Let G be a finite group. A subgroup H of G is a permutable subgroup of G if HK = KH for all subgroups K of G. It will be shown that if all subgroups not contained in the Frattini subgroup are permutable in a group G, then all subgroups are permutable in G. 相似文献
In this paper, we employ a technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain
the asymptotic behavior (in the limit of large representation index J) of generic Wigner matrix elements DJMM¢(g){D^{J}_{MM'}(g)} . We use this result to derive asymptotic formulae for the character χJ(g) of an SU(2) group element and for Wigner’s 3j symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for
χJ(g) is in fact exact. The result hints at a “Duistermaat-Heckman like” localization property for discrete sums. 相似文献
The Ramanujan Journal - In this paper, we study the harmonic continued fractions. These form an infinite family of ordinary continued fractions with coefficients $$\frac{t}{1}, \frac{t}{2},... 相似文献
A family of mem-models, including the mem-dashpots, mem-springs, and most recently, mem-inerters, is emerging as a new and powerful way of capturing complex nonlinear behaviors of materials and systems under various types of dynamic loads involving different frequency, amplitude, and loading histories (e.g., hysteresis). Under the framework of nonlinear state-space representation and hybrid dynamical systems, mem-springs may be formulated to effectively represent an inherent degradation of material state. It is shown in this study, for the first time, how the absement (time integral of strain/displacement), a signature state variable for a mem-spring, can be connected with the damage variable, a key quantity in continuum damage mechanics. The generalized momentum (time integral of stress), on the other hand, is shown to be efficient in modeling strain ratcheting via the concept of mem-dashpot. It is also shown in this study, for the first time, how two formulations of the memcapacitive system models (for mem-springs) are special cases of the Preisach model.
Zanthoxylum species (Syn. Fagara species) of the Rutaceae family are widely used in many countries as food and in trado-medicinal practice due to their wide geographical distribution and medicinal properties. Peer reviewed journal articles and ethnobotanical records that reported the traditional knowledge, phytoconstituents, biological activities and toxicological profiles of Z. species with a focus on metabolic and neuronal health were reviewed. It was observed that many of the plant species are used as food ingredients and in treating inflammation, pain, hypertension and brain diseases. Over 500 compounds have been isolated from Z. species, and the biological activities of both the plant extracts and their phytoconstituents, including their mechanisms of action, are discussed. The phytochemicals responsible for the biological activities of some of the species are yet to be identified. Similarly, biological activities of some isolated compounds remain unknown. Taken together, the Z. species extracts and compounds possess promising biological activities and should be further explored as potential sources of new nutraceuticals and drugs. 相似文献
The low-temperature single-crystal spectrum of TMCBD has revealed a low-lying triplet state at 25 718 cm-1 (72·5 kcal/mol). The observed band is ascribed to a 3Au(3A2) ← 1Agnπ* transition on the basis of its small singlet-triplet splitting, its polarization behaviour, and its vibrational structure. The 3Au state is first-order spin-orbit coupled to either or both of the 1B2u or 1B3u states. No evidence for two or more nπ* transitions was found. Several multi-membered progressions in the carbonyl wagging mode indicate the presence of a distorted excited state, in which the carbonyl carbons attain a pyramidal conformation. Analysis of the site symmetry shows that TMCBD is distorted to a boat-shaped C2v structure in its triplet nπ* state. 相似文献
We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on U(1)4 is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the ${\phi^6}$ rather than of the ${\phi^4}$ type, since two different ${\phi^6}$-type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new locality principle is established for this category of graphs which allows to renormalize their divergences through counterterms of the form of the bare Lagrangian interactions. The model also has an unexpected anomalous log-divergent ${(\int \phi^2)^2}$ term, which can be interpreted as the generation of a scalar matter field out of pure gravity. 相似文献
The two known cadinanes 2-hydroxy-8α-hydroxycalamenene and 2-hydroxy-8α-angeloyloxycalamenene were isolated from a Louisiana population of Heterotheca subaxillaris. Their 13C NMR spectra were fully assigned by the application of HETCOR, COLOC, COSY, NOESY and DEPT experiments. It was shown on the basis of NOESY experiments that both cadinanes require revision at the stereogenic centre C-7. 相似文献
Abstract Salts of the [Eu(2,6-pyridinedicarboxylate)3]3- complex anion and various monovalent inorganic and organic counterions (Li+, Na+, K+, Rb+, Cs+, NH4+, and pyridinium+) have been synthesized and studied by emission spectroscopy. The Eu3+ ion emission spectra exhibited by these salts have been observed with high resolution (less than 1.0 cm?1) and at low temperature (77 K). The emission spectra of these compounds indicate that changing the attached counterion does not affect the site symmetry observed by the europium ion beyond slight distortions indicated by small shifts in the energies of the Eu3+ electronic levels. 相似文献