If we have a discrete spectrum of orthonormal basis vectors then the resolution of the identity is given by:

And if we have a continuous spectrum then the resolution of the identity is given by: 11 more words

If we have a discrete spectrum of orthonormal basis vectors then the resolution of the identity is given by:

And if we have a continuous spectrum then the resolution of the identity is given by: 11 more words

http://arxiv.org/abs/1511.06532

Cosmography represents an important branch of cosmology which aims to describe the universe without the need of postulating \emph{a priori} any particular cosmological model. All quantities of interest are expanded as a Taylor series around here and now, providing in principle, a way of directly matching with cosmological data. 189 more words

**4***th ***Law-***every* *objects* *tend* *to* *be* *elastic* *with* *respect* *to* *its* *rest* *position* *and* *its* *initial* *motion*…Since seventeen centuries we have learned about Newton’s Three laws of Motions. 62 more words

http://arxiv.org/abs/1511.06164

The onset of dynamo action is investigated within the context of a newly developed low Rossby, low magnetic Prandtl number, convection-driven dynamo model. The model represents an asymptotically exact form of an $\alpha^2$ mean field dynamo model in which the small-scale convection is represented explicitly by the finite amplitude, single mode convective solutions first investigated by Bassom and Zhang (Geophys.~Astrophys.~Fluid Dyn., \textbf{76}, p.223, 1994). 151 more words

In this post we will see the book *Generalized Functions in Mathematical Physics* by *V. S. Vladimirov.*

82 more words… modern mathematical physics makes extensive use of the latest attainments of mathematics, one of which is the theory of generalized functions.

A linear operator that takes the form:

Restricted to functions satisfying the boundary condition:

(note that other (less stringent) boundary conditions can be applied).

The SL eigenvalue problem is the following: 10 more words

Guest Editors for the issue are Tobias Kuna at Reading University and Sandro Vaienti at Aix-Marseille University* *– we would like to thank them for their hard work to bring the issue together. 194 more words