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
This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the correspon...This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).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
Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)an...Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.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 relevance of studying the storage coefficient variable brings with it the updating of this value in the hydraulic characteristics as part of the hydrogeological parameters applied to each country, where recommende...The relevance of studying the storage coefficient variable brings with it the updating of this value in the hydraulic characteristics as part of the hydrogeological parameters applied to each country, where recommended values for the storage coefficient to be used in hydrogeological studies are presented. And the application of a methodology adapted to the conditions of each country, is done under current conditions resulting in reference values. For this research work, an adequate methodology was sought for calculating the storage coefficient with a natural logarithm (LN) arrangement. To achieve this, first, the variables that affect the storage coefficient were identified, then the model was described with the natural logarithm (LN) arrangement, and as a third point the storage coefficient was calculated. In conclusion, in points 1 and 2 it was possible to calculate the storage coefficient from the Natural Logarithm arrangement model, with a correlation equal to R<sup>2</sup> = 0.99, and R<sup>2</sup> = 0.97 respectively, indicating that this method can be applied as long as there is free aquifer conditions and that manipulation of data alteration is not frequent.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 nonclassical law of iterated logarithm that holds for a stationary negatively associated sequence of random variables with finite variance is proved in this paper. The proof is based on a Rosenthal type maximal ineq...A nonclassical law of iterated logarithm that holds for a stationary negatively associated sequence of random variables with finite variance is proved in this paper. The proof is based on a Rosenthal type maximal inequality and the subsequence method.This result extends the work of Klesov,Rosalsky (2001) and Shao,Su (1999).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
Let {X,X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set S n=n k=1X k,M n=max k≤n|S k|,n≥1. Suppose lim n→∞ES2 n/n=∶σ2>0 and ∞...Let {X,X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set S n=n k=1X k,M n=max k≤n|S k|,n≥1. Suppose lim n→∞ES2 n/n=∶σ2>0 and ∞n=1ρ 2/d(2n)<∞, where d=2,if -1<b<0 and d>2(b+1),if b≥0. It is proved that,for any b>-1, limε0ε 2(b+1)∞n=1(loglogn)bnlognP{M n≥εσ2nloglogn}= 2(b+1)πГ(b+3/2)∞k=0(-1)k(2k+1) 2b+2,where Г(·) is a Gamma function.展开更多
For p ∈ R, the generalized logarithmic mean Lp(a, b) and Seiffert's mean T(a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p ...For p ∈ R, the generalized logarithmic mean Lp(a, b) and Seiffert's mean T(a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality Lp(a, b) 〈 T(a,b) 〈 Lq(a,b) holds for all a,b 〉 0 and a ≠ b.展开更多
Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general erro...Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.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.
文摘This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).
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 by the National Natural Science Foundation of China(11771178 and 12171198)the Science and Technology Development Program of Jilin Province(20210101467JC)+1 种基金the Science and Technology Program of Jilin Educational Department during the“13th Five-Year”Plan Period(JJKH20200951KJ)the Fundamental Research Funds for the Central Universities。
文摘Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.
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 relevance of studying the storage coefficient variable brings with it the updating of this value in the hydraulic characteristics as part of the hydrogeological parameters applied to each country, where recommended values for the storage coefficient to be used in hydrogeological studies are presented. And the application of a methodology adapted to the conditions of each country, is done under current conditions resulting in reference values. For this research work, an adequate methodology was sought for calculating the storage coefficient with a natural logarithm (LN) arrangement. To achieve this, first, the variables that affect the storage coefficient were identified, then the model was described with the natural logarithm (LN) arrangement, and as a third point the storage coefficient was calculated. In conclusion, in points 1 and 2 it was possible to calculate the storage coefficient from the Natural Logarithm arrangement model, with a correlation equal to R<sup>2</sup> = 0.99, and R<sup>2</sup> = 0.97 respectively, indicating that this method can be applied as long as there is free aquifer conditions and that manipulation of data alteration is not frequent.
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。
文摘A nonclassical law of iterated logarithm that holds for a stationary negatively associated sequence of random variables with finite variance is proved in this paper. The proof is based on a Rosenthal type maximal inequality and the subsequence method.This result extends the work of Klesov,Rosalsky (2001) and Shao,Su (1999).
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Research supported by the National Natural Science Foundation of China (1 0 0 71 0 72 )
文摘Let {X,X n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set S n=n k=1X k,M n=max k≤n|S k|,n≥1. Suppose lim n→∞ES2 n/n=∶σ2>0 and ∞n=1ρ 2/d(2n)<∞, where d=2,if -1<b<0 and d>2(b+1),if b≥0. It is proved that,for any b>-1, limε0ε 2(b+1)∞n=1(loglogn)bnlognP{M n≥εσ2nloglogn}= 2(b+1)πГ(b+3/2)∞k=0(-1)k(2k+1) 2b+2,where Г(·) is a Gamma function.
基金Project Supported by NSFC (10131040)SRFDP (2002335090)
文摘A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown.
基金supported by the National Natural Science Foundation of China (11071069 and 11171307)Natural Science Foundation of Hunan Province(09JJ6003)Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924)
文摘For p ∈ R, the generalized logarithmic mean Lp(a, b) and Seiffert's mean T(a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality Lp(a, b) 〈 T(a,b) 〈 Lq(a,b) holds for all a,b 〉 0 and a ≠ b.
基金Supported by the National Natural Science Foundation of China(11171275)the Natural Science Foundation Project of CQ(cstc2012jj A00029)the Doctoral Grant of University of Shanghai for Science and Technology(BSQD201608)
文摘Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.