scholarly journals Self-Dual Effective Compact and True Compacton Configurations in Generalized Abelian Higgs Models

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Rodolfo Casana ◽  
Guillermo Lazar ◽  
Lucas Sourrouille
Keyword(s):  
Dielectric Function ◽  
Higgs Sector ◽  
Asymptotic Decay ◽  
And Mathematics ◽  
The One ◽  
Electrically Charged ◽  
Chern Simons ◽  
Explicit Determination

We have studied the existence of self-dual effective compact and true compacton configurations in Abelian Higgs models with generalized dynamics. We have named an effective compact solution the one whose profile behavior is very similar to the one of a compacton structure but still preserves a tail in its asymptotic decay. In particular, we have investigated the electrically neutral configurations of the Maxwell-Higgs and Born-Infeld-Higgs models and the electrically charged ones of the Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs models. The generalization of the kinetic terms is performed by means of dielectric functions in gauge and Higgs sectors. The implementation of the BPS formalism without the need to use a specific Ansatz has led us to the explicit determination for the dielectric function associated with the Higgs sector to be proportional to λϕ2λ-2, λ>1. Consequently, the followed procedure allows us to determine explicitly new families of self-dual potential for every model. We have also observed that, for sufficiently large values of λ, every model supports effective compact vortices. The true compacton solutions arising for λ=∞ are analytical. Therefore, these new self-dual structures enhance the space of BPS solutions of the Abelian Higgs models and they probably will imply interesting applications in physics and mathematics.

scholarly journals LORENTZ-SYMMETRY VIOLATION AND ELECTRICALLY CHARGED VORTICES IN THE PLANAR REGIME

2006 ◽  
Vol 21 (11) ◽  
pp. 2415-2429 ◽  
Author(s):  
H. BELICH ◽  
T. COSTA-SOARES ◽  
M. M. FERREIRA ◽  
J. A. HELAYËL-NETO ◽  
M. T. D. ORLANDO
Keyword(s):  
Lorentz Violation ◽  
Symmetry Violation ◽  
Gauge Sector ◽  
Neutral Particles ◽  
Planar Model ◽  
Vortex Solutions ◽  
The One ◽  
Electrically Charged ◽  
Chern Simons ◽  
Scalar Sector

We start from a Lorentz noninvariant Abelian-Higgs model in 1+3 dimensions, and carry out its dimensional reduction to D = 1+2. The planar model resulting thereof is composed by a Maxwell—Chern—Simons–Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background, vμ) that realizes Lorentz violation for the reduced model. Vortex-type solutions of the planar model are investigated, revealing charged vortex configurations that recover the usual Nielsen–Olesen configuration in the asymptotic regime. The Aharonov–Casher Effect in layered superconductors, that shows interference of neutral particles with a magnetic moment moving around a line charge, is also studied. Our charged vortex solutions exhibit a screened electric field that induces the same phase shift as the one caused by the charged wire.

scholarly journals Arithmetic Word Problems Revisited: Cognitive Processes and Academic Performance in Secondary School

2021 ◽  
Vol 11 (4) ◽  
pp. 155
Author(s):  
Gonzalo Duque de Blas ◽  
Isabel Gómez-Veiga ◽  
Juan A. García-Madruga
Keyword(s):  
Academic Performance ◽  
Word Problems ◽  
Spatial Reasoning ◽  
Deductive Reasoning ◽  
Executive Processes ◽  
Mathematical Operation ◽  
Visual Spatial ◽  
And Mathematics ◽  
The One ◽  
Memory Resources

Solving arithmetic word problems is a complex task that requires individuals to activate their working memory resources, as well as the correct performance of the underlying executive processes involved in order to inhibit semantic biases or superficial responses caused by the problem’s statement. This paper describes a study carried out with 135 students of Secondary Obligatory Education, each of whom solved 5 verbal arithmetic problems: 2 consistent problems, whose mathematical operation (add/subtract) and the verbal statement of the problem coincide, and 3 inconsistent problems, whose required operation is the inverse of the one suggested by the verbal term(s). Measures of reading comprehension, visual–spatial reasoning and deductive reasoning were also obtained. The results show the relationship between arithmetic problems and cognitive measures, as well as the ability of these problems to predict academic performance. Regression analyses confirmed that arithmetic word problems were the only measure with significant power of association with academic achievement in both History/Geography (β = 0.25) and Mathematics (β = 0.23).

TETRAHEDRA AND POLYNOMIAL EQUATIONS IN TOPOLOGICAL FIELD THEORY

1991 ◽  
Vol 06 (20) ◽  
pp. 3571-3598 ◽  
Author(s):  
NOUREDDINE CHAIR ◽  
CHUAN-JIE ZHU
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Fundamental Representation ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Witten Theory ◽  
Topological Field ◽  
General Program ◽  
The One ◽  
Chern Simons

Some tetrahedra in SUk(2) Chern-Simons-Witten theory are computed. The results can be used to compute an arbitrary tetrahedron inductively by fusing with the fundamental representation. The results obtained are in agreement with those of quantum groups. By associating a (finite) topological field theory (FTFT) to every rational conformal field theory (RCFT), we show that the pentagon and hexagon equations in RCFT follow directly from some skein relations in FTFT. By generalizing the operation of surgery on links in FTFT, we also derive an explicit expression for the modular transformation matrix S(k) of the one-point conformal blocks on a torus in RCFT and the equations satisfied by S(k), in agreement with those required in RCFT. The implication of our results on the general program of classifying RCFT is also discussed.

When Mathematics Teacher Educators Come Under Attack

2018 ◽  
Vol 6 (2) ◽  
pp. 68-74
Author(s):  
Rochelle Gutiérrez
Keyword(s):  
Teacher Education ◽  
Mathematics Education ◽  
Mathematics Teacher ◽  
Teacher Educators ◽  
Mathematics Teacher Education ◽  
Professional Organizations ◽  
Mathematics Teacher Educators ◽  
And Mathematics ◽  
The One ◽  
Historical Moment

We are in an interesting historical moment in mathematics teacher education. On the one and, there is greater realization within our field of the connections between systems of power and mathematics (O'Neil, 2016). We are starting to acknowledge how mathematics education can be viewed as dehumanizing for both students and teachers as well as what might constitute rehumanizing practices (Gutiérrez, in press). Our professional organizations are calling for teachers to move beyond simplistic notions of equity to understand these power dimensions and challenge the system on behalf of (and in community with) Black,1 Indigenous,2 and Latinx3 students in particular

scholarly journals Testing Economic Theory

2018 ◽  
pp. 303-313
Author(s):  
Christopher P. Guzelian
Keyword(s):  
A Priori ◽  
Number System ◽  
Physical Reality ◽  
Economic Research ◽  
Economic Knowledge ◽  
Fractional Reserve Banking ◽  
Physical Universe ◽  
And Mathematics ◽  
Reserve Banking ◽  
The One

Two years ago, Bob Mulligan and I empirically tested whether the Bank of Amsterdam, a prototypical central bank, had caused a boom-bust cycle in the Amsterdam commodities markets in the 1780s owing to the bank’s sudden initiation of low-fractional-re-serve banking (Guzelian & Mulligan 2015).1 Widespread criticism came quickly after we presented our data findings at that year’s Austrian Economic Research Conference. Walter Block representa-tively responded: «as an Austrian, I maintain you cannot «test» apodictic theories, you can only illustrate them».2 Non-Austrian, so-called «empirical» economists typically have no problem with data-driven, inductive research. But Austrians have always objected strenuously on ontological and epistemolog-ical grounds that such studies do not produce real knowledge (Mises 1998, 113-115; Mises 2007). Camps of economists are talking past each other in respective uses of the words «testing» and «eco-nomic theory». There is a vital distinction between «testing» (1) an economic proposition, praxeologically derived, and (2) the rele-vance of an economic proposition, praxeologically derived. The former is nonsensical; the latter may be necessary to acquire eco-nomic theory and knowledge. Clearing up this confusion is this note’s goal. Rothbard (1951) represents praxeology as the indispensible method for gaining economic knowledge. Starting with a Aristote-lian/Misesian axiom «humans act» or a Hayekian axiom of «humans think», a voluminous collection of logico-deductive eco-nomic propositions («theorems») follows, including theorems as sophisticated and perhaps unintuitive as the one Mulligan and I examined: low-fractional-reserve banking causes economic cycles. There is an ontological and epistemological analog between Austrian praxeology and mathematics. Much like praxeology, we «know» mathematics to be «true» because it is axiomatic and deductive. By starting with Peano Axioms, mathematicians are able by a long process of creative deduction, to establish the real number system, or that for the equation an + bn = cn, there are no integers a, b, c that satisfy the equation for any integer value of n greater than 2 (Fermat’s Last Theorem). But what do mathematicians mean when they then say they have mathematical knowledge, or that they have proven some-thing «true»? Is there an infinite set of rational numbers floating somewhere in the physical universe? Naturally no. Mathemati-cians mean that they have discovered an apodictic truth — some-thing unchangeably true without reference to physical reality because that truth is a priori.

Electron Correlation Effects on the Lattice Dynamics of Sodium and Potassium

1975 ◽  
Vol 53 (16) ◽  
pp. 1507-1512 ◽  
Author(s):  
V. K. Jindal
Keyword(s):  
Dielectric Function ◽  
Lattice Dynamics ◽  
Phonon Dispersion ◽  
Matrix Elements ◽  
Correlation Effects ◽  
Phonon Dispersion Curves ◽  
Electron Correlation Effects ◽  
Experimental Values ◽  
The One ◽  
Sodium And Potassium

The phonon dispersion curves for sodium and potassium have been calculated using the one OPW (orthogonalized plane wave) bare electron matrix elements and the dielectric function of Vashishta and Singwi. Results are compared with experimental results as well as with similar calculations using the dielectric function of Geldart and Taylor. It is found that the screening function of Vashishta and Singwi gives at least as good an agreement with experimental values as obtained from the screening function of Geldart and Taylor. The interionic potentials for these metals have also been calculated and compared with similar calculations done previously. The reason for the appreciable difference between the potentials is discussed.

Computational Thinking and Mathematics

2016 ◽  
pp. 853-865
Author(s):  
Thiago Schumacher Barcelos ◽  
Ismar Frango Silveira
Keyword(s):  
Problem Solving ◽  
Computer Science ◽  
Basic Education ◽  
National Curriculum ◽  
Computational Thinking ◽  
Thinking Skills ◽  
Educational Systems ◽  
Curriculum Guidelines ◽  
And Mathematics ◽  
The One

On the one hand, ensuring that students archive adequate levels of Mathematical knowledge by the time they finish basic education is a challenge for the educational systems in several countries. On the other hand, the pervasiveness of computer-based devices in everyday situations poses a fundamental question about Computer Science being part of those known as basic sciences. The development of Computer Science (CS) is historically related to Mathematics; however, CS is said to have singular reasoning mechanics for problem solving, whose applications go beyond the frontiers of Computing itself. These problem-solving skills have been defined as Computational Thinking skills. In this chapter, the possible relationships between Math and Computational Thinking skills are discussed in the perspective of national curriculum guidelines for Mathematics of Brazil, Chile, and United States. Three skills that can be jointly developed by both areas are identified in a literature review. Some challenges and implications for educational research and practice are also discussed.

scholarly journals Self-Esteem and Motivation for Learning in Academic Achievement: The Mediating Role of Reasoning and Verbal Fluidity

2020 ◽  
Vol 12 (14) ◽  
pp. 5768
Author(s):  
Nieves Moyano ◽  
Alberto Quílez-Robres ◽  
Alejandra Cortés Pascual
Keyword(s):  
Academic Achievement ◽  
Cognitive Abilities ◽  
Verbal Fluency ◽  
Self Esteem ◽  
Cognitive Factors ◽  
Mediating Role ◽  
Motivation For Learning ◽  
And Mathematics ◽  
The One

The goal of the present study was to analyze the joint role that non-cognitive (motivation and self-esteem) and cognitive (verbal fluency and reasoning) factors play on academic achievement, both as a global score and in relation to specific subjects, such as language and literature and mathematics. We also analyzed the mediating role of cognitive factors. We recruited a sample of 133 primary education students (aged 6–9 years old) (47.6% girls, 52.6% boys), to whom various measures of the above-indicated variables were administered. Several predictive models were tested through a mediational regression analysis. The results indicated the relevance of intrinsic motivation together with self-esteem as predictors of academic achievement mediated by the cognitive abilities verbal fluency and reasoning. These relationships differed depending on the specific subject. We discuss the educational implications of these findings and emphasize, on the one hand, that academic achievement depends on both cognitive and non-cognitive factors and, on the other hand, the malleability of cognitive factors, as they seem to improve based on motivation and self-esteem.

LOW ENERGY EFFECTIVE LAGRANGIAN FOR SUPERSYMMETRIC SEESAW MODEL

2007 ◽  
Vol 16 (05) ◽  
pp. 1437-1443
Author(s):  
AKINA KATO ◽  
TAKUYA MOROZUMI ◽  
NORIMI YOKOZAKI ◽  
SYN KYU KANG
Keyword(s):  
Neutrino Mass ◽  
Higgs Mass ◽  
Higgs Sector ◽  
Low Energy ◽  
Seesaw Model ◽  
Mass Correction ◽  
Effective Lagrangian ◽  
The One ◽  
The Right ◽  
Higgs Fields

Seesaw model is an attractive model because it may explain baryogenesis through leptogenesis and also may explain the small neutrino mass. The supersymmetric seesaw model may be more attractive because the naturalness problem is absent in supersymmetric theory. Recently, the higgs mass correction due to leptons and sleptons loops is computed.1 In this talk, we report on the preliminary results on the one loop corrections of leptons and sleptons loops to the effective action of Higgs sector for super symmetric seesaw model. Our results show that the corrections to the mass parameters for Higgs sector are proportional to the soft breaking parameters of supersymmetric seesaw model, while for the quartic couplings of Higgs fields, the corrections are suppressed by inverse powers of the right-handed neutrino mass.

Future Supply of Science and Mathematics Students

1953 ◽  
Vol 46 (4) ◽  
pp. 225-240
Author(s):  
Dael Wolfle
Keyword(s):  
Technological Progress ◽  
Direct Relationship ◽  
Mathematics Students ◽  
Men And Women ◽  
Jet Engine ◽  
Technological Advances ◽  
Future Supply ◽  
Scientists And Engineers ◽  
And Mathematics ◽  
The One

The technological advances of this country during the Twentieth Century have been made possible by a steadily increasing number of men and women engaged in engineering, the sciences, and mathematics. Without a substantial number of trained and competent workers in these fields we could not have brought the antibiotics, television, radar, the jet engine, and countless other products and processes to their high state of development. While the supply of scientists and engineers has made possible these products of research and development, those products have, in turn, created increasing demands for more scientists, more engineers, more mathematicians, and more technicians. We might go even further in exploring the relationships between technological progress on the one hand and the supply of and demand for scientists on the other. If we had adequate methods of measuring the variables involved, I suspect that we would find some kind of direct relationship between the rate at which we are experiencing technological change and the size of the resulting demand for scientists and technologists.

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