Search results for "Theorem"
showing 10 items of 1250 documents
Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces
2007
This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…
Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space
2002
AbstractIn an infinite-dimensional real Hilbert space, we introduce a class of fourth-degree polynomials which do not satisfy Rolle's Theorem in the unit ball. Extending what happens in the finite-dimensional case, we show that every fourth-degree polynomial defined by a compact operator satisfies Rolle's Theorem.
Impacts of piscicide-induced fish removal on resource use and trophic diversity of lake invertebrates
2022
Chemical eradication of non-native species has become a widely used method to mitigate the potential negative im- pacts of altered competitive or predatory dynamics on biodiversity and natural ecosystem processes. However, the re- sponses of non-target species can vary from rapid full recovery to delayed or absent recolonization, and little is known about the potential shifts in resource use and trophic diversity of native species following chemical treatments. We used a before-after-control-impact approach to study the effects of rotenone piscicide treatment on abundance and tro- phic niche of benthic invertebrates in three untreated and three treated lakes in central Norway, the latter gr…
New chronology for Ksâr ‘Akil (Lebanon) supports Levantine route of modern human dispersal into Europe
2015
Modern human dispersal into Europe is thought to have occurred with the start of the Upper Paleolithic around 50,000-40,000 y ago. The Levantine corridor hypothesis suggests that modern humans from Africa spread into Europe via the Levant. Ksâr 'Akil (Lebanon), with its deeply stratified Initial (IUP) and Early (EUP) Upper Paleolithic sequence containing modern human remains, has played an important part in the debate. The latest chronology for the site, based on AMS radiocarbon dates of shell ornaments, suggests that the appearance of the Levantine IUP is later than the start of the first Upper Paleolithic in Europe, thus questioning the Levantine corridor hypothesis. Here we report a seri…
Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
2013
We formulate the general approach based on the Lindblad equation to calculate the full counting statistics of work and heat produced by driven quantum systems weakly coupled with a Markovian thermal bath. The approach can be applied to a wide class of dissipative quantum systems driven by an arbitrary force protocol. We show the validity of general fluctuation relations and consider several generic examples. The possibilities of using calorimetric measurements to test the presence of coherence and entanglement in the open quantum systems are discussed. QC 20141010
On the irreducibility of Hurwitz spaces of coverings with an arbitrary number of special points
2013
In this paper we study Hurwitz spaces of coverings of Y with an arbitrary number of special points and with monodromy group a Weyl group of type D_d, where Y is a smooth, complex projective curve. We give conditions for which these spaces are irreducible.
Generalized countable iterated function systems
2011
One of the most common and most general way to generate fractals is by using iterated function systems which consists of a finite or infinitely many maps. Generalized countable iterated function systems (GCIFS) are a generalization of countable iterated function systems by considering contractions from X ? X into X instead of contractions on the metric space X to itself, where (X, d) is a compact metric space. If all contractions of a GCIFS are Lipschitz with respect to a parameter and the supremum of the Lipschitz constants is finite, then the associated attractor depends continuously on the respective parameter.
Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths
2018
Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets a…
Assessing Stage-Discharge Relationships for Circular Overflow Structure
2018
Circular overflow structures are used in irrigation and drainage networks as water measuring structures. Different approaches can be found in the literature to formulate the stage-discharge relationship of the circular weir. They are mainly categorized in three groups: (1)methods trying to simplify the complex elliptic integrals coming from the theoretical discharge equation; (2)methods that use the orifice formula and a discharge coefficient specific for the circular weir; and (3)approaches using dimensional analysis and Buckingham's Theorem. In this study, a nondimensional stage-discharge formula was obtained using Buckingham's Theorem to define the flow over the sharp-crested circular we…