Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.

A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).

By Vyjayanthi Chari and Andrew Pressley: 651 pp., £22.95 (US$34.95), isbn 0 521 55884 0 (Cambridge University Press, 1994).

A guide to quantum groups

Volume II J. S. R. Chisholm and Rosa M. Morris Amsterdam: North-Holland. 1964 Pp. xviii + 717. Price 72s. This book is a valuable addition to an ever-growing collection of mathematical texts written expressly for the physicist. The authors suggest that the book might also be useful to undergraduates in chemistry and engineering and research workers in other fields, but the content is clearly chosen to meet the needs of modern undergraduate physics.

http://iopscience.iop.org/article/10.1088/0031-9112/16/8/015/pdf

Mathematical Methods in Physics

Basic Algebraic Geometry

https://www.ime.unicamp.br/~jardim/publicados/jgp04b.pdf

A survey on Nahm transform

We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear monads and are shown to be semistable if its rank is not too large, while semistable torsion-free sheaves satisfying certain cohomological conditions are instanton. We also study a few examples of moduli spaces of instanton sheaves.

/pdf/instanton-sheaves-on-complex-projective-spaces-3f7j0ophqf.pdf

Instanton sheaves on complex projective spaces

We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line ℂ, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to T×ℙ1. The converse statement is also true, namely a holomorphic bundle on T×ℙ1 which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton. Finally, we study the hyperkahler geometry of the moduli space of doubly-periodic instantons, and prove that the Nahm transform previously defined by the second author is a hyperkahler isometry with the moduli space of certain meromorphic Higgs bundles on the dual torus.

/pdf/asymptotic-behaviour-and-the-moduli-space-of-doubly-periodic-1c1v164dz4.pdf

Asymptotic behaviour and the moduli space of doubly-periodic instantons

A trisymplectic structure on a complex 2n-manifold is a triple of holomorphic symplectic forms such that any linear combination of these forms has rank 2n, n or 0. We show that a trisymplectic manifold is equipped with a holomorphic 3-web and the Chern connection of this 3-web is holomorphic, torsion-free, and preserves the three symplectic forms. We construct a trisymplectic structure on the moduli of regular rational curves

/pdf/trihyperkahler-reduction-and-instanton-bundles-on-22qeuoh1gh.pdf

Trihyperkähler reduction and instanton bundles on

We construct finite-energy instanton connections over ℝ4 which are periodic in two directions via an analogue of the Nahm transform for certain singular solutions of Hitchin's equations defined over a 2-torus.

/pdf/construction-of-doubly-periodic-instantons-1us3fi9v9f.pdf

Marcos Jardim

Papers

A survey on Nahm transform

Instanton sheaves on complex projective spaces

Asymptotic behaviour and the moduli space of doubly-periodic instantons

Trihyperkähler reduction and instanton bundles on

Construction of doubly-periodic instantons