Matrix formulation of vector operations

An efficient technique is developed to simplify the computations in the area of vector analysis. The evaluation of vector algebraic and differential operations becomes more simple and straightforward by simply converting the vector operations into matrix operations. The matrix formulation technique is especially useful when there are mixed coordinate basis involved in the vector operations.     

Focusing of electromagnetic waves into a uniaxial crystal

We derive integral representations suitable for studying the focusing of electromagnetic waves through a plane interface into a uniaxial crystal. To that end we start from existing exact solutions for the transmitted fields due to an arbitrary three-dimensional (3D) wave that is incident upon a plane interface separating two uniaxial crystals with arbitrary orientation of the optical axis in each medium. Then we specialize to the case in which the medium of the incident wave is isotropic and derive explicit expressions for the dyadic Green's functions associated with the transmitted fields as well as integral representations suitable for asymptotic analysis and efficient numerical evaluation. Relevant integral representations for focused 3D electromagnetic waves are also given. Next we consider the special case in which (i) the incident field is a two-dimensional (2D) TM wave and (ii) the optical axis in the crystal lies in the plane of incidence, implying that we have a 2D vectorial problem, and derive dyadic Green's functions, integral representations suitable for asymptotic and numerical treatment, and integral representations for focused TM fields. Numerical results for focused 2D TM fields based on these integral representations as well as corresponding experimental results will be presented in forthcoming papers.     

Seismic gyrotropy as a result of rock-microstructure dissymmetry

Seismic investigations show that rocks exhibit not only anisotropic properties but also gyrotropic ones. Recently, the phenomenological theory has been developed to describe the phenomenon ‘seismic gyrotropy'. The paper gives a possible explanation of the gyrotropic properties of rocks on a microlevel. A gyrotropic model of grainy rock with dissymetry in its microstructure is presented. The model is built on a principle ‘azimuthal turn plus translation'. The mathematical and physical formulations of the problem are discussed. An algorithm is constructed to find the displacements, their first and second derivatives with respect to spatial coordinates as well as stresses inside a grain, an element of the model. Mathematical modelling of elastic-wave propagation in the model considered enabled to demonstrate that the model possesses gyrotropic properties, i.e., it rotates on a polarization vector. Gyration constants are determined.     

A Note on Cyclic Vectors for the Shift

We strengthen a result in the literature that gives a necessary condition for the shift on the Hardy space H 2 ( G ) of some bounded, simply connected region G to be cyclic. Part of this involves a characterization, in terms of ‘ G , of what it means for G to be the image of under a conformal map whose boundary values are univalent a.e. m (normalized Lebesgue measure on ).     

Microplastics and associated emerging contaminants in the environment: Analysis,sorption mechanisms and effects of co-exposure

Microplastics (MPs) and other emerging pollutants exist together in the environment and their co-exposure represents a source of increasing concern as MPs have been reported to act as carriers of pollutants due to their high sorption capacity. The ingestion of contaminated MPs by organisms can enhance the desorption of pollutants, increasing their bioavailability and toxicity. This review examines the role of MPs as vectors of environmental emerging contaminants. First, the main tools used to identify and characterise MPs and the analytical methods used for the determination of associated emerging contaminants are discussed. Insightful explanations of the sorption interaction between several groups of emerging pollutants and MPs are provided. MP type (polarity, crystallinity, size) and aging process together with the environmental conditions and pollutant properties (hydrophobicity and dissociated forms) are key factors influencing the sorption process. The literature review showed that polyethylene and polystyrene were the most commonly studied polymers. Antibiotics, perfluoroalkyl compounds and triclosan showed high sorption capacities onto MPs. Finally, the effect of co-exposure to MPs-emerging pollutants and bioaccumulation in aquatic and terrestrial organisms is discussed. The combined exposure may impact the toxic effects in different ways, through synergistic or antagonic interactions. Examples of different scenarios are provided, but in general the research conducted on terrestrial systems is scarce. The results revealed a lack of standardization in laboratory studies and in the testing conditions that reflect actual environmental exposure.     

On the Best Approximation in Non-Archimedean Normed Linear Spaces

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Local asymptotic normality for multivariate nonlinear AR processes

In this paper, we establish local asymptotic normality (LAN) for the log-likelihood ratio of a class of multivariate nonlinear autoregressive processes generated by independent identically distributed (i.i.d.) random vectors. This result generalizes LAN for multivariate linear processes to multivariate nonlinear autoregressive processes.     

分子纳米技术与金属有机分子纳米体系

基于超分子自组装的分子纳米技术是一种新兴的高新技术。本文从金属矢量操纵的自组装分子纳米体系、自组装的纳米微反应器与超分子催化和自组装金属超分子高分子纳米材料等三个方面评述了分子纳米技术及其在构筑金属有机分子纳米体系中的发展现状 ,进一步阐述了“金属矢量”的概念 ,并首次提出建立“自组装子工具箱” ,探讨了分子纳米技术的发展方向。     

Entomological repercussions of increasing environmental temperatures: Reply to comments on “Modeling the impact of global warming on vector-borne infections”

Global warming will certainly affect the abundance and distribution of disease vectors. The effect of global warming, however, depends on the complex interaction between the human host population and the causative infectious agent. In this work we review some mathematical models that were proposed to study the impact of the increase in ambient temperature on the spread and gravity of some insect-transmitted diseases.     

f3组态离子在四角场中的基矢矩阵元

通过选用与群链[(O⊃D₄⊃C₄)×SU(2)]相匹配的单电子基矢,使其直积构成多电子fN体系的O⊃D₄⊃C₄旋量群的不可约表示的基矢,并讨论了有关的Coulomb矩阵元、Casimir矩阵元、旋-轨偶合矩阵元和晶体场作用矩阵元.