素数幂和形式的卢卡斯平衡数

对于卢卡斯平衡数C_(n),研究了丢番图方程C_(n)=2^(a)+3^(b)+5^(c)+7^(d),0≤max{a,b,c}≤d的整数解问题.通过Matveev定理和缩减方法得到方程仅有解(n,a,b,c,d)=(2,1,1,1,1).

High—Dimensional Integrable Models with Infinitely Dimensional Virasoro—Type Symmetry Algebra

Using every realization of the Virasoro-type symmetry algebra , we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries. By means of a concrete realization, many -dimensional equations which possess Kac–Moody–Virasoro-type infinite dimensional symmetry algebras are obtained.

A Storm Surge Intensity Classification Based on Extreme Water Level and Concomitant Wave Height

Storm surge is one of the predominant natural threats to coastal communities. Qingdao is located on the southern coast of the Shandong Peninsula in China. The storm surge disaster in Qingdao depends on various influencing factors such as the intensity, duration, and route of the passing typhoon, and thus a comprehensive understanding of natural coastal hazards is essential. In order to make up the defects of merely using the warning water level, this paper presents two statistical distribution models(Poisson Bi- variable Gumbel Logistic Distribution and Poisson Bi-variable Log-normal Distribution) to classify the intensity of storm surge. We emphasize the joint return period of typhoon-induced water levels and wave heights measured in the coastal area of Qingdao since 1949. The present study establishes a new criterion to classify the intensity grade of catastrophic storms using the typhoon surge estimated by the two models. A case study demonstrates that the new criterion is well defined in terms of probability concept, is easy to implement, and fits well the calculation of storm surge intensity. The procedures with the proposed statistical models would be useful for the disaster mitigation in other coastal areas influenced by typhoons.

Volatility-volume relationship of Chinese copper and aluminum futures market

Following Bessembinder and Seguins,trading volume is separated into expected and unexpected components.Meanwhile,realized volatility is divided into continuous and discontinuous jump components.We make the empirical research to investigate the relationship between trading volume components and various realized volatility using1min high frequency data of Shanghai copper and aluminum futures.Moreover,the asymmetry of volatility-volume relationship is investigated.The results show that there is strong positive correlation between volatility and trading volume when realized volatility and its continuous component are considered.The relationship between trading volume and discontinuous jump component is ambiguous.The expected and unexpected trading volumes have positive influence on volatility.Furthermore,the unexpected trading volume,which is caused by arrival of new information,has a larger influence on price volatility.The findings also show that an asymmetric volatility-volume relationship indeed exists,which can be interpreted by the fact that trading volume has more explanatory power in positive realized semi-variance than negative realized semi-variance.The influence of positive trading volume shock on volatility is larger than that of negative trading volume shock,which reflects strong arbitrage in Chinese copper and aluminum futures markets.

Two New Multi-component BKP Hierarchies

We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable （1＋1）-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of hi-directional SK equations with self-consistent

LOGARITHMIC GAUSS NORMAL DISTRIBUTION OF MICROLATEX PARTICLE OF EMULSION EXPLOSIVES

Microlatex particles of emulsion explosives determined by microphotography were studied with the law of logarithmic Gauss normal distribution, and results obtained showed that the microlatex particle just possessed the law of logarithmic Gauss normal distribution. The particle diameter in statistical average value, such as DNL, DNS, DLS, DSV and DVM was calculated through the diagram of logarithmic Gauss normal distribution of microlatex particles of emulsion explosives, so was SW.

A Method for Alpine Wetland Delineation and Features of Border: Zoigê Plateau, China

Accurate wetland delineation is the basis of wetland definition and mapping, and is of great importance for wetland management and research. The Zoige Plateau on the Qinghai-Tibet Plateau was used as a research site for research on alpine wetland delineation. Several studies have analyzed the spatiotemporal pattern and dynamics of these alpine wetlands, but none have addressed the issues of wetland boundaries. The objective of this work was to discriminate the upper boundaries of alpine wetlands by coupling ecological methods and satellite observations. The combination of Landsat 8 images and supervised classification was an effective method for rapid identification of alpine wetlands in the Zoig6 Plateau. Wet meadow was relatively stable compared with hydric soils and wetland hydrology and could be used as a primary indicator for discriminating the upper boundaries of alpine wetlands. A slope of less than 4.5° could be used as the threshold value for wetland delineation. The normalized difference vegetation index （NDVI） in 434 field sites showed that a threshold value of 0.3 could distinguish grasslands from emergent marsh and wet meadow in September. The median normalized difference water index （NDWI） of emergent marsh remained more stable than that of wet meadow and grasslands during the period from September until July of the following year. The index of mean density in wet meadow zones was higher than the emergent and upland zones. Over twice the number of species occurred in the wet meadow zone compared with the emergent zone, and close to the value of upland zone. Alpine wetlands in the three reserves in 2014 covered 1175.19 kin2 with a classification accuracy of 75.6%. The combination of ecological methods and remote sensing technology will play an important role in wetland delineation at medium and small scales. The correct differentiation between wet meadow and grasslands is the key to improving the accuracy of future wetland delineation.

Non-Gaussian Phase Screen Based on log-Poisson Distribution and Effect on Imaging

Gaussian models without intermittency are extensively used in estimating the effect of turbulence,but italso brings some puzzles,for example the observed pulse shape that disagrees with the result of the standard theoryof interstellar scintillations.Indeed the property of intermittency is inherent in turbulence,i.e.,all the quantities thatcharacterize it suffer from strong fluctuations.So it is necessary to consider turbulent intermittency in many applications.In this paper we propose a non-Gaussian phase screen,which obeys log-Poisson statistics,and also offers the correspondingpoint spread function(PSF).These results describe that intermittency leads to the more extent and different directionaldistribution of PSF.Theoretical analysis is made under the hypothesis of the phase difference satisfying log-Poissonstatistics,and the average point spread function,which accord qualitatively with the result of the above generated phasescreen,is derived.

Spatial and temporal variation of drought index in a typical steep alpine terrain in Hengduan Mountains

This study describes the spatial and temporal variation of a drought index and makes inferences regarding the environmental factors that influence this variability in the Hengduan Mountains. A drought index is typically used to determine the moisture conditions and the magnitude of water deficiency in a given area. Based on data from 26 meteorological stations over the period 1960-2012, the spatial and temporal variations of the drought index were analyzed using a thin plate smoothing splines method that considered elevation as a covariate. The drought index was estimated based on the potential evapotranspiration(E0) as defined by the Penman Monteith model modified by FAO(1998). The results of the reported analysis showed that the drought index in the Hengduan Mountains has been decreasing since 1960 at a rate of-0.008/a. This represented a progressive shift from the "sub-humid" class, which typified the wider area in the Hengduan Mountains, toward the "humid" class, which appeared in the Hengduan Mountains areas. The drought index was relatively high in the north and low in the south and the variation of the drought index varied with seasons. The drought index showed increasing trends in summer and autumn and it is greater in autumn than in summer, while it showed a decreasing trend in spring and winter. Drought index is inversely proportional to the soil relative humidity and Normalized Difference Vegetation Index(NDVI).

Influence of wave normal angle on gyroresonance between chorus waves and outer radiation belt electrons

In this paper, using a Gaussian distribution of wave normal angle X=tan0, and considering contributions of harmonic resonances n up to ＋5, we analyze the effect of normal angle on diffusion coefficients induced by gyroresonance between chorus waves and electrons with energies 0.1 and 1.0 MeV on the dayside and nightside at L=4.5. When pitch angle a~〉10~, for 0.1 and 1,0 MeV electrons on the dayside and nightside, diffusion coefficients of five orders （-2, -1, 0, 1, 2） decrease with in- creasing normal angle peak, leading to the total diffusion coefficients decreasing with increasing peak. When ae〈10~, for 1.0 MeV electrons on the dayside and 0.1 MeV electrons on the dayside and nightside, the positive order diffusion coefficients are generally smaller than the same negative order ones; in the meanwhile, diffusion coefficients of orders （-2, 1, 2） are very small, the dominant order n=-I diffusion coefficients change very little, hence the total diffusion coefficients almost remain un- changed. However, for 1.0 MeV electrons on the nightside, diffusion coefficients of orders （-2, 1, 2） which are larger than those of the order （-1） resonance increase with increasing peak, hence the total diffusion coefficients increase with increasing peak. The current results show that the wave normal angle plays an important role in the quantitative analysis of gyroresonance between chorus waves and electrons in the outer radiation belt.

HIGHER-ORDER DUALITY FOR A CLASS OF NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING PROBLEMS INVOLVING GENERALIZED TYPE I AND RELATED FUNCTIONS

This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi（2000） to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-objective programming problem and establishes higher-order duality results under the higher-order generalized type I functions introduced in the present paper, A special case that appears repeatedly in the literature is that the support function is the square root of a positive semi-definite quadratic form. This and other special cases can be readily generated from these results.