497 research outputs found
Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds
Given a finite dimensional manifold , the group
of diffeomorphism of which fall
suitably rapidly to the identity, acts on the manifold of submanifolds
on of diffeomorphism type where is a compact manifold with . For a right invariant weak Riemannian metric on
induced by a quite general operator
, we
consider the induced weak Riemannian metric on and we compute its
geodesics and sectional curvature. For that we derive a covariant formula for
curvature in finite and infinite dimensions, we show how it makes O'Neill's
formula very transparent, and we use it finally to compute sectional curvature
on .Comment: 28 pages. In this version some misprints correcte
Possible canted antiferromagnetism in UCuSn
We report on the new compound UCuSn which crystallizes in the
tetragonal structure \emph{I}4/\emph{mcm} with lattice parameters and . This compound is isotyp to the
ferromagnetic systems RECuSn (RE = Ce, Pr, Nd) with Curie
temperatures = 5.5 K, 10.5 K and 15 K, respectively.
UCuSn exhibits an uncommon magnetic behavior resulting in three
different electronic phase transitions. Below 105 K the sample undergoes a
valence transition accompanied by an entropy change of 0.5 Rln2. At 32 K a
small hump in the specific heat and a flattening out in the susceptibility
curve probably indicate the onset of helical spin order. To lower temperatures
a second transition to antiferromagnetic ordering occurs which develops a small
ferromagnetic contribution on lowering the temperature further. These results
are strongly hinting for canted antiferromagnetism in UCuSn.Comment: 2 pages, 3 figures, SCES0
Construction of completely integrable systems by Poisson mappings
Pulling back sets of functions in involution by Poisson mappings and adding
Casimir functions during the process allows to construct completely integrable
systems. Some examples are investigated in detail.Comment: AmsTeX, 9 page
The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy
We discuss the algebro-geometric initial value problem for the Ablowitz-Ladik
hierarchy with complex-valued initial data and prove unique solvability
globally in time for a set of initial (Dirichlet divisor) data of full measure.
To this effect we develop a new algorithm for constructing stationary
complex-valued algebro-geometric solutions of the Ablowitz-Ladik hierarchy,
which is of independent interest as it solves the inverse algebro-geometric
spectral problem for general (non-unitary) Ablowitz-Ladik Lax operators,
starting from a suitably chosen set of initial divisors of full measure.
Combined with an appropriate first-order system of differential equations with
respect to time (a substitute for the well-known Dubrovin-type equations), this
yields the construction of global algebro-geometric solutions of the
time-dependent Ablowitz-Ladik hierarchy.
The treatment of general (non-unitary) Lax operators associated with general
coefficients for the Ablowitz-Ladik hierarchy poses a variety of difficulties
that, to the best of our knowledge, are successfully overcome here for the
first time. Our approach is not confined to the Ablowitz-Ladik hierarchy but
applies generally to (1+1)-dimensional completely integrable soliton equations
of differential-difference type.Comment: 47 page
Completely integrable systems: a generalization
We present a slight generalization of the notion of completely integrable
systems to get them being integrable by quadratures. We use this generalization
to integrate dynamical systems on double Lie groups.Comment: Latex, 15 page
Towards a Lagrange-Newton approach for PDE constrained shape optimization
The novel Riemannian view on shape optimization developed in [Schulz, FoCM,
2014] is extended to a Lagrange-Newton approach for PDE constrained shape
optimization problems. The extension is based on optimization on Riemannian
vector space bundles and exemplified for a simple numerical example.Comment: 16 pages, 4 figures, 1 tabl
A quantum-group-like structure on noncommutative 2-tori
In this paper we show that in the case of noncommutative two-tori one gets in
a natural way simple structures which have analogous formal properties as Hopf
algebra structures but with a deformed multiplication on the tensor product
People in Nature: Environmental History of the Kennebec River, Maine
The quality of a river affects the tributaries, lakes, and estuary it feeds; it affects the wildlife and vegetation that depend on the river for energy, nutrients, and habitat, and also affects the human community in the form of use, access, pride, and sustainability. In an age of mass consumerism and materialism, dwindling natural resources and wild spaces, and advanced technology, the ability to make a living and at the same time enjoy the benefits of rural living is increasingly difficult. Using the entire Kennebec River watershed as the scale of investigation with particular focus on the river corridor itself, my project looks at the interconnectedness of the river and the surrounding human community in a whole ecosystem analysis. Through coordinated efforts in the 1960s and 1970s in pollution abatement control and natural resource management, the communities of central Maine improved water quality in the Kennebec River from what was once described as an open sewer to conditions that provide for thriving aquatic life and improved access, enjoyment and economic health for the people. Vibrant commercial districts appeared, and tourism, fishing, boating and swimming all increased as a result of the improved river quality. Based on Mainer\u27s values of economy, rural living, and environmental health, management of the Kennebec met the needs and values of the whole ecosystem (social, economic, biogeophysical). Providing the river with conditions necessary for clean water, the people were in turn, sustained by the it as a natural resource; this resembles cutting-edge ecological theory called supply-side sustainability: maintaining, or fostering the development of, the systemic contexts that produce the goods, services, and amenities that people need or value, at an acceptable cost, for as long as they are needed or valued. My project provides an example of how people can translate their values of economic well being, ecological integrity, and the enjoyment of nature in their everyday lives into a sustainable system which provides for their every value
Poisson structures on double Lie groups
Lie bialgebra structures are reviewed and investigated in terms of the double
Lie algebra, of Manin- and Gau{\ss}-decompositions. The standard R-matrix in a
Manin decomposition then gives rise to several Poisson structures on the
correponding double group, which is investigated in great detail.Comment: AmSTeX, 37 page
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