Grid movies

2014 ◽  
Vol 23 (08) ◽  
pp. 1450038 ◽  
Author(s):  
Matthew Graham
Keyword(s):  
Planar Grid ◽  
Grid Algorithm ◽  
One To One ◽  
Definition Of

We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that grid planar isotopy classes are in one-to-one correspondence with smooth planar isotopy classes by using a new planar grid algorithm that takes a smooth knot diagram to a grid diagram. We then present generalizations of both the smooth and grid movie theorems that apply to surfaces with boundary.

scholarly journals Object-Free Definition of Categories

2013 ◽  
Vol 21 (3) ◽  
pp. 193-205
Author(s):  
Marco Riccardi
Keyword(s):  
Binary Relation ◽  
Category Theory ◽  
Final Part ◽  
One To One ◽  
Definition Of

Summary Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. In this article is proposed a new definition of an object-free category, introducing the two properties: left composable and right composable, and a simplification of the notation through a symbol, a binary relation between morphisms, that indicates whether the composition is defined. In the final part we define two functions that allow to switch from the two definitions, with and without objects, and it is shown that their composition produces isomorphic categories.

scholarly journals TIME AND TACHYON

2003 ◽  
Vol 18 (26) ◽  
pp. 4869-4888 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Canonical Quantization ◽  
Recent Analysis ◽  
Late Time ◽  
Classical Dynamics ◽  
One To One ◽  
Definition Of

Recent analysis suggests that the classical dynamics of a tachyon on an unstable D-brane is described by a scalar Born–Infeld type action with a runaway potential. The classical configurations in this theory at late time are in one to one correspondence with the configuration of a system of noninteracting (incoherent), nonrotating dust. We discuss some aspects of canonical quantization of this field theory coupled to gravity, and explore, following an earlier work on this subject, the possibility of using the scalar field (tachyon) as the definition of time in quantum cosmology. At late "time" we can identify a subsector in which the scalar field decouples from gravity and we recover the usual Wheeler–de Witt equation of quantum gravity.

scholarly journals A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Wei ◽  
Yan Qiang ◽  
Jing Zhang
Keyword(s):  
Universal Algebra ◽  
Residuated Lattices ◽  
One To One ◽  
Definition Of

The aim of this paper is to study relations between lattice-valued filters and lattice-valued congruences in residuated lattices. We introduce a new definition of congruences which just depends on the meet∧and the residuum→. Then it is shown that each of these congruences is automatically a universal-algebra-congruence. Also, lattice-valued filters and lattice-valued congruences are studied, and it is shown that there is a one-to-one correspondence between the set of all (lattice-valued) filters and the set of all (lattice-valued) congruences.

scholarly journals On asymptotic symmetries in higher dimensions for any spin

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Andrea Campoleoni ◽  
Dario Francia ◽  
Carlo Heissenberg
Keyword(s):  
Minkowski Space ◽  
Higher Dimensions ◽  
Maximal Depth ◽  
Dimensional Minkowski Space ◽  
Higher Spin ◽  
One To One ◽  
Definition Of ◽  
Celestial Sphere ◽  
Asymptotic Symmetries

Abstract We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four. For spin two we provide the counterpart of the extended BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski space. We then identify higher-spin supertranslations and generalised superrotations in any dimension. These symmetries are in one-to-one correspondence with spin-s partially-massless representations on the celestial sphere, with supertranslations corresponding in particular to the representations with maximal depth. We discuss the definition of the corresponding asymptotic charges and we exploit the supertranslational ones in order to prove the link with Weinberg’s soft theorem in even dimensions.

scholarly journals What is an alliance?

2020 ◽  
Vol 1 ◽  
pp. 139-144
Author(s):  
Wolfgang Willner
Keyword(s):  
Basic Unit ◽  
Similar Frequency ◽  
Character Species ◽  
Vegetation Surveys ◽  
One To One ◽  
The One ◽  
Definition Of ◽  
Broad Scale

The alliance is the basic unit of the EuroVegChecklist, and it often serves as the lowest rank in broad-scale vegetation surveys. However, there is hardly any literature about the concept and definition of this syntaxonomic rank, leading to uncertainty in its application. Here, I explore the original association concept of Braun-Blanquet, which was based on absolute character species, and I show that this concept is more or less identical with the units that we now call alliances. By also incorporating the concept of central syntaxa, I propose the following definition: “An alliance is a moderately broad vegetation unit that either has one or several absolute character taxa or that can be interpreted as the central alliance of an order.” The one-to-one relationship between character taxa and vegetation units gives the latter a clear biogeographical and evolutionary meaning. Restrictions to the validity of character taxa – either to certain geographical areas or to physiognomic types – cause theoretical and practical problems and should be avoided. Possible exceptions are species with similar frequency in two formations or species introduced to other continents. Taxonomic reference: Euro+Med PlantBase (http://ww2.bgbm.org/EuroPlusMed/) [accessed 1 July 2020].

scholarly journals ALGORITHMS FOR CONSTRUCTING EDGE MAGIC TOTAL LABELING OF COMPLETE BIPARTITE GRAPHS

2015 ◽  
pp. 55-58
Author(s):  
KRISHNAPPA H. K ◽  
N K. SRINATH ◽  
S. Manjunath ◽  
RAMAKANTH KUMAR P
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Bipartite Graphs ◽  
Graph Labeling ◽  
Constant Independent ◽  
Magic Square ◽  
Complete Bipartite Graphs ◽  
One To One ◽  
Definition Of

The study of graph labeling has focused on finding classes of graphs which admits a particular type of labeling. In this paper we consider a particular class of graphs which demonstrates Edge Magic Total Labeling. The class we considered here is a complete bipartite graph Km,n. There are various graph labeling techniques that generalize the idea of a magic square has been proposed earlier. The definition of a magic labeling on a graph with v vertices and e edges is a one to one map taking the vertices and edges onto the integers 1,2,3,………, v+e with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of edge. We use m x n matrix to construct edge magic total labeling of Km,n.

scholarly journals The points and diameters of quantales

2018 ◽  
Vol 16 (1) ◽  
pp. 636-645
Author(s):  
Shaohui Liang
Keyword(s):  
Spatial Quantale ◽  
One To One ◽  
Definition Of ◽  
Induced Topology ◽  
Prime Elements

AbstractIn this paper, we investigate some properties of points on quantales. It is proved that the two sided prime elements are in one to one correspondence with points. By using points of quantales, we give the concepts of p-spatial quantales, and some equivalent characterizations for P-spatial quantales are obtained. It is shown that two sided quantale Q is a spatial quantale if and only if Q is a P-spatial quantale. Based on a quantale Q, we introduce the definition of diameters. We also prove that the induced topology by diameter coincides with the topology of the point spaces.

AN AXIOMATIC DEFINITION OF FUZZY DIVERGENCE MEASURES

2008 ◽  
Vol 16 (01) ◽  
pp. 1-17 ◽  
Author(s):  
INÉS COUSO ◽  
SUSANA MONTES
Keyword(s):  
Real Number ◽  
Divergence Measure ◽  
Essential Information ◽  
Divergence Measures ◽  
Axiomatic Definition ◽  
One To One ◽  
Definition Of ◽  
Fuzzy Divergence ◽  
Fuzzy Subsets

The representation of the degree of difference between two fuzzy subsets by means of a real number has been proposed in previous papers, and it seems to be useful in some situations. However, the requirement of assigning a precise number may lead us to the loss of essential information about this difference. Thus, (crisp) divergence measures studied in previous papers may not distinguish whether the differences between two fuzzy subsets are in low or high membership degrees. In this paper we propose a way of measuring these differences by means of a fuzzy valued function which we will call fuzzy divergence measure. We formulate a list of natural axioms that these measures should satisfy. We derive additional properties from these axioms, some of them are related to the properties required to crisp divergence measures. We finish the paper by establishing a one-to-one correspondence between families of crisp and fuzzy divergence measures. This result provides us with a method to build a fuzzy divergence measure from a crisp valued one.

Normalization of Relations with Nulls in Candidate Keys

2011 ◽  
pp. 128-140
Author(s):  
George C. Philip
Keyword(s):  
Normal Form ◽  
Missing Information ◽  
Satisfactory Solution ◽  
Current Definition ◽  
One To One ◽  
Definition Of

This chapter discusses normalization of relations when the candidate keys of a relation have missing information represented by nulls. The chapter shows that problems and confusion can arise in normalizing relations with nulls in candidate keys. Candidate keys with missing information commonly are found in relations that represent information on two entities with a one-to-one relationship between them. The current definition of Boyce-Codd Normal Form (BCNF) is ineffective in identifying poor designs in such relations that may have insertion/deletion anomalies. Domain Key Normal Form (DKNF) also suffers from the same problem. It is shown that the above problem can be corrected by incorporating the concept of entity integrity rule into the definitions of BCNF and DKNF. This chapter also shows that incorporating the entity integrity rule into the definition of either a relation or a candidate key does not provide a satisfactory solution to the problem.

Matching with Transfers: Basic Notions

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Metric Spaces ◽  
Transferable Utility ◽  
Equilibrium Concept ◽  
Matching Problem ◽  
Basic Equilibrium ◽  
One To One ◽  
Definition Of ◽  
Matching Models

This chapter describes the basic notions of matching with transfers. It first introduces the notations that will be used throughout the book, including two compact, separable metric spaces: the space of female characteristics and the space of male characteristics. In particular, it outlines a framework that is common to all (bipartite, one-to-one) matching models. It then considers how a matching problem is defined in the nontransferable utility, transferable utility, and imperfectly transferable utility cases. It also explains how the solution is defined in all three cases, noting that there are differences in the definition of an equilibrium. In all cases, the basic equilibrium concept is stability.

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