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151.
Stavros Garoufalidis Piotr Kucharski Piotr Sułkowski 《Communications in Mathematical Physics》2016,346(1):75-113
We analyze relations between BPS degeneracies related to Labastida-Mariño-Ooguri-Vafa (LMOV) invariants and algebraic curves associated to knots. We introduce a new class of such curves, which we call extremal A-polynomials, discuss their special properties, and determine exact and asymptotic formulas for the corresponding (extremal) BPS degeneracies. These formulas lead to nontrivial integrality statements in number theory, as well as to an improved integrality conjecture, which is stronger than the known M-theory integrality predictions. Furthermore, we determine the BPS degeneracies encoded in augmentation polynomials and show their consistency with known colored HOMFLY polynomials. Finally, we consider refined BPS degeneracies for knots, determine them from the knowledge of super-A-polynomials, and verify their integrality. We illustrate our results with twist knots, torus knots, and various other knots with up to 10 crossings. 相似文献
152.
We give a complete derived equivalence classification of all nonstandard representation-infinite domestic selfinjective algebras over an algebraically closed field. As a consequence, a complete stable equivalence classification of these algebras is obtained. 相似文献
153.
We develop a theoretical framework for projection-iterative methods to solve operator equations of the form Au + Bu = f, where A is a Toeplitz operator in a Banach space , B is considered as a perturbation (of general form) of A, and f is a given element in this space. The methods are adopted for application to general situations, in particular, to the equations
in which A need not be a Fredholm operator. The idea to involve iteration procedures and the technique which we apply allow to obtain
conditions on perturbations for convergence and effective error estimates in terms of some weighted spaces (without any restrictions
on the norms for perturbations). Based on established evaluations we derive further information about decaying properties
of the solutions. The obtained results are illustrated by considering concrete classes of equations as, for instance, equations
corresponding to Jacobi type operators.
相似文献
154.
We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. 相似文献
155.
Emma Kushtina Oleg Zaikin Przemysław Różewski Bartłomiej Małachowski 《European Journal of Operational Research》2009
The decision about curriculum modification usually takes place at the knowledge level, mainly with consideration of individual academic staff competences and qualifications. However, traditional approaches to cost estimation of curriculum modification are focused on material resources only. In this paper we present a cost estimation method and decision model for curriculum modification in educational organizations. The proposed method works at the knowledge level and employs competence sets as knowledge representation models in educational organizations. Authors used the theory of hierarchical, multilevel systems in order to define the model of the decision-making process of curriculum modification and its dimension. Basing on this and also using a fuzzy competence model the cost estimation algorithm in the form of a group competences expansion algorithm is proposed. The algorithm focuses on the cost of staff competence expansion caused by the knowledge development process. 相似文献
156.
A weighting of the edges of a hypergraph is called vertex‐coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e. every edge contains at least two vertices with different weighted degrees. In this article, we show that such a weighting is possible from the weight set for all hypergraphs with maximum edge size and not containing edges solely consisting of identical vertices. The number is best possible for this statement. 相似文献
157.
We present the experimental realization of a method to generate predetermined, arbitrary pulse shapes after transmission through an optical fiber in the nonlinear regime. The method is based on simulating the reverse propagation of the desired pulse shape in the fiber. First, linear and nonlinear parameters of a single-mode step-index fiber required for the simulation are determined. The calculated pulse shapes are then generated in a pulse shaper. 相似文献
158.
159.
Ting Zhao Katarzyna Kurpiewska Justyna Kalinowska‐Tłuścik Eberhardt Herdtweck Prof. Dr. Alexander Dömling 《Chemistry (Weinheim an der Bergstrasse, Germany)》2016,22(9):3009-3018
The synthesis of all 20 common natural proteinogenic and 4 otherα‐amino acid‐isosteric α‐amino tetrazoles has been accomplished, whereby the carboxyl group is replaced by the isosteric 5‐tetrazolyl group. The short process involves the use of the key Ugi tetrazole reaction followed by deprotection chemistries. The tetrazole group is bioisosteric to the carboxylic acid and is widely used in medicinal chemistry and drug design. Surprisingly, several of the common α‐amino acid‐isosteric α‐amino tetrazoles are unknown up to now. Therefore a rapid synthetic access to this compound class and non‐natural derivatives is of high interest to advance the field. 相似文献
160.
Joanna Kobyłecka Bogdan Ptaszyński Anna Zwolinńska 《Monatshefte für Chemie / Chemical Monthly》2000,131(1):1-11
Summary. Sparingly water soluble complexes of lead(II), cadmium(II), and zinc(II) with N-phosphonomethylglycine (glyphosate, NPMG) of the general formulae C3H6O5NPPb, C3H6O5NPCdċ2H2O, and C3H6O5NPZn were synthesized. The complexes were also precipited from a dilute Roundup solution, and their solubility in water was
determined. Thermal, diffractometric, and IR spectrophotometric analyses were carried out. It was found that the metal is
bonded to glyphosate through the oxygen atoms of the carboxylic and phosphonate groups; metal-nitrogen binding is absent in
the above compounds. Studying the complexing behaviour in solution by UV spectrophotometry pointed out that a complex of the
composition Pb(II) : NPMG=1:1 with an absorption band at 232 nm is formed. Its stability constant as determined by Job’s method is logK=5.9±0.1. Using potentiometric techniques, the dissociation constant of N-phosphonomethylglycine and the stability constants
of its complexes with cadmium (II) and zinc (II) were determined.
Received June 30, 1999/Accepted July 21, 1999. 相似文献