Active design of tooth profiles using parabolic curve as the line of action

This paper proposes a method for the design of gear tooth profiles using parabolic curve as its line of action. A mathematical model, including the equation of the line of action, the equation of the tooth profile, and the equation of the conjugate tooth profile, is developed based on the meshing theory. The equation of undercutting condition is derived from the model. The influences of the two design parameters, that present the size (or shape) of the parabolic curve relative to the gear size, on the shape of tooth profiles and on the contact ratio are also studied through the design of an example drive. The strength, including the contact and the bending stresses, of the gear drive designed by using the proposed method is analyzed by an FEA simulation. A comparison of the above characteristics of the gear drive designed with the involute gear drive is also carried out in this work. The results confirm that the proposed design method is more flexible to control the shape of the tooth profile by changing the parameters of the parabola.

[Recueil]

S. Augustinus, De baptismo parvulorum (1-30). - S. Anselmus Cantuariensis, Epistola ad monasterium Sancti Albani super Trinitatem (30-30v). - S. Gregorius, Epistolae (30v-31). - Remigius Autissiodorensis, Tractatus in Cantica canticorum (32-58). - Alcuinus, Expositio super Ecclesiastem (58-79v). - S. Augustinus, Altercatio contra Felicianum Arriomantem de unitate Trinitatis (79v-87). - Pseudo-Augustinus, De quattuor virtutibus caritatis (87-87v). - Alcuinus, De virtutibus et vitiis (88-94).- Liber Scintillarum (94-116v). - Isidorus Hispalensis, Sententiae de exemplis sanctorum (116v-121v). - De sacramentis ecclesiae (121v-124). - Teobaldus Stapensis, Epistola ad abbatem Saloberiensem (124-124v). - S. Bernardus Claraevallensis, Parabola de conflictu civitatis Babilonie et Jerusalem (124v-132v). - S. Augustinus, De incarnatione Domini contra Judeos (132v-133), Liber de predestinatione (133-136). - Hugo de Sancto Victore, Quaestio ("De eo quod dicitur: funes ceciderunt mihi in praeclaris") (136-136v). - S. Gregorius, Regula pastoralis (136v-137v). - S. Anselmus Cantuariensis, Cur Deus homo (138-155). - Robertus Pullus, Sermo (155-156). - Elucidarium (156-173v). - Adso Dermensis, D761De Antichristo ejusque signis (173v-174). - S. Augustinus, De libero arbitrio (174v). - Anselmus Lauduniensis, Sententiae de matrimonio (174v-177). - Sententiae variae (177-181).

Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certain assumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur in the proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p. There are many statistical tests being used to check whether empirical marker data obeys the Hardy-Weinberg principle. Among these are the classical xi-square test (with or without continuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combination with Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE) are numerical in nature, requiring the computation of a test statistic and a p-value. There is however, ample space for the use of graphics in HWE tests, in particular for the ternary plot. Nowadays, many genetical studies are using genetical markers known as Single Nucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the counts one typically computes genotype frequencies and allele frequencies. These frequencies satisfy the unit-sum constraint, and their analysis therefore falls within the realm of compositional data analysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotype frequencies can be adequately represented in a ternary plot. Compositions that are in exact HWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected in a statistical test are typically “close" to the parabola, whereas compositions that differ significantly from HWE are “far". By rewriting the statistics used to test for HWE in terms of heterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted in the ternary plot. This way, compositions can be tested for HWE purely on the basis of their position in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphical representations where large numbers of SNPs can be tested for HWE in a single graph. Several examples of graphical tests for HWE (implemented in R software), will be shown, using SNP data from different human populations

Utilizaci??n did??ctica de las TIC en las Matem??ticas en 1 y 2 de la ESO

Resumen basado en la publicaci??n

Mejora de las actitudes de los alumnos de ESO en grupos de riesgo mediante el trabajo con pizarra digital interactiva y miniportátiles en geometría.

Seleccionado en la convocatoria: Ayudas a la innovación e investigación educativa en centros docentes de niveles no universitarios, Gobierno de Aragón 2010-11

Exercises B pdf

Exercises and solutions in PDF

Exercises B

Exercises and solutions in LaTex

Taller matemático de costura.

Se combinan las matemáticas y el arte de coser para llegar a ver cómo con la combinación de segmentos rectilíneos se obtiene la envolvente de ciertas figuras matemáticas como cónicas, epicicloides e hipocicloides. Las composiciones han sido hechas sobre madera con agujeros, o puntas e hilos. Se ha diseñado una página web interactiva con Geogebra con la que se pueden elegir diversos patrones y ver cómo se construyen paso a paso.

Aproximación al concepto de función primitiva : un experimento de enseñanza con applets de geometría dinámica.

Resumen tomado de la pubicación

La influencia del SGD en las estrategias de resoluci??n de los problemas de geometr??a anal??tica

Resumen basado en el de la publicaci??n

Gauss : recursos interactivos de Matemáticas : Primaria y ESO.

Resumen basado en el de la publicación

Cómo descubrir las mates y no morir en el intento! : guía de enseñanza-aprendizaje con software libre y gratuito.

Resumen basado en el de la publicación

Materiales para la enseñanza de las matemáticas con la pizarra digital interactiva.

Se incluye documentación de los dos tipos de PDIs utilizadas, así como del programa Geogebra

Actualización científica del profesorado mediante la inmersión y participación de programas científicos de ámbito internacional.

Resumen basado en el de la publicación

La par??bola de las Competencias

Bibliograf??a al final del cap??tulo