2,620 research outputs found
The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories
The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown
S-Lemma with Equality and Its Applications
Let and be two quadratic functions
having symmetric matrices and . The S-lemma with equality asks when the
unsolvability of the system implies the existence of a real
number such that . The
problem is much harder than the inequality version which asserts that, under
Slater condition, is unsolvable if and only if for some . In this paper, we
show that the S-lemma with equality does not hold only when the matrix has
exactly one negative eigenvalue and is a non-constant linear function
(). As an application, we can globally solve as well as the two-sided generalized trust region subproblem
without any condition. Moreover, the
convexity of the joint numerical range where is a (possibly non-convex) quadratic
function and are affine functions can be characterized
using the newly developed S-lemma with equality.Comment: 34 page
Quantum planes and quantum cylinders from Poisson homogeneous spaces
Quantum planes and a new quantum cylinder are obtained as quantization of
Poisson homogeneous spaces of two different Poisson structures on classical
Euclidean group E(2).Comment: 13 pages, plain Tex, no figure
Hessian Matrix-Based Shape Extraction and Volume Growing for 3D Polyp Segmentation in CT Colonography
Local Index Formula on the Equatorial Podles Sphere
We discuss spectral properties of the equatorial Podles sphere. As a
preparation we also study the `degenerate' (i.e. ) case (related to the
quantum disk). We consider two different spectral triples: one related to the
Fock representation of the Toeplitz algebra and the isopectral one. After the
identification of the smooth pre--algebra we compute the dimension
spectrum and residues. We check the nontriviality of the (noncommutative) Chern
character of the associated Fredholm modules by computing the pairing with the
fundamental projector of the -algebra (the nontrivial generator of the
-group) as well as the pairing with the -analogue of the Bott
projector. Finally, we show that the local index formula is trivially
satisfied.Comment: 18 pages, no figures; minor correction
Nanoengineered Curie Temperature in Laterally-Patterned Ferromagnetic Semiconductor Heterostructures
We demonstrate the manipulation of the Curie temperature of buried layers of
the ferromagnetic semiconductor (Ga,Mn)As using nanolithography to enhance the
effect of annealing. Patterning the GaAs-capped ferromagnetic layers into
nanowires exposes free surfaces at the sidewalls of the patterned (Ga,Mn)As
layers and thus allows the removal of Mn interstitials using annealing. This
leads to an enhanced Curie temperature and reduced resistivity compared to
unpatterned samples. For a fixed annealing time, the enhancement of the Curie
temperature is larger for narrower nanowires.Comment: Submitted to Applied Physics Letters (minor corrections
Operator algebra quantum homogeneous spaces of universal gauge groups
In this paper, we quantize universal gauge groups such as SU(\infty), as well
as their homogeneous spaces, in the sigma-C*-algebra setting. More precisely,
we propose concise definitions of sigma-C*-quantum groups and sigma-C*-quantum
homogeneous spaces and explain these concepts here. At the same time, we put
these definitions in the mathematical context of countably compactly generated
spaces as well as C*-compact quantum groups and homogeneous spaces. We also
study the representable K-theory of these spaces and compute it for the quantum
homogeneous spaces associated to the universal gauge group SU(\infty).Comment: 14 pages. Merged with [arXiv:1011.1073
- …