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Smoothness of the Gradient of Weak Solutions of Degenerate linear Equations

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Acta Mathematica Sinica,English Series 2018年第1期34卷 42-62页

作者： richard l.WHEEDEN Department of Mathematics Rutgers University

let Q（x） be a nonnegative definite, symmetric matrix such that √Q（X） is lipschitz con- tinuous. Given a real-valued function b（x） and a weak solution u（x） of div（QVu） = b, we find sufficient conditions in order that √Qu has some first order smoothness. Specifically, if is a bounded open set in Rn, we study when the components of vVu belong to the first order Sobolev space W1＇2（Ω） defined by Sawyer and Wheeden. Alternately we study when each of n first order lipschitz vector field derivatives Xiu has some first order smoothness if u is a weak solution in Ω of ^-^-1 X^Xiu ＋ b = O. We do not assume that {Xi}is a HSrmander collection of vector fields in ~. The results signal ones for more general equations.

关键词： Degenerate elliptic differential equations degenerate quadratic forms weak solutions,second order regularity

The characteristics, origins, and geodynamic settings of supergiant gold metallogenic provinces

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Science China Earth Sciences 2000年第S1期43卷 1-68页

作者： robert Kerrich richard Goldfarb David Groves Steven Garwin Department of Geological Sciences University of Saskatchewan Saskatoon SK S7N 5E2 Canada United States Geological Survey Box 25046 MS 964 Denver Federal Center Denver CO 80225-0046 USA Centre for Strategic Mineral Resources Department of Geology and Geophysics University of Western Australia Nedlands 6907 Western Australia Newmont Mining Corporation 1700 Lincoln Street Denver Colorado 80203 USA Correspondence should be addressed to Kerrich

There are six distinct classes of gold deposits, each represented by metallogenic provinces, having 100's to > 1 000 tonne gold production. The deposit classes are: (1) erogenic gold; (2) Carlin and Carlin-like gold deposits; (3) epithermal gold-silver deposits; (4) copper-gold porphyry deposits; (5) iron-oxide copper-gold deposits; and (6) gold-rich volcanic hosted massive sul-fide (VMS) to sedimentary exhalative (SEDEX) deposits. This classification is based on ore and alteration mineral assemblages; ore and alteration metal budgets; ore fluid pressure(s) and compositions; crustal depth or depth ranges of formation; relationship to structures and/or magmatic intrusions at a variety of scales; and relationship to the P-T-t evolution of the host terrane. These classes reflect distinct geodynamic settings. Orogenic gold deposits are generated at mid-crustal (4-16 km) levels proximal to terrane boundaries, in transpressional subduction-accretion complexes of Cordilleran style erogenic belts; other orogenic gold provinces form inboard by delamina-tion of mantle lithosphere, or plume impingement. Carlin and Carlin-like gold deposits develop at shallow crustal levels (l convergent margin continental arcs or back arcs; some provinces may involve asthenosphere plume impingement on the base of the lithosphere. Epithermal gold and copper-gold porphyry deposits are sited at shallow crustal levels in continental margin or intraoceanic arcs. Iron oxide copper-gold deposits form at mid to shallow crustal levels; they are associated with extensional intracratonic anorogenic magmatism. Proterozoic examples are sited at the transition from thick refractory Archean mantle lithosphere to thinner Proterozoic mantle lithosphere. Gold-rich VMS deposits are hydrothermal accumulations on or near the sea-floor in continental or intraoceanic back arcs.The compressional tectonics of orogenic gold deposits is generated by terrane accretion; high heat flow stems

关键词： gold deposit orogenic gold deposit geodynamics tectonic setting supercontinent.

SO(n)-Invariant Special lagrangian Submanifolds of C^(n+1) with Fixed loci

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Chinese Annals of Mathematics,Series B 2006年第1期27卷 95-112页

作者： robert l. BRYANT Dedicated to the memory of Shiing-Shen Chern

let SO（n） act in the standard way on C^n and extend this action in the usual way to C^n＋l = C＋ C^n. It is shown that a nonsingular special lagrangian submanifold l→∪ C^n＋l that is invariant under this SO（n）-action intersects the fixed C→∪ C^n＋1 in a nonsingular real-analytic arc A （which may be empty）. If n 〉 2, then A has no compact component. Conversely, an embedded, noncompact nonsingular real-analytic arc A→∪ C lies in an embedded nonsingular special lagrangian submanifold that is SO（n）-invariant. The same existence result holds for compact A if n =2. nonsingular SO（n）-invariant special lagrangian nonsingular SO（n）-invariant special lagrangian extensions in some open neighborhood of A. If A is connected, there exist n distinct extensions of A such that any embedded extension of A agrees with one of these n The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gerard and Tahara to prove the existence of the extension.

关键词： Calibrations Special lagrangian submanifolds

SlC11A1 polymorphisms in inflammatory bowel disease and Mycobacterium avium subspecies paratuberculosis status

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World Journal of Gastroenterology 2010年第45期16卷 5727-5731页

作者： lucy C Stewart Andrew S Day John Pearson Murray l Barclay richard B Gearry Rebecca l roberts robert W Bentley Department of Paediatrics University of OtagoChristchurch 8140New Zealand Department of Paediatrics Christchurch HospitalChristchurch 8140New Zealand Department of Pathology University of OtagoChristchurch 8140New Zealand Department of Medicine University of OtagoChristchurch 8140New Zealand Department of Gastroenterology Christchurch HospitalChristchurch 8140New Zealand Department of Biochemistry University of OtagoDunedin 9054New Zealand

AIM: To test for association of SlC11A1 with inflammatory bowel disease (IBD) and Mycobacterium avium subspecies paratuberculosis (MAP) status in a Caucasian cohort. METHODS: Five hundred and seven Crohn's disease (CD) patients, 474 ulcerative colitis (UC) patients, and 569 healthy controls were genotyped for SlC11A1 1730G>A and SlC11A1 469+14G>C using pre-designed TaqMan  SNP assays. χ 2 tests were applied to test for association of single nucleotide polymorphisms (SNPs) with disease, and the presence of MAP ***:SlC11A1 1730G>A and SlC11A 1469+14G>C were not associated with CD, UC, or IBD. The SlC11A1 1730A minor allele was over-represented in patients who did not require immunomodulator therapy (P = 0.002, OR: 0.29, 95% CI: 0.13-0.66). The frequency of the SlC11A1 469+14C allele was higher in the subset of study participants who tested positive for MAP DNA (P = 0.02, OR: 1.56, 95% CI: 1.06-2.29). No association of SlC11A1 1730G>A with MAP was ***: Although SlC11A1 was not associated with IBD, association with MAP suggests that SlC11A1 is important in determining susceptibility to bacteria implicated in the etiology of CD.

关键词： NRAMP1 Crohn’s disease Ulcerative colitis IS900 polymerase chain reaction

Boundary element method (BEM) applied to the rough surface contact vs. BEM in computational mechanics

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Friction 2019年第4期7卷 359-371页

作者： Yang XU robert l.JACKSON Mechanical Engineering Department Auburn University

In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method(BEM). The boundary integral equations(BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space(or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.

关键词： boundary element method rough surface contact half-space half-plane Flamant solution Boussinesq-Cerruti solution

Utilization of α-olefins obtained by pyrolysis of waste high density polyethylene to synthesize α-olefin-succinic-anhydride based cold flow improvers

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燃料化学学报 2009年第3期37卷 302-310页

作者： Norbert MISKOlCZI richard SAGI lászló BARTHA lívia FORCEK University of Pannonia Chemical Engineering and Process Engineering Institute Department of Hydrocarbon and Coal Processing Egyetem street 10 Veszprém H-8200 HUNGARY

浪费聚合物热分解获得的石蜡富人烃部分的利用的一条新线路被调查。-olefin-succinic-anhydride 基于中介倒点镇静剂添加剂因为柴油被综合，在哪个反应需要的石蜡被废物的热分解获得高密度的聚乙烯(HDPE ) 。石蜡的部分被塑料废物的de... 详细信息

浪费聚合物热分解获得的石蜡富人烃部分的利用的一条新线路被调查。-olefin-succinic-anhydride 基于中介倒点镇静剂添加剂因为柴油被综合，在哪个反应需要的石蜡被废物的热分解获得高密度的聚乙烯(HDPE ) 。石蜡的部分被塑料废物的de聚合在 500 滓鲥?在一个试管反应堆生产???????????????????????禧?????迋????骤??????吗鲥??????禧哉????嫪????滓?????篤?廯??????可??????????????裍??妢???????臙???????蚨?蚨？？

关键词：添加剂石油炼制成份燃料化学高温分解

Biomechanical response of skeletal muscle to eccentric contractions

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Journal of Sport and Health Science 2018年第3期7卷 294-309页

作者： richard l.lieber Shirley Ryan Ability lab Department of Veterans Affairs Departments of Biomedical Engineering and PhysiologyNorthwestern University

The forced lengthening of an activated skeletal muscle has been termed an eccentric contraction(EC).This review highlights the mechanically unique nature of the EC and focuses on the specific disruption of proteins within the cell known as cytoskeletal *** major intermediate filament cytoskeletal protein,desmin,has been the focus of work in this area because changes to desmin occur within minutes of ECs and because desmin has been shown to play both a mechanical and biologic role in a muscle's response to *** is hoped that these types of studies will assist in decreasing the incidence of muscle injury in athletes and facilitating the development of new therapies to treat muscle injuries.

关键词： Cytoskeleton Eccentric contraction Inflammation Muscle injury Muscle mechanics

Morphologic features of the cerebellum of the Atlantic stingray, and their possible evolutionary significance

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Integrative Zoology 2009年第1期4卷 110-122页

作者： richard l.PUZDROWSKI Stephen GRUBER School of Science and Computer Engineering The University of HoustonHoustonTexasUSA

The morphology of the cerebellar corpus in cartilaginous fishes varies from a smooth,relatively simple structure to a complex,multilobed *** stingrays possess a trilobed corpus that includes an anterior lobe,divided into rostral and caudal lobules,and a posterior *** corpus in this stingray is *** asymmetry was examined in the stingray population of Galveston *** 49%of the animals the axis of the caudal lobule was right of the midline,in 27%it was across the midline,and in 24%it was to the *** variation is not related to size,sex,or an asymmetry in the cranial volume,but might reflect a variation in the cerebellar developmental *** gain insight into the factors that have driven cerebellar hypertrophy in cartilaginous fishes,the neural connections of the lobules of the cerebellum of the Atlantic stingray were examined using biotinylated *** was found that,for the most part,the stingray cerebellum receives inputs from the same diencephalic and brainstem nuclei as in cartilaginous fishes with a bilobed ***,in stingrays there is greater segregation of *** anterior lobe rostral lobule receives inputs from the accessory optic nuclei,the caudal lobule receives inputs from trigeminal and octavolateral nuclei,and the posterior lobe receives inputs from the spinal *** rostral lobule and posterior lobe also receive input from midbrain nuclei that do not appear to be present in carti-laginous fishes with a morphologically simple ***,it is proposed that the complex hypertrophy of the corpus in stingrays might result from a combination of functional specialization of the lobes,and the acquisition of new inputs.

关键词： anatomy brain chondrichthyan elasmobranch evolution.

Modeling of an Internal Stress and Strain Distribution of an Inverted Staggered Thin-Film Transistor Based on Two-Dimensional Mass-Spring-Damper Structure

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Computer Modeling in Engineering & Sciences 2020年第11期125卷 515-539页

作者： Yi Yang robert Nawrocki richard Voyles Haiyan H.Zhang School of Engineering Technology Purdue UniversityWest Lafayette47906USA

Equipped with a two-dimensional topological structure,a group of masses,springs and dampers can be demonstrated to model the internal dynamics of a thin-film transistor(TFT).In this paper,the two-dimensional Mass-Spring-Damper(MSD)representation of an inverted staggered TFT is proposed to explore the TFT’s internal stress/strain distributions,and the stress-induced effects on TFT’s electrical *** 2DMSD model is composed of a finite but massive number of interconnected cellular *** parameters,such as mass,stiffness,and damping ratios,of each cellular unit are approximated from constitutive equations of the compositematerials,while the electrical properties of the inverted staggered TFT are characterized by utilizing an electro-mechanical coupling relation derived from the quantum *** are often used in biomedical sensors/transducers attached to human skins,and,for the purpose of simulation and validation,the boundary conditions on the interface between the TFT and the human skin were modeled as a spatially distributed sinusoidal excitation with a frequency of 50 Hz,assuming the TFT thickness is more than tens of *** fidelity of the 2D MSD structure in the modeling of an inverted staggered TFT is verified by comparing its simulated total displacement fieldwith that of a finite element analysis(FEA)*** advantages of the MSD model include a dramatic reduction in memory use by up to 60%and faster computation times that are up to 80%*** importantly,the MSD model is better suited than FEA to many problems in accurate tissue modeling for medical applications,for which FEA is becoming a *** work develops a novel modeling approach,which can be extended to other types of flexible thin film transistors.

关键词： Mass-spring-damper structure inverted staggered thin-film transistor electro-mechanical coupling relation quantum mechanics finite element analysis