Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Towards an Intrinsic Doppler Correction for X-ray Spectroscopy of Stored Ions at CRYRING@ESR

We report on a new experimental approach for the Doppler correction of X-rays emitted by heavy ions, using novel metallic magnetic calorimeter detectors which uniquely combine a high spectral resolution with a broad bandwidth acceptance. The measurement was carried out at the electron cooler of CRYRING@ESR at GSI, Darmstadt, Germany. The X-ray emission associated with the radiative recombination of cooler electrons and stored hydrogen-like uranium ions was investigated using two novel microcalorimeter detectors positioned under 0∘ and 180∘ with respect to the ion beam axis. This new experimental setup allowed the investigation of the region of the N, M → L transitions in helium-like uranium with a spectral resolution unmatched by previous studies using conventional semiconductor X-ray detectors. When assuming that the rest-frame energy of at least a few of the recorded transitions is well-known from theory or experiments, a precise measurement of the Doppler shifted line positions in the laboratory system can be used to determine the ion beam velocity using only spectral information. The spectral resolution achievable with microcalorimeter detectors should, for the first time, allow intrinsic Doppler correction to be performed for the precision X-ray spectroscopy of stored heavy ions. A comparison with data from a previous experiment at the ESR electron cooler, as well as the conventional method of conducting Doppler correction using electron cooler parameters, will be discussed

Метилмалоновая ацидурия у детей: клинические рекомендации

Methylmalonic acidemia (aciduria) is an inherited metabolic disturbance from the group of organic acidemias (acidurias). The article presents etiopathogenetic, epidemiological, diagnostic, and therapeutic aspects of the problem. The possibilities of laboratory and instrumental diagnostic methods the tactics of dietary correction of metabolic disorders in acute and interstitial periods of the disease are described in details; features of drug treatment are outlined. The necessary information for clinical practice and patients’ everyday life is given in the article.Метилмалоновая ацидемия (ацидурия) — генетически гетерогенное наследственное заболевание группы органических ацидемий (ацидурий). В статье представлены этиопатогенетические, эпидемиологические, диагностические и терапевтические аспекты данной проблемы. Подробно освещены возможности лабораторных и инструментальных методов диагностики и особенности медикаментозного лечения, изложена тактика диетической коррекции метаболических нарушений в острый и межприступный периоды заболевания. Дана необходимая информация для практических врачей и родителей пациентов

Aluminum and gallium chloride stabilized arene-mercury complexes

Reaction of HgCl2 with two equivalents of MCl3 in an aromatic solvent yields Hg(arene)2(MCl4) 2 where arene = C6H5Me, C6H5Et, o-C6H4Me2, C6H3 -1,2,3-Me3, M = Al, Ga. Reaction of HgCl2 with MCl3 in benzene, m-xylene, and p-xylene results in the formation of liquid clathrates whose spectroscopic characterization is reported. In the solid state, all compounds, with the exception of o-xylene complexes, exist as neutral complexes in which two arenes are bound to the mercury and the MCl3 groups are bound through bridging chlorides to the mercury. o-xylene complex exists as a cation anion pair [Hg(o-C6H4Me 2)2(AlCl4)][AlCl4]. However, in solution all mercury-arene compounds exist as neutral complexes. The structures of Hg(arene)2(AlCl4)2 and [Hg(arene)2(AlCl 4)]+ have been optimized by DFT calculations to facilitate the assignment of the 13C CPMAS NMR spectra, and are in good agreement with the X-ray diffraction structures. Dissolution of Hg(arene)2(MCl4)2 in C6D6 results in a rapid H/D exchange and the formation of the appropriate dn-arene and C6D5H. H/D exchange between excess arene and C6D6 is also found to be catalyzed by Hg(arene)2(MCl4)2 including those with a different arene ligand. Based on DTF calculations the inter- and intra-molecular mechanism of the exchange is proposed. Mercury-arene complexes are found to be very active catalysts for the alkylation of arenes by olefins. Ethylene, propylene, and cyclohexene reacts with benzene or toluene to form mono- and polyalkylated products, the distribution being dependent on the nature of olefin. Based on the deuterium labeling experiments two different mechanisms of arene alkylation are discussed. Reaction of K[CpFe(CO)2] with a large excess of GaCl 3 yields [{CpFe(CO)2}Ga(Cl·GaCl3)(mu-Cl)] 2, while reactions with 1 and 0.5 equivalents yields [{CpFe(CO) 2}GaCl2]n, and [{CpFe(CO)2}2Ga(mu-Cl)] infinity, respectively. [{CpFe(CO)2}GaCl2] n reacts with MeCN to yield [CpFe(CO)2]GaCl2(MeCN). Reduction of [{CpFe(CO)2}2Ga(mu-Cl)]infinity with potassium in Et2O yields the previously reported [CpFe(CO) 2]3Ga and gallium metal. Reaction of K[CpFe(CO)2] with GaI3 yields [CpFe(CO)2]GaI2, which upon hydrolysis gives the unusual galloxane, [CpFe(CO)2]6Ga 6(mu3-O)4(mu-OH)2I2. Reaction of K[CpFe(CO)2] with InCl in toluene results in the formation of previously reported [CpFe(CO)2]3In and indium metal. Reaction of CpMo(CO)3H with Ga(tBu)3 yields [CpMo(CO)3]Ga(tBu)2 which forms a Lewis acid-base complex with MeCN: [CpMo(CO)3]Ga(tBu) 2(MeCN). The structure of [CpMo(CO)3]Ga(tBu) 2 shows evidence of unusual intra- and inter-molecular carbonyl &cdots; gallium interactions

Clasificación de los grupos simples de rango de Morley finito

IP 1204-05-552-9