Topological properties of regular generalized function algebras

We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.Comment: 6 page

New exact quasi-classical asymptotic beyond WKB approximation and beyond Maslov formal expansion

New exact quasi-classical asymptotic of solutions to th

Highly conductive Sb-doped layers in strained Si

The ability to create stable, highly conductive ultrashallow doped regions is a key requirement for future silicon-based devices. It is shown that biaxial tensile strain reduces the sheet resistance of highly doped n-type layers created by Sb or As implantation. The improvement is stronger with Sb, leading to a reversal in the relative doping efficiency of these n-type impurities. For Sb, the primary effect is a strong enhancement of activation as a function of tensile strain. At low processing temperatures, 0.7% strain more than doubles Sb activation, while enabling the formation of stable, ~10-nm-deep junctions. This makes Sb an interesting alternative to As for ultrashallow junctions in strain-engineered complementary metal-oxide-semiconductor device

The partition bundle of type A_{N-1} (2, 0) theory

Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometric data (i.e. an orientation, a spin structure, a conformal structure, and an R-symmetry bundle with connection). We discuss the nature of the object that generalizes the partition function of a more conventional quantum theory. This object takes its values in a certain complex vector space, which fits together into the total space of a complex vector bundle (the `partition bundle') as the data on the six-manifold is varied in its infinite-dimensional parameter space. In this context, an important role is played by the middle-dimensional intermediate Jacobian of the six-manifold endowed with some additional data (i.e. a symplectic structure, a quadratic form, and a complex structure). We define a certain hermitian vector bundle over this finite-dimensional parameter space. The partition bundle is then given by the pullback of the latter bundle by the map from the parameter space related to the six-manifold to the parameter space related to the intermediate Jacobian.Comment: 15 pages. Minor changes, added reference

Products of Distributions in Colombeau Algebra

The problem about product of two arbitrary distributions is one of the main problems that classical theory of distributions had came across. Many attempts have been done for overcoming this problem. The construction of the Colombeau algebra seems to be an optimal solution until now for dealing with products of distributions. Colombeau algebra is an associative, differential algebra and the space of Schwartz distributions is embedded in it. The most important feature of the Colombeau algebra is that the product of elements in it generalises the classical product of distributions, thus the classical product of two distributions, if it exists, and the new one obtained in Colombeau algebra (Colombeau product of distributions) are equal. Furthermore, in Colombeau algebra we can obtain many products of two singular distributions which in the classical theory are not defined. One of the advantages of Colombeau theory of generalized functions is that we can operate with singular distributions easily as well as with smooth functions. I will present the idea for the construction of such algebra and some examples with results about products of two singular distributions that can not be calculated in the classical theory of distributions

Distributional sources for black hole initial data

Black hole initial data is usually produced using Bowen-York type puncture initial data or by applying an excision boundary condition. The benefits of the Bowen-York initial data are the ability to specify the spin and momentum of the system as parameters of the initial data. In an attempt to extend these benefits to other formulations of the Einstein constraints, the puncture method is reformulated using distributions as source terms. It is shown how the Bowen-York puncture black hole initial data and the trumpet variation is generated by distributional sources. A heuristic argument is presented to argue that these sources are the general sources of spin and momentum. In order to clarify the meaning of other distributional sources, an exact family of initial data with generalized sources to the Hamiltonian constraint are studied; spinning trumpet black hole initial data and black hole initial data with higher order momentum sources are also studied.Comment: Code available at https://github.com/SwampWalker/LeapingMonke