22,022 research outputs found
Symbolic calculus on the time-frequency half-plane
The study concerns a special symbolic calculus of interest for signal
analysis. This calculus associates functions on the time-frequency half-plane
f>0 with linear operators defined on the positive-frequency signals. Full
attention is given to its construction which is entirely based on the study of
the affine group in a simple and direct way. The correspondence rule is
detailed and the associated Wigner function is given. Formulas expressing the
basic operation (star-bracket) of the Lie algebra of symbols, which is
isomorphic to that of the operators, are obtained. In addition, it is shown
that the resulting calculus is covariant under a three-parameter group which
contains the affine group as subgroup. This observation is the starting point
of an investigation leading to a whole class of symbolic calculi which can be
considered as modifications of the original one.Comment: 25 pages, Latex, minor changes and more references; to be published
in the "Journal of Mathematical Physics" (special issue on "Wavelet and
Time-Frequency Analysis"
Computer program performs rectangular fitting stress analysis
Computer program simulates specific bulkhead fittings by subjecting the desired geometry configuration to a membrane force, an external force, an external moment, an external tank pressure, or any combination of the above. This program generates a general model of bulkhead fittings for the Saturn booster
Exponential convergence to equilibrium for subcritical solutions of the Becker-D\"oring equations
We prove that any subcritical solution to the Becker-D\"{o}ring equations
converges exponentially fast to the unique steady state with same mass. Our
convergence result is quantitative and we show that the rate of exponential
decay is governed by the spectral gap for the linearized equation, for which
several bounds are provided. This improves the known convergence result by
Jabin & Niethammer (see ref. [14]). Our approach is based on a careful spectral
analysis of the linearized Becker-D\"oring equation (which is new to our
knowledge) in both a Hilbert setting and in certain weighted spaces.
This spectral analysis is then combined with uniform exponential moment bounds
of solutions in order to obtain a convergence result for the nonlinear
equation
A Z_3-graded generalization of supermatrices
We introduce Z_3-graded objects which are the generalization of the more
familiar Z_2-graded objects that are used in supersymmetric theories and in
many models of non-commutative geometry. First, we introduce the Z_3-graded
Grassmann algebra, and we use this object to construct the Z_3-matrices, which
are the generalizations of the supermatrices. Then, we generalize the concepts
of supertrace and superdeterminant
Entropy dissipation estimates for the linear Boltzmann operator
We prove a linear inequality between the entropy and entropy dissipation
functionals for the linear Boltzmann operator (with a Maxwellian equilibrium
background). This provides a positive answer to the analogue of Cercignani's
conjecture for this linear collision operator. Our result covers the physically
relevant case of hard-spheres interactions as well as Maxwellian kernels, both
with and without a cut-off assumption. For Maxwellian kernels, the proof of the
inequality is surprisingly simple and relies on a general estimate of the
entropy of the gain operator due to Matthes and Toscani (2012) and Villani
(1998). For more general kernels, the proof relies on a comparison principle.
Finally, we also show that in the grazing collision limit our results allow to
recover known logarithmic Sobolev inequalities
Copper-catalyzed dehydrogenative borylation of terminal alkynes with pinacolborane.
LCuOTf complexes [L = cyclic (alkyl)(amino)carbenes (CAACs) or N-heterocyclic carbenes (NHCs)] selectively promote the dehydrogenative borylation of C(sp)-H bonds at room temperature. It is shown that σ,π-bis(copper) acetylide and copper hydride complexes are the key catalytic species
Flat rank of automorphism groups of buildings
The flat rank of a totally disconnected locally compact group G, denoted
flat-rk(G), is an invariant of the topological group structure of G. It is
defined thanks to a natural distance on the space of compact open subgroups of
G. For a topological Kac-Moody group G with Weyl group W, we derive the
inequalities: alg-rk(W)\le flat-rk(G)\le rk(|W|\_0). Here, alg-rk(W) is the
maximal -rank of abelian subgroups of W, and rk(|W|\_0) is the
maximal dimension of isometrically embedded flats in the CAT0-realization
|W|\_0. We can prove these inequalities under weaker assumptions. We also show
that for any integer n \geq 1 there is a topologically simple, compactly
generated, locally compact, totally disconnected group G, with flat-rk(G)=n and
which is not linear
- …