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

Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.

Arithmetic duality theorems

Determine the value of the variable in each equation.

Basic Algebra = 代数学入門

/pdf/handbook-of-magma-functions-5anhrdxxj3.pdf

Handbook of magma functions

http://www.epa.gov/oppfead1/labeling/lrm/ individual chapters of the Pesticide Label Review Manual, 3rd Edition Pesticide Label Review Manual, 3rd Edition. Utilized by the EPA Office of Pesticide Programs (OPP) to improve the quality and consistency of pesticide labels. This document provides guidance on how the US EPA interprets the Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA) and its specific requirements for label language and format. Chapters include: • Precautionary labeling (including Signal Word, Personal Protective Equipment, and First Aid Statements) • Physical or Chemical Hazards • Worker Protection Labeling • Directions for Use • Labeling Claims • Storage and Disposal • Identification numbers (including EPA registration number)

Appendix A: informational sources on pesticides and health.

In this paper we consider models for genus one curves of degree n for n = 2, 3 and 4, which arise in explicit n-descent on elliptic curves. We prove theorems on the existence of minimal models with the same invariants as the minimal model of the Jacobian elliptic curve and provide simple algorithms for minimising a given model, valid over general number fields. Finally, for genus one models defined over Q, we develop a theory of reduction and again give explicit algorithms for n = 2, 3 and 4.

/pdf/minimisation-and-reduction-of-2-3-and-4-coverings-of-3tgi57kwpg.pdf

Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves

We perform descent calculations for the families of elliptic curves over Q with a rational point of order n = 5 or 7. These calculations give an estimate for the Mordell-Weil rank which we relate to the parity conjecture. We exhibit explicit elements of the Tate-Shafarevich group of order 5 and 7, and show that the 5-torsion of the Tate-Shafarevich group of an elliptic curve over Q may become arbitrarily large.

https://www.ems-ph.org/journals/show_pdf.php?issn=1435-9855&vol=3&iss=2&rank=3

Some examples of 5 and 7 descent for elliptic curves over Q

It was first pointed out by Weil that we can use classical invariant theory to compute the Jacobian of a genus one curve. The invariants required for curves of degree n=2, 3, 4 were already known to the nineteenth century invariant theorists. We have succeeded in extending these methods to curves of degree n=5, where although the invariants are too large to write down as explicit polynomials, we have found a practical algorithm for evaluating them.

/pdf/the-invariants-of-a-genus-one-curve-53ovcixfdl.pdf

The invariants of a genus one curve

This is the first in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as genus one normal curves of degree n. The methods we describe are practical in the case n = 3 for elliptic curves over the rationals, and have been implemented in MAGMA .

EXPLICIT n-DESCENT ON ELLIPTIC CURVES I. ALGEBRA

We continue our development of the invariant theory of genus one curves with the aim of computing certain twists of the universal family of elliptic curves parametrised by the modular curve X(n) for n = 2, 3, 4, 5. Our construction makes use of a covariant we call the Hessian, generalising the classical Hessian that exists in degrees 2 and 3. In particular we give explicit formulae and algorithms for computing the Hessian in degrees 4 and 5. This leads to a practical algorithm for computing equations for visible elements of order n in the Tate-Shafarevich group of an elliptic curve. Taking Jacobians we also recover the formulae of Rubin and Silverberg for families of n-congruent elliptic curves.

/pdf/the-hessian-of-a-genus-one-curve-1ptvuedddj.pdf

Tom Fisher

Papers

Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves

Some examples of 5 and 7 descent for elliptic curves over Q

The invariants of a genus one curve

EXPLICIT n-DESCENT ON ELLIPTIC CURVES I. ALGEBRA

The Hessian of a genus one curve