REGULARITY OF POISSON EQUATION IN SOME LOGARITHMIC SPACE

In this note, the regularity of Poisson equation -△u = f with f lying in logarithmic function space L^P（LogL）^a（Ω）（1 〈 p 〈 ∞, a ∈ R） is studied. The result of the note generalizes the W^2,p estimate of Poisson equation in L^P（Ω）.

A New Function for Modelling Diameter Frequency Distribution in the Tropical Rain Forest of Xishuangbanna,Southwest of China

Permanent plots in the montane tropical rain forests in Xishuangbanna, southwest China, were established, and different empirical models, based on observation data of these plots in 1992, were built to model diameter frequency distributions. The focus of this study is on predicting accuracy of stem number in the larger diameter classes, which is much more important than that of the smaller trees, from the view of forest management, and must be adequately considered in the modelling and estimate. There exist 3 traditional ways of modelling the diameter frequency distribution: the negative exponential function model, limiting line function model, and Weibull distribution model. In this study, a new model, named as the logarithmic J-shape function, together with the others, was experimented and was found as a more suitable model for modelling works in the tropical forests.

A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).

Beach Profiles Characteristics Along Giao Thuy and Hai Hau Coasts,Vietnam:A Field Study

Giao Thuy and Hai Hau coasts are located in Nam Dinh province, Vietnam, with a total coastline of 54.42 km in length. The sea-dike system has been seriously damaged and there have been many dike breaches which caused floods and losses. This situation is considered of a general representative for coastal area in the northern part of Vietnam. A variety of studies have shown that the gradient in the longshore sediment transport rate and the offshore fine sediment lost are the main mechanisms causing the beach erosion. This study presents a field investigation of the beach profiles at Giao Thuy and Hai Hau beaches. Three types of empirical functions for the equilibrium beach profile are applied and compared with the observations. Results show that all observed beach profiles can be described by a single function. However, one specific equilibrium profile equation is not sufficient to assess all beach profiles. In Section 1 of Giao Thuy and Section 3 of Hai Thinh beaches, beach profiles are consistent with the logarithmic function, while the exponential function fits well in Section 2. This difference is explained with respect to coastal morphology, sediment characteristics and hydrodynamic conditions which vary in site. An analysis of the validity of the beach profile functions is recommended for the numerical modeling and engineering designs in this area.

Two-Stage Resource Allocation Scheme for Three-Tier Ultra-Dense Network

In 5 G Ultra-dense Network(UDN), resource allocation is an efficient method to manage inter-small-cell interference. In this paper, a two-stage resource allocation scheme is proposed to supervise interference and resource allocation while establishing a realistic scenario of three-tier heterogeneous network architecture. The scheme consists of two stages: in stage I, a two-level sub-channel allocation algorithm and a power control method based on the logarithmic function are applied to allocate resource for Macrocell and Picocells, guaranteeing the minimum system capacity by considering the power limitation and interference coordination; in stage II, an interference management approach based on K-means clustering is introduced to divide Femtocells into different clusters. Then, a prior sub-channel allocation algorithm is employed for Femtocells in diverse clusters to mitigate the interference and promote system performance. Simulation results show that the proposed scheme contributes to the enhancement of system throughput and spectrum efficiency while ensuring the system energy efficiency.

Estimation of postseismic deformation parameters from continuous GPS data in northern Sumatra after the 2004 Sumatra-Andaman earthquake

Continuous global positioning system （GPS） in northern Sumatra detected signal of the ongoing physical process of postseismic deformation after the M9.2 2004 Sumatra-Andaman earthquake. We analyze the character- istics of postseismic deformation of the 2004 earthquake based on GPS networks operated by BIG, and the others named AGNeSS, and SuGAr networks located in northern Sumatra. We use a simple analytical logarithmic and exponential function to evaluate the postseismic deforma- tion parameters of the 2004 earthquake. We find that GPS data in northern Sumatra during time periods of 2005-2012 are fit better using the logarithmic function with dog of 104.2 ± 0.1 than using the exponential function. Our result clearly indicates that other physical mechanisms of post- seismic deformation should be taken into account rather than a single physical mechanism of afterslip only.

Application of Physics Phenomenon Model Towards Economic Symptoms in Indonesia （Spring Oscillation Model and Rupiah Rate Exchange）

A physical phenomenon can be duplicated similarly to different phenomenon. Based on these facts, the application of physics phenomenon model towards the economic cases that occurred in Indonesia will be discussed. Physical phenomenon to be discussed is the loaded oscillation spring, while the economic case is the dynamics of the Rupiah against foreign currencies, namely U.S. Dollars. Symptoms of the analyzed oscillations involve vibration load on the spring, with the mass load changes against time; for free oscillation, damped oscillation, forced oscillation, as well as forced damped oscillation. Oscillation is modeled into a non homogenous second order differential equation, which results in a solution of the deviation function of time in the form of logarithmic harmonic function. Obtained solutions of physical phenomenon model are matched with the dynamics of the exchange rate data for both steady state, as well as to the condition shortly after the surge （crash）. Models are quite satisfactory, especially when being associated with the occurrence of momentary interruption followed by a relaxation mechanism, both for amplitude and period.

An improve d smoothe d particle hydrodynamics approach using new inverse kernel function

The main limitation of Smoothed Particle Hydrodynamics(SPH)method that resists the method’s poten-tial is its lack of providing stability and accuracy to the numerical technique.We improve the accuracy of the standard SPH technique,by formulating a new inverse logarithmic kernel function.This new kernel function is derived based on the underlying properties of kernel functions.The approximation technique used here is based on the Moving Least Squares based technique.The adequacy of the proposed ker-nel function is tested by simulation of 2D shock wave propagation and 3D dam-break free surface flow against a cuboidal obstacle.The method was validated against experimental data by Kleefsman et al.,[1].The numerical results reveal that our new SPH approach using inverse logarithmic kernel function outper-forms existing ones in particle restoration,zero error,better accuracy and enhanced efficiency in kernel approximation.This new kernel function showed some improvement over existing kernels by showing very less error approximation value of 0.035h 2.The results showed some improvements over standard technique by being capable of handling problems with large deformations accurately and precisely.

Complete monotonicity of a function involving the divided diference of digamma functions

In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.

A Functional LIL for Integrated α Stable Process

Let {X（t）,t ∈ R＋} be an integrated α stable process. In this paper, a functional law of the iterated logarithm （LIL） is derived via estimating the small ball probability of X. As a corollary,, the classical Chung LIL of X is obtained. Furthermore, some results about the weighted occupation measure of X（t） are established.

Chung’s functional law of the iterated logarithm for the Brownian sheet

In this paper,we investigate functional limit problem for path of a Brownian sheet,Chung’s functional law of the iterated logarithm for a Brownian sheet is obtained.The main tool in the proof is large deviation and small deviation for a Brownian sheet.

A Functional LIL for m-Fold Integrated Brownian Motion

Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This extends the classic Chung type liminf result for this process. Furthermore, a result about the weighted occupation measure for Xm（t） is also obtained.

FUNCTIONAL LAW OF ITERATED LOGARITHM FOR ADDITIVE FUNCTIONALS OF REVERSIBLE MARKOV PROCESSES

Using the forward-backward martingale decomposition and the martingale limit theorems, we establish the functional law of iterated logarithm for an additive functional (At) of a reversible Markov process, under the minimal condition that σ~2(A)= tim BA_t~2/t exists in R. We extend also t →∞ the previous remarkable functional central limit theorem of Kipnis and Varadhan.

The Further Development and Application of Grey Forecasting Model

In this paper, the method which forecasts original sequences {x (0)(k)} with logarithmic function or with power function has been complemented, and the method which handles original sequences by logarithmic function-power function transformation or by power function-logarithmic function transformation has been presented, then smooth degree and precision of forecasting of discrete data have been improved.

A CORPUS-BASED STUDY ON VOCABULARY GROWTH MODEL FOR ENGLISH OF SCIENCE AND TECHNOLOGY

本文采用语料库证据支持的方法,重点考察了科技英语的篇际词汇增长模型。研究表明,现有的数学模型(Brunet模型,Guiraud模型,Tuldava模型及Herdan模型)不能精确地描述科技英语词汇增长曲线。通过对幂函数和对数函数的比较分析,本文构建了新的词汇增长模型,并应用此模型推导出科技英语的理论词汇增长曲线及其95%双向置信区间。本研究对EFL教学有显著意义。新的词汇增长模型可用于推断任意给定语篇的词汇量以及生成任意词汇量需要的语篇数。

Hyperspectral image unmixing algorithm based on endmember-constrained nonnegative matrix factorization

The objective function of classical nonnegative matrix factorization （NMF） is non-convexity, which affects the obtaining of optimal solutions. In this paper, we proposed a NMF algorithm, and this algorithm was based on the constraint of endmember spectral correlation minimization and endmember spectral difference max- imization. The size of endrnember spectral overall- correlation was measured by the correlation function, and correlation function was defined as the sum of the absolute values of every two correlation coefficient between the spectra. In the difference constraint of the endmember spectra, the mutation of matrix trace was slowed down by introducing the natural logarithm function. Combining the image decomposition error with the influences of end- member spectra, in the objective function the projection gradient was used to achieve NMF. The effectiveness of algorithm was verified by the simulated hyperspeetral images and real hyperspectral images.

How big are the Csorgo-Revesz increments of two-parameter Wiener processes?

In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.