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11.
Andrei S. Rapinchuk Yoav Segev Gary M. Seitz 《Journal of the American Mathematical Society》2002,15(4):929-978
We prove that finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Let be a finite dimensional division algebra having center , and let be a normal subgroup of finite index. Suppose is not solvable. Then we may assume that is a minimal nonsolvable group (MNS group for short), i.e. a nonsolvable group all of whose proper quotients are solvable. Our proof now has two main ingredients. One ingredient is to show that the commuting graph of a finite MNS group satisfies a certain property which we denote Property . This property includes the requirement that the diameter of the commuting graph should be , but is, in fact, stronger. Another ingredient is to show that if the commuting graph of has Property , then is open with respect to a nontrivial height one valuation of (assuming without loss of generality, as we may, that is finitely generated). After establishing the openness of (when is an MNS group) we apply the Nonexistence Theorem whose proof uses induction on the transcendence degree of over its prime subfield to eliminate as a possible quotient of , thereby obtaining a contradiction and proving our main result.
12.
Myron H. Miller DeLyle Eastwood Martha Schulz Hendrick 《Spectrochimica Acta Part B: Atomic Spectroscopy》1984,39(1):13-56
Experimental data and theoretical criteria are used to critically review existing models for analyte emission enhancement in the 3-electrode d.c. plasma (DCP). The analytical zone is characterized as a non-optically thin recombining plasma in partial thermodynamic equilibrium (PTE). Spectrochemical excitation the authors ascribe largely to: (1) argon resonance line radiative transport; (2) inversion of optically pumped argon states; (3) inversion of analyte populations by Franck-Condon collisions with argon; (4) energy cascading in analytes via a multitude of channels. Adding an easily ionized element (EIE): (1) induces additional resonance line radiative transfer; (2) raises electron densities in cooler, analyte-rich plasma margins; (3) locally increases argon optical absorption cross sections via Stark broadening; (4) redistributes ohmic heating. Coupling between the proposed mechanisms is non-linear. Relationships between radiative transfer and collisional redistribution and (1) background suppression by EIE and (2) analyte emission enhancement by helium are also examined. Similarities between DCP and inductively coupled plasma (ICP) excitation mechanisms are noted and practical implications are addressed. 相似文献
13.
Emil S. Koteles 《Fiber and Integrated Optics》1999,18(4):211-244
A review is presented of state-of-the-art optical planar waveguide demultiplexers (DEMUXes), that is, phasars (arrayed waveguide) and etched grating devices designed for high-density (narrow channel spacing) wavelength division multiplexing (WDM) systems. Their advantages and disadvantages are discussed in comparison with other techniques for demultiplexing WDM signals. The advances made in their performance are reviewed, and ultimate limitations, set by technological constraints, are proposed. Finally, a comparison is made of the advantages and disadvantages of etched grating as opposed to phasar planar waveguide DEMUXes. 相似文献
14.
Vikas Kumar Mehak Gupta Sumit G. Gandhi Sonali S. Bharate Ajay Kumar Ram A. Vishwakarma Sandip B. Bharate 《Tetrahedron letters》2017,58(42):3974-3978
Herein we report isolation of a new chromone alkaloid chrotacumine K (12) from fruits and a chromone glycoside schumaniofioside A (13) from leaves of Dysoxylum binectariferum Hook f. Schumaniofioside A is reported for the first time from Meliaceae family. Other known alkaloids isolated include rohitukine (1) and chrotacumine E (6). The structure of new alkaloid 12 was elucidated on the basis of extensive 1D and 2D NMR analysis, synthesis and chemical hydrolysis. Chemically, chrotacumine K (12) is a 3′-O-acetyl rohitukine which on chemical or enzymatic hydrolysis produces rohitukine. The new alkaloid 12 is also present in seeds and stem-barks of this plant. The glycoside schumaniofioside A (13) is present only in leaves, and in abundance (~1% w/w of dried leaves). The isolated compounds and extracts were evaluated for in vitro effect on the proinflammatory cytokines (TNF-α and IL-6) in human monocytic THP-1 cells. The alkaloid 12 displayed potent inhibition (57%) of TNF-α at 0.3 µM, and was non-toxic to THP-1 cells up to 40 µM, indicating its excellent therapeutic window. Furthermore, a nitrobenzoyl ester analog 15e showed better inhibition of IL-6 than parent natural product chrotacumine K. 相似文献
15.
16.
Jairo Z. Goncalves 《代数通讯》2017,45(12):5193-5201
Let k(t) be the field of rational functions over the field k, let σ be a k-automorphism of K = k(t), let D = K(X;σ) be the ring of fractions of the skew polynomial ring K[X;σ], and let D? be the multiplicative group of D. We show that if N is a noncentral normal subgroup of D?, then N contains a free subgroup. We also prove that when k is algebraically closed and σ has infinite order, there exists a specialization from D to a quaternion algebra. This allows us to explicitly present free subgroups in D?. 相似文献
17.
《Indagationes Mathematicae》2021,32(4):797-812
In this text, we study factorizations of polynomials over the tropical hyperfield and the sign hyperfield, which we call tropical polynomials and sign polynomials, respectively. We classify all irreducible polynomials in either case. We show that tropical polynomials factor uniquely into irreducible factors, but that unique factorization fails for sign polynomials. We describe division algorithms for tropical and sign polynomials by linear terms that correspond to roots of the polynomials. 相似文献
18.
Huang Liping 《东北数学》1998,(4)
§1.IntroductionAlongwiththeadvanceinalgebra,thematrixtheoryoveradivisionringbecomesanactivedirection.Inthispaper,wediscussthe... 相似文献
19.
Nitrite ion at low concentrations is determined spectrophotometrically by diazotization of p-nitroaniline and coupling of the diazonium salt with 2-methyl-8-quinolinol. The resulting dye is solubilized in hexadecyltrimethylammonium bromide micelles. The molar absorptivity is 4.72 × 104 l mol-1 cm-1, and the Sandell sensitivity is 9.7 × 10-4 μg cm-2. Some interferences are reported, and preconcentration by evaporation is evaluated. The solubility of hexadecyltrimethylammonium bromide in water was determined as a function of temperature; the Krafft point is 19.6°C. Salting-in of the surfactant by potassium nitrate is described. 相似文献
20.
E. M. Chance G. M. Clore A. R. Curtis E. P. Shephard 《Journal of computational physics》1981,40(2):318-326
The theory required for the solution of the Hodgkin-Huxley equations for the transmission of the nerve impulse in a moving coordinate system are presented. Using this theory, simulations of the transmission of the nerve impulse over large distances (e.g., 1 m) may be carried out rapidly and accurately. The above theory may be applied to other diffusion problems by appropriate modification to the problem concerned. 相似文献