scholarly journals Facts indicate that Fermat had a simpler proof for his last theorem!

2019 ◽  
Author(s):  
Jayaram as
Keyword(s):  
Simple Proof ◽  
Present Form ◽  
Geometrical Proof

1.Fermat really had a simple proof for his last theorem. This is because, at that time, the knowledge of “elliptical curves” used for present proof was not there. So, he never had proof in its present form. The present proof is so complicated to write even in a book having a big margin!2.He never had the wrong proof.His ability of solving his previous tricky puzzles and theorems proves that he used to check very proof perfectly before telling it to his friends. In fact, he proved the above theorem for a particular case of n=4.3.His comment of “the margin of this book is insufficient to write the proof” indicates to me that it must be a geometrical proof, using some triangles.

Anyon Networks from Geometric Models of Matter

2021 ◽  
Author(s):  
Michael Atiyah ◽  
Matilde Marcolli
Keyword(s):  
Normal Bundle ◽  
Present Form ◽  
Joint Work ◽  
Geometric Models ◽  
Tensor Networks

Abstract This paper, completed in its present form by the second author after the first author passed away in 2019, describes an intended continuation of the previous joint work on anyons in geometric models of matter. This part outlines a construction of anyon tensor networks based on four-dimensional orbifold geometries and braid representations associated with surface-braids defined by multisections of the orbifold normal bundle of the surface of orbifold points.

scholarly journals Cogalois theory and drinfeld modules

2019 ◽  
Vol 19 (01) ◽  
pp. 2050001
Author(s):  
Marco Antonio Sánchez–Mirafuentes ◽  
Julio Cesar Salas–Torres ◽  
Gabriel Villa–Salvador
Keyword(s):  
Class Number ◽  
Present Form ◽  
Drinfeld Modules ◽  
Carlitz Module ◽  
Rank One

In this paper, we generalize the results of [M. Sánchez-Mirafuentes and G. Villa–Salvador, Radical extensions for the Carlitz module, J. Algebra 398 (2014) 284–302] to rank one Drinfeld modules with class number one. We show that, in the present form, there does not exist a cogalois theory for Drinfeld modules of rank or class number larger than one. We also consider the torsion of the Carlitz module for the extension [Formula: see text].

The Relief of Poverty in Mid Nineteenth-Century Colyton

Rural History ◽  
1990 ◽  
Vol 1 (2) ◽  
pp. 193-218 ◽  
Author(s):  
Jean Robin
Keyword(s):  
Nineteenth Century ◽  
Welfare State ◽  
Present Form ◽  
Poor Law ◽  
The Poor ◽  
Poor Person ◽  
The Welfare State

The welfare state emerged in 1948 when the National Assistance Act finally abolished the New Poor Law Forty-two years later, as politicians and bureaucrats struggle to keep increasing expenditure within bounds, the existence of the welfare state in its present form is under threat. Just over 150 years ago, the Old Poor Law was presenting parish ratepayers with a similar problem of rising costs, leading in 1834 to a fundamental reorganisation into the New Poor Law It may therefore be profitable to see how effective in practice the New Poor Law was when it replaced a system widely regarded as profligate, and to consider the extent to which benefits payable through the welfare state were available a hundred years or more ago.This study examines in detail how the New Poor Law, and other forms of relief, affected the whole population of the rural parish of Colyton, in south Devonshire, during the thirty years from 1851 to 1881. It will first describe the sources from which a poor person in Colyton in the mid nineteenth century could look for relief; next discuss how widespread poverty was and who the poor were; then look at what kinds of relief were available, under what conditions; and finally assess the comparative importance to the poor of the different agencies providing assistance.

scholarly journals A simple proof of Andrews’s 5 F 4 evaluation

2013 ◽  
Vol 36 (1-2) ◽  
pp. 165-170 ◽  
Author(s):  
Ira M. Gessel
Keyword(s):  
Simple Proof

A simple proof of existence of weak and statistical solutions of Navier–Stokes equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 1-11 ◽  
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Natural Number ◽  
Simple Proof ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Proofs ◽  
Statistical Solutions

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

Philippine Archaeology: Status and Prospects

1987 ◽  
Vol 18 (2) ◽  
pp. 235-249 ◽  
Author(s):  
Karl L. Hutterer
Keyword(s):  
Present Form ◽  
Historical Events ◽  
Research Practices ◽  
Future Directions ◽  
Historical Perspectives ◽  
Present Essay ◽  
History Of ◽  
Future Potential ◽  
Made In

The purpose of the present essay is not to present a history of Philippine archaeology; several preliminary attempts have been made in this regard which may be consulted. Rather, the aim of this paper is to pause for a moment and look across the landscape of Philippine archaeology to assess what has been accomplished to date, to ponder strength and weaknesses of the field at this time, and to consider future directions. Nevertheless, the shape of any landscape is the result of historical events and processes that need to be taken into account if we want to understand its present form and assess its future potential and development. Thus, it will be necessary to include in the following thoughts historical perspectives which will help to explain how and why certain concepts, methods and research practices arose in the context of Philippine archaeology and came to determine our picture of Philippine prehistory.

scholarly journals A representation theorem for the linear quasi-differential equation(py′)′+qy=0

2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Simple Proof ◽  
Representation Theorem ◽  
Second Order ◽  
Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

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