1. Three Greek problems 2. Field extensions 3. Solution by radicals 4. Polynomials with symmetry groups.

Field theory and its classical problems, by Charles Robert Hadlock (Carus Mathematical Monograph No. 19). Pp xvi, 323. £8·80. 1979. SBN 0 88385 020 6 (Mathematical Association of America/Wiley)

We introduce equivariant Burnside groups, new invariants in equivariant birational geometry, generalizing birational symbols groups for actions of finite abelian groups, due to Kontsevich, Pestun, and the second author, and study their properties. We establish a specialization map for the equivariant birational type of a smooth algebraic variety with an action of a finite group.

Equivariant birational types and Burnside volume

We prove that if two complex affine irreducible varieties are birational (that is their coordinate rings have isomorphic fields of fractions) then their rings of differential operators are birationally equivalent. It allows to address the Noncommutative Noether’s Problem on the invariants of Weyl fields for linear actions of finite groups. In fact, we show for any field 
$${\mathsf {k}}$$

 of characteristic 0 that rationality of the quotient variety 
$${\mathbb {A}}^n({\mathsf {k}})/G$$

 implies that the Noncommutative Noether’s Problem is positively solved for G. In particular, this gives affirmative answer for all pseudo-reflections groups, for the alternating groups (
$$n=3, 4, 5$$

) and for any finite group when 
$$n=3$$

 and 
$${\mathsf {k}}$$

 is algebraically closed (covering and generalizing all previously known cases). Alternative proofs are given for the complex field and for all pseudo-reflections groups. In the later case an effective algorithm of finding the Weyl generators is described.

Noncommutative Noether’s problem vs classic Noether’s problem

On iterated extensions of number fields arising from quadratic polynomial maps

Image registration is the process of overlaying two or more images of the same scene taken at different times, from different viewpoints, and/or by different sensors. Registration is among the most fundamental operations to generate almost all data products from remotely sensed scenes. It is a challenging task due to inevitable geometric and radiometric distortions during the data acquisition process. The presence of clouds makes the problem even more complicated. This article presents the development of operational software for multitemporal and multiband image registration for KALPANA-1 and INSAT-3A at the Indian Space Research Organization (ISRO).

Image Registration for Meteorological Applications: Development of a Generalized Software for Sensor Data Registration at ISRO

book describes a constructive approach to the inverse Galois problem: Given a finite group G and a field K, determine whether there exists a Galois extension of K whose Galois group is isomorphic to G. Further, if there is such a Galois extension, find an explicit polynomial over K whose Galois group is the prescribed group G. The main theme of the book is an exposition of a family of " generic " poly-nomials for certain finite groups, which give all Galois extensions having the required group as their Galois group. The existence of such generic polyno-mials is discussed, and where they do exist, a detailed treatment of their construction is given. The book also introduces the notion of " generic dimension " to address the problem of the smallest number of parameters required by a generic polynomial. published by the press syndicate of the university of cambridge A catalogue record for this book is available from the British Library.

Generic Polynomials Constructive Aspects Of The Inverse Galois Problem

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Generic Polynomials Constructive Aspects Of The Inverse Galois Problem