Some Mathematical Expressions Probability and Statisties

1 Probability1.1 Some definitions (1)Outcome A result of an experiment is called an outcome. (2)Sample space The set of possible outcomes of an experiment is the sample space for the experiment. (3) Fair experiment If a sample space has n possi-     

Some Mathematical Expressions of Probability and Statistics

1.1 Some definitions (1)Outcome A result of an experiment is called an outcome. (2)Sample space The set of possible outcomes of an experiment is the sample space for the experiment.     

Degradation process of coated tinplate by phase space reconstruction theory

The degradation process of organosol coated tinplate in beverage was investigated by electrochemical noise (EN) technique combined with morphology characterization.EN data were analyzed using phase space reconstruction theory.With the correlation dimensions obtained from the phase space reconstruction,the chaotic behavior of EN was quantitatively evaluated.The results show that both electrochemical potential noise (EPN) and electrochemical current noise (ECN) have chaotic properties.The correlation dimensions of EPN increase with corrosion extent,while those of ECN seem nearly unchanged.The increased correlation dimensions of EPN during the degradation process are associated with the increased susceptibility to local corrosion.     

Low-Temperature Selective Catalytic Reduction of NO with NH_3 over Fe–Ce–O_x Catalysts

In this study,we used a simple impregnation method to prepare Fe-Ce-O_x catalysts and tested them regarding their low-temperature(200-300 ℃) selective catalytic reduction(SCR) of NO using NH_3.We investigated the effects of Fe/Ce molar ratio,the gas hourly space velocity(GHSV),the stability and SO_2/H_2O resistance of the catalysts.The results showed that the FeCe(1:6)O_x(Ce/Fe molar ratio is 1:6) catalyst,which has some ordered parallel channels,exhibited good SCR performance.The FeCe(1:6)O_x catalyst had the highest NO conversion with an activity of 94-99%at temperatures between 200 and300 ℃ at a space velocity of 28,800 h~(-1).The NO conversion for the FeCe(1:6)O_x catalyst also reached 80-98%between 200 and 300 ℃ at a space velocity of204,000h~(-1).In addition,the FeCe(1:6)O_x catalyst demonstrated good stability in a 10-h SCR reaction at200-300 ℃.Even in the presence of SO_2 and H_2O,the FeCe(1:6)O_x catalyst exhibited good SCR performance.     

On the Traditional Architecture Couplets to Create the Type of Space

Couplets financial literature,calligraphy and seal carving is an important part of traditional Chinese culture.To create a space of traditional architecture couplets attaches great importance to the overall order of;convey the connotation,but also to convey a visual space;Joining Sentences people across time and space of unlimited imagination,greatly sublimation of the people’s psychological space and beyond time and spaceextension,easy to create an image space.The couplet has become to create one of the indispensable element of traditional Chinese architectural conception of space.     

趣味英语谜语(英文)

1.What's the beginning of eternity(永恒),the end of time and space;the beginning of end,and the end of every place?     

Extreme points of norm closed nest algebra modules

INTRODUCTION During the last decade there has been an in-terest in the Banach space geometry of non-selfadjoint operator algebras. Subjects of investigationthere include the extreme point structure of the unitball (Hudson et al., 1997; Moore and Trent, 1987)and the isometries between such algebras (Arazyand Solel, 1990; Kadison, 1951; Moore and Trent,1989). One possible application of a characteriza-tion of extreme points is in the study of isometries.Kadison (1951) used the char…     

Comparative mapping of QTLs for Al tolerance in rice and identification of positional Al-induced genes

INTRODUCTION Aluminum (Al) toxicity is one of the mostimportant yield-limiting factors for crop grown onacid upland and lowland acid sulphate soils (IRRI,1978). Al toxicity results in a reduced and damagedroot system, which in turn causes the affectedplants to be susceptible to drought stress and min-eral nutrient deficiencies (Foy, 1988). The physio-logical and biochemical mechanisms of the toxiceffect of Al on root elongation had been extensivelyinvestigated (Matsumoto, 2000). T…     

My Wishes

The first manned Chinese sphceship (载人航天飞船) succeeded on October 16, 2003. When the astronaut (宇航员), Yang Liwei, came out of the space capsule(密     

Parallel Spectral-Domain Optical Coherence Tomography for Non-Scattering Object Imaging

The parallel spectral-domain optical coherence tomography(PSDOCT) is described for high-speed optical coherence tomography(OCT) without lateral scanning. In this setup, the self-elimination of auto-correlation(AC) interference algorithm was used for eradicating the AC interference and ghost images. However, when performed in free space OCT, this algorithm still generated a weak DC component. The algorithm was improved by adding the background intensity part to compensate for the mutual interference between object and reference arms. The results demonstrate that the DC component can be eradicated. Compared with conventional OCT and complex Fourier-domain optical coherence tomography, the advantages of PSDOCT with the improved algorithm in free space are that it has no moving parts to generate consecutive phase shift, the structure of the object can be reconstructed immediately and automatically, and the speed is approximately 16 times faster than those of the other two in the same case.     

Composition operator from logarithmic Bloch-type space to Bergman space on unit polydisc

In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc, the classic Bergman norm is firstly changed into another equivalent norm. Then according to some common inequalities, the properties of logarithmic Bloch-type space and the absolute continuity of the general integral, the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations, and the boundedness and compactness are proved to be equivalent.     

Spatio-temporal reconstruction of air temperature maps and their application to estimate rice growing season heat accumulation using multi-temporal MODIS data

The accumulation of thermal time usually represents the local heat resources to drive crop growth.Maps of temperature-based agro-meteorological indices are commonly generated by the spatial interpolation of data collected from meteorological stations with coarse geographic continuity.To solve the critical problems of estimating air temperature(T a) and filling in missing pixels due to cloudy and low-quality images in growing degree days(GDDs) calculation from remotely sensed data,a novel spatio-temporal algorithm for T a estimation from Terra and Aqua moderate resolution imaging spectroradiometer(MODIS) data was proposed.This is a preliminary study to calculate heat accumulation,expressed in accumulative growing degree days(AGDDs) above 10 ℃,from reconstructed T a based on MODIS land surface temperature(LST) data.The verification results of maximum T a,minimum T a,GDD,and AGDD from MODIS-derived data to meteorological calculation were all satisfied with high correlations over 0.01 significant levels.Overall,MODIS-derived AGDD was slightly underestimated with almost 10% relative error.However,the feasibility of employing AGDD anomaly maps to characterize the 2001-2010 spatio-temporal variability of heat accumulation and estimating the 2011 heat accumulation distribution using only MODIS data was finally demonstrated in the current paper.Our study may supply a novel way to calculate AGDD in heat-related study concerning crop growth monitoring,agricultural climatic regionalization,and agro-meteorological disaster detection at the regional scale.     

Precise asymptotics in the law of the logarithm for random fields in Hilbert space

Consider the positive d-dimensional lattice d (d≥2) with partial ordering ≤, let {XK; K ∈ d } be i.i.d. random vari- ables taking values in a real separable Hilbert space (H, ||·||) with mean zero and covariance operator ∑, and set partial sums SN =∑K≤NXK, K , N ∈ d . Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε 0 by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of (Gut and Spǎtaru, 2003).     

Stress analysis of anisotropic thick laminates in cylindrical bending using a semi-analytical approach

Semi-analytical elasticity solutions for bending of angle-ply laminates in cylindrical bending are presented using the state-space-based differential quadrature method (SSDQM). Partial differential state equation is derived from the basic equations of elasticity based on the state space concept. Then, the differential quadrature (DQ) technique is introduced to discretize the longitu- dinal domain of the plate so that a series of ordinary differential state equations are obtained at the discrete points. Meanwhile, the edge constrained conditions are handled directly using the stress and displacement components without the Saint-Venant principle. The thickness domain is solved analytically based on the state space formalism along with the continuity conditions at interfaces. The present method is validated by comparing the results to the exact solutions of Pagano’s problem. Numerical results for fully clamped thick laminates are presented, and the influences of ply angle on stress distributions are discussed.     

关于Orlicz-Bochner序列空间的一些注记

In this paper, we discuss some basic properties of the Orlicz-Bochner sequence space lM (X) and its subspace hM (X). We present the equivalent definition of hM (X), the sufficient and necessary conditions under which l(M) (X) is complete, and lM (X) and hM (X) are separable respectively, and also give the sufficient condition that hM (X) has a basis. All these results generalize the results for the classical Orlicz sequence spaces.     

Separation axioms in topological ordered spaces

The Ti-axiom,the Ti-ordered axiom and Ti-pairwise axiom(i = 0,1,2,3,4) of topological ordered space are discussed and proved that they are equivalence under the certain conditions.     

Screening of field pea （Pisum sativum） selections for their reactions to root-knot nematode （Meloidogyne incognita）

INTRODUCTION Fieldpea (Pisum sativum L.) is one of the im-portant pulse crops of the world and is cultivated over 5.9 million hectares with a production of about 11.7 million tons (Singh, 1983). In India it is grown over 0.7 million hectares yielding about 0.6 million tons (Singh, 1983). Among various obstacles in cultivating this crop, root-knot nematode Meloidogyne incognita (Kofoid & White) Chitwood has been reported to cause severe yield losses of up to 20%~33% (Upadhyay and Dwiv…     

Characterizing and estimating rice brown spot disease severity using stepwise regression,principal component regression and partial least-square regression

Detecting plant health conditions plays a key role in farm pest management and crop protection. In this study, measurement of hyperspectral leaf reflectance in rice crop (Oryzasativa L.) was conducted on groups of healthy and infected leaves by the fungus Bipolaris oryzae (Helminthosporium oryzae Breda. de Hann) through the wavelength range from 350 to 2 500 nm. The percentage of leaf surface lesions was estimated and defined as the disease severity. Statistical methods like multiple stepwise regression, principal component analysis and partial least-square regression were utilized to calculate and estimate the disease severity of rice brown spot at the leaf level. Our results revealed that multiple stepwise linear regressions could efficiently estimate disease severity with three wavebands in seven steps. The root mean square errors (RMSEs) for training (n=210) and testing (n=53) dataset were 6.5% and 5.8%, respectively. Principal component analysis showed that the first principal component could explain approximately 80% of the variance of the original hyperspectral reflectance. The regression model with the first two principal components predicted a disease severity with RMSEs of 16.3% and 13.9% for the training and testing dataset, respec-tively. Partial least-square regression with seven extracted factors could most effectively predict disease severity compared with other statistical methods with RMSEs of 4.1% and 2.0% for the training and testing dataset, respectively. Our research demon-strates that it is feasible to estimate the disease severity of rice brown spot using hyperspectral reflectance data at the leaf level.     

L2 Teaching and Learning in the Classroom Space

L2 teaching and learning is a way of using language,but it happens in a particular space—the classroom space,which,to some extent,has a restriction to language using.This paper provides a valuable sight into L2 teaching and learning in the classroom space,and discusses the viewpoint of how to make an actual learning of L2 under the way of teaching.     

Web-based interactive visualization of 3D video mosaics using X3D standard

INTRODUCTION The visualization of roadside buildings in virtual space using synthetic photorealistic view is one of the common methods for representing the background scene of Car Navigation Systems (CNS) and Internet map services. Since most of these background scenes are implemented by two-dimensional (2D) images, they may give somewhat monotonous impression due to fixed viewpoint position and orientation. For more interactive visualizations that enable arbitrary ad- justment of the …