analysis is given.It assumes that the motion of all clutch components can be expressed by a model of epicyclic gearing.It takes advantage of Hunt-Crossley contact impact theory to calculate the contact forces between sprags and races,and it can be used for optimization of design and comparison with other types of sprag clutches.A good deal of analysis shows that the parameters of the steady windup angle,the steady contact force,the natural frequency and natural cycle of clutch have nothing to do with the initial velocity of outer race,while the parameters of the maximum transient windup angle,the maximum transient impact force and the steady engagement time increase linearly in the mode of engaging operation of clutch.It is also shown that the strut angle has great influence on the dynamic engagement performance of clutch.The parameters of the steady windup angle,the maximum transient windup angle,the steady engaging time,the steady contact force,the maximum transient impact force and the natural cycle of clutch decrease linearly nearly with the inner strut angle,while the natural frequency of the system increases linearly with the inner strut angle.
基金funded by the Doctoral Scientific Research Foundation of Liaoning Province(Grant No.20170520341)the Fundamental Research Funds for the Central Universities(Grant No.N170103015)
文摘In this study, a modified logarithmic spiral method is proposed to determine the passive earth pressure and failure surface of cohesionless sloping backfill, with presence of wallesoil interface friction. The proposed method is based on a limit equilibrium analysis wherein the assumed profile of the backfill failure surface is a composite of logarithmic spiral and its tangent. If the wallesoil interface is smooth, a straight line does not need to be assumed for the failure surface. The geometry of the failure surface is determined using the Mohr circle analysis of the soil. The resultant passive earth thrust is computed considering equilibrium of moments. The passive earth pressure coefficients are calculated with varied values of soil internal friction angle and cohesion, wall friction angle and inclination angle, and sloping backfill angle. This method is verified with the finite element method(FEM) by comparing the horizontal passive earth pressure and failure surface. The results agree well with other solutions, particularly with those obtained by the FEM. The implementation of the present method is efficient. The logarithmic spiral theory is rigorous and self-explanatory for the geotechnical engineer.
文摘AIM:To compare the results of visual acuity(VA)measured by Early Treatment Diabetic Retinopathy Study(ETDRS)chart,5 m Standard Logarithm Visual Acuity(5 SL)chart,and 2.5 m Standard Logarithm Visual Acuity(2.5 SL)chart in outpatients of age 12-80 y.METHODS:Each patient(totally 2000 outpatients)had both eyes tested with ETDRS chart at 4 m,5 SL chart at 5 m,and 2.5 SL chart at 2.5 m in random order.The VA values of outpatients were categorized by ages.VA values were expressed by log MAR recording method.RESULTS:The mean VA results of ETDRS charts,5 SL,and 2.5 SL chart were 0.52±0.28,0.50±0.30,and 0.46±0.28 log MAR,respectively.There was a statistically significant difference in the three eye charts in the whole group(P<0.001).For all subjects,the correlation of VA tested with three charts was statistically significant(Spearman correlation coefficient=0.944,0.937,0.946,all P<0.001).Bland–Altman analysis shows the 95%limits of agreement between the 5 SL and 2.5 SL chart were-0.182 to 0.210,-0.139 to 0.251,and-0.151 to 0.235 log MAR,respectively.CONCLUSION:The agreement between the three eye charts is not high.The VA measured by 5 SL chart is slightly better than that by ETDRS chart and 5 SL chart would be a suitable alternative when ETDRS chart are not available in the clinical situation.The VA measured by 2.5 SL chart is about 0.5 line better than VA tested with ETDRS chart,which may overestimate VA.
基金This project is supported by National Natural Science Foundation of China (No.59475037).
文摘An account of numerical solutions to the isothermal and flooded elastohydrodynamic lubrication(EHL)of a logarithmic profile roller,which is rolling over a flat plane,is given The analysis takes account of sideways flow of lubricant in the inlet region of the contact When the results are presented in suitable non dimensional groups,it is shown that more uniformly pressure and shape of the film distributing in axial direction is taken place under light loading As the increase of the load,the end closure is displayed and the oil pressure rises sharply at the ends The seal action formed by the end closure makes the film thickness a little And the minimum film thickness is transferred from the central to the ends and the value is reduced rapidly As the increase of the speed,the end closure becomes much serious The optimum crowning value obtained in EHL state is larger than the design value obtained in elastostatic contact state for the same working conditions In order to verify the correctness of theory,optical interferometry is applied to measure the oil film thickness between a logarithmic profiled roller and a glass plate under pure rolling conditions It is found the agreement between numerical solutions and experiments is very good.
文摘Form milling cutter is built-for-purpose cutter which process the form surface, for example, usually process male and female circular arc face and form trench and so on. From the traditional concept, form milling cutter is divided into pointed tooth and relieving follow its structure. Relieving shaped cutter is more convenient than pointed tooth milling cutter, because only its rake face is needed to grind after it turn into blunting, so the current books which are used in college almost select relieving shaped cutter in order to introduce how to design the form milling cutter.The curve of the back of tooth of relieving cutter is the transversal which is formed by the rear face of tooth in the end cut plane of the milling cutter. In the past, because of the limit of the manufacturing technology, the curve of the back of tooth is often selected Archimedes’ curve, in order that the shovel-nose tool acquire the uniform motion when the cutter shovel the back, in other word, the rear face of the milling cutter rotate its axis by the new cutting lip, in the same time, it move uniformly to the axis in order to form the surface. Although this curve of the back of tooth meet the fixedness of the form of blade around grinding the cutter, the rear angle of the dot of the cutting lip don’t keep fixedness. With the development of the modern manufacturing technology, the unmanageable problem of many complex curves is already easily solved. So it is need to study the optimum profile of the curve of the back of tooth in theory, and study the design theory of the relieving shaped cutter under the condition of new manufacture, in order to ensure that the rear angle of the dot of the cutting lip keep fixedness after the relieving shaped cutter is grinded. The paper derive the curve profile of tooth of the form cutter and the modifier calculation formula of the profile of the cutter edge from the definition of the rear angle of the cutter, which establish the foundation for the precision design and manufacture of other form cutter.
基金supported by Natural Science Foundation of Guizhou Minzu University(20185773-YB03)supported by Fundamental Research Funds of China West Normal University(18B015)+2 种基金Innovative Research Team of China West Normal University(CXTD2018-8)supported by National Natural Science Foundation of China(11861021)supported by National Natural Science Foundation of China(11661021)。
文摘We consider the logarithmic elliptic equation with singular nonlinearity {Δu+ulogu^(2)+λ/u^(γ)=0,in Ω,u>0,in Ω,u=0,on δΩ,where Ω⊂R^(N)(N≥3)is a bounded domain with a smooth boundary,0<γ<1 andλis a positive constant.By using a variational method and the critical point theory for a nonsmooth functional,we obtain the existence of two positive solutions.This result generalizes and improves upon recent results in the literature.
基金supported by the National Key R&D Program of China(Grant Nos.2017YFA0303302 and 2018YFA0305602)the National Natural Science Foundation of China(Grant No.11921005)Shanghai Municipal Science and Technology Major Project(Grant No.2019SHZDZX01)。
文摘We investigate a time-independent many-boson system,whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit.Out of these quasi-degenerate ground states we construct a quantum state that evolves in time with a period that is logarithmically proportional to the number of particles,that is,T~log N.This boson system in such a state is a quantum time crystal as it approaches the ground state in the thermodynamic limit.The logarithmic dependence of its period on the total particle number N makes it observable experimentally even for systems with very large number of particles.Possible experimental proposals are discussed.
