The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

DYNAMIC VARIATION OF NITROGEN CONTENT IN THE SECOND SONGHUA RIVER

The space time variation laws of nitrogen content in different river sections, water periods and years in the Second Songhua River in China is described in detail. The results show that there is direct relation between the nitrogen content variation in river water and that in wastewater from cities and runoff water of both banks of the river. Nitrate and nitrite contents in water in flood period are higher than that in mid and low water periods. In flood period, nitrate content in water increases gradually with the extension of river section, ammonia content in polluted river section is higher than that in unpolluted river section. Nitrate and nitrite contents in water in the flood, mid and low water periods from 1985 to 1989 were slightly higher than that from 1980 to 1984 and from 1990 to 1994, ammonia content in water increased annually.

Some Results on the Space of Bounded Second Variation Functions in the Sense of Shiba

In this paper, we study the structure of the space of functions of bounded second variation in the sense of Shiba;an integral representation theorem is also proved and necessary conditions are given for that the space be closed under composition of functions. Another significant result is the proof that this space of bounded second variation in the sense of Shiba is a Banach algebra, which is not immediate as it happens in other spaces of generalized bounded variation.

Root Canal System Variation in Mandibular Second Molar: Middle-Mesial Canal

Middle-mesial canals in mandibular molars are present in the population depending on age, sex and ethnicity. However, limited literature alludes to its prevalence. Troughing procedures may enhance identification, cleaning and shaping. This case report expresses the recognition and management of middle-mesial canal in a mandibular second molar of 24 years old Hispanic-Latino male.

The Sociolinguistic Research on the Second Personal Pronouns "Ni" and "Nin" in Chinese

The personal pronoun is the indispensable and essential component in all languages.In modern standard Chinese,the second personal pronouns encompass two variations:the generic term "Ni" and the honorific term "Nin".No matter the speaker choose "Ni" or "Nin",it indicates the relationship between two interlocutors.This paper,based on the theories of sociolinguistics,mainly explores the pragmatic meanings of the second personal pronouns "Ni" and "Nin".The research obtain these conclusions:even if this pair of personal pronoun received the contextual constraints in the concrete utilization,but they can also derive a lot of pragmatic variations and deixis variations,the interlocutors will select distinct second personal pronouns to achieve the particular communicative goals.

Idioms,Collocations,Formulaic Phrases and Second Language Acquisition

Idioms,collocations,and formulaic phrases are three factors playing the important role in the second language acquisition(SLA).This essay firstly deals with the definitions of these concepts,then it illustrates the importance of them to SLA on two perspectives—idioms,collocations,and formulaic phrases respectively and they regarded as a whole.Therefore,in this way,the essay may lead to the answer the question“How are idioms,collocations,and formulaic phrases important to SLA?”

RANDOM SINGULAR INTEGRAL OF RANDOM PROCESS WITH SECOND ORDER MOMENT

This paper discussses the random singular integral of random process with second order moment, establishes the concepts of the random singular integral and proves that it's a linear bounded operator of space Ha(L)(m, s). Then Plemelj formula and some other properties for random singular integral are proved.

An FEM approximation for a fourth-order variational inequality of second kind

A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.

A variational formula for controlled backward stochastic partial differential equations and some application

An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.

Anatomic Variation in Palatal Root of Maxillary Second Molar: Endodontic Management

The aim of the present clinical case report is to describe the singular root canal anatomy and endodontic management of a maxillary second molar with two palatal roots and two separate canal orifices. A 60 years-old female Hispanic/Latino patient attended the Endodontic Department at University of Buenos Aires School of Dentistry with acute pain in her maxillary left second molar. Clinical radiographs examination revealed unusual root morphology. Cleaning and shaping were completed with 5.25% NaOCl irrigation, 15% EDTA solution and hand/rotary instruments. Filling was performed with gutta-percha points and resin-based sealer. After one year follow-up periapical radiographs and CBCT images showed healing in the area and patient was asymptomatic.

General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems

First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.

On Second Riesz Φ-Variation of Normed Space Valued Maps

In this article we present a Riesz-type generalization of the concept of second variation of normed space valued functions defined on an interval [a,b]R. We show that a function f [a,b], where X is a reflexive Banach space, is of bounded second Φ-variation, in the sense of Riesz, if and only if it can be expressed as the (Bochner) integral of a function of bounded (first) $\Phi$-variation. We provide also a Riesz lemma type inequality to estimate the total second Riesz-Φ-variation introduced.

二阶非完整系统Vacco动力学的Herglotz型Noether定理

研究二阶非完整系统Vacco动力学的Herglotz型Noether定理.首先,基于Herglotz广义变分原理,建立了二阶非完整系统Vacco动力学的Herglotz型运动微分方程.其次,根据Hamilton-Herglotz作用量的非等时变分公式,给出了二阶非完整系统Vacco动力学的Herglotz型Noether对称性和准对称性的概念及其判据方程,并推导了系统的Herglotz型Noether定理及其逆定理.最后,举例说明了该结果的应用.

关于第二类Smarandache伪5倍数数列

目的研究伪5倍数数列的均值性质。方法初等及解析的方法。结果给出伪5倍数数列的一个有趣的渐近公式。结论对于类似第二类Smarandache伪5倍数集合上的均值性质,可以利用讨论数列特性的方法给出均值公式。

Variational formulas and approximation theorems for the first eigenvalue in dimension one

Some complete variational formulas and approximation theorems for the first eigenvalue of elliptic operators in dimension one or a class of Markov chains are presented.

Spatial variation of reference crop evapotranspiration on Tibetan Plateau

This study is based on meteorological observation data collected at 38 weather stations on the Tibetan Plateau over several decades. Daily reference crop evapotranspiration （ETo） was calculated with the FAO-56 standard Penman-Monteith formula. A test of normality was performed with Statistica 6.0 software, isotropic and anisotropic semi-variogram analysis was conducted with the GS＋ （geostatistics for the environmental sciences） system for Windows 7.0, and the characteristics of spatial variation of daily ETo were obtained. The following results can be obtained Daily ETo for different periods on the Tibetan Plateau are distributed normally; Except for daily ETo in the E-W （east-west） direction in the summer, which showed a slight negative correlation with distance change, the Moran＇s indexes of daily ETo for different periods in all directions on the Tibetan Plateau within a 100-km distance were positive, demonstrating a positive correlation with distance change; Variograms of daily ETo in June, the dry season, the wet season, as well as annual average daily ETo fit well with the Gaussian model; A variogram of daily ETo in December fit well with the exponential model; Variograms of daily ETo for the four seasons fit well with the linear With sill model.

SRV constraint based FIB design for wideband linear array

Frequency-invariant beamformer （FIB） design is a key issue in wideband array signal processing. To use commonly wideband linear array with tapped delay line （TDL） structure and complex weights, the FIB design is provided according to the rule of minimizing the sidelobe level of the beampattern at the reference frequency while keeping the distortionless response constraint in the mainlobe direction at the reference frequency, the norm constraint of the weight vector and the amplitude constraint of the averaged spatial response variation （SRV）. This kind of beamformer design problem can be solved with the interior-point method after being converted to the form of standard second order cone programming （SOCP）. The computer simulations are presented which illustrate the effectiveness of our FIB design method for the wideband linear array with TDL structure and complex weights.

Explicit Shifted Second-kind Chebyshev Spectral Treatment for Fractional Riccati Differential Equation

This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method.A new explicit formula for approximating the fractional derivatives of shifted Chebyshev polynomials of the second kind in terms of their original polynomials is established.This formula is expressed in terms of a certain terminating hypergeometric function of the type_(4)F_(3)(1).This hypergeometric function is reduced in case of the integer case into a certain terminating hypergeometric function of the type 3 F 2(1)which can be summed with the aid of Watson’s identity.Six illustrative examples are presented to ensure the applicability and accuracy of the proposed algorithm.

A General Linear Wave Theory for Water Waves Propagating over Uneven Porous Bottoms

Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green's second identity. This theory can be reduced to a number of the most typical mild-slope equations currently in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms.

VARIATIONAL IMAGE FUSION WITH FIRST AND SECOND-ORDER GRADIENT INFORMATION

Image fusion is important in computer vision where the main goal is to integrate several sources images of the same scene into a more informative image. In this paper, we propose a variational image fusion method based on the first and second-order gradient information. Firstly, we select the target first-order and second-order gradient information from the source images by a new and simple salience criterion. Then we build our model by requiring that the first-order and second-order gradient information of the fused image match with the target gradient information, and meanwhile the fused image is close to the source images. Theoretically, we can prove that our variational model has a unique minimizer. In the numerical implementation, we take use of the split Bregman method to get an efficient algorithm. Moreover, four-direction difference scheme is proposed to discrete gradient operator, which can dramatically enhance the fusion quality. A number of experiments and comparisons with some popular existing methods demonstrate that the proposed model is promising in various image fusion applications.