Linear discriminant analysis with worst between-class separation and average within-class compactness

Linear discriminant analysis （LDA） is one of the most popular supervised dimensionality reduction （DR） tech- niques and obtains discriminant projections by maximizing the ratio of average-case between-class scatter to average- case within-class scatter. Two recent discriminant analysis algorithms （DAS）, minimal distance maximization （MDM） and worst-case LDA （WLDA）, get projections by optimiz- ing worst-case scatters. In this paper, we develop a new LDA framework called LDA with worst between-class separation and average within-class compactness （WSAC） by maximiz- ing the ratio of worst-case between-class scatter to average- case within-class scatter. This can be achieved by relaxing the trace ratio optimization to a distance metric learning prob- lem. Comparative experiments demonstrate its effectiveness. In addition, DA counterparts using the local geometry of data and the kernel trick can likewise be embedded into our frame- work and be solved in the same way.

VITEK■ 2 Compact全自动微生物鉴定药敏分析仪虚拟仿真教学软件的开发与应用

文章主要介绍了VITEK■2 Compact全自动微生物鉴定药敏分析仪虚拟仿真教学软件的设计与开发,以及虚拟仿真融合线上线下混合教学模式在医学微生物检验实验教学中的应用。结果表明,该仿真教学软件的实际应用既有利于培养学生的实践操作能力及思维方式,又能弥补学校实训环境与临床实际不符的缺陷,为微生物检验实验教学质量的提升开辟新的思路。

A NOTE IN APPROXIMATIVE COMPACTNESS AND MIDPOINT LOCALLY K-UNIFORM ROTUNDITY IN BANACH SPACES

In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.

Compactness for the commutators of multilinear singular integral operators with non-smooth kernels

In this paper, the behavior for commutators of a class of bilinear singular integral operators associated with non-smooth kernels on the product of weighted Lebesgue spaces is considered. By some new maximal functions to control the commutators of bilinear singular integral operators and CMO(Rn) functions, compactness for the commutators is proved.

COMPACTNESS FOR THE COMMUTATOR OF BOCHNER-RIESZ OPERATOR

Let α ∈0,(n-1)/2 and T~α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz operator generated by CMO(R^n) function and T~α.

ON COMPACTNESS FOR ITERATED COMMUTATORS

The authors study the iterated commutators on the weighted Bergman spaces A2（φ）, and prove that Cnh is compact on A2（φ） if and only if h ∈ B0.

Measurement and Spatial Distribution of Urban Agglomeration Industrial Compactness in China

Urban agglomeration (UA) compactness means spatial concentration degree of physical entities, such as cities (towns), industries, resources, funds, traffic and technologies, whose concentration is formed according to specified economic and technologic association in the process of UA formation and development. The UA industrial compactness means the concentration degree of industry and industry clusters with reference to the industrial, technologi- cal and economic relations among the cities in the UA in the process of rational industrial division and with the exten- sion of industrial chain. After analyzing the researches on compactness, this paper finds that the relevant measurement coefficient and methods reflecting industrial geographical concentration fail to link industries spatial concentration with urban spatial concentration. Taking 23 UAs as samples and classifying them by development degree, this paper probes into UA compactness and spatial distribution characteristics from the perspective of industry by adopting UA index systems of industry and measurement models. The research finds out: 1) there is obvious positive correlation between UA industrial compactness and UA development degree; 2) the spatial distribution difference of UA industrial compactness is relatively great; and 3) UA industrial compactness shows a gradually decreasing tendency from the eastern part, the middle part to the western part of China. From the research thoughts and approaches, this article suggests that studies on the UA integrated compactness measurement should be enhanced from a multidimensional perspective involving space, traffic, population density and so on.

STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION

Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measurevalued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes.

Degree of Compactness in I-fuzzy Topological Spaces

In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spaces accordingly.

EQUI-ATTRACTION AND BACKWARD COMPACTNESS OF PULLBACK ATTRACTORS FOR POINT-DISSIPATIVE GINZBURG-LANDAU EQUATIONS

A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynam- ical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force.

Compactness of Composition Operators from the p-Bloch Space to the q-Bloch Space on the Classical Bounded Symmetric Domains

In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.

THE COMPACTNESS OF A KIND OF GENERALIZED HANKEL OPERATORS ON THE BERGMAN SPACE OF THE UNIT BALL

This paper gives the compactness criteria for a kind of generalized Hankel operators on Bergman spaces Lpa(B) defined by M. M. Peloso.

Study on mechanical properties of soil-rock mixture of various compactness subjected to freeze-thaw cycles

The soil-rock mixture,a collection of soil particles and rock blocks,is inherently heterogeneous and anisotropic due to significant particle size and material strength differences.This study conducts triaxial tests on soil-rock mixture samples of various compactness subjected to varying freeze-thaw cycles.A mesoscopic simulation is carried out by particle flow code(PFC)to analyze the effects of freeze-thaw cycles on the mechanical properties of soil and rock particles.The results show that the mechanical properties of the soil-rock mixture under freeze-thaw cycles are greatly affected by the initial compaction.In general,when the degree of compaction is higher,the influence of freeze-thaw cycles on the soil-rock mixture is greater.The stress-strain curves of the samples with different compactness demonstrate strain-softening behavior.The freeze-thaw cycles greatly influence the failure strength of the samples with a higher degree of compaction but have little impact on the samples with a lower degree of compaction.On the microscopic level,during freeze-thaw cycles,the pore volume in the highly compacted sample is too small to accommodate the volume expansion from ice crystal formation,causing significant strength loss among the soil and rock particles and deterioration of the macroscopic properties of the soil-rock mixture.

Measurement and Spatial Distribution of Urban Land Use Compactness in Chaoyang District of Beijing,China

China is in the process of rapid urbanization,and wise land use is critical to the long-term sustainability of Chinese cities.Promotion of a compact city is typically believed to be helpful for sustainable land use management.However,given the fact that Chinese cities are characterized by high population densities,the applicability of a more compact solution to expand cities in China remains questionable;there is little evidence to support the many claims in its favor.In seeking to provide empirical data to explore the application of compact city theory in China,one of the key problems researchers face is the task of measuring the urban compactness,in order to objectively investigate the current characteristics of urban compactness.To meet this need,indices were developed for measuring the urban land use compactness,by which the spatial distribution characteristics of urban land use compactness were identified and applied to the Chaoyang District of Beijing.The conclusions can be made as follows:(1) comprehensive land use compactness in Chaoyang District has increased during the period of 2001-2007,especially the population density;(2) the spatial distribution of land use compactness has the characteristics of a ring structure,which shows a decreasing trend with its distance to the city center;(3) there is a strong positive correlation between urban land use compactness and location.The better the location is,the higher the land use compactness is.

Application of Compactness Detection to Complicated Concrete-Filled Steel Tube by Ultrasonic Method

An example of using ultrasonic method to detect the compactness of complicated concrete-filled steel tube in certain high-rise building was discussed in this study.Because of the particularity of the complicated concrete-filled steel tubular column,the plane detection method and embedded sounding pipe method were adopted in the process of effectively detecting the column.According to the results of the plane detection method and embedded sounding pipe method,the cementing status of steel tube and concrete can be concluded,which cannot be judged by the hammering method in the rectangular steel tube-reinforced concrete.

A Short Note on Compactness in Aligned Spaces and Higgs Spaces

We generalize to aligned spaces and to Higgs spaces the concept of compact topological spaces.

Almost Fuzzy Compactness in L-fuzzy Topological Spaces

In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented.

COMPENSATED COMPACTNESS APPLIED TO PERTURBED FOURTH AND SIXTH ORDER P.D.E

In the paper, by using the methods of compensated compactness and energy estimate, the convergence of class of fourth and sixth orders singular perturbed, partial differential equations is obtained, and furthermore, the regularity of solutions are improved.

COMPENSATED COMPACTNESS AND THE STRATIFIED LIE GROUP

In this paper we prove that the Jacobian J（F） of a map F（f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY（G）,whereQ/Q＋1〈r〈1,and Q is the homogeneous dimension of the stratified Lie group G.

Driver at 10 MJ and 1 shot/30 min for inertial confinement fusion at high gain:Efficient,compact,low-cost,low laser-plasma instabilities,beam color selectable from 2ω/3ω/4ω,applicable to multiple laser fusion schemes

The achievement of ignition at the National Ignition Facility(NIF)has prompted a global wave of further research on inertial fusion energy(IFE).However,IFE requires a target gain G of 30-100,and it is hard to achieve fusion at such high gain with the energy,configuration,and technical approach of the NIF.Here,we present a conceptual design for a next-generation laser driver that is applicable to multiple laser fusion schemes and provides 10 MJ,2-3 PW at 3ω(or 2ω,in which case the energy and power can be higher),and one shot per 30 min,with the aim of achieving G>30.It is also efficient,compact,and low in cost,and it has low susceptibility to laser-plasma instabilities.