Secciones cónicas tangentes a la gráfica de una función y sus derivadas

The geometric problem of the tangent line to the graph of a function at a point P is studied within the derivative concept. The geometric problem of the tangent can be extended to other tangent curves and not only to the simplest curve (the tangent straight line). The tangent line is a specific case of a tangent conic section since a line is a degenerate conic section. Therefore a tangent conic section is a more general solution as this contains also the geometric problem of the tangent line. Here, the tangent conic sections to the graph of a function are determined. The tangent conic section contains the point P as its vertex whose tangent line is equal to the tangent line of the function at that point P. The second-degree equation of a tangent conic section is an implicitly defined function. So, the parametric equations are used to obtain the graphs and the derivatives easily. Tangent conic sections to a given point P of a function are calculated in illustrative examples.El problema geométrico de la recta tangente a la gráfica de una función en un punto P se estudia en el concepto de derivada. El problema geométrico de la tangente se puede extender a otras curvas tangentes y no solo a la curva más simple (la recta tangente). La línea tangente es un caso específico de una sección cónica tangente ya que una línea es una sección cónica degenerada. Por lo tanto, una sección cónica tangente es una solución más general, ya que también contiene el problema geométrico de la recta tangente. En este artículo, las secciones cónicas tangentes a la gráfica de una función son determinadas. La sección cónica tangente contiene el punto P como su vértice, cuya línea tangente es igual a la línea tangente de la función en ese punto P. La ecuación de segundo grado de una sección cónica tangente es una función definida implícitamente. Entonces, las ecuaciones paramétricas son usadas para obtener las gráficas y las derivadas fácilmente. Las secciones cónicas tangentes a un punto P dado de una función se calculan en ejemplos ilustrativos

Uma simples extensão do teorema de Rolle e sua relação com múltiplas taxas internas de retorno (TIR)

This paper presents a simple extension of Rolle’s Theorem. This extension allows determining the amount of numbers ξi in which f'(ξi) = 0 in a given interval, using the characteristics of the function f in that interval. The extension has been proved, and the geometric interpretation has been presented. Illustrative examples have also been developed for each case that can be obtained by applying the extension. Finally, the study examines the relation of this theorem with the problem of multiple internal rates of return (IRR).En este artículo se presenta una extensión simple del teorema de Rolle. Esta extensión permite determinar la cantidad de números ξi en los que f'(ξi) = 0 en un intervalo dado utilizando las características de la función f en ese intervalo. La extensión ha sido probada y se presenta la interpretación geométrica. Se han desarrollado ejemplos ilustrativos para cada uno de los casos que se pueden obtener aplicando la extensión. Se presenta la relación de este teorema con el problema de las múltiples tasas internas de retorno (TIR).Apresenta-se uma simples extensão do teorema de Rolle, a qual permite determinar a quantidade de Números ξi em que f'(ξi) = 0, num intervalo dado, utiliza as características da função nesse intervalo. A extensão foi testada e é apresentada a interpretação geométrica. Exemplos ilustrativos foram desenvolvidos para cada um dos casos que podem ser obtidos a partir da extensão. Além disso, é apresentada a relação desse teorema com o problema das múltiplas taxas internas de retorno

Apollonius' problem using equations of tangent circles

Secciones cónicas tangentes a la gráfica de una función son usadas para resolver el problema de Apolonio. Este artículo presenta un nuevo método para resolver este problema. El planteamiento del problema de Apolonio puede originar diez casos. Aqui, se resuelven tres casos. A saber, tres líneas (LLL), una línea y dos puntos (LPP) y tres círculos (CCC). Estas tres combinaciones consideran los tres objetos: círculo, línea y punto. La solución es similar en los otros siete casos del problema. Cuando los objetos, línea o círculo, son parte de los elementos del problema, la línea o el círculo se toman como funciones. Cuando un punto es un elemento del problema, la ecuación del círculo tangente debe contener este punto. A estas funciones se les aplican las ecuaciones de los círculos tangentes en la forma centro-radio. Dado que el desconocido círculo tangente es tangente a los otros objetos (o pasa por los eventuales puntos dados) del problema, las diferentes ecuaciones producen un sistema de ecuaciones no lineales. De la solución de este sistema de ecuaciones se puede obtener el centro-radio del círculo tangente desconocido y los puntos de tangencia.Tangent conic sections to the graph of a function are used to solve the Apollonius' problem. The statement of the Apollonius' problem can originate ten types of the problem. Here, three types are solved. Namely, three lines (LLL), one line and two points (LPP) and three circles (CCC). These three combinations consider the three objects: circle, line and point. The solution strategy is similar in the other seven cases of the problem. When the objects, line or circle, are part of the elements of the problem, the line or circle are taken as functions. The equations of the tangent circles in the form center-radius are applied to these functions. Since the unknown tangent circle is tangent to the other objects (or passes through the eventual given points) of the problem, the different equations produce a system of non-linear equations. From the solution of this system of equations can be obtained the center-radius of the unknown tangent circle and the points of tangency. When a point is an element of the problem, the equation of the (tangent) circle must contain this point

Expansionary Policy in Pandemics, a Dynamic Model Examination

The objective of this paper is to examine the issue of expansionary policies during the pandemic in Mexico. To do so, we use a dynamic model of the interaction between Covid-19 and economic output. We find that expansionary policies are desirable but that they alone cannot prevent the acceleration of the pandemic. We also model supplementary policies, especially public health policies, and find that in their presence expansionary economic policies can put the economy on track while simultaneously addressing the pandemic. Our analysis’s implications are straightforward: countercyclical economic policies are desirable when there are other supplementary policies. A limitation of our analysis is that it is circumscribed to the Mexican context. The paper is a novel contribution to the burgeoning literature on Covid-19 in Mexico because it is the first which formally examines the issue of expansionary policies during the pandemic. We conclude that both expansionary policies and supplementary policies are needed to achieve a sustainable recovery.Política expansiva en pandemia, una investigación con un modelo dinámico.El objetivo de este artículo es examinar el problema de las políticas expansivas durante la pandemia en México. Para hacer eso, usamos un modelo dinámico de la interacción entre Covid-19 y la producción económica. Encontramos que las políticas expansivas son deseables pero que, solas, no pueden prevenir la aceleración de la pandemia. También modelamos políticas suplementarias, particularmente de salud pública, y encontramos que en su presencia las políticas económicas expansivas pueden poner a la economía en buen camino mientras que simultáneamente enfrentan a la pandemia. Las implicaciones de nuestro análisis son claras: políticas contracíclicas son deseables cuando existen otras políticas suplementarias. Una limitación de nuestro análisis es que está circunscrito al contexto de la economía mexicana. El artículo es una contribución original en la floreciente literatura sobre Covid-19 en México, porque es el primero que examina formalmente el problema de las políticas expansivas durante la pandemia. Nuestra conclusión es que tanto políticas expansivas como políticas suplementarias son necesarias para lograr una recuperación sostenible

La solución del pacífico como el resultado de la secutirización de la migración por asilo en Australia entre 2001 y 2013

Actualmente, la migración internacional es vista como un fenómeno multidimensional, pero que posee un carácter humanitario, en especial, cuando se aborda desde el asilo y el refugio. Sin embargo, esta investigación sugiere que esta temática ha sido vista en los últimos años como una creciente amenaza para la seguridad de los Estados de destino. El asilo se ha ido securitizando como un asunto que vulnera la seguridad nacional del Estado, y su soberanía, haciendo necesaria una serie de medidas más drásticas para el control de los flujos de refugiados. En este orden de ideas, la investigación analiza la implementación de la ‘Solución del Pacífico’ en Australia, como el resultado de acciones securitizadoras dirigidas por el gobierno para aminorar los costos en los que se incurre al cumplir con las obligaciones internacionales con los solicitantes de asilo.Traditionally, international migration is seen as a multidimensional phenomenon, but has a humanitarian character. In particular, asylum and refuge. However, this research suggests that the topic has been seen in recent years as a growing threat to receiving countries. That is why, asylum has been securitized as a matter that violates the national security of the state and his sovereignty, making necessary a series of more drastic measures for the control of refugee flows. Therefore, the research analyzes the implementation of the Pacific Solution in Australia as the result of government-led securitization actions to reduce the costs incurred in complying with international obligations with asylum-seekers

Characterization of Defects and Designed Flaws in Metal Additive Manufacturing (AM) Parts with X-ray Computed Tomography (XCT)

Metal Additive Manufacturing (AM) has great potential to revolutionize manufacturing industries, but a reliable method to detect defects in AM-produced parts with complex internal structures must be developed prior to its widespread adoption. In this research, defects occurring in additively manufactured metal parts are characterized with X-ray Computed Tomography (XCT). In addition, the concept of metrological XCT is introduced, with the goal of providing more accurate dimensional measurements of the internal features. Preliminary experiments have been conducted toward the larger goal of evaluating XCT as a viable option for nondestructive evaluation of AM-produced components. Critical to this evaluation is the principle of the Probability of Detection (PoD), which has not been previously determined for typical AM defects using XCT. The first step in determining the PoD for XCT is to develop a suitable artifact with embedded features that are representative of the defects occurring in AM-produced parts. Two sets of samples were built by AM and their embedded defects measured by XCT. In the first set of samples, the chosen AM processing parameters were suboptimal, ensuring that defects would be present in the parts. These parameters were also varied to understand their effect on the resulting microstructure and defect formation. Measurements of porosity and the pore size distribution were determined from the XCT images. In the second set of samples, synthetic internal features were added, some approximating typical AM defects. Dimensional XCT was used to evaluate the quality of these features. Based on the results, a future experiment with the goal of estimating the PoD of critical AM defects with an XCT system is suggested

Influence of Hyrax screw position on dental movement and cortical bone : a study of finite elements

Rapid maxillary expansion (RME) has effects on the dental and periodontal structures of the parts involved, which vary according to the design and position of the expansion screw. The purpose of the study was to determine the optimal three-dimensional position of the Hyrax screw to obtain precise control of the dental movement and effect on the bone cortex using the finite element method (FEM). RME was performed from the patient whom two Cone-Beam computerized tomography scans (CBCT) were obtained: T1 before expansion, and T2 three months after stabilization of RME. The FEM model was designed with T1 and of Hyrax photographs. FEM was obtained by comparing the simulation, T2, and clinical results. Three sagittal screw positions (anterior-middle-posterior) and vertical (upper-medium-low) were evaluated. A coronal- buccal displacement of premolars and first molars was found which decreased in the occlusal-apical direction, presenting different types of dental movement in the screw positions; besides, a tendency of translational movement in the posterior-high location was observed. In the posterior-high position a higher concentration of efforts and homogeneous deformations in the periodontal ligament and vestibular cortex of the cervical area of first molars, first and second premolars were observed, with variations according to the screw position and the distribution of stresses. The ideal location of the expansion screw for controlling dental movement and periodontal side effects was the high-posterior position

Evolución Reciente del Endeudamiento Externo de los Bancos Colombianos - Junio de 2023

En este informe se describe la evolución reciente de las líneas de crédito en moneda extranjera (M/E) del sistema bancario colombiano con información a junio de 2023 y se presentan los principales resultados de la Encuesta de endeudamiento externo y cupos aplicada por el Banco de la República

Evolución Reciente del Endeudamiento Externo de los Bancos Colombianos - Marzo de 2023

En este informe se describe la evolución reciente de las líneas de crédito en moneda extranjera (M/E) del sistema bancario colombiano con información a marzo de 2023 y se presentan los principales resultados de la Encuesta de endeudamiento externo y cupos aplicada por el Banco de la República

Comparison of frictional resistance between passive self-ligating brackets and slide-type low-friction ligature brackets during the alignment and leveling stage

To compare the frictional resistance between passive self-ligating brackets and conventional brackets with low-friction ligature under bracket/archwire and root/bone interface during dental alignment and leveling. A tridimensional model of the maxilla and teeth of a patient treated with conventional brackets, and slide ligatures was generated employing the SolidWorks modeling software. SmartClip self-ligating brackets and Logic Line conventional brackets were assembled with slide low-friction ligatures, utilizing archwires with different diameters and alloys used for the alignment and leveling stage. Friction caused during the bracket/archwire interface and stress during the bone/root interface were compared through a finite element model. SmartClip and Logic Line brackets with slide elastomeric low-friction elastomeric ligature showed similar frictional stress values of 0.50 MPa and 0.64 MPa, respectively. Passive self-ligating brackets transmitted a lower load along the periodontal ligament, compared to conventional brackets with a low-friction ligature. Slide low-friction elastomeric ligatures showed frictional forces during the bracket/archwire interface similar to those of the SmartClip brackets, while the distribution of stresses and deformations during the root/bone interface were lower in the passive self-ligating brackets