3,066 research outputs found
Numerical homogenization of H(curl)-problems
If an elliptic differential operator associated with an
-problem involves rough (rapidly varying)
coefficients, then solutions to the corresponding
-problem admit typically very low regularity, which
leads to arbitrarily bad convergence rates for conventional numerical schemes.
The goal of this paper is to show that the missing regularity can be
compensated through a corrector operator. More precisely, we consider the
lowest order N\'ed\'elec finite element space and show the existence of a
linear corrector operator with four central properties: it is computable,
-stable, quasi-local and allows for a correction of
coarse finite element functions so that first-order estimates (in terms of the
coarse mesh-size) in the norm are obtained provided
the right-hand side belongs to . With these four
properties, a practical application is to construct generalized finite element
spaces which can be straightforwardly used in a Galerkin method. In particular,
this characterizes a homogenized solution and a first order corrector,
including corresponding quantitative error estimates without the requirement of
scale separation
Coalgebraic Behavioral Metrics
We study different behavioral metrics, such as those arising from both
branching and linear-time semantics, in a coalgebraic setting. Given a
coalgebra for a functor , we define a framework for deriving pseudometrics on which
measure the behavioral distance of states.
A crucial step is the lifting of the functor on to a
functor on the category of pseudometric spaces.
We present two different approaches which can be viewed as generalizations of
the Kantorovich and Wasserstein pseudometrics for probability measures. We show
that the pseudometrics provided by the two approaches coincide on several
natural examples, but in general they differ.
If has a final coalgebra, every lifting yields in a
canonical way a behavioral distance which is usually branching-time, i.e., it
generalizes bisimilarity. In order to model linear-time metrics (generalizing
trace equivalences), we show sufficient conditions for lifting distributive
laws and monads. These results enable us to employ the generalized powerset
construction
Towards Trace Metrics via Functor Lifting
We investigate the possibility of deriving metric trace semantics in a
coalgebraic framework. First, we generalize a technique for systematically
lifting functors from the category Set of sets to the category PMet of
pseudometric spaces, showing under which conditions also natural
transformations, monads and distributive laws can be lifted. By exploiting some
recent work on an abstract determinization, these results enable the derivation
of trace metrics starting from coalgebras in Set. More precisely, for a
coalgebra on Set we determinize it, thus obtaining a coalgebra in the
Eilenberg-Moore category of a monad. When the monad can be lifted to PMet, we
can equip the final coalgebra with a behavioral distance. The trace distance
between two states of the original coalgebra is the distance between their
images in the determinized coalgebra through the unit of the monad. We show how
our framework applies to nondeterministic automata and probabilistic automata
Coalgebraic Trace Semantics for Continuous Probabilistic Transition Systems
Coalgebras in a Kleisli category yield a generic definition of trace
semantics for various types of labelled transition systems. In this paper we
apply this generic theory to generative probabilistic transition systems, short
PTS, with arbitrary (possibly uncountable) state spaces. We consider the
sub-probability monad and the probability monad (Giry monad) on the category of
measurable spaces and measurable functions. Our main contribution is that the
existence of a final coalgebra in the Kleisli category of these monads is
closely connected to the measure-theoretic extension theorem for sigma-finite
pre-measures. In fact, we obtain a practical definition of the trace measure
for both finite and infinite traces of PTS that subsumes a well-known result
for discrete probabilistic transition systems. Finally we consider two example
systems with uncountable state spaces and apply our theory to calculate their
trace measures
Transformation of Ammonium Dicyanamide into Dicyandiamide in the Solid
Ammonium dicyanamide NH4[N(CN)2] was synthesized through aqueous ion exchange. The crystal structure was investigated by single-crystal X-ray diffraction (P21/c, a = 378.67(6) pm, b = 1240.9(3) pm, c = 911.84(14) pm, ÎČ = 91.488(18)°, Z = 4). It derives from the CsCl structure type. Medium strong hydrogen bonds between NH4+ and [N(CN)2]- ions are indicative of the observed formation of dicyandiamide H4C2N4 during heating. According to DSC and temperature-dependent X-ray powder diffractometry, this isomerization is exothermic and occurs between 102 and 106°C in the solid. The reaction represents the isolobal analogue to the classical synthesis of urea by heating NH4OCN. While other alkali and alkaline earth dicyanamides undergo trimerization or polymerization of their anions during heating, ammonium dicyanamide thus shows a different reactivity
"Der Frau GrÀfin Moszinska Garten, ..., gehört mit Recht unter die schönen und reizenden GÀrten der Residenz." Ein Garten des 18. Jahrhunderts in Dresden
Höhenatmung, Phosphat-Protein-Wechselwirkung: Die Sequenz der HÀmoglobine des Goldhamsters (Mesocricetus aureatus) und des zweihöckerigen Kamels (Trampeltier, Camelus ferus, Camelidae)
The sequence of the main component of the hemoglobin of the hamster and that of
the camel (Camelus ferus) is given. The sequence is obtained automatically by the sequenator using
the quadrol and the propyne programme. The sequence of the α-and ÎČ-chains of the hamster is compared
with the human hemoglobin; the sequence of the hemoglobin of the camel (Camelus ferus,
Cameiidae), in comparison to the llama, there are to be found in the α-chains five amino acid exchanges,
in the ÎČ-chains are two exchanges - in ÎČ2 and ÎČ76 - only. The sequence ÎČ2 in camel - the P2-glycerate contact - is histidine: This sequence sustains the interpretation of the high altitude respiration
of the llama as mutation ÎČ2His to Asn. The amino acid sequence of the hemoglobin of Camelus
ferus and Camelus dromedarius is identical
In design we trust: dealing with the innovation imperative
This research was funded by the Arts and Humanities Research Council (Grant number: AH/J005126/1).Preprin
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