Search results for "algebra"
showing 10 items of 4129 documents
Pseudodifferential Analysis on Manifolds with Boundary — a Comparison of b-Calculus and Cone Algebra
2001
We establish a relation between two different approaches to a complete pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary respectively conical singularities: Melrose’s (overblown) b-calculus and Schulze’s cone algebra. Though quite different in their definition, we show that these two pseudodifferential calculi basically contain the same operators.
Singular integrals and rectifiability
2002
We shall discuss singular integrals on lower dimensional subsets of Rn. A survey of this topic was given in [M4]. The first part of this paper gives a quick review of some results discussed in [M4] and a survey of some newer results and open problems. In the second part we prove some results on the Riesz kernels in Rn. As far as I know, they have not been explicitly stated and proved, but they are very closely related to some earlier results and methods. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
Numerical evaluation of multiple polylogarithms
2004
Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for arbitrary complex arguments and without any restriction on the weight. We have implemented these algorithms with arbitrary precision arithmetic in C++ within the GiNaC framework.
Finite Braid Groups for the SU(2) Knizhnik Zamolodchikov Equation
1995
We consider the monodromy representations of the mapping class group B 4 of the 2-sphere with 4 punctures acting in the solutions space of the zu(2) Knizhnik-Zamolodchikov equation [3] (note that the monodromy representations of the braid group have a more general geometric definition [4]).
Hodge Numbers for the Cohomology of Calabi-Yau Type Local Systems
2014
We determine the Hodge numbers of the cohomology group \(H_{L^{2}}^{1}(S, \mathbb{V}) = H^{1}(\bar{S},j_{{\ast}}\mathbb{V})\) using Higgs cohomology, where the local system \(\mathbb{V}\) is induced by a family of Calabi-Yau threefolds over a smooth, quasi-projective curve S. This generalizes previous work to the case of quasi-unipotent, but not necessarily unipotent, local monodromies at infinity. We give applications to Rohde’s families of Calabi-Yau 3-folds.
Miscellaneous Periods: An Outlook
2017
In this chapter, we collect several other important examples of periods in the literature for the convenience of the reader.
Closedness properties in team learning of recursive functions
1997
This paper investigates closedness properties in relation with team learning of total recursive functions. One of the first problems solved for any new identification types is the following: “Does the identifiability of classes U1 and U2 imply the identifiability of U1∪U2?” In this paper we are interested in a more general question: “Does the identifiability of every union of n−1 classes out of U1,...,Un imply the identifiability of U1∪...∪Un?” If the answer is positive, we call such identification type n-closed. We show that n-closedness can be equivalently formulated in terms of team learning. After that we find for which n team identification in the limit and team finite identification t…
On the representation theory of quantum Heisenberg group and algebra
1994
We show that the quantum Heisenberg groupH q (1) and its *-Hopf algebra structure can be obtained by means of contraction from quantumSU q (2) group. Its dual Hopf algebra is the quantum Heisenberg algebraU q (h(1)). We derive left and right regular representations forU q (h(1)) as acting on its dualH q (1). Imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. Realized in the Bargmann-Hilbert space of analytic functions the unitarity of regular representation is also shown. By duality, left and right regular representations for quantum Heisenberg group with the quantum Heis…
Improvement of Grüss and Ostrowski type inequalities
2015
Several inequalities of Ostrowski-Gr?ss-type available in the literature are generalized considering the weighted case of them. The inequality of Gr?ss type proved by P. Cerone and S.S. Dragomir [3] is extended for the weighted case.