Mathematical Properties of Gromov Hyperbolic Graphs

2010 ◽  
Author(s):  
Sergio Bermudo ◽  
José M. Rodríguez ◽  
José M. Sigarreta ◽  
Jean-Marie Vilaire ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Mathematical Properties ◽  
Gromov Hyperbolic ◽  
Hyperbolic Graphs

Scaled Gromov hyperbolic graphs

2007 ◽  
Vol 57 (2) ◽  
pp. 157-180 ◽  
Author(s):  
Edmond Jonckheere ◽  
Poonsuk Lohsoonthorn ◽  
Francis Bonahon
Keyword(s):  
Gromov Hyperbolic ◽  
Hyperbolic Graphs

scholarly journals Gromov hyperbolic graphs

2013 ◽  
Vol 313 (15) ◽  
pp. 1575-1585 ◽  
Author(s):  
Sergio Bermudo ◽  
José M. Rodríguez ◽  
José M. Sigarreta ◽  
Jean-Marie Vilaire
Keyword(s):  
Gromov Hyperbolic ◽  
Hyperbolic Graphs

scholarly journals Gromov hyperbolic graphs arising from iterations

2021 ◽  
Vol 389 ◽  
pp. 107908
Author(s):  
Shi-Lei Kong ◽  
Ka-Sing Lau ◽  
Xiang-Yang Wang
Keyword(s):  
Gromov Hyperbolic ◽  
Hyperbolic Graphs

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

Rotating Shallow-Water Models with Moist Convection

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Baroclinic Instability ◽  
Potential Temperature ◽  
Moist Convection ◽  
Mathematical Properties ◽  
Vertical Fluxes ◽  
Equivalent Potential ◽  
Shallow Water Models ◽  
Wave Emission ◽  
Rotating Shallow Water ◽  
Convective Fluxes

It is shown how the standard RSW can be ’augmented’ to include phase transitions of water. This chapter explains how to incorporate extra (convective) vertical fluxes in the model. By using Lagrangian conservation of equivalent potential temperature condensation of the water vapour, which is otherwise a passive tracer, is included in the model and linked to convective fluxes. Simple relaxational parameterisation of condensation permits the closure of the system, and surface evaporation can be easily included. Physical and mathematical properties of thus obtained model are explained, and illustrated on the example of wave scattering on the moisture front. The model is applied to ’moist’ baroclinic instability of jets and vortices. Condensation is shown to produce a transient increase of the growth rate. Special attention is paid to the moist instabilities of hurricane-like vortices, which are shown to enhance intensification of the hurricane, increase gravity wave emission, and generate convection-coupled waves.

scholarly journals Students’ agency, creative reasoning, and collaboration in mathematical problem solving

2021 ◽  
Author(s):  
Ellen Kristine Solbrekke Hansen
Keyword(s):  
Problem Solving ◽  
Driving Forces ◽  
Mathematical Reasoning ◽  
Mathematical Problem ◽  
Linear Functions ◽  
Shared Understanding ◽  
Interaction Patterns ◽  
Collaborative Processes ◽  
Mathematical Properties ◽  
Shared Agency

AbstractThis paper aims to give detailed insights of interactional aspects of students’ agency, reasoning, and collaboration, in their attempt to solve a linear function problem together. Four student pairs from a Norwegian upper secondary school suggested and explained ideas, tested it out, and evaluated their solution methods. The student–student interactions were studied by characterizing students’ individual mathematical reasoning, collaborative processes, and exercised agency. In the analysis, two interaction patterns emerged from the roles in how a student engaged or refrained from engaging in the collaborative work. Students’ engagement reveals aspects of how collaborative processes and mathematical reasoning co-exist with their agencies, through two ways of interacting: bi-directional interaction and one-directional interaction. Four student pairs illuminate how different roles in their collaboration are connected to shared agency or individual agency for merging knowledge together in shared understanding. In one-directional interactions, students engaged with different agencies as a primary agent, leading the conversation, making suggestions and explanations sometimes anchored in mathematical properties, or, as a secondary agent, listening and attempting to understand ideas are expressed by a peer. A secondary agent rarely reasoned mathematically. Both students attempted to collaborate, but rarely or never disagreed. The interactional pattern in bi-directional interactions highlights a mutual attempt to collaborate where both students were the driving forces of the problem-solving process. Students acted with similar roles where both were exercising a shared agency, building the final argument together by suggesting, accepting, listening, and negotiating mathematical properties. A critical variable for such a successful interaction was the collaborative process of repairing their shared understanding and reasoning anchored in mathematical properties of linear functions.

scholarly journals On monotonicity and search strategies in face-based copositivity detection algorithms

2021 ◽  
Author(s):  
B. G.-Tóth ◽  
E. M. T. Hendrix ◽  
L. G. Casado
Keyword(s):  
Research Question ◽  
Quadratic Function ◽  
Mixed Integer ◽  
Quadratic Program ◽  
Matrix Methods ◽  
Detection Algorithms ◽  
Standard Simplex ◽  
Mathematical Properties ◽  
The Face ◽  
Spatial Branch And Bound

AbstractOver the last decades, algorithms have been developed for checking copositivity of a matrix. Methods are based on several principles, such as spatial branch and bound, transformation to Mixed Integer Programming, implicit enumeration of KKT points or face-based search. Our research question focuses on exploiting the mathematical properties of the relative interior minima of the standard quadratic program (StQP) and monotonicity. We derive several theoretical properties related to convexity and monotonicity of the standard quadratic function over faces of the standard simplex. We illustrate with numerical instances up to 28 dimensions the use of monotonicity in face-based algorithms. The question is what traversal through the face graph of the standard simplex is more appropriate for which matrix instance; top down or bottom up approaches. This depends on the level of the face graph where the minimum of StQP can be found, which is related to the density of the so-called convexity graph.

Perception of Mathematical Properties of Interpersonal Relations

1958 ◽  
Vol 8 (3) ◽  
pp. 279-286 ◽  
Author(s):  
Clinton B. De Soto ◽  
James L. Kuethe
Keyword(s):  
Interpersonal Relations ◽  
Mathematical Properties

scholarly journals Mathematical Properties of Variable Topological Indices

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 43
Author(s):  
José M. Sigarreta
Keyword(s):  
Real Number ◽  
Large Class ◽  
Symmetric Functions ◽  
Topological Indices ◽  
Current Interest ◽  
Zagreb Indices ◽  
Mathematical Properties ◽  
Connectivity Indices ◽  
Optimal Bounds ◽  
New Framework

A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices Aα and Bα, defined for each graph H=(V(H),E(H)) by Aα(H)=∑ij∈E(H)f(di,dj)α and Bα(H)=∑i∈V(H)h(di)α, where di denotes the degree of the vertex i and α is any real number. Many important topological indices can be obtained from Aα and Bα by choosing appropriate symmetric functions and values of α. This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of Aα (respectively, Bα) involving Aβ (respectively, Bβ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.

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