scholarly journals A Natural Generalization of Bounded Tree-Width and Bounded Clique-Width

2014 ◽  
pp. 72-83 ◽  
Author(s):  
Martin Fürer
Keyword(s):  
Natural Generalization ◽  
Tree Width

On mappings with finite length distortion on Riemann surfaces

2019 ◽  
Vol 33 ◽  
Author(s):  
Serhii Volkov ◽  
Vladimir Ryazanov
Keyword(s):  
Finite Length ◽  
Riemann Surfaces ◽  
Boundary Behavior ◽  
Main Tool ◽  
Natural Generalization ◽  
Finite Distortion ◽  
Lipschitz Mappings ◽  
Geometric Function ◽  
Mappings With Finite Distortion ◽  
Length Distortion

The present paper is a natural continuation of our previous paper (2017) on the boundary behavior of mappings in the Sobolev classes on Riemann surfaces, where the reader will be able to find the corresponding historic comments and a discussion of many definitions and relevant results. The given paper was devoted to the theory of the boundary behavior of mappings with finite distortion by Iwaniec on Riemannian surfaces first introduced for the plane in the paper of Iwaniec T. and Sverak V. (1993) On mappings with integrable dilatation and then extended to the spatial case in the monograph of Iwaniec T. and Martin G. (2001) devoted to Geometric function theory and non-linear analysis. At the present paper, it is developed the theory of the boundary behavior of the so--called mappings with finite length distortion first introduced in the paper of Martio O., Ryazanov V., Srebro U. and Yakubov~E. (2004) in the spatial case, see also Chapter 8 in their monograph (2009) on Moduli in modern mapping theory. As it was shown in the paper of Kovtonyuk D., Petkov I. and Ryazanov V. (2017) On the boundary behavior of mappings with finite distortion in the plane, such mappings, generally speaking, are not mappings with finite distortion by Iwaniec because their first partial derivatives can be not locally integrable. At the same time, this class is a generalization of the known class of mappings with bounded distortion by Martio--Vaisala from their paper (1988). Moreover, this class contains as a subclass the so-called finitely bi-Lipschitz mappings introduced for the spatial case in the paper of Kovtonyuk D. and Ryazanov V. (2011) On the boundary behavior of generalized quasi-isometries, that in turn are a natural generalization of the well-known classes of bi-Lipschitz mappings as well as isometries and quasi-isometries. In the research of the local and boundary behavior of mappings with finite length distortion in the spatial case, the key fact was that they satisfy some modulus inequalities which was a motivation for the consideration more wide classes of mappings, in particular, the Q-homeomorphisms (2005) and the mappings with finite area distortion (2008). Hence it is natural that under the research of mappings with finite length distortion on Riemann surfaces we start from establishing the corresponding modulus inequalities that are the main tool for us. On this basis, we prove here a series of criteria in terms of dilatations for the continuous and homeomorphic extension to the boundary of the mappings with finite length distortion between domains on arbitrary Riemann surfaces.

A Relative Notion of Natural Generalization

1975 ◽  
Vol 42 (1) ◽  
pp. 46-48 ◽  
Author(s):  
Nathan Stemmer
Keyword(s):  
Natural Generalization ◽  
Relative Notion

Generalized Commutativity of Lattice-Ordered Groups

2015 ◽  
Vol 65 (2) ◽  
Author(s):  
M. R. Darnel ◽  
W. C. Holland ◽  
H. Pajoohesh
Keyword(s):  
Theorem Proving ◽  
Natural Generalization ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Weak Commutativity

AbstractIn this paper we explore generalizations of Neumann’s theorem proving that weak commutativity in ordered groups actually implies the group is abelian. We show that a natural generalization of Neumann’s weak commutativity holds for certain Scrimger ℓ-groups.

scholarly journals On polytopes and generalizations of the KLT relations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nikhil Kalyanapuram
Keyword(s):  
Scattering Amplitudes ◽  
Large Class ◽  
Moduli Space ◽  
Differential Forms ◽  
Natural Generalization ◽  
Intersection Theory ◽  
Hyperplane Arrangements ◽  
Number Of Solutions ◽  
Scalar Theories ◽  
Double Copy

Abstract We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT). To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on ℳ0, n — the moduli space of marked Riemann spheres — the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

scholarly journals Flexible models for overdispersed and underdispersed count data

2021 ◽  
Author(s):  
Dexter Cahoy ◽  
Elvira Di Nardo ◽  
Federico Polito
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Hypergeometric Functions ◽  
Natural Generalization ◽  
Model Parameters ◽  
Probability Models ◽  
Limiting Behavior ◽  
Poisson Models ◽  
Special Cases ◽  
Flexible Models

AbstractWithin the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.

scholarly journals Three-Dimensional Morphological Measurement Method for a Fruit Tree Canopy Based on Kinect Sensor Self-Calibration

Agronomy ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 741 ◽  
Author(s):  
Haihui Yang ◽  
Xiaochan Wang ◽  
Guoxiang Sun
Keyword(s):  
Intelligent Control ◽  
Point Cloud ◽  
Three Dimensional ◽  
Fruit Tree ◽  
Tree Canopy ◽  
Morphological Parameters ◽  
Kinect Sensor ◽  
Self Calibration ◽  
Morphological Measurement ◽  
Tree Width

Perception of the fruit tree canopy is a vital technology for the intelligent control of a modern standardized orchard. Due to the complex three-dimensional (3D) structure of the fruit tree canopy, morphological parameters extracted from two-dimensional (2D) or single-perspective 3D images are not comprehensive enough. Three-dimensional information from different perspectives must be combined in order to perceive the canopy information efficiently and accurately in complex orchard field environment. The algorithms used for the registration and fusion of data from different perspectives and the subsequent extraction of fruit tree canopy related parameters are the keys to the problem. This study proposed a 3D morphological measurement method for a fruit tree canopy based on Kinect sensor self-calibration, including 3D point cloud generation, point cloud registration and canopy information extraction of apple tree canopy. Using 32 apple trees (Yanfu 3 variety) morphological parameters of the height (H), maximum canopy width (W) and canopy thickness (D) were calculated. The accuracy and applicability of this method for extraction of morphological parameters were statistically analyzed. The results showed that, on both sides of the fruit trees, the average relative error (ARE) values of the morphological parameters including the fruit tree height (H), maximum tree width (W) and canopy thickness (D) between the calculated values and measured values were 3.8%, 12.7% and 5.0%, respectively, under the V1 mode; the ARE values under the V2 mode were 3.3%, 9.5% and 4.9%, respectively; and the ARE values under the V1 and V2 merged mode were 2.5%, 3.6% and 3.2%, respectively. The measurement accuracy of the tree width (W) under the double visual angle mode had a significant advantage over that under the single visual angle mode. The 3D point cloud reconstruction method based on Kinect self-calibration proposed in this study has high precision and stable performance, and the auxiliary calibration objects are readily portable and easy to install. It can be applied to different experimental scenes to extract 3D information of fruit tree canopies and has important implications to achieve the intelligent control of standardized orchards.

A system of constructor classes: overloading and implicit higher-order polymorphism

1995 ◽  
Vol 5 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Mark P. Jones
Keyword(s):  
Type System ◽  
Type Systems ◽  
Natural Generalization ◽  
Higher Order ◽  
Functional Language ◽  
Effective Algorithm ◽  
Prototype Implementation ◽  
Type Classes

AbstractThis paper describes a flexible type system that combines overloading and higher-order polymorphism in an implicitly typed language using a system of constructor classes—a natural generalization of type classes in Haskell. We present a range of examples to demonstrate the usefulness of such a system. In particular, we show how constructor classes can be used to support the use of monads in a functional language. The underlying type system permits higher-order polymorphism but retains many of the attractive features that have made Hindley/Milner type systems so popular. In particular, there is an effective algorithm that can be used to calculate principal types without the need for explicit type or kind annotations. A prototype implementation has been developed providing, amongst other things, the first concrete implementation of monad comprehensions known to us at the time of writing.

scholarly journals NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d${\mathcal N} = (2, 0)$ THEORIES

2013 ◽  
Vol 28 (03n04) ◽  
pp. 1340006 ◽  
Author(s):  
OSCAR CHACALTANA ◽  
JACQUES DISTLER ◽  
YUJI TACHIKAWA
Keyword(s):  
Lie Algebra ◽  
Young Diagram ◽  
Central Charge ◽  
Outer Automorphism ◽  
Natural Generalization ◽  
Nilpotent Orbits ◽  
Coulomb Branch ◽  
Local Properties

We study the local properties of a class of codimension-2 defects of the 6d [Formula: see text] theories of type J = A, D, E labeled by nilpotent orbits of a Lie algebra [Formula: see text], where [Formula: see text] is determined by J and the outer-automorphism twist around the defect. This class is a natural generalization of the defects of the six-dimensional (6d) theory of type SU (N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the four-dimensional (4d) central charges a and c and to the flavor central charge k.

Sign in / Sign up

Export Citation Format

Share Document