Higher-order expansions of powered extremes of logarithmic general error distribution

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).

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

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.

Radial solution of the Logarithmic Laplacian system

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.

Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

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.

Existence of a Sigh-Changing Solution Result for Logarithmic Schrödinger Equations with Weight Function

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).

Vertical deformation model on postseismic phase using exponential and logarithmic function based on InSAR

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.

CLOSURE OF ANALYTIC FUNCTIONS OF THE BOUNDED MEAN OSCILLATION IN LOGARITHMIC BLOCH SPACES

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.

Nyström kernel algorithm based on least logarithmic hyperbolic cosine loss

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.

Pricing European Options Based on a Logarithmic Truncated t-Distribution

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.

基于Logarithmic方程的干燥参数对稻谷水分扩散特性影响分析

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。

一种新的寿命分布——Rayleigh-Logarithmic分布

提出了一种新的带有两个参数的寿命分布——Rayleigh-logarithmic分布(RL分布),研究了RL分布的各种性质,同时给出了其参数的极大似然估计的渐近方差——协方差阵以及EM算法的迭代方程。

混合Pareto-logarithmic分布

基于元件的寿命服从双参数的混合Pareto分布,而元件的个数服从Logarithmic分布.本文提出了一种新的寿命分布:混合Pareto-logarithmic分布(MPL分布),研究了MPL分布的各种性质,同时给出了其参数的极大似然估计的渐近协方差阵和近似置信区间.

Design and analysis of logarithmic spiral type sprag one-way clutch

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.

THE OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR SEIFFERT'S MEAN

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.

Distributional expansion of maximum from logarithmic general error distribution

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.

ELASTOHYDRODYNAMIC LUBRICATION OF LOGARITHMIC PROFILE ROLLER CONTACTS

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.

Study on the double-logarithmic profile of tidal flow velocity in the near-bed layers

Tidal current velocity profile in the near-bed layers has been widely studied. The results showed that velocity profile in the near-bed layer obviously departure from the traditional logarithmic profile, due to the acceleration or deceleration. Although the logarithmic linear profile can reduce the rate of deviation from this, only it is a lower-order approximate solution. In this paper, considering the unsteady and non-linear features of tidal motion, the double logarithmic profile near-bed layers in estuarine and coastal waters is established on the assumption that the turbulent shear stress along the water depth was parabolic distribution, and on the basis of Prandtl＇s mixing length theory and yon Karman＇s self-similar theory. Having been verified the data observed at the West Solent in the south of England, and comparison of the logarithmic linear profile, it found that the double logarithmic profile is more precious than the latter. At last, the discussed results showed that： （1） The parabolic distribution of the tidal shear stresses verified good by the field data and experimental data, can be better reflected the basic features of the tidal shear stress deviating from linear distribution that is downward when to accelerate, upward when to decelerate. （2） The traditional logarithmic velocity profile is the zero-order approximation solution of the double logarithmic profile, the logarithmic linear profile is the first order, and the logarithmic parabolic profile is the second order. （3） Ignoring the conditions of diffusion and convection in the tida movement, the double logarithmic profile can reflect the tidal properties of acceleration or deceleration, so that the calculation of the friction velocity and roughness length are more reasonable. When the acceleration or the deceleration is about zero, the double logarithmic profile becomes the logarithmic profile.

A modified logarithmic spiral method for determining passive earth pressure

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.

A comparison of visual acuity measured by ETDRS chart and Standard Logarithmic Visual Acuity chart among outpatients

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.

凸体的最小Logarithmic函数

为了解决Logarithmic Minkowski问题,已对球面上的任意有限偶Borel测度引入了Logarithmic函数.考虑单位球面上旋转不变概率测度的Logarithmic函数,并考虑它的最小值问题.