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Perturbation Theory for Solutions to Second Order Elliptic Operators with Complex Coefficients and the L^p Dirichlet Problem

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Acta Mathematica Sinica,English Series 2019年第6期35卷 749-770页

作者： martin DINDO? Jill PIPHER School of Mathematics The University of Edinburgh and Maxwell Institute of Mathematical Sciences Department of Mathematics Brown University

We establish a Dahlberg-type perturbation theorem for second order divergence form elliptic operators with complex coefficients. In our previous paper, we showed the following result: If L_0 = div A^0(x)? + B^0(x) · ? is a p-elliptic operator satisfying the assumptions of Theorem 1.1 then the LpDirichlet problem for the operator L_0 is solvable in the upper half-space Rn+. In this paper we prove that the Lpsolvability is stable under small perturbations of L_0. That is if L_1 is another divergence form elliptic operator with complex coefficients and the coefficients of the operators L_0 and L_1 are sufficiently close in the sense of Carleson measures, then the LpDirichlet problem for the operator L_1 is solvable for the same value of p. As a corollary we obtain a new result on Lpsolvability of the Dirichlet problem for operators of the form L = div A(x)? + B(x) · ? where the matrix A satisfies weaker Carleson condition(expressed in term of oscillation of coefficients). In particular the coefficients of A need no longer be differentiable and instead satisfy a Carleson condition that controls the oscillation of the matrix A over Whitney boxes. This result in the real case has been established by Dindoˇs,Petermichl and Pipher.

关键词： Complex coefficients elliptic PDEs perturbation theory boundary value problems

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3D mixed finite elements for curved,flat piezoelectric structures

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International Journal of Smart and Nano Materials 2019年第4期10卷 249-267页

作者： martin Meindlhumer Astrid Pechstein Institute of Technical Mechanics Johannes Kepler University LinzLinzAustria

The Tangential-Displacement Normal-Normal-Stress(TDNNS)method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric *** uses tangential components of the displacement and normal components of the normal stress vector as degrees of freedom for *** the electric field,the electric potential is *** TDNNS method has been shown to provide elements which do not suffer from shear *** thin structures(*** patch actuators)can be modeled *** and prismatic elements of arbitrary polynomial order are provided in the current *** show that these elements can be used to discretize curved,shelllike geometries by curved elements of high aspect *** order of geometry approximation can be chosen independently from the polynomial order of the shape *** present two examples of curved geometries,a circular patch actuator and a radially polarized piezoelectric *** results of the TDNNS method are compared to results gained in *** obtain good results for displacements and electric potential as well as for stresses,strains and electric field when using only one element in thickness direction.

关键词： Piezoelasticity mixed finite elements curved elements locking free

A novel methodology for finding the regulation on gene expression data

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Progress in Natural Science:Materials International 2009年第2期19卷 267-272页

作者： Jarka Glassey Elaine martin School of Chemical Engineering and Advanced Materials University of Newcastle upon TyneMerz Court

DNA microarray technology is a high throughput and parallel technique for genomic investigation due to its advantages of simul-taneously surveying features of large scales complex data in biology. This paper aims to find feature subset to build the classifier for gene expression data analysis. At first,K-means clustering algorithm was carried out on the dataset of yeast cell cycle. Based on Rand cal-culation,a statistical method was used to pick out the data points (genes) for classifier design. Meanwhile,the principal component anal-ysis was applied to help to construct the classifier. For the validation of classifier built and prediction of a target subset of genes,discriminant analysis in terms of partial least square regression and artificial neural network were also performed.

关键词： Classifier design Discriminant analysis Gene expression data Rand calculation

Is sympatric speciation in nature only possible with micro-parapatry? A new case study of glacial lake cyprinid fishes

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National Science Review 2022年第12期9卷 21-23页

作者： Christopher H.martin Department of Integrative Biology University of California Museum of Vertebrate Zoology University of California

Although numerous theoretical models of the feasibility and necessary conditions for sympatric speciation abound in the literature,clear-cut examples in nature remain ***,as always in speciation research,this statement strongly depends on your definition of sympatric speciation [1-3].If using the biogeographic definition of sympatric speciation as divergence between individuals in a population within’cruising range’of each other [4],

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Early Jurassic Coleopterans from the Mintaja Insect Locality,Western Australia

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Acta Geologica Sinica(English Edition) 2010年第4期84卷 925-953页

作者： Sarah K.martin School of Geosciences Building 28Monash UniversityClayton Victoria 3800Australia

Beetles （Coleoptera） are the most common insects recovered from the Lower Jurassic Mintaja insect locality of Western Australia, with over half of the fossils recorded from this site being isolated coleopteran elytra. A range of partial beetle bodies and other isolated beetle sclerites have also been recovered from the locality; much of this material is taxonomically unidenitifiable due to its disarticulation and poor preservation. A number of the Mintaja coleopterans are assigned to the archostematan family Ommatidae, including Zygadenia westraliensis （Riek, 1968） comb. nov, previously placed in the morphogenus Mesothoris, and an unnamed species of Tetraphalerus. Also recorded is a new species of elaterid, Lithomerus wunda sp. nov., along with other fragments likely attributable to the same family. The remaining material is assigned into morphospecies, separated primarily on preserved body parts - specifically, there are three morphospecies based on partially articulated coleopteran bodies, two morphospecies based on isolated head capsules, three morphospecies based on isolated thoracic sclerites, three morphospecies based on isolated abdominal sclerites, and 13 morphospecies based on isolated elytra. Overall, the ecology of these fossils is difficult to interpret due to poor preservation, although some of the beetles were likely aquatic, and the Ommatidae and Elateridae were both likely xylophilous. There is a strong similarity between the Mintaja coleopterans and those from the Late Triassic Denmark Hill locality of Queensland, though many of these similarities are based on morphotaxa and may be superficial in nature. Of the species that have been assigned to named taxa, all are generally typical of the Late Mesozoic worldwide, with Zygadenia, Tetraphalerus and Lithomerus all long-ranging, cosmopolitan genera.

关键词： Coleoptera Early Jurassic Mintaja insect locality Western Australia

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Controversies in testosterone replacement therapy： testosterone and cardiovascular disease

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Asian Journal of Andrology 2015年第2期17卷 187-191,I0006页

作者： Kathleen Hwang martin Miner Department of Surgery (Urology) The Alpert Medical School of Brown University Providence Rhode Island USA Department of Family Medicine The Alpert Medical School of Brown University Providence Rhode Island USA.

The role of testosterone in the cardiovascular （CV） health of men is controversial. Data suggest that both the condition and treatment of clinical hypogonadism is associated with decreased CV mortality; however, two recent studies suggest that hypogonadal subjects treated with testosterone replacement therapy have a higher incidence of new CV events. There has been increased media attention concerning the risk of CV disease in men treated with testosterone. Until date, there are no long-term prospective studies to determine safety. Literature spanning over the past 30 years has suggested that not only is there a possible increased CV risk in men with low levels of testosterone, but the benefits from testosterone therapy may even lower this risk. We review here the recent studies that have garnered such intense scrutiny. This article is intended as a thorough review of testosterone levels and CV risk, providing the clinician with the facts needed to make informed clinical decisions in managing patients with clinical hypogonadism.

关键词： cardiovascular disease hypogonadism testosterone

Developing a web-based spatial decision support system for geothermal exploration at the Olkaria geothermal field

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International Journal of Digital Earth 2017年第11期10卷 1118-1145页

作者： Daniel Mwaur martin Kad Institute of Geodesy and Geoinformation Science Technische Universität BerlinBerlinGermany

Geothermal exploration is a complex process that spans a number of *** a decision is made to drill a geothermal well,there is need for an extensive exploration process to determine the most suitable *** process of evaluating and analyzing data from individual scientific disciplines can be complex and *** have been made at solving this problem using GIS-based tools but the uptake of these tools is often hindered by the limited knowledge of GIS by decision *** paper presents an approach for solving the geothermal exploration question through a web-based spatial decision support system(SDSS)that incorporates the various geosciences through a multi-criteria spatial decision analysis *** results reveal a decision-making gap that is to be filled using a novel,automated exploration *** approach hypothesizes an easier and faster decision-making *** research focuses on Olkaria,an active geothermal area in Kenya,East Africa and highlights a pragmatic approach to identifying priority areas for *** evaluates contributions made by many disciplines in identifying potential sites ideal for harnessing geothermal energy and the gaps that emerge in an effort to synergize the results from the different disciplines.

关键词： GIS SDSS geothermal web based multi-criteria decision analysis

Addressing administrative units in international tsunami early warning systems: shortcomings in international geocode standards

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International Journal of Digital Earth 2012年第4期5卷 356-371页

作者： Matthias Lendholt martin Hammitzsch German Research Centre for Geosciences Centre for GeoInformation TechnologyPotsdamGermany

Administrative units reflect the territorial hierarchies established within all countries of the *** units are addressable with geocodes that provide a bijective mapping between territories and unique identification *** warning systems for natural or man-made hazards often map affected or threatened areas to administrative units to establish a spatial reference that is comprehensible to all parts of the *** these territories in an international context has several requirements,such as worldwide coverage,completeness and topicality,which must be met by geocode *** this paper,the practicability and suitability of international geocode standards are examined in the context of the requirements of large-scale early warning *** paper exposes the insufficiencies and limitations of existing geocode standards International Organization for Standardization(ISO)-3166,Second Administrative Level Boundaries data set project(SALB)and Nomenclature of the Territorial Units for Statistics(NUTS)and emphasises the suitability of the non-official hierarchical administrative subdivision codes(HASC).The analysis is framed in the context of addressing affected areas for an Indian Ocean tsunami early warning *** system was developed within the Distant Early Warning Systems project according to the requirements of the United Nations Educational,Scientific and Cultural Organization(UNESCO)Intergovernmental Oceanic Commission for Regional Tsunami Watch Providers(RTWPs).

关键词： digital earth early warning system spatial reference geocode SALB HASC ISO-3166

Finding a home for hyoliths

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National Science Review 2020年第2期7卷 470-471页

作者： martin R.Smith Department of Earth Sciences Durham University NSR

Many of the animal lineages that arose during the Cambrian evolutionary radiation, 540 million years ago, are difficult to relate to living taxa. Constraining the phylogenetic position of these highly disparate taxa allows their idiosyncratic morphologies to illuminate the stepwise establishment of modern body plans[1–3].Hyoliths are one such lineage; their operculate conical shells

关键词： Finding a home for hyoliths