Search results for " math"
showing 10 items of 11183 documents
Operators in Rigged Hilbert Spaces, Gel’fand Bases and Generalized Eigenvalues
2022
Given a self-adjoint operator A in a Hilbert space H, we analyze its spectral behavior when it is expressed in terms of generalized eigenvectors. Using the formalism of Gel’fand distribution bases, we explore the conditions for the generalized eigenspaces to be one-dimensional, i.e., for A to have a simple spectrum.
Towards a global view of dynamical systems, for the C1-topology.
2010
This paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits Diff1(M) in disjoint C1-open regions whose union is C1-dense, and conjectures state that these open set, and their complement, are characterized by the presence of • either a robust local phenomenon • or a global structure forbiding this local phenomenon. Other conjectures states that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.
8-parameter solutions of fifth order to the Johnson equation
2019
We give different representations of the solutions of the Johnson equation with parameters. First, an expression in terms of Fredholm determinants is given; we give also a representation of the solutions written as a quotient of wronskians of order 2N. These solutions of order N depend on 2N − 1 parameters. When one of these parameters tends to zero, we obtain N order rational solutions expressed as a quotient of two polyno-mials of degree 2N (N +1) in x, t and 4N (N +1) in y depending on 2N −2 parameters. Here, we explicitly construct the expressions of the rational solutions of order 5 depending on 8 real parameters and we study the patterns of their modulus in the plane (x, y) and their …
From first to fourth order rational solutions to the Boussinesq equation
2020
Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in x and t. For each positive integer N , the numerator is a polynomial of degree N (N + 1) − 2 in x and t, while the denominator is a polynomial of degree N (N + 1) in x and t. So we obtain a hierarchy of rational solutions depending on an integer N called the order of the solution. We construct explicit expressions of these rational solutions for N = 1 to 4.
Rule of the One: Avicenna, Bahmanyār, and al-Rāzī on the Argument from the Mubāḥathāt
2020
Avicenna is a strong proponent of what some of the later ones call qāʻidat al-wāḥid or ‘rule of the one’ (RO). The gist of RO states: from the one only one directly proceeds. In the secondary literature, discussion of this Avicennian rule is usually limited to a particular application of it i.e., the issue of emanation. As result, it’s not really clear what RO means, nor why Avicenna endorsed it. In this paper, I try and remedy this situation by doing two things – one on the taṣawwur front, the other on the tasdīq. First, explain just what the terms of RO amount to – that is, its subject and predicate. In doing this, I distinguish between a narrow and a broad understanding of RO, and the sh…
On overall sampling plan for small area estimation
2017
The time and budget restrictions in survey sampling can impose limits on the area sample sizes. This may reduce the possibility to obtain area-specific and population parameters estimates with adequate precision. Market research companies and institutes for producing official statistics face frequently this problem. Various models and methods for small area estimation (SAE) have been developed to solve this problem. The sample allocation must support the selected model and method to ensure efficient estimation and must be implemented in the design phase of the survey. The proposed allocation is developed by incorporating auxiliary information, a model, and an estimation method. The estimate…
The Joint Distribution Criterion and the Distance Tests for Selective Probabilistic Causality
2010
A general definition and a criterion (a necessary and sufficient condition) are formulated for an arbitrary set of external factors to selectively influence a corresponding set of random entities (generalized random variables, with values in arbitrary observation spaces), jointly distributed at every treatment (a set of factor values containing precisely one value of each factor). The random entities are selectively influenced by the corresponding factors if and only if the following condition, called the joint distribution criterion, is satisfied : there is a jointly distributed set of random entities, one entity for every value of every factor, such that every subset of this set that corr…
A black-box, general purpose quadratic self-consistent field code with and without Cholesky Decomposition of the two-electron integrals
2021
We present the implementation of a quadratically convergent self-consistent field (QCSCF) algorithm based on an adaptive trust-radius optimisation scheme for restricted open-shell Hartree���Fock (ROHF), restricted Hartree���Fock (RHF), and unrestricted Hartree���Fock (UHF) references. The algorithm can exploit Cholesky decomposition (CD) of the two-electron integrals to allow calculations on larger systems. The most important feature of the QCSCF code lies in its black-box nature ��� probably the most important quality desired by a generic user. As shown for pilot applications, it does not require one to tune the self-consistent field (SCF) parameters (damping, Pulay's DIIS, and other simil…
Diseño de un sistema de apoyo a la regulación social del aprendizaje en los xMOOC
2019
Esta investigación tiene como objetivo estudiar los procesos de regulación del aprendizaje, atendiendo tanto a su dimensión individual como social, en entornos de xMOOC. En concreto, se propone analizar cómo los procesos de autorregulación, corregulación y regulación social compartida pueden apoyarse y promoverse en este tipo de contextos abiertos y masivos para conseguir un aprendizaje más profundo. Para ello, se aplica un modelo de investigación basada en el diseño que permite intervenir directamente en la práctica pedagógica, a través de un proceso cíclico de cuatro etapas: diseño, intervención, evaluación y reflexión y rediseño de un sistema de apoyo a la regulación del aprendizaje en u…
Comparing male and female students’ self-efficacy and self-regulation skills in two undergraduate mathematics course contexts
2018
International audience; Students' efficacy beliefs have a positive influence on students' academic achievement and retention, especially for female students. These beliefs are closely linked to students' ability to regulate their learning. In this quantitative study, students' self-efficacy and self-regulation of learning are compared in two university mathematics courses that differ in content but also in their pedagogical setting: one is a more traditional lecture-based course, and the other course is taught with the Extreme Apprenticeship (XA) method. The analysis is based on the same cohort of students in the two contexts (N=91). The results suggest that students have higher self-effica…