scholarly journals Characterization of Graphs Associated with the Ideal of Numerical Semigroups

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Peng Xu ◽  
Muhammad Ahsan Binyamin ◽  
Adnan Aslam ◽  
Wajid Ali ◽  
Hasan Mahmood ◽  
...  
Keyword(s):  
Undirected Graph ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Vertex Set ◽  
The Ideal

Let I be an ideal of a numerical semigroup Λ. We define an undirected graph GIΛ with vertex set vi:i∈Λ∖I∗=Λ∖I−0 and edge set vivj⟺i+j∈I. The aim of this article is to discuss the connectedness, girth, completeness, and some other related properties of the graph GIΛ.

scholarly journals Characterization of Graphs Associated with Numerical Semigroups

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 557 ◽  
Author(s):  
Muhammad Ahsan Binyamin ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Nida Munawar Khan ◽  
Adnan Aslam ◽  
Yongsheng Rao
Keyword(s):  
Undirected Graph ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Vertex Set

Let Γ be a numerical semigroup. We associate an undirected graph G ( Γ ) with a numerical semigroup Γ with vertex set { v i : i ∈ N \ Γ } and edge set { v i v j ⇔ i + j ∈ Γ } . In this article, we discuss the connectedness, diameter, girth, and some other related properties of the graph G ( Γ ) .

scholarly journals Numerical semigroups of small and large type

2021 ◽  
pp. 1-20
Author(s):  
Deepesh Singhal
Keyword(s):  
Numerical Semigroup ◽  
Frobenius Number ◽  
Numerical Semigroups ◽  
Natural Numbers ◽  
Type Formula ◽  
Explicit Characterization ◽  
Large Type ◽  
Number Formula ◽  
Genus Formula

A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number [Formula: see text], genus [Formula: see text] and type [Formula: see text]. It is known that for any numerical semigroup [Formula: see text]. Numerical semigroups with [Formula: see text] are called almost symmetric, we introduce a new property that characterizes them. We give an explicit characterization of numerical semigroups with [Formula: see text]. We show that for a fixed [Formula: see text] the number of numerical semigroups with Frobenius number [Formula: see text] and type [Formula: see text] is eventually constant for large [Formula: see text]. The number of numerical semigroups with genus [Formula: see text] and type [Formula: see text] is also eventually constant for large [Formula: see text].

Hamiltonian trace graph of matrices

2021 ◽  
pp. 2250001
Author(s):  
M. Sivagami ◽  
T. Tamizh Chelvam
Keyword(s):  
Positive Integer ◽  
Commutative Ring ◽  
Undirected Graph ◽  
Matrix Ring ◽  
Ideal Formula ◽  
The Matrix ◽  
Vertex Set ◽  
Matrix Formula ◽  
The Ideal

Let [Formula: see text] be a commutative ring with identity, [Formula: see text] be a positive integer and [Formula: see text] be the set of all [Formula: see text] matrices over [Formula: see text] For a matrix [Formula: see text] Tr[Formula: see text] is the trace of [Formula: see text] The trace graph of the matrix ring [Formula: see text] denoted by [Formula: see text] is the simple undirected graph with vertex set [Formula: see text][Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if Tr[Formula: see text] The ideal-based trace graph of the matrix ring [Formula: see text] with respect to an ideal [Formula: see text] of [Formula: see text] denoted by [Formula: see text] is the simple undirected graph with vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if Tr[Formula: see text] In this paper, we investigate some properties and structure of [Formula: see text] Further, it is proved that both [Formula: see text] and [Formula: see text] are Hamiltonian.

scholarly journals Zero-Divisor Graphs with respect to Ideals in Noncommutative Rings

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Shahabaddin Ebrahimi Atani ◽  
Ahmad Yousefian Darani
Keyword(s):  
Commutative Ring ◽  
Zero Divisor ◽  
Undirected Graph ◽  
Noncommutative Rings ◽  
Zero Divisor Graph ◽  
Vertex Set ◽  
Definition Of ◽  
The Ideal

Let R be a commutative ring and I an ideal of R. The zero-divisor graph of R with respect to I, denoted ΓI(R), is the undirected graph whose vertex set is {x∈R∖I|xy∈I for some y∈R∖I} with two distinct vertices x and y joined by an edge when xy∈I. In this paper, we extend the definition of the ideal-based zero-divisor graph to noncommutative rings.

scholarly journals On the star forest polytope for trees and cycles

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1773
Author(s):  
Meziane Aider ◽  
Lamia Aoudia ◽  
Mourad Baïou ◽  
A. Ridha Mahjoub ◽  
Viet Hung Nguyen
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Discrete Math ◽  
Complete Characterization ◽  
Facial Structure ◽  
Maximum Weight ◽  
Single Node ◽  
End Node ◽  
Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

The genus of graphs associated with vector spaces

2019 ◽  
Vol 19 (05) ◽  
pp. 2050086 ◽  
Author(s):  
T. Tamizh Chelvam ◽  
K. Prabha Ananthi
Keyword(s):  
Finite Field ◽  
Vector Space ◽  
Undirected Graph ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Vertex Connectivity ◽  
Dimensional Vector Space ◽  
Nonzero Component ◽  
Vertex Set ◽  
Component Graph

Let [Formula: see text] be a k-dimensional vector space over a finite field [Formula: see text] with a basis [Formula: see text]. The nonzero component graph of [Formula: see text], denoted by [Formula: see text], is a simple undirected graph with vertex set as nonzero vectors of [Formula: see text] such that there is an edge between two distinct vertices [Formula: see text] if and only if there exists at least one [Formula: see text] along which both [Formula: see text] and [Formula: see text] have nonzero scalars. In this paper, we find the vertex connectivity and girth of [Formula: see text]. We also characterize all vector spaces [Formula: see text] for which [Formula: see text] has genus either 0 or 1 or 2.

Towards 3D image-based nanocrystallography by means of transmission electron goniometry

2004 ◽  
Vol 839 ◽  
Author(s):  
Peter Moeck ◽  
Wentao Qin ◽  
Philip B. Fraundorf
Keyword(s):  
Lattice Structure ◽  
Three Dimensions ◽  
Structural Defects ◽  
Transmission Electron ◽  
Means Of Transmission ◽  
Z Contrast ◽  
Individual Nanoparticles ◽  
Nanocrystal Model ◽  
The Ideal

ABSTRACTIt is well known that the crystallographic phase and morphology of many materials changes with the crystal size in the tens of nanometer range and that many nanocrystals possess structural defects in excess of their equilibrium levels. A need to determine the ideal and real structure of individual nanoparticles, therefore, arises. High-resolution phase-contrast transmission electron microscopy (TEM) and atomic resolution Z-contrast scanning TEM (STEM) when combined with transmission electron goniometry offer the opportunity of develop dedicated methods for the crystallographic characterization of nanoparticles in three dimensions. This paper describes tilt strategies for taking data from individual nanocrystals “as found”, so as to provide information on their lattice structure and orientation, as well as on the structure and orientation of their surfaces and structural defects. Internet based java applets that facilitate the application of this technique for cubic crystals with calibrated tilt-rotation and double-tilt holders are mentioned briefly. The enhanced viability of image-based nanocrystallography in future aberration-corrected TEMs and STEMs is illustrated on a nanocrystal model system.

Gobernanza económica europea y modelo territorial de distribución del poder

2013 ◽  
pp. 153-191
Author(s):  
Ainhoa LASA LÓPEZ
Keyword(s):  
European Union ◽  
The European Union ◽  
European Level ◽  
Euro Pean ◽  
Economic Constitution ◽  
The One ◽  
The Impact ◽  
The Relationship ◽  
The Ideal

LABURPENA: Artikulu honetan, Europar Batasuneko botere-artikulazio berriak erkidegotan osatutako Espainian zer eragin daukan aztertuko dugu. Europa mailako politika-ekonomia erlazioak funtsezko bi koordenatu izan behar ditu ezinbestean. Alde batetik, Europako konstituzio-ordena ez dela gizartearen konstituzionalismoaren koordenatuetan ernatutako ordenaren berdina. Bestetik, Europako konstituzio ekonomikoa Europa bat egiteko proiektuak berarekin dakartzan aldaketa berriak gorpuzteko eremua dela. Izan ere, funtsean, Europako konstituzio ekonomikoa plataforma ezin hobea delako boterearen artikulazioa berria nola artikulatu asmatzeko, Europa guztirako. RESUMEN: el objetivo de este artículo es analizar el impacto que tiene la nueva articulación del poder en la Unión Europea en el Estado español de las autonomías. La relación política-economía a nivel europeo debe tener en cuenta dos coordenadas fundamentales. Por una parte, la consideración del orden constitucional europeo como un orden distinto al gestado bajo las coordenadas del constitucionalismo social. Por otra, la caracterización de la constitución económica europea como ámbito de materialización de las nuevas transformaciones que incorpora el proyecto de integración europeo. Fundamentalmente, porque la constitución económica europea representa la plataforma idónea desde la que dilucidar la nueva articulación del poder desde el espacio supranacional europeo. ABSTRACT: The aim of this paper is to analyse the impact of the new articula tion of power in the European Union in the Spanish state of autonomies. The relationship between politics and economy at European level must take into consideration two fundamental coordinates. On the one hand, the Euro pean constitucional system appears as a system opposite to that of social constitutionalism. Moreover, the characterization of the European economic constitution as a field of realization of the new transformations incorporated by the European project. Specially, because this represents the ideal platform in order to analyse the new articulation of power from European supranational space.

scholarly journals Percepción de los entrenadores de alto rendimiento de atletismo: caracterización de su perfil polifacético (Perception of high performance track and field coaches: characterization of their multifaceted profile)

Retos ◽  
2015 ◽  
pp. 42-47
Author(s):  
Angeles Filgueira Perez
Keyword(s):  
High Performance ◽  
Target Population ◽  
Track And Field ◽  
Personal Qualities ◽  
High Level ◽  
Almost All ◽  
Methodological Aspects ◽  
The Ideal

En el presente estudio se ha tratado de obtener una aproximación al perfil ideal del entrenador de alto rendimiento en atletismo. En el mundo del deporte de alta competición, el entrenador debe desarrollar funciones de maestro, técnico y líder, lo cual hace difícil delimitar sus competencias (conocimientos, habilidades y cualidades personales). Por tanto, la principal motivación de este trabajo es establecer el papel que debe desempeñar el entrenador para la preparación física, técnica, táctica, psicológica y moral del deportista de alto nivel. Para ello, se ha considerado como población objeto de estudio al conjunto de entrenadores de alto rendimiento que en el momento de la investigación estuviesen activo, ya que interesaba realizar este estudio desde su propia perspectiva. Los datos recogidos forman parte de una investigación más amplia, llevada a cabo mediante encuesta, para la que se diseñó un cuestionario de 78 preguntas en el que se abarcaban tres temas: el perfil del entrenador y del deportista, así como la figura del formador de entrenadores en el Practicum. En este trabajo nos centramos en el primer tema y el análisis de la información obtenida nos permite concluir que la que práctica totalidad de los entrenadores de atletismo consideran necesario dominar con precisión los aspectos técnico-metodológicos. Además, consideran que su ética profesional debe estar regida por los principios de autonomía y beneficencia, de modo que valores como la honestidad y la justicia deben primar en el desarrollo de sus funciones.Abstract: In the current study, we have tried to get an approximation of the ideal profile of high performance coaches in athletics. In the high-level sports world, the coach must develop the role of teacher, technician and leader,  which makes it difficult to delimit  his/her competencies (knowledge, skills and personal qualities). Therefore, the main motivation of this work is to define the role that the coach plays in relation  to the physical, technical, tactical, psychological and moral preparation of elite athletes. Keeping this aim as an objective, we have considered as the target population the high performance coaches who are active at the time of the investigation, since we were interested  in knowing their own perspective. The data that was collected is a part of a wider investigation, conducted by a survey, for which we designed a questionnaire of 78 questions divided on three topics: the profile of the coach and the athlete, as well as the figure of the coach educator in the Practicum. In this work, we focus on the first topic and the analysis of the information that we obtained allows us to conclude that almost all the track and field coaches find it necessary to dominate the technical and methodological aspects. They also consider that professional ethics must be governed by the principles of autonomy and care that values   like honesty and justice must prevail in the performance of their work.

scholarly journals Playing the Whack-A-Mole Game: ERK5 Activation Emerges Among the Resistance Mechanisms to RAF-MEK1/2-ERK1/2- Targeted Therapy

2021 ◽  
Vol 9 ◽  
Author(s):  
Alessandro Tubita ◽  
Ignazia Tusa ◽  
Elisabetta Rovida
Keyword(s):  
Tyrosine Kinases ◽  
Resistance Mechanism ◽  
Resistance Mechanisms ◽  
Mitogen Activated Protein Kinase ◽  
Cancer Therapies ◽  
New Era ◽  
Mitogen Activated Protein ◽  
The Impact ◽  
The Ideal

Molecularly tailored therapies have opened a new era, chronic myeloid leukemia being the ideal example, in the treatment of cancer. However, available therapeutic options are still unsatisfactory in many types of cancer, and often fail due to the occurrence of resistance mechanisms. With regard to small-molecule compounds targeting the components of the Mitogen-Activated Protein Kinase (MAPK) cascade RAF-MEK1/2-ERK1/2, these drugs may result ineffective as a consequence of the activation of compensatory pro-survival/proliferative signals, including receptor tyrosine kinases, PI3K, as well as other components of the MAPK family such as TPL2/COT. The MAPK ERK5 has been identified as a key signaling molecule in the biology of several types of cancer. In this review, we report pieces of evidence regarding the activation of the MEK5-ERK5 pathway as a resistance mechanism to RAF-MEK1/2-ERK1/2 inhibitors. We also highlight the known and possible mechanisms underlying the cross-talks between the ERK1/2 and the ERK5 pathways, the characterization of which is of great importance to maximize, in the future, the impact of RAF-MEK1/2-ERK1/2 targeting. Finally, we emphasize the need of developing additional therapeutically relevant MEK5-ERK5 inhibitors to be used for combined treatments, thus preventing the onset of resistance to cancer therapies relying on RAF-MEK1/2-ERK1/2 inhibitors.

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