scholarly journals Double Solids, Categories and Non-Rationality

2013 ◽  
Vol 57 (1) ◽  
pp. 145-173 ◽  
Author(s):  
Atanas Iliev ◽  
Ludmil Katzarkov ◽  
Victor Przyjalkowski
Keyword(s):  
Category Theory ◽  
Mirror Symmetry ◽  
Homology Group ◽  
Hochschild Homology ◽  
Singular Points ◽  
Double Covering ◽  
Homological Mirror Symmetry ◽  
New Approach ◽  
The Third

AbstractThis paper suggests a new approach to questions of rationality of 3-folds based on category theory. Following work by Ballard et al., we enhance constructions of Kuznetsov by introducing Noether–Lefschetz spectra: an interplay between Orlov spectra and Hochschild homology. The main goal of this paper is to suggest a series of interesting examples where the above techniques might apply. We start by constructing a sextic double solid X with 35 nodes and torsion in H3(X, ℤ). This is a novelty: after the classical example of Artin and Mumford, this is the second example of a Fano 3-fold with a torsion in the third integer homology group. In particular, X is non-rational. We consider other examples as well: V10 with 10 singular points, and the double covering of a quadric ramified in an octic with 20 nodal singular points. After analysing the geometry of their Landau–Ginzburg models, we suggest a general non-rationality picture based on homological mirror symmetry and category theory.

scholarly journals How to Solve the Problem of Evil

2019 ◽  
Vol 36 (4) ◽  
pp. 442-462 ◽  
Author(s):  
Justin Mooney ◽  
Keyword(s):  
Problem Of Evil ◽  
New Approach ◽  
Gratuitous Evil ◽  
The Third ◽  
The Problem Of Evil ◽  
Argument From Evil

One paradigmatic argument from evil against theism claims that (1) if God exists, then there is no gratuitous evil. But (2) there is gratuitous evil, so (3) God does not exist. I consider three deontological strategies for resisting this argument. Each strategy restructures existing theodicies which deny (2) so that they instead deny (1). The first two strategies are problematic on their own, but their primary weaknesses vanish when they are combined to form the third strategy, resulting in a promising new approach to the problem of evil.

scholarly journals VII. A memoir on cubic surfaces

1869 ◽  
Vol 159 ◽  
pp. 231-326 ◽  
Keyword(s):  
Singular Points ◽  
Third Order ◽  
Cubic Surface ◽  
The Third ◽  
Cubic Surfaces ◽  
Present Subject

The present Memoir is based upon, and is in a measure supplementary to that by Pro­fessor Schläfli, “On the Distribution of Surfaces of the Third Order into Species, in reference to the presence or absence of Singular Points, and the reality of their Lines,” Phil. Trans, vol. cliii. (1863) pp. 193—241. But the object of the Memoir is different. I disregard altogether the ultimate division depending on the reality of the lines, attend­ing only to the division into (twenty-two, or as I prefer to reckon it) twenty-three cases depending on the nature of the singularities. And I attend to the question very much on account of the light to be obtained in reference to the theory of Reciprocal Surfaces. The memoir referred to furnishes in fact a store of materials for this purpose, inasmuch as it gives (partially or completely developed) the equations in plane-coordinates of the several cases of cubic surfaces, or, what is the same thing, the equations in point-coor­dinates of the several surfaces (orders 12 to 3) reciprocal to these repectively. I found by examination of the several cases, that an extension was required of Dr. Salmon’s theory of Reciprocal Surfaces in order to make it applicable to the present subject ; and the preceding “Memoir on the Theory of Reciprocal Surfaces” was written in connexion with these investigations on Cubic Surfaces. The latter part of the Memoir is divided into sections headed thus:— “Section I = 12, equation (X, Y, Z, W ) 3 = 0” &c. referring to the several cases of the cubic surface; but the paragraphs are numbered continuously through the Memoir. The twenty-three Cases of Cubic Surfaces—Explanations and Table of Singularities . Article Nos. 1 to 13. 1. I designate as follows the twenty-three cases of cubic surfaces, adding to each of them its equation:

scholarly journals Computing the fundamental group of a higher-rank graph

2021 ◽  
pp. 1-12
Author(s):  
Sooran Kang ◽  
David Pask ◽  
Samuel B.G. Webster
Keyword(s):  
Fundamental Group ◽  
Homology Group ◽  
Klein Bottle ◽  
Fundamental Groups ◽  
The Third ◽  
Higher Rank ◽  
The One ◽  
Standard Presentation

Abstract We compute a presentation of the fundamental group of a higher-rank graph using a coloured graph description of higher-rank graphs developed by the third author. We compute the fundamental groups of several examples from the literature. Our results fit naturally into the suite of known geometrical results about higher-rank graphs when we show that the abelianization of the fundamental group is the homology group. We end with a calculation which gives a non-standard presentation of the fundamental group of the Klein bottle to the one normally found in the literature.

scholarly journals Rehydration of Dried-Out Specimens: a New Approach

2020 ◽  
Vol 34 (1) ◽  
pp. 73-86
Author(s):  
F. Neisskenwirth
Keyword(s):  
Water Vapor ◽  
Soft Tissue ◽  
Second Step ◽  
Phosphate Solution ◽  
Glycerol Solution ◽  
New Approach ◽  
The Third ◽  
Demineralized Water ◽  
Chemically Induced

Abstract Different procedures are proposed in the literature for the rehydration of dried-out specimens. These procedures vary greatly in their efficiency and application. This work describes a new procedure that is inspired by the literature but that avoids heating the specimens. This method was applied to reconditioning dried-out specimens from a historical collection (Swiss freshwater fishes, bird brains, and bird eyes), stored at the Naturhistorisches Museum Bern in Switzerland. The procedure consists of five steps. The first step is the softening of hardened soft tissue with benzaldehyde and demineralized water. The second step is an indirect rehydration with water vapor. The third step is a chemically induced direct hydration using a trisodium phosphate solution that allows the specimen to swell in size before being washed with water to remove all additives. Finally, the rehydrated specimen is transferred into new preserving fluid. Because the dehydrating properties of ethanol as a preservative are problematic, this paper presents the results of an experimental case study using a glycerol solution as a preservation fluid.

scholarly journals Negating as turning upside down

2018 ◽  
Vol 54 (1) ◽  
pp. 115-129 ◽  
Author(s):  
Bartłomiej Skowron ◽  
Wiesław Kubiś
Keyword(s):  
Category Theory ◽  
Contravariant Functor ◽  
States Of Affairs ◽  
Truth Values ◽  
Paper Making ◽  
The Third ◽  
Entire Structure ◽  
Ontological Problem

Abstract In order to understand negation as such, at least since Aristotle’s time, there have been many ways of conceptually modelling it. In particular, negation has been studied as inconsistency, contradictoriness, falsity, cancellation, an inversion of arrangements of truth values, etc. In this paper, making substantial use of category theory, we present three more conceptual and abstract models of negation. All of them capture negation as turning upside down the entire structure under consideration. The first proposal turns upside down the structure almost literally; it is the well known construction of opposite category. The second one treats negation as a contravariant functor and the third one captures negation as adjointness. Traditionally, negation was investigated in the context of language as negation of sentences or parts of sentences, e.g. names. On the contrary we propose to negate structures globally. As a consequence of our approach we provide a solution to the ontological problem of the existence of negative states of affairs.

Puzzles: Noisy Prisoners, Manhattan Locations, and More

1987 ◽  
Vol 1 (1) ◽  
pp. 185-191 ◽  
Author(s):  
Barry Nalebuff
Keyword(s):  
Category Theory ◽  
Prisoner's Dilemma ◽  
Location Problem ◽  
Prisoner’S Dilemma ◽  
Optimal Location ◽  
The Third ◽  
Economic Interpretation ◽  
Mathematical Problems

Each “Puzzles” will begin with a few speed problems. These puzzles have answers provided in the same issue. Puzzles 1 and 2 will give you a chance to get up to speed. Then, we continue with longer puzzles taken from two very broadly defined categories: strategy puzzles and theory puzzles. Strategy puzzles will give the readers an opportunity to compete against each other in problems of coordination and competition. The third puzzle, a noisy prisoner's dilemma tournament, falls dead center in this category. Theory puzzles are meant to offer mathematical problems that have an economic interpretation. The fourth puzzle, an optimal location problem, is in this category.

scholarly journals A new approach to glycan targeting: enzyme inhibition by oligosaccharide metalloshielding

2014 ◽  
Vol 50 (31) ◽  
pp. 4056-4058 ◽  
Author(s):  
John B. Mangrum ◽  
Brigitte J. Engelmann ◽  
Erica J. Peterson ◽  
John J. Ryan ◽  
Susan J. Berners-Price ◽  
...  
Keyword(s):  
Enzyme Inhibition ◽  
Systematic Study ◽  
Coordination Compounds ◽  
Bioinorganic Chemistry ◽  
Structure And Function ◽  
New Approach ◽  
The Third ◽  
Major Class ◽  
And Function

Metalloglycomics – the effects of defined coordination compounds on oligosaccharides and their structure and function opens new areas for bioinorganic chemistry and expands its systematic study to the third major class of biomolecules after DNA/RNA and proteins.

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