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.

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.

THE LAW OF THE ITERATED LOGARITHM FOR SPATIAL AVERAGES OF THE STOCHASTIC HEAT EQUATION

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.

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.

Determination of the Storage or Porosity Coefficient Using the Natural Logarithm Curve by Means of in Situ Measurements

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 R2 = 0.99, and R2 = 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.

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。

A NONCLASSICAL LAW OF ITERATED LOGARITHM FOR NEGATIVELY ASSOCIATED RANDOM VARIABLES

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).

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 LAW OF ITERATED LOGARITHM FOR R/S STATISTICS

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.

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.

PRECISE ASYMPTOTICS IN SELF-NORMALIZED SUMS OF ITERATED LOGARITHM FOR MULTIDIMENSIONALLY INDEXED RANDOM VARIABLES

In the case of Z＋^d（d ≥ 2）-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z＋^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/｜n｜（log｜n｜dP（｜Sn/Vn｜≥ε√log log｜n｜） and ∑n（logn｜）b/｜n｜（log｜n｜）^d-1P（｜Sn/Vn｜≥ε√log n）,as ε↓0,is established.

PRECISE RATES IN THE LAW OF THE ITERATED LOGARITHM FOR R/S STATISTICS

Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.