22 results
Search Results
2. Sobre funciones convexas, casi-convexas y pseudo-convexas
- Author
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J. P. Vilaplana and O. Herrero
- Subjects
Pure mathematics ,General Mathematics ,Differentiable function ,Convex function ,Convexity ,Mathematics - Abstract
In this paper, the basic properties of the convex functions are discussed, such as continuity, directional differentiability, and supportability properties. Also the relations with the quasi-convex, and pseudo-convex functiona are given. Both weaker and stronger forma of convexity are also given.
- Published
- 1980
3. Teoremas de existencia de la programacion lineal
- Author
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J. P. Vilaplana
- Subjects
Algebra ,Lemma (mathematics) ,Development (topology) ,Linear programming ,General Mathematics ,Duality (optimization) ,Mathematics ,Dual (category theory) - Abstract
One of the most important facts to solve a linear programming model is that the solutions of the primal and dual must verify some conditions so that the solution may be optimum. In this paper, the Existence and Duality Theorems of the linear programming are proved, without using the Farkas-Minkowski's Lemma . This provides a great simplification in the following theoretical development.
- Published
- 1980
4. Aproximación aleatoria de cuerpos convexos
- Author
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Fernando Affentranger
- Subjects
Combinatorics ,Convex hull ,General Mathematics ,Regular polygon ,Convex body ,Polytope ,Expected value ,Random variable ,Mean width ,Integral geometry ,Mathematics - Abstract
Problems related to the random approximation of convex bodies fall into the field of integral geometry and geometric probabilities. The aim of this paper is to give a survey of known results about the stochastic model that has received special attention in the literature and that can be described as follows: Let K be a d-dimensional convex body in Eucliden space Rd, d = 2. Denote by Hn the convex hull of n independent random points X1, ..., Xn distributed identically and uniformly in the interior of K. If f is a random variable on d-dimensional polytopes on Rd, we define the random variable fn by: fn = f (conv {X1, ..., Xn}), where conv denotes the convex hull. Typical random variables studied in the literature are numbers of vertices and facets, volume, surface area and mean width. Our main interest concerns the study of the mathematical expectation E(fn) of fn. Some further stochastic models and other problems related to random points studied in the literature will be presented.
- Published
- 1992
5. A COMPACTNESS EMBEDDING LEMMA, A PRINCIPLE OF SYMETRIC CRITICALITY AND APPLICATIONS TO ELLIPTIC PROBLEMS
- Author
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D. C. de Morais Filho, Marco A. S. Souto, and João Marcos Do O.
- Subjects
Discrete mathematics ,Sobolev space ,Lemma (mathematics) ,Compact space ,General Mathematics ,Embedding ,Symmetry (geometry) ,Subspace topology ,Sobolev inequality ,Mathematics ,Variable (mathematics) - Abstract
In this paper, we present a compactness embedding theorem of a subspace of a the Sobolev space W 1;p (R N ) into L s (R N ) spaces, formed by functions u(x;y) which are spherically symmetry with respect to Þrst variable and R a(z)juj p dz a0 > 0 if jzj i R; for a large R > 0 and such that lim jyj!1 a(x;y) = +1 uniformly for x: Moreover, we give two
- Published
- 2000
6. Sensitivity analysis in linear semi-infinite programming via partitions
- Author
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Tamás Terlaky, Miguel A. Goberna, M. I. Todorov, Universidad de Alicante. Departamento de Estadística e Investigación Operativa, Lehigh University. Department of Industrial and Systems Engineering, Universidad de las Américas Puebla. Departamento de Física y Matemáticas, and Programación Semi-infinita
- Subjects
Mathematical optimization ,Linear programming ,General Mathematics ,Regular polygon ,Linear semi-infinite programming ,Management Science and Operations Research ,Semi-infinite programming ,Computer Science Applications ,Linear-fractional programming ,Effective domain ,Optimal value function ,Bellman equation ,Estadística e Investigación Operativa ,Applied mathematics ,Partition (number theory) ,Sensitivity analysis ,Mathematics - Abstract
This paper provides sufficient conditions for the optimal value function of a given linear semi-infinite programming (LSIP) problem to depend linearly on the size of the perturbations, when these perturbations involve either the cost coefficients or the right-hand side function or both, and they are sufficiently small. Two kinds of partitions are considered. The first concerns the effective domain of the optimal value as a function of the cost coefficients and consists of maximal regions on which this value function is linear. The second class of partitions considered in this paper concerns the index set of the constraints through a suitable extension of the concept of optimal partition from ordinary to LSIP. These partitions provide convex sets, in particular, segments, on which the optimal value is a linear function of the size of the perturbations, for the three types of perturbations considered in this paper. Research of the first author was supported by MEC and FEDER, Grant MTM2005-08572-C03-01; the second author was supported by NSERC, MITACS, the Canada Research Chair Program, and a grant from Lehigh University; the third author was partially supported by CONACyT of MX.Grant 55681.
- Published
- 2009
7. Fixed points for cyclic orbital generalized contractionson complete metric spaces
- Author
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Kenan Taş, Salvador Romaguera, and Erdal Karapınar
- Subjects
Discrete mathematics ,Pure mathematics ,Cyclic generalized contraction ,General Mathematics ,Mathematics::General Topology ,Fixed-point theorem ,54e50 ,Fixed point ,Fixed-point property ,46t99 ,Complete metric space ,Metric space ,54h25 ,Schauder fixed point theorem ,QA1-939 ,Kakutani fixed-point theorem ,Brouwer fixed-point theorem ,MATEMATICA APLICADA ,47h10 ,Mathematics - Abstract
We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir–Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir–Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and Agrawal, The authors are very grateful to the referee since his/her corrections and suggestions have fairly improved the first version of the paper. Salvador Romaguera also acknowledges the support of the Spanish Ministry of Science and Technology, grant MTM2009-12872-C02-01.
- Published
- 2013
8. Central quasipolar rings
- Author
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Mete Burak Calci, Abdullah Harmanci, and Burcu Ungor
- Subjects
Discrete mathematics ,central quasipolar ring ,Pure mathematics ,Ring (mathematics) ,central clean ring ,Mathematics::Commutative Algebra ,General Mathematics ,Triangular matrix ,Local ring ,Commutative ring ,anillo casi-polar central ,Anillo casi-polar ,clean ring ,51 Matemáticas / Mathematics ,Diagonal matrix ,Dedekind cut ,Element (category theory) ,anillo limpio ,anillo limpio central ,Mathematics ,Quasipolar ring - Abstract
In this paper, we introduce a kind of quasipolarity notion for rings, namely, an element a of a ring R is called central quasipolar if there exists p² = p ∈ R such that a+p is central in R, and the ring R is called central quasipolar if every element of R is central quasipolar. We give many characterizations and investigate general properties of central quasipolar rings. We determine the conditions that some subrings of upper triangular matrix rings are central quasipolar. A diagonal matrix over a local ring is characterized in terms of being central quasipolar. We prove that the class of central quasipolar rings lies between the classes of commutative rings and Dedekind finite rings, and a ring R is central quasipolar if and only if it is central clean. Further we show that several results of quasipolar rings can be extended to central quasipolar rings in this general setting. Resumen En este trabajo, se presenta una noción de un tipo de casi-polaridad en anillos, esto es, un elemento a de un anillo R se dice casi-polar central si existe p² = p ∈ R tal que a + p es central en R, y el anillo R es llamado casi-polar central si todo elemento de R es casi-polar central. Se dan algunas caracterizaciones y se investigan propiedades generales de los anillos centrales casi-polares. Se determinan las condiciones bajo las cuales algunos subanillos de anillos de matrices triangulares superiores son casi-polares centrales. Una matriz diagonal sobre un anillo local se caracteriza en términos de ser casi-polar central. Se demuestra que la clase de anillos casi-polares centrales se encuentra dentro de la clase de los anillos conmutativos y los anillos finitos de Dedekind, y un anillo R es casi-polar central si es limpio central. Además se muestra que varios resultados de anillos casi-polares se pueden extender a anillos casi-polares centrales en un contexto general.
- Published
- 2015
9. Principal spin-bundles and triality
- Author
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Alvaro Antón Sancho
- Subjects
Triality ,Spin-principal bundles ,Subvariety ,General Mathematics ,fixed points ,SO(8) ,Outer automorphism group ,Lie group ,estabilidad ,Fixed point ,stability ,Automorphism ,Trialidad ,Moduli space ,Combinatorics ,Mathematics::Group Theory ,51 Matemáticas / Mathematics ,espacio de moduli ,triality ,Spin-fibrado principal ,moduli space ,puntos fijos ,Mathematics - Abstract
In this paper we construct a family of spin Lie groups G with an outer automorphism of order three (triality automorphism) and we describe the subgroups of fixed points for this kind of automorphisms. We will take advantage of this work to study the action of the group of outer automorphisms of G on the moduli space of principal G-bundles and describe the subvariety of fixed points in M(G) for the action of the outer automorphism of order three of G. Finally, we further study the case of Spin(8, C). Resumen En este artículo construimos una familia de grupos de Lie espinoriales G dotados de un automorfismo externo de orden tres (trialidad) y describimos los subgrupos de puntos fijos para esta clase de automorfismos. Usaremos esto para estudiar la acción del grupo de automorfismos externos de G en el espacio de moduli de G-fibrados principales y describir la subvariedad de puntos fijos en M(G) para la acción del automorfismo externo de orden tres de G. Finalmente, profundizaremos en el estudio del caso Spin(8, C).
- Published
- 2015
10. Operator-valued Fourier multipliers on toroidal Besov spaces
- Author
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Jairo Hernández Monzón, Bienvenido Barraza Martínez, and Ivan González Martínez
- Subjects
Toroid ,General Mathematics ,Operator (physics) ,Mathematical analysis ,espacios de Besov toroidales ,símbolos operador-valuados ,Multiplicadores de Fourier ,symbols.namesake ,Fourier transform ,51 Matemáticas / Mathematics ,symbols ,UMD- spaces ,Fourier multipliers ,toroidal Besov spaces ,espacios UMD ,Mathematics ,operator-valued symbols - Abstract
We prove in this paper that a sequence M: Zn → L(E) of bounded variation is a Fourier multiplier on the Besov space Bsp, q(Tn, E) for s ∈ R, 1 p ∞, 1 ≤ q ≤ ∞ and E a Banach space, if and only if E is a UMD-space. This extends the Theorem 4.2 in [3] to the n-dimensional case. As illustration of the applicability of this results we study the solvability of two abstract Cauchy problems with periodic boundary conditions. En el presente artículo se prueba que una sucesión M: Zn → L(E) de variación acotada, es un multiplicador de Fourier sobre el espacio de Besov Bsp, q(Tn, E) para s ∈ R, 1 p ∞, 1 ≤ q ≤ 1 y E un espacio de Banach, si y solo si, E es un espacio UMD. Este resultado extiende el Teorema 4.2 en [3] al caso n-dimensional. Como ilustración de la aplicabilidad de este resultado, se estudia la solubilidad de dos problemas de Cauchy abstractos con condiciones de frontera periódicas.
- Published
- 2016
11. Ecuación del calor y funciones de Morse minimales y estables en espacios proyectivos reales y complejos
- Author
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Alexander Quintero Vélez and Sebastián Muñoz Muñoz
- Subjects
Pure mathematics ,Minimal Morse function ,General Mathematics ,Heat equation ,Móetrica de Fubini-Study ,Torus ,Funcioón estable ,Fubini–Study metric ,Laplace–Beltrami operator ,Funcióon de Morse minimal ,51 Matemáticas / Mathematics ,Laplace-Beltrami operator ,Stable function ,SPHERES ,Fubini-Study metric ,Morse theory ,Mathematics ,Ecuación del calor ,Operador de Laplace-Beltrami - Abstract
Following similar results in (7) for flat tori and round spheres, in this paper is presented a proof of the fact that, for "arbitrary" initial conditions f 0 , the solution f t at time t of the heat equation on real or complex projective spaces eventually becomes (and remains) a minimal Morse function. Furthemore, it is shown that the solution becomes stable. RESUMEN Siguiendo resultados similares en (7) para toros planos y esferas redondas, en este artículo se presenta una demostración del hecho de que, para condiciones iniciales "arbitrarias" f 0 , la solución f t en el tiempo t de la ecuación del calor en espacios proyectivos reales y complejos eventualmente se convierte en (y permanece siendo) una función de Morse minimal con valores críticos distintos. Ademas, se muestra que la solucion se vuelve una función estable.
- Published
- 2017
12. On Property (Saw) and others spectral properties type Weyl-Browder theorems
- Author
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José Sanabria, Carlos Carpintero, Ennis Rosas, and Orlando García
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Operador semi-B-Fredholm ,teorema de a-Weyl ,Pure mathematics ,Property (philosophy) ,General Mathematics ,010102 general mathematics ,Spectral properties ,propiedad (Sab) ,Type (model theory) ,a-Weyl's theorem ,01 natural sciences ,property (Saw) ,010101 applied mathematics ,property (Sab) ,propiedad (Saw) ,51 Matemáticas / Mathematics ,0101 mathematics ,Semi B-Fredholm operator ,Mathematics - Abstract
An operator T acting on a Banach space X satises the property (aw) if σ(T) \ σW(T) = E0a(T), where σW (T) is the Weyl spectrum of T and E0a(T) is the set of all eigenvalues of T of finite multiplicity that are isolated in the approximate point spectrum of T. In this paper we introduce and study two new spectral properties, namely (Saw) and (Sab), in connection with Weyl-Browder type theorems. Among other results, we prove that T satisfies property (Saw) if and only if T satisfies property (aw) and σSBF-+ (T) = σW (T), where σSBF-+ (T) is the upper semi B-Weyl spectrum of T. Un operador T actuando sobre un espacio de Banach X satisface la propiedad (aw) si σ(T) \ σW(T) = E0a(T), donde σW (T) es el espectro de Weyl de T y E0a(T) es el conjunto de todos los autovalores de T de multiplicidad finita que son aislados en el espectro aproximado puntual de T. En este artículo introducimos y estudiamos dos nuevas propiedades espectrales, llamadas (Saw) y (Sab), en conexión con teoremas tipo Weyl-Browder. Entre otros resultados, mostramos que T satisface la propiedad (Saw) si y sólo si T satisface la propiedad (aw) y σSBF-+ (T) = σW (T), donde σSBF-+ (T) es el espectro superiormente semi B-Weyl de T.
- Published
- 2017
13. Solución numérica de un modelo Black-Scholes no local y no lineal por molificación discreta
- Author
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Lorena Aguirre, Harold Contreras, and Carlos D. Acosta
- Subjects
51 Matemáticas / Mathematics ,finite differences ,General Mathematics ,molificación discreta ,Non local Black-Scholes equation ,discrete mollification ,Mathematics ,Ecuación Black-Scholes no local y no lineal ,diferencias finitas - Abstract
En el presente trabajo se presenta el desarrollo numérico para un modelo Blacks-Scholes no lineal y no local utilizando los métodos de diferencias finitas, integración numérica y molificación discreta. De dicho modelo, se analizan las condiciones de estabilidad y convergencia para la discretización propuesta. In this paper, we study a nonlinear nonlocal Black-Scholes model by means of the methods of finite differences, numerical integration and discrete mollification. In this model, conditions for stability and convergence of the discretization proposed are discussed.
- Published
- 2017
14. Género y matemáticas. Colombianas pioneras en el campo de las matemáticas
- Author
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Clara Helena Sánchez-B. and Academia Colombiana de Ciencias Exactas, Físicas y Naturales
- Subjects
Historia de las matemáticas ,Matemáticas ,General Mathematics ,General Physics and Astronomy ,Gender ,General Chemistry ,General Biochemistry, Genetics and Molecular Biology ,History of Mathematics ,General Energy ,History and Philosophy of Science ,General Earth and Planetary Sciences ,Género ,General Agricultural and Biological Sciences ,Mathematics - Abstract
En este trabajo me propongo destacar a las primeras colombianas que obtuvieron un doctorado en matemáticas; para ello es relevante tener en cuenta el contexto nacional e internacional, pues revela la importancia de ese hecho. Una breve reflexión sobre las matemáticas y el género permite hallar respuestas sobre la baja representación femenina en la comunidad matemática en Colombia y en el mundo, y sobre la invisibilidad de las mujeres en este campo. In this paper, I intend to enhance the place of the first Colombian women who obtained a PhD degree in Mathematics contextualizing its importance both in the national and the international contexts. A brief discussion on the relation between gender and Mathematics allows to find answers regarding the low representation of women in the mathematical community and their invisibility in this field.
- Published
- 2017
15. A note on the controllability of linear first order systems with holomorphic initial functions in elliptic complex numbers
- Author
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Luis Gerardo Mármol and Judith Vanegas
- Subjects
Pure mathematics ,General Mathematics ,Elliptic complex numbers ,Semigrupos Fuertemente Continuos ,Holomorphic function ,Constrained null-controllability ,First order ,Strongly continuous semigroups ,Controllability ,Initial value problems ,Problemas a Valor Inicial ,51 Matemáticas / Mathematics ,Elliptic complex ,Controlabilidad restringida en el origen ,Mathematics ,Números Complejos Elípticos - Abstract
In this paper we characterize the constrained null-controllability of a large family of linear first order systems with holomorphic initial functions in a more general context of holomorphicity given by the elliptic complex numbers. Resumen: En este trabajo se caracteriza la controlabilidad restringida en el origen para una familia grande de Sistemas Lineales de Primer Orden con funciones iniciales holomorfas, en un contexto más general de holomorficidad dado por los números complejos elípticos.
- Published
- 2018
16. Mathematics teachers’ Specialized Knowledge: A Case Study about Teaching of the Basic Concepts of Function
- Author
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Nielka Rojas-González, Miguel Picado-Alfaro, Jonathan Espinoza-González, and Ariana Rodríguez-Flores
- Subjects
General Computer Science ,General Mathematics ,Funciones ,Formación de profesores ,General Physics and Astronomy ,enseñanza de las matemáticas ,General Biochemistry, Genetics and Molecular Biology ,matemáticas ,matemática ,lcsh:Science ,lcsh:Science (General) ,Secondary teachers training ,formação de docentes de secundária ,Secondary teachers ,Docente de secundária ,formación de docentes de secundaria ,mathematics ,Docente de secundaria ,General Social Sciences ,General Chemistry ,Sistemas de representación ,ensino da matemática ,Análisis didáctico ,Mathematics teaching ,General Earth and Planetary Sciences ,lcsh:Q ,General Agricultural and Biological Sciences ,Estudio de casos ,lcsh:Q1-390 - Abstract
Resumen Esta investigación enfoca el conocimiento especializado que muestra un profesor de matemática de secundaria al enseñar los conceptos básicos de función. Se enmarca en las investigaciones sobre el conocimiento matemático del profesor para la enseñanza (Hill, Ball y Schilling, 2008). Además, emplea el análisis didáctico (Gómez, 2007) para determinar indicadores que permitan identificar y caracterizar este conocimiento. Los resultados muestran la riqueza de la estructura conceptual presentada durante la enseñanza, así como un uso preciso del lenguaje matemático por parte del docente y la utilización de diversos sistemas de representación, enfatizando la relación entre ellas. Abstract This research draws its attention to the specialized knowledge a secondary school teacher of mathematics demonstrates while teaching the basic concepts of function. This paper falls within the research field of teachers’ mathematical knowledge for teaching (Hill, Ball y Schilling, 2008). In addition, it uses didactic analysis (Gómez, 2007) to determine indicators that allow the identification and the characterization of this knowledge. The results show the richness of the conceptual structure taught when teaching, as well as the precise use of the mathematical language by the teacher, and the use of diverse systems of representation that emphasize the relation between them. Resumo Esta pesquisa enfoca o conhecimento especializado que um professor de matemática da secundária mostra ensinando os conceitos básicos de função. Enquadra-se nas pesquisas sobre o conhecimento matemático do professor para o ensino (Hill, Ball e Schilling, 2008). Além disso, emprega a análise didática (Gómez, 2007) para determinar indicadores que permitam identificar e caracterizar este conhecimento. Os resultados mostram a riqueza da estrutura conceptual apresentada durante o ensino, assim como um uso preciso da linguagem matemática por parte do docente e a utilização de diversos sistemas de representação, enfatizando a relação entre elas.
- Published
- 2018
17. Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects
- Author
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Yony Raúl Santaria Leuyacc and Jorge Luis Crisostomo Parejas
- Subjects
Thesaurus (information retrieval) ,Dynamical systems theory ,General Mathematics ,010102 general mathematics ,General Engineering ,Nonlinear equations ,01 natural sciences ,Viscoelasticity ,010101 applied mathematics ,Nonlinear system ,Data storage equipment ,Attractor ,Dynamical systems ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
This paper is devoted to showing the upper semicontinuity of global attractors associated with the family of nonlinear viscoelastic equations (Formula presented.) in a three-dimensional space, for f growing up to the critical exponent and dependent on ρ ∈ [0,4), as ρ→0+. This equation models extensional vibrations of thin rods with nonlinear material density ϱ(∂tu) = |∂tu|ρ and presence of memory effects. This type of problems has been extensively studied by several authors; the existence of a global attractor with optimal regularity for each ρ ∈ [0,4) were established only recently. The proof involves the optimal regularity of the attractors combined with Hausdorff's measure. Revisado por pares
- Published
- 2019
18. On asymptotic commutativity degree of finite groups
- Author
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Rajat Kanti Nath
- Subjects
Pure mathematics ,Degree (graph theory) ,biology ,General Mathematics ,Problema ,Commutativity degree ,biology.organism_classification ,Commutative property ,Finite groups ,Mathematics - Abstract
The aim of this paper is to give a detailed account of a problema posed by P. Lescot regarding asymptotic commutativity degree of finite groups.
- Published
- 2019
19. On graded 2-classical prime submodules of graded modules over graded commutative rings
- Author
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Khaldoun Al-Zoubi and Farah Al-Turman
- Subjects
Pure mathematics ,Mathematics::Commutative Algebra ,Group (mathematics) ,Graded 2-classical prime submodule ,General Mathematics ,Mathematics::Rings and Algebras ,010103 numerical & computational mathematics ,Commutative ring ,Graded classical prime submodule ,01 natural sciences ,Prime (order theory) ,010101 applied mathematics ,Identity (mathematics) ,Graded prime submodule ,0101 mathematics ,Mathematics - Abstract
Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded 2-classical prime submodules. Various properties of graded 2-classical prime submodules are considered.
- Published
- 2019
20. El conocimiento matemático del profesor acerca de la parábola: diseño de un instrumento para investigación
- Author
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Advíncula Clemente, E., Beteta Salas, M., León Ríos, J. C., Torres Céspedes, I., Montes, M., Advincula Clemente, Elizabeth Milagro, Beteta Salas, Marisel Rocio, León Ríos, José Carlos, and Torres Céspedes, Isabel
- Subjects
teacher's knowledge ,General Computer Science ,Matemáticas ,Computer science ,General Mathematics ,purl.org/pe-repo/ocde/ford#5.03.01 [http] ,conocimiento del profesor ,General Physics and Astronomy ,Ciencias sociales / Educación ,cuestionario ,educación matemática ,mtsk ,General Biochemistry, Genetics and Molecular Biology ,conhecimento matemático ,mathematical knowledge ,Mathematics education ,parabola, questionnaire, MTSK, teacher’s knowledge ,lcsh:Science ,lcsh:Science (General) ,funções ,educação matemática ,functions ,parábola ,questionnaire ,Teaching ,conocimiento matemático ,General Social Sciences ,Profesores ,Teachers ,parábola, questionário, MTSK, conhecimento do professor ,General Chemistry ,funciones ,conhecimento do professor ,General Earth and Planetary Sciences ,lcsh:Q ,parábola, cuestionario, MTSK, conocimiento del profesor ,General Agricultural and Biological Sciences ,Mathematics ,Enseñanza ,lcsh:Q1-390 - Abstract
Resumen La investigación en Educación Matemática suele centrarse en compartir los resultados de la aplicación de instrumentos de obtención de información. Si bien dichos instrumentos suelen describirse en la sección de metodología, el proceso de su desarrollo no suele ser muy transparente para el lector. En esta investigación el objetivo es abordar dicha problemática y describir con todo detalle el proceso de generación de un cuestionario, basado en el modelo MTSK, para la exploración del conocimiento del profesor acerca de la parábola, entendida como cónica. Se presenta el diseño de un instrumento de carácter cualitativo que permite hacer una aproximación al conocimiento matemático del profesor acerca de la parábola, poniendo énfasis tanto en el uso de la teoría, como de la triangulación, interna y externa, como elementos clave en el diseño metodológico. El principal aporte fue determinar pautas para el diseño de cuestionarios basados en el modelo MTSK, las cuales pueden ser tomadas en cuenta al margen de los contenidos matemáticos. Abstract Research in mathematics education usually focuses on sharing results from the application of instruments to obtain data. Even though these instruments are usually described in the methodology section, their development process tends to not be transparent for the reader. The objective of this paper is to study this problem and describe in detail the process of creating a questionnaire based on the MTSK model, in order to explore the teacher's knowledge of parabolas, understood as conic sections. We present the design of a qualitative instrument that allows for the approximation of the teacher's mathematical knowledge of parabolas, emphasizing on the use of theory, as well as both internal and external triangulation, as key elements in the methodological design. The main contribution of this paper is to give guidelines for the design of questionnaires based on the MTSK model, which can be taken into account regardless of the mathematical contents. Resumo A pesquisa na Educação Matemática tende a estar centrada no compartilhamento dos resultados da aplicação de instrumentos de alcance de informação. Embora tais instrumentos se inclinem a estar descritos na seção de metodologia, o processo de seu desenvolvimento tende a não ser muito transparente para o leitor. Nesta pesquisa o objetivo é abordar essa problemática e descrever detalhadamente o processo de criação de um questionário, com base no modelo MTSK, para a exploração do conhecimento do professor sobre a parábola, entendida como cônica. É apresentado o desenho de um instrumento de carácter qualitativo, que permite fazer uma aproximação ao conhecimento matemático do professor sobre a parábola, colocando ênfase tanto no uso da teoria quanto da triangulação, interna e externa, como elementos-chave no desenho metodológico. A principal contribuição foi determinar pautas para o desenho de questionários baseados no modelo MTSK, que podem ser levadas em consideração independentemente dos conteúdos matemáticos.
- Published
- 2021
21. La implementación de los programas de estudio de Matemática en primaria desde la visión de la persona docente
- Author
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Mario Castillo-Sánchez, Randall Hidalgo-Mora, and Ronny Gamboa-Araya
- Subjects
Science (General) ,elementary education ,General Computer Science ,Science ,General Mathematics ,ensino fundamental ,General Physics and Astronomy ,General Biochemistry, Genetics and Molecular Biology ,matemática ,Q1-390 ,professor ,avaliação ,study programs ,programas de estudio ,docente ,programas de estudo ,metodología ,evaluation ,mathematics ,metodologia ,General Social Sciences ,methodology ,General Chemistry ,evaluación ,educación primaria ,General Earth and Planetary Sciences ,teacher ,General Agricultural and Biological Sciences - Abstract
Resumen Este artículo tiene como objetivo analizar, desde la perspectiva del personal docente de primaria, los procesos que este lleva a cabo en las aulas en los aspectos metodológicos y de evaluación en el área de Matemática, como parte del desarrollo de los programas de estudio de la disciplina. El estudio se enmarca en el enfoque mixto, con un diseño secuencial. El muestreo utilizado fue no probabilístico por conveniencia. En una primera etapa de la investigación, se encuestó a 117 docentes de educación primaria de centros educativos de Costa Rica. En la segunda etapa, se realizó una entrevista a tres docentes. Para la recolección de los datos se utilizó un cuestionario y se realizaron entrevistas semiestructuradas. Los resultados obtenidos muestran que la implementación de los programas de estudio de Matemática provocó en el personal docente cambios metodológicos y ajustes en la evaluación, pero también generó dificultades. La pizarra continúa siendo el recurso más utilizado, pero se ha diversificado el uso de otros adicionales. Hay poco uso de la tecnología y la historia de la matemática como recurso didáctico. No hay un conocimiento adecuado de los programas de estudio, se prioriza en conocimientos y no necesariamente en el desarrollo de habilidades. El personal docente posee dificultad para planificar y desarrollar actividades de resolución de problemas. Además, existe una necesidad, por parte del profesorado, de participar en procesos de formación continua en áreas como conocimientos matemáticos, estrategias metodológicas y de evaluación, uso de la tecnología, resolución de problemas, entre otras. Abstract The objective of this paper is to analyze, from the perspectives of elementary school teachers, the processes they carry out in their classrooms in terms of methodologies and evaluations used in the development of programs for the study of mathematics. A mixed approach was used in the study, which was based on a sequential design. Non-probabilistic sampling was used for convenience. In the first phase of the research, 117 elementary school teachers from schools in Costa Rica were surveyed. In the second phase, interviews were conducted with three teachers. A questionnaire was used to collect data, and semi-structured interviews were also carried out. The results obtained show that implementation of the Mathematics curriculum led to methodological changes and adjustments in the process of evaluation among the teaching staff, but also created problems. In general, the blackboard was the most used resource, but the use of additional tools has diversified. There is little use of technology and discussion of the history of mathematics as teaching resources. Knowledge of the curriculum is not adequate; priority is given to content, rather than to the development of skills. The teaching staff has difficulty in planning and developing problem-solving activities. Teachers should participate in continuous training processes in areas including mathematical knowledge, methodological and evaluation strategies, use of technology, and problem solving. Resumo Este artigo tem como objetivo analisar, a partir da perspectiva de professores do ensino fundamental, os processos realizados em sala de aula nos aspectos metodológicos e avaliativos na área da Matemática, como parte do desenvolvimento dos programas de estudos da disciplina. O estudo está enquadrado na abordagem mista, com um desenho sequencial. A amostra utilizada foi não probabilística por conveniência. Na primeira etapa da pesquisa, foram entrevistados 117 professores do ensino fundamental de centros educacionais da Costa Rica. Na segunda etapa, foi realizada uma entrevista com três professores. Para a coleta de dados, foi utilizado um questionário e realizadas entrevistas semiestruturadas. Os resultados obtidos mostram que a implementação dos programas de estudo da Matemática provocou alterações metodológicas e adequações na avaliação do corpo docente, mas também gerou dificuldades. A lousa continua sendo o recurso mais amplamente utilizado, porém, o uso de outros adicionais se diversificou. Há pouco uso da tecnologia e da história da matemática como recurso didático. Não existe um conhecimento adequado dos programas de estudo, é priorizado no conhecimento e não necessariamente no desenvolvimento de competências. O corpo docente tem dificuldade em planejar e desenvolver atividades de resolução de problemas. Além disso, há necessidade, por parte dos professores, de participarem de processos de formação contínua em áreas como conhecimento matemático, estratégias metodológicas e de avaliação, uso de tecnologia, resolução de problemas, entre outras.
- Published
- 2022
22. Statistical convergence in measure for triple sequences of fuzzy-valued functions
- Author
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Carlos Granados
- Subjects
espacio de medida ,General Mathematics ,Triple sequence ,Sucesiones triples ,Outer and inner statistical convergence ,General Physics and Astronomy ,General Chemistry ,General Biochemistry, Genetics and Molecular Biology ,Egorov’s theorem ,General Energy ,Measure space ,History and Philosophy of Science ,General Earth and Planetary Sciences ,Fuzzy-valued function ,teorema de Egorov ,General Agricultural and Biological Sciences ,funciones con valores difusos ,Mathematics ,interna y externa estadística convergence - Abstract
Resumen En este artículo, definimos y extendemos las nociones de dos tipos de convergencia en medida, estos son interna y externa estadística convergencia para sucesiones triples de funciones medibles con valores difusos. Además, mostramos que ambas sucesiones son equivalentes en un espacio de medida finita. Adicionalmente, definimos y estudiamos la noción de estadística convergencia en medida para sucesiones triples de funciones medibles con valores difusos. En adición, mostramos y probamos la versión estadística del teorema de Egorov para sucesiones triples de funciones con valores difusos sobre un espacio de medida finita. Abstract In this paper, we define and extend the notions of two kinds of convergence in measure, these are inner and outer statistical convergence for triple sequences of fuzzy-valued measurable functions. Besides, we show that both kinds of convergence are equivalent in a finite measurable space. Additionally, we define and study the notion of statistical convergence in measure for triple sequences of fuzzy-valued measurable functions. In addition, we show and prove the statistical version of Egorov’s theorem for triple sequences of fuzzy-valued functions on a finite measure space.
- Published
- 2022
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