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Airy, Beltrami, Maxwell, Einstein and Lanczos Potentials Revisited

j.urnal of.Modern Physics 2016年第7期7卷 699-728页

作者： j.-f. Pommaret CERMICS Ecole des Ponts ParisTech Marne-la-Vallée France

The purpose of.this paper is to revisit the well known potentials, also called stress f.nctions, needed in order to study the parametrizations of.the stress equations, respectively provided by G.B. Airy (1863) f.r 2-dimensional elasticity, then by E. Beltrami (1892), j.C. Maxwell (1870) f.r 3-dimensional elasticity, f.nally by A. Einstein (1915) f.r 4-dimensional elasticity, both with a variational procedure introduced by C. Lanczos (1949, 1962) in order to relate potentials to Lagrange multipliers. Using the methods of.Algebraic Analysis, namely mixing dif.erential geometry with homological algebra and combining the double duality test involved with the Spencer cohomology, we shall be able to extend these results to an arbitrary situation with an arbitrary dimension n. We shall also explain why double duality is perf.ctly adapted to variational calculus with dif.erential constraints as a way to eliminate the corresponding Lagrange multipliers. f.r example, the canonical parametrization of.the stress equations is j.st described by the f.rmal adj.int of.the components of.the linearized Riemann tensor considered as a linear second order dif.erential operator but the minimum number of.potentials needed is equal to f.r any minimal parametrization, the Einstein parametrization being “in between” with potentials. We provide all the above results without even using indices f.r writing down explicit f.rmulas in the way it is done in any textbook today, but it could be strictly impossible to obtain them without using the above methods. We also revisit the possibility (Maxwell equations of.electromagnetism) or the impossibility (Einstein equations of.gravitation) to obtain canonical or minimal parametrizations f.r various equations of.physics. It is nevertheless important to notice that, when n and the algorithms presented are known, most of.the calculations can be achieved by using computers f.r the corresponding symbolic computations. f.nally, though the paper is mathemati

关键词： Stress Equations Stress f.nctions Elasticity Theory Lagrange Multipliers f.rmal Adj.int Control Theory General Relativity Einstein Equations Lanczos Potentials Algebraic Analysis Riemann Tensor Weyl Tensor

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Nonlinear Conf.rmal Gravitation

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j.urnal of.Modern Physics 2023年第11期14卷 1464-1496页

作者： j.-f. Pommaret CERMICS Ecole des Ponts ParisTech Paris France

In 1909 the brothers E. and f. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with the only experimental need to measure the EL constants. In a modern f.amework, they used the nonlinear Spencer sequence instead of.the nonlinear j.net sequence f.r the Lie groupoid def.ning the group of.rigid motions of.space. f.llowing H. Weyl, our purpose is to compute f.r the f.rst time the linear and nonlinear Spencer sequences f.r the Lie groupoid def.ning the conf.rmal group of.space-time in order to provide the mathematical f.undations of.both electromagnetism (EM) and gravitation (GR), with the only experimental need to measure the EM and GR constants. With a manif.ld of.dimension n ≥ 3, the dif.iculty is to deal with the n nonlinear transf.rmations that have been called “elations” by E. Cartan in 1922. Using the f.ct that dimension n = 4 has very specif.c properties f.r the computation of.the Spencer cohomology, we also prove that there is no conceptual dif.erence between the (nonlinear) Cosserat EL f.eld or induction equations and the (linear) Maxwell EM f.eld or induction equations. As f.r gravitation, the dimension n = 4 also allows to have a conf.rmal f.ctor def.ned everywhere but at the central attractive mass because the inversion law of.the isotropy subgroupoid made by second order j.ts transf.rms attraction into repulsion. The mathematical f.undations of.both electromagnetism and gravitation are thus only depending on the structure of.the conf.rmal pseudogroup of.space-time.

关键词： Nonlinear Dif.erential Sequences Linear Dif.erential Sequences Lie Groupoids Lie Algebroids Conf.rmal Geometry Spencer Cohomology Maxwell Equations Cosserat Equations

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The song remains the same： j.venile Richardson＇s ground squirrels do not respond dif.erentially to mother＇s or colony member＇s alarm calls

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Current Zoology 2012年第5期58卷 773-780页

作者： j.mes f. HARE Kurtis j. WARKENTIN Department of.Biological Sciences University of Manitoba Winnipeg MB Canada R3T 2N2 Department of.Zoology Brandon University Brandon MB R7A 6A9

Alarm calls are emitted by Richardson＇s ground squirrels Urocitellus richardsonii in response to avian and terrestrial predators. Conspecif.cs detecting these calls respond with increased vigilance, promoting predator detection and evasion, but in doing so, lose time f.om f.raging. That loss can be minimized if.alarm call recipients discriminate among signalers, and weight their response accordingly. f.r j.venile ground squirrels, we predicted that the trade-of. between f.raging and vigilance could be optimized via selective response to alarm calls emitted by their own dam, and/or neighboring colony members over calls broad- cast by less f.miliar conspecif.cs. Alarm calls of.adult f.male Richardson＇s ground squirrels were elicited in the f.eld using a predator model and recorded on digital audio tape. f.ee-living f.cal j.veniles were subj.cted to playbacks of.a call of.their mother, and on a separate occasion a call f.om either another adult f.male f.om their own colony, or an adult f.male f.om another colony. Neither immediate postural responses and escape behavior, nor the duration of.vigilance manif.sted by j.veniles dif.ered with exposure to alarm calls of.the three adult f.male signaler types. Thus, j.veniles did not respond pref.rentially to alarm calls emitted by their mothers or colony members, likely ref.ecting the high cost of.ignoring alarm signals where receivers have had limited opportunity to establish past signaler reliability [Current Zoology 58 （5）： 773-780, 2012].

关键词： Alarm Signal Communication Maternal Call Recognition Signal Reliability Ground Squirrel Social Discrimination

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Ef.ect of.dif.erent pigmented cooked common beans on glucose and lipid metabolism in obese rats and 3T3 L1 cells

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f.OD BIOSCIENCE 2023年第3期53卷 463-471页

作者： Perez-Ramirez, Iza f. Herrera, Mayra D. Mora, Of.lia Ramos-gomez, Minerva Martinez-Alarcon, Dania Reynoso-Camacho, Rosalia Univ Autonoma Queretaro Fac Quim Queretaro 76010 Queretaro Mexico Campo Expt Zacatecas CEZAC INIf.P Zacatecas 98500 Zacatecas Mexico Univ Nacl Autonoma Mexico Inst Neurobiol Queretaro 76230 Queretaro Mexico

The ef.ect of.Azuf.asin (yellow coat seed) and f.or de j.nio (f.0} Dalia (pink-cream coat seed) cooked bean varieties was evaluated in high f.t and f.uctose diet-f.d rats to identif. their health benef.cial ef.ects on obesity-related metabolic alterations. f.0}Dalia and Azuf.asin daily supplementation (10%) f.r six months decreased body weight (5-7%), serum triglycerides (28.5-36.4%), HOMA insulin resistance index (59.6-62.3%), and serum TNf.alpha (40.5-45.0%);moreover, f.0}Dalia increased serum adiponectin (77.5%). Polyphenol-, phytosterol-, and saponin-rich extracts f.om Azuf.asin and f.0}Dalia were evaluated in 3T3 L1 cells. Both varieties up-regulated, Cpt1a and Acadm (f.tty acid beta-oxidation), and Glut4, Irs1, and Pi3k (insulin signaling cascade) and down-regulated Pparg and Cebpa (adipogenesis) and f.sn and Acaca (lipogenesis). These activities were associated with their high content of.soyasaponins A3, Af. and Be f.r adipogenesis and lipid metabolism, as well as erio-dictyol, ellagic acid, hesperidin and (+)-catechin and (-)-epicatechin and their derivatives, and beta-campesterol hexoside f.r insulin signaling cascade. f.0}Dalia and Azuf.asin cooked beans could be consumed to ameliorate obesity and its metabolic complications.

关键词： Common beans Phaseolus vulgaris L Dyslipidemia Insulin resistance Phytochemicals

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UV/visible spectroscopic analysis of.CO^(3+) and CO^(2+) during the dissolution of.cobalt f.om mixed Co-Cu oxidized ores

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International j.urnal of.Minerals,Metallurgy and Materials 2011年第3期18卷 260-269页

作者： j. Ndalamo A.f. Mulaba-Baf.biandi B.B. Mamba Department of.Chemical Technology University of Johannesburg Department of.Extraction Metallurgy University of Johannesburg

The leaching of.cobalt f.om f.ur-mixed Co-Cu oxidized ores containing cobalt at levels ranging f.om 0.5wt% to 34wt% was studied and the results has been reported. Conventional dissolution of.these oxidized Co-Cu ores with diluted H2SO4 and SO2 as a reducing agent resulted in a substantial improvement in the solution based recovery of.cobalt. UV/visible spectroscopic analysis of.the leached solu-tions indicated that the increased cobalt content in the solution was a result of.f.ushing the acidif.ed cobalt leaching solution with SO2. f.r-thermore, UV/visible spectroscopy conf.rmed that as SO2 was f.ushed into the acidif.ed leaching solution, Co3＋ bearing minerals were re-duced to the readily soluble Co2＋ bearing minerals, and this resulted in the increase of.total cobalt in the collected solution. The mechanism of.the reduction of.Co3＋ to Co2＋ bearing minerals when SO2 is f.ushed during the leaching of.mixed Co-Cu oxidized ores, including the stability trends of.Co3＋, Co2＋, and Cu2＋ complexes, as shown by their UV/visible spectra, are also discussed.

关键词： cobalt metallurgy dissolution leaching reaction kinetics spectroscopic analysis

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PRECIPITATION BEHAVIOR Of.M_(2)N IN A HIGH-NITROGEN AUSTENITIC STAINLESS STEEL DURING ISOTHERMAL AGING

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Acta Metallurgica Sinica(English Letters) 2007年第2期20卷 95-101页

作者： f. Shi L.j. Wang W.f. Cui C.M. Liu School of.Materials ＆ Metallurgy Northeastern UniversityShenyang 110004 China

The precipitation behavior of.M2N and the microstructural evolution in a Cr-Mn austenitic stainless steel with a high nitrogen content of.0.43mass% during isothermal aging has been investigated using optical microscopy （ OM）, scanning electron microscopy （SEM）, and transmission electron microscopy （TEM）. The aging treatments have led to the decomposition of.nitrogen supersaturated austenitic matrix through discontinuous cellular precipitation. The precipitated cells comprise alternate lamellae of.M2N precipitate and austenitic matrix. This kind of.precipitate morphology is similar to that of.pearlite. However, owing to the non-eutectoidic mechanism of.the reaction, the growth characteristic of.the cellular precipitates is dif.erent f.om that of.pearlite in f.-C binary alloys. M2N precipitate in the cell possesses a hexagonal crystal structure with the parameters a = 0.4752nm and c = 0.4429nm, and the orientation relationship between the M2V precipitates and austenite determined f.om the SADP is [01^-10]M2N//[101]γ, [2^-1^-10]M2N//[010]γ.

关键词： austenitic stainless steel high nitrogen microstructureisothermal aging precipitation

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Analysis of.Heat Transf.r Phenomenon in Magnetohydrodynamic Casson f.uid f.ow Through Cattaneo–Christov Heat Dif.usion Theory

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Communications in Theoretical Physics 2017年第7期67卷 91-95页

作者： G. K. Ramesh j. Gireesha, S. A. Shehzad, f. M. Abbasi Department of.Mathematics School of Engineering Presidency University Bengaluru-560089 Karnataka India Department of.Studies and Research in Mathematics Kuvempu University Shankaraghatta-577451 Shimoga Karnataka India Department of.Mathematics COMSATS Institute of Information Technology Sahiwal-57000 Pakistan Department of.Mathematics COMSATS Institute of Information Technology Islamabad-44000 Pakistan

Heat transport phenomenon of.two-dimensional magnetohydrodynamie Casson f.uid f.ow by employing Cattaneo-Christov heat dif.usion theory is described in this work. The term of.heat absorption/generation is incorporated in the mathematical modeling of.present f.ow problem. The governing mathematical expressions are solved f.r velocity and temperature prof.les using RKf.45 method along with shooting technique. The importance of.arising nonlinear quantities namely velocity, temperature, skin-f.iction and temperature gradient are elaborated via plots. It is explored that the Casson parameter retarded the liquid velocity while it enhances the f.uid temperature. f.rther, we noted that temperature and thickness of.temperature boundary layer are weaker in case of.Cattaneo-Christov heat dif.usion model when matched with the prof.les obtained f.r f.urier＇s theory of.heat f.ux.

关键词： Hydromagnetic f.ow Casson f.uid heat transf.r Cattaneo-Christov heat dif.usion model numer-ical solution

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Application of.RNA interf.rence in triatomine （Hemiptera： Reduviidae） studies

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Insect Science 2013年第1期20卷 40-52页

作者： Raf.ela M. M. Paim Ricardo N. Arauj. Michael j. Lehane Nelder f. Gontij. MarcosH. Pereira Departamento de Parasitologia Instituto de Ciencias Biologicas Universidade Federal de Minas Gerais Bloco 14 Sala 177 Av. AntonioCarlos 6627 Pampulha CEP 30270-901 Belo Horizonte MG Brazil Liverpool School of.Tropical Medicine Pembroke Place LiverpoolL3 5QA UK

Triatomines （Hemiptera： Reduviidae） are obligate hematophagous insects. They are of.medical importance because they are vectors of.Trypanosoma cruzi, the causative agent of.Chagas disease in the Americas. In recent years, the RNA interf.rence （RNAi） technology has emerged as a practical and usef.l alternative means of.studying gene f.nction in insects, including triatomine bugs. RNAi research in triatomines is still in its early stages, several issues still need to be elucidated, including the description of.the molecules involved in the RNAi machinery and aspects related to phenotype evaluation and persistence of.the knockdown in dif.erent tissues and organs. This review considers recent applications of.RNAi to triatomine research, describing the maj.r methods that have been applied during the knockdown process such as the double-stranded RNA delivery mechanism （inj.ction, microinj.ction, or ingestion） and the phenotype characterization （mRNA and target protein levels） in studies conducted with the intent to provide greater insights into the biology of.these insects. In addition to the characterization of.insect biomolecules, some with biopharmacological potential, RNAi may provide a new view of.the interaction between triatomine and trypanosomatids, enabling the development of.new measures f.r vector control and transmission of.the parasite.

关键词： dsRNA knockdown phenotype RNAi triatomine

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Nanoparticle migration ef.ects on f.lly developed f.rced convection of.TiO2-water nanof.uid in a parallel plate microchannel

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Particuology 2016年第1期14卷 96-107页

作者： f. Hedayati G. Domairry Young Researchers and Elite Club Neyshabur Branch Islamic Azad University Neyshabur Iran Mechanical Engineering Department Babol University of Technology Babol lran

This study considers the f.rced convection of.laminar TiO2-water nanof.uid f.ow in a parallel plate microchannel. The small length scale associated with microchannels dictates the use of.slip condition at the f.id-solid interf.ce. The modif.ed Buongiorno model was employed f.r the nanof.uid to f.lly account f.r the ef.ects of.non-unif.rm viscosity and thermal conductivity. The partial dif.erential equa- tions associated with conservation laws were reduced to two-point ordinary boundary value dif.erential equations bef.re being numerically solved. Considering Brownian motion and thermophoresis, the ef.ects of.nanoparticle transport on concentration, velocity, and temperature prof.les were analyzed f.r three dif.erent values of.wall heat f.ux. To assess the ef.iciency of.adding nanoparticles, the ratios of.the pres- sure drop and the heat transf.r coef.icient of.the nanof.uid to that of.the base f.uid were studied in detail. f.om analyzing dif.erent heat f.ux ratios, one-sided heating was f.und to be most ef.icient at enhancing the heat transf.r rate in the microchannel. Additionally, in the presence of.the slip velocity, the increase in the value of.the heat transf.r coef.icient f.r the nanof.uid was smaller than that f.r the base f.uid.

关键词： Nanof.uid Microchannel Nanoparticles migration Slip velocity Brownian motion Thermophoresis

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Antibacterial properties of.copper-substituted cobalt f.rrite nanoparticles synthesized by co-precipitation method

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Particuology 2017年第1期15卷 158-163页

作者： Alireza Samavati A. f. Ismail Advanced Membrane Technology Research Centre (AMTEC) Universiti Teknologi Malaysia 81310 Skudai Johor Malaysia

Controlled growth and caref.l characterization of.cobalt f.rrite nanoparticles f.r antibacterial applica- tions are challenging. Copper-substituted cobalt f.rrite nanoparticles （CuxCo1-xf.2O4）, where x = 0.0, 0.3, 0.5, 0.7 and 1.0, were synthesized using an economical and simple co-precipitation technique. The crys- tal structure and antibacterial properties of.the samples as a f.nction of.Cu-substituted content were systematically studied. With increasing Cu concentration, the nanopartide size decreased f.om ~30 to ~20 nm. The f.urier transf.rm inf.a-red spectra exhibit two prominent f.ndamental absorption bands, at ~595 and 419 cm^-1. These bands correspond to intrinsic stretching vibrations of.metals at tetrahedral and octahedral sites, respectively. The Raman scattering results reveal that increasing the Cu content enhances the local disorder at both tetrahedral and octahedral sub lattices. The results indicate that the substitution of.Co with Cu in cobalt f.rrite nanoparticles strongly inf.uences the microstructure, crystal structure, and oarticle diameter, and also improves the antibacterial properties.

关键词： Cobalt f.rrite nanoparticles X-ray dif.raction Raman spectroscopy Antibacterial properties

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