Let G be a finite group and f : U ⊂ M → M a compactly fixed G-equivariant self-map of a G-manifold M ; the aim of the paper is to give an answer to the following question: if for every subgroup H ⊂ G the restricted map f : U →M can be deformed (non-equivariantly and via a compactly fixed homotopy) to be fixed point free, is it true that f can be deformed (via a compactly fixed homotopy) equivar...

 Ab initio calculations were employed to investigate nitrogen inversion as a configuration change that can supply an infinitely useful switchable control mechanism for some <span style="letter-sp...

Abstract We derive explicit formulae for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulae are important for problems of thermoand photo-acoustic tomography. A closed-form inversion formula of a filtrationbackprojection type is found for the case when the centres of the integration spheres lie ...

The problem of image reconstruction in thermoacoustic tomography requires inversion of a generalized Radon transform, which integrates the unknown function over circles in 2D or spheres in 3D. The paper investigates implementation of the recently discovered backprojection type inversion formulas for the case of spherical acquisition in 3D. A numerical simulation of the data acquisition with sub...

The forward problem of focusing light using a high numerical aperture lens can be described using the Debye-Wolf integral, however a solution to the inverse problem does not currently exist. In this work an inversion formula based on an eigenfunction representation is derived and presented which allows a field distribution in a plane in the focal region to be specified and the appropriate pupil...

A survey of the q-Lagrange inversion formula is given, including recent work of Garsia, Gessel, Hofbauer, Krattenthaler, Remmel, and Stanton. Some applications to identities of Rogers-Ramanujan type are stated.

Let An be the n’th Weyl algebra and Pm be a polynomial algebra in m variables over a field K of characteristic zero. The following characterization of the algebras {An⊗Pm} is proved: an algebra A admits a finite set δ1, . . . , δs of commuting locally nilpotent derivations with generic kernels and ∩i=1ker(δi) = K iff A ≃ An ⊗ Pm for some n and m with 2n + m = s, and vice versa. The inversion fo...

In this paper, we present concise proofs of several recently developed exact cone-beam reconstruction methods in the Tuy inversion framework, including both filtered-backprojection and backprojection-filtration formulas in the cases of standard spiral, nonstandard spiral, and more general scanning loci. While a similar proof of the Katsevich formula was previously reported, we present a new pro...

PURPOSE Gel'fand and Graev performed classical work on the inversion of integral transforms in different spaces [Gel'fand and Graev, Funct. Anal. Appl. 25(1) 1-5 (1991)]. This paper discusses their key results for further research and development. METHODS The Gel'fand-Graev inversion formula reveals a fundamental relationship between projection data and the Hilbert transform of an image to be...