433 research outputs found
Parametric Euler Sum Identities
We consider some parametrized classes of multiple sums first studied by
Euler. Identities between meromorphic functions of one or more variables
generate reduction formulae for these sums.Comment: 12 page
Log-sine evaluations of Mahler measures, II
We continue the analysis of higher and multiple Mahler measures using
log-sine integrals as started in "Log-sine evaluations of Mahler measures" and
"Special values of generalized log-sine integrals" by two of the authors. This
motivates a detailed study of various multiple polylogarithms and worked
examples are given. Our techniques enable the reduction of several multiple
Mahler measures, and supply an easy proof of two conjectures by Boyd.Comment: 35 page
Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator
The most famous open problem in Monotone Operator Theory concerns the maximal
monotonicity of the sum of two maximally monotone operators provided that
Rockafellar's constraint qualification holds.
In this paper, we prove the maximal monotonicity of provided that are maximally monotone and is a linear relation, as soon as
Rockafellar's constraint qualification holds: \dom A\cap\inte\dom
B\neq\varnothing. Moreover, is of type (FPV).Comment: 16 pages. arXiv admin note: substantial text overlap with
arXiv:1010.4346, arXiv:1005.224
Nearest points and delta convex functions in Banach spaces
Given a closed set in a Banach space , a point
is said to have a nearest point in if there exists such that
, where is the distance of from . We shortly
survey the problem of studying how large is the set of points in which have
nearest points in . We then discuss the topic of delta-convex functions and
how it is related to finding nearest points.Comment: To appear in Bull. Aust. Math. So
Log-sine evaluations of Mahler measures
We provide evaluations of several recently studied higher and multiple Mahler
measures using log-sine integrals. This is complemented with an analysis of
generating functions and identities for log-sine integrals which allows the
evaluations to be expressed in terms of zeta values or more general
polylogarithmic terms. The machinery developed is then applied to evaluation of
further families of multiple Mahler measures.Comment: 25 page
A Cyclic Douglas-Rachford Iteration Scheme
In this paper we present two Douglas-Rachford inspired iteration schemes
which can be applied directly to N-set convex feasibility problems in Hilbert
space. Our main results are weak convergence of the methods to a point whose
nearest point projections onto each of the N sets coincide. For affine
subspaces, convergence is in norm. Initial results from numerical experiments,
comparing our methods to the classical (product-space) Douglas-Rachford scheme,
are promising.Comment: 22 pages, 7 figures, 4 table
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