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991.
Jerzy Browkin with an appendix by Karim Belabas Herbert Gangl. 《Mathematics of Computation》2000,69(232):1667-1683
J. Tate has determined the group (called the tame kernel) for six quadratic imaginary number fields where Modifying the method of Tate, H. Qin has done the same for and and M. Skaba for and
In the present paper we discuss the methods of Qin and Skaba, and we apply our results to the field
In the Appendix at the end of the paper K. Belabas and H. Gangl present the results of their computation of for some other values of The results agree with the conjectural structure of given in the paper by Browkin and Gangl.
992.
Damian Mikulski Jerzy Konarski Krzysztof Eder Marcin Molski Stanisław Kabaciński 《Journal of mathematical chemistry》2015,53(9):2018-2027
The study involves finding exact eigenvalues of the radial Schrödinger equation for new expansion of the anharmonic potential energy function. All analytical calculations employ the mathematical formalism of the supersymmetric quantum mechanics. The novelty of this study is underlined by the fact that for the first time the recurrence formulas for rovibrational bound energy levels have been derived employing factorization method and algebraic approach. The ground state and the excited states have been determined by means of the hierarchy of the isospectral Hamiltonians. The Riccati nonlinear differential equation with superpotentials has been solved analytically. It has been shown that exact solutions exist when the potential and superpotential parameters satisfy certain supersymmetric constraints. The results obtained can be utilized both in computations of quantum chemistry and theoretical spectroscopy of diatomic molecules. 相似文献
993.
Roman Dabrowski Katarzyna Garbat Stanisław Urban Tomasz R. Woliński Jerzy Dziaduszek Tomasz Ogrodnik 《Liquid crystals》2017,44(12-13):1911-1928
ABSTRACTSeries of low-birefringence liquid crystal mixtures composed of alkyl alkylbicyclohexyl carbonates and modified mixtures with other compounds have been formulated, their refractive indices and electric permittivity measured upon temperature. They exhibit the ordinary refraction index no lower than the refractive index of silica glass in a different range of temperature. This enables to observe in photonic liquid crystal fibres (PLCFs) a change in the light propagation mechanism from photonic band gap guiding to modified total internal reflection at different temperatures. Selected applications of PLCFs are also discussed. 相似文献
994.
Dewei Chen Christopher Copeland D. Majumdar Szczepan Roszak Jerzy Leszczynski 《Structural chemistry》2017,28(2):379-389
Functionalized graphene – metal nano-conjugates are used as Raman probes, in recent years, for trace level identification of materials having specific Raman active modes. In the present paper, model Raman probes were modeled through conjugation of Au4 and Ag4 clusters with functionalized graphene systems. In silico models of functionalized (5,5)-graphene sheets were designed at the density functional theory (DFT) level through attachments of epoxy, -OH and –NH(CH3)2SH/-CONH(CH3)2SH groups. Model Raman probes were designed through attachment of Au4 and Ag4 clusters to the functional sites. Full geometry optimizations followed by vibrational analysis were carried out to ensure that the designed Raman probes have acceptable geometric characteristics to attach Raman-active molecules to the metal site. Pyridine was used as a test system to investigate the functionality of such model Raman probes through attachment with the metal clusters. It was observed that the chemical effects due to such attachments increase the Raman intensities (RI) of specific Raman modes of pyridine (in-plane symmetric bending (1040 cm-1) and asymmetric stretch-bend (1634 cm-1)), which are too weak in the isolated molecule. Furthermore, the suggested in silico system could provide an important model for basic understanding of RI-enhancements of molecules through increase of the size of the metal clusters, as the observed enhancement was found to be dependent on the polarizability of the metal clusters attached to the molecule of interest. 相似文献
995.
996.
The main goal of this paper is to initiate study of analytic monoids as a general framework for quantitative theory of factorization. So far the latter subject was developed either in concrete settings, for instance in orders of number fields, or abstractly, in an axiomatic way. Some of the abstract approaches are too general to address delicate problems concerning oscillatory nature of the related counting functions, or are too restrictive in the sense that they suffer from the lack of examples except classical ones i.e. the Hilbert monoids of algebraic integers and their products. The notion of an analytic monoid is enough flexible to allow constructions of many other examples, and also ensures sufficiently rich analytic structure. In particular, we construct examples of such monoids with the associated L-functions being products of classical Dirichlet L-functions and L-functions of twisted irreducible unitary cuspidal automorphic representations of \(GL_d({\mathbb {A}}_{\mathbb {Q}})\) satisfying the Ramanujan conjecture and having real coefficients. Finally, to illustrate how a typical problem from the quantitative theory of factorization can be studied in the framework of analytic monoids, we formulate several results concerning oscillations of the remainder term in the asymptotic formula for the number of irreducible elements with norms less or equal x, as x tends to infinity. 相似文献
997.
Tomasz Jachowicz Tomasz Garbacz Aneta Tor-Świątek Ivan Gajdoš Andrzej Czulak 《International Journal of Polymer Analysis and Characterization》2015,20(4):307-315
This article provides general information about the aging process of polymer plastics. It also reports the experimental results of investigations undertaken to determine changes in the mechanical properties of polypropylene injection-molded samples with the oxo-biodegradable additive d2w which were subjected to natural aging for two years. A decrease of tensile strength and elongation at yield as well as an increase of hardness were observed during the experiment. 相似文献
998.
Generalizing the result in Lemma of Baksalary and Baksalary [J.K. Baksalary, O.M. Baksalary, Commutativity of projectors, Linear Algebra Appl. 341 (2002) 129-142], Baksalary et al. [J.K. Baksalary, O.M. Baksalary, T. Szulc, Linear Algebra Appl. 354 (2002) 35-39] have shown that if P1 and P2 are orthogonal projectors, then, in all nontrivial situations, a product of any length having P1 and P2 as its factors occurring alternately is equal to another such product if and only if P1 and P2 commute, in which case all products involving P1 and P2 reduce to the orthogonal projector P1P2 (= P2P1). In the present paper, further generalizations of this property are established. They consist in replacing a product of the type specified above, appearing on the left-hand side (say) of the equality under considerations, by an affine combination of two or three such products. Comments on the problem when the number of components in a combination exceeds three are also given. 相似文献
999.
We find minimal generators for the ideals of secant varietiesof Segre varieties in the cases of k(1 x n x m) for all k, n,m, 2(n x m x p x r) for all n, m, p, r (GSS conjecture for fourfactors), and 3(n x m x p) for all n, m, p and prove they arenormal with rational singularities in the first case and arithmeticallyCohen–Macaulay in the second two cases. 相似文献
1000.
Grzegorz Graff Jerzy Jezierski 《Proceedings of the American Mathematical Society》2007,135(10):3249-3254
Let be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension . We show that in the homotopy class of there is a map with less then periodic points, up to any given fixed period .