111 research outputs found
Large Scales - Long Times: Adding High Energy Resolution to SANS
The Neutron Spin Echo (NSE) variant MIEZE (Modulation of IntEnsity by Zero
Effort), where all beam manipulations are performed before the sample position,
offers the possibility to perform low background SANS measurements in strong
magnetic fields and depolarising samples. However, MIEZE is sensitive to
differences \DeltaL in the length of neutron flight paths through the
instrument and the sample. In this article, we discuss the major influence of
\DeltaL on contrast reduction of MIEZE measurements and its minimisation.
Finally we present a design case for enhancing a small-angle neutron scattering
(SANS) instrument at the planned European Spallation Source (ESS) in Lund,
Sweden, using a combination of MIEZE and other TOF options, such as TISANE
offering time windows from ns to minutes. The proposed instrument allows
studying fluctuations in depolarizing samples, samples exposed to strong
magnetic fields, and spin-incoherently scattering samples in a straightforward
way up to time scales of \mus at momentum transfers up to 0.01 {\AA}-1, while
keeping the instrumental effort and costs low.Comment: 5 pages, 8 figure
A cyclopentadienyl functionalized silylene-a flexible ligand for Si- And C-coordination
The synthesis of a 1,2,3,4-tetramethylcyclopentadienyl (Cp) substituted four-membered N-heterocyclic silylene [{PhC(NtBu) }Si(CMeH)] is reported first. Then, selected reactions with transition metal and a calcium precursor are shown. The proton of the Cp-unit is labile. This results in two different reaction pathways: (1) deprotonation and (2) rearrangement reactions. Deprotonation was achieved by the reaction of [{PhC(NtBu) }Si(CMeH)] with suitable zinc precursors. Rearrangement to [{PhC(NtBu) }(CMe)SiH], featuring a formally tetravalent silicon RCSi(RâČ)-H unit, was observed when the proton of the Cp ring was shifted from the Cp-ring to the silylene in the presence of a Lewis acid. This allows for the coordination of the Cp-ring to a calcium compound. Furthermore, upon reaction with transition metal dimers [MCl(cod)] (M = Rh, Ir; cod = 1,5-cyclooctadiene) the proton stays at the Cp-ring and the silylene reacts as a sigma donor, which breaks the dimeric structure of the precursors
The structure of the infinite models in integer programming
The infinite models in integer programming can be described as the convex
hull of some points or as the intersection of halfspaces derived from valid
functions. In this paper we study the relationships between these two
descriptions. Our results have implications for corner polyhedra. One
consequence is that nonnegative, continuous valid functions suffice to describe
corner polyhedra (with or without rational data)
Integer polyhedra for program analysis
Polyhedra are widely used in model checking and abstract interpretation. Polyhedral analysis is effective when the relationships between variables are linear, but suffers from imprecision when it is necessary to take into account the integrality of the represented space. Imprecision also arises when non-linear constraints occur. Moreover, in terms of tractability, even a space defined by linear constraints can become unmanageable owing to the excessive number of inequalities. Thus it is useful to identify those inequalities whose omission has least impact on the represented space. This paper shows how these issues can be addressed in a novel way by growing the integer hull of the space and approximating the number of integral points within a bounded polyhedron
A parametric integer programming algorithm for bilevel mixed integer programs
We consider discrete bilevel optimization problems where the follower solves
an integer program with a fixed number of variables. Using recent results in
parametric integer programming, we present polynomial time algorithms for pure
and mixed integer bilevel problems. For the mixed integer case where the
leader's variables are continuous, our algorithm also detects whether the
infimum cost fails to be attained, a difficulty that has been identified but
not directly addressed in the literature. In this case it yields a ``better
than fully polynomial time'' approximation scheme with running time polynomial
in the logarithm of the relative precision. For the pure integer case where the
leader's variables are integer, and hence optimal solutions are guaranteed to
exist, we present two algorithms which run in polynomial time when the total
number of variables is fixed.Comment: 11 page
Nonlinear Integer Programming
Research efforts of the past fifty years have led to a development of linear
integer programming as a mature discipline of mathematical optimization. Such a
level of maturity has not been reached when one considers nonlinear systems
subject to integrality requirements for the variables. This chapter is
dedicated to this topic.
The primary goal is a study of a simple version of general nonlinear integer
problems, where all constraints are still linear. Our focus is on the
computational complexity of the problem, which varies significantly with the
type of nonlinear objective function in combination with the underlying
combinatorial structure. Numerous boundary cases of complexity emerge, which
sometimes surprisingly lead even to polynomial time algorithms.
We also cover recent successful approaches for more general classes of
problems. Though no positive theoretical efficiency results are available, nor
are they likely to ever be available, these seem to be the currently most
successful and interesting approaches for solving practical problems.
It is our belief that the study of algorithms motivated by theoretical
considerations and those motivated by our desire to solve practical instances
should and do inform one another. So it is with this viewpoint that we present
the subject, and it is in this direction that we hope to spark further
research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G.
Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50
Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art
Surveys, Springer-Verlag, 2009, ISBN 354068274
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