Relative Morsification Theory

In this paper we develope a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known Morsification results for non-isolated singulatities and generalize them to a much wider context. We also show that deforming functions of finite codimension with respect to an ideal within the same ideal respects the Milnor fibration. Furthermore we present some applications of the theory: we introduce new numerical invariants for non-isolated singularities, which explain various aspects of the deformation of functions within an ideal; we define generalizations of the bifurcation variety in the versal unfolding of isolated singularities; applications of the theory to the topological study of the Milnor fibration of non-isolated singularities are presented. Using intersection theory in a generalized jet-space we show how to interprete the newly defined invariants as certain intersection multiplicities; finally, we characterize which invariants can be interpreted as intersection multiplicities in the above mentioned generalized jet space.Comment: 56 pages, some typos correcte

The ring compression test: Analysis of dimensions and canonical geometry

The compression ring test is universally accepted as a perfectly valid method by which determine simply and reliably the adhesion friction factor in a plastic deformation process. Its methodology is based on the application of geometric changes as both the reduction in thickness as the decrease in bore inner diameter in the strained ring itself. In this paper the performance of that test is the basis for establishing the coefficient of friction on a forging process so that, given this, its application to Upper Bound Theorem (UBT) by model Triangular Rigid Zones (TRZ), enable the establishment an intercomparison with empirical force, reaching a cuasivalidation of this Theorem in a certain range.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

The L\^e numbers of the square of a function and their applications

L\^e numbers were introduced by Massey with the purpose of numerically controlling the topological properties of families of non-isolated hypersurface singularities and describing the topology associated with a function with non-isolated singularities. They are a generalization of the Milnor number for isolated hypersurface singularities. In this note the authors investigate the composite of an arbitrary square-free f and $z^2$. They get a formula for the L\^e numbers of the composite, and consider two applications of these numbers. The first application is concerned with the extent to which the L\^e numbers are invariant in a family of functions which satisfy some equisingularity condition, the second is a quick proof of a new formula for the Euler obstruction of a hypersurface singularity. Several examples are computed using this formula including any X defined by a function which only has transverse D(q,p) singularities off the origin.Comment: 14 page

An exploration of student mentoring to motivate and to enhance interactive learning in undergraduate engineering courses

Algunos de los objetivos establecidos por las directrices de la Universidad son la promoción de la tutoría entre pares, desarrollada principalmente entre estudiantes de cursos avanzados y estudiantes de primer año. Si bien es cierto que este tipo de experiencia se difunde ampliamente en las Facultades de Pedagogía y Psicología, su implementación limitada en las Escuelas de Ingeniería no es menos cierta. Esta comunicación describe la experiencia de tutoría que se ha llevado a cabo entre los estudiantes de pregrado de tercer y segundo año para mejorar los resultados académicos de los de segundo año en la asignatura de "Automatización", incluida en el programa del segundo curso de El Grado en Tecnología de Ingeniería Industrial, todo ello basado en la experiencia adquirida por los alumnos de tercer año. Para lograr este objetivo, los mentores de los estudiantes han utilizado herramientas en línea que ya podían manejar con habilidad, como MATLAB y SIMULINK, para el aprendizaje de conceptos fundamentales de la asignatura "Automatización". Para este propósito, han propuesto tareas de aprendizaje explicativas basadas en problemas sobre ejercicios tratados en clase, asesorando a sus compañeros supervisados ​​en la mejora de su propio aprendizaje y maximizando su potencial, para así obtener las competencias necesarias antes de la evaluación general. Los datos de una encuesta de estudiantes indican la opinión positiva de los estudiantes de pregrado sobre el proceso de tutoría. De hecho, la experiencia de la mentoría realizada ha llevado a una mejor adaptación del estudiante a la materia y le ha permitido al profesor conocer las dificultades en el manejo por parte de los estudiantes de las herramientas de aprendizaje en línea. También ha demostrado una mejora en las relaciones y la comunicación entre estudiantes y profesores gracias a la función de intermediación de los estudiantes mentores.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Tax collection in Spain in the 18th century: the case of the “décima”

If we compare the Castilian fiscal system with English, French or Dutch, two basic differences are apparent: in one hand, in England, France and Holland the fiscal system was a mixture of indirect taxes and direct taxes and in the other hand, the financial revolution had been carried out in the 16th century in Castilia (central Spain), when for different reasons national short-term debt was turned into juros - or long-term debt. But the Dutch Republic in the 16th century and England by the end of 17th century and the beginning of 18th century were able to finance wars thanks to an efficient financial revolution. Traditionally, wars have been the excuse to impose new taxes or to reorganize public funds in order to obtain greater economic resources for financing the deficit originated by the war. Since most of the monarchies’ tax expenses stemmed from war, it is no surprise that the conflict known as the Jenkins´ Ear (1739) contributed to increase the deficit and fuelled a debate regarding a tax reform that would augment income and would be collected in a more egalitarian way. The Castilian tax system was based almost exclusively on indirect taxes. The taxation (alcabalas, millones, cientos, tobacco monopolies, customs…) of consumables ensured that whilst some taxes affected primarily rich consumers (for example tobacco), most taxes targeted the masses. Increasing the fiscal charge via indirect taxes seemed like an unfeasible and damaging option for trade and craftwork. This is the reason why there was an attempt to create a direct tax, similar to the Catalan cadastre. One of these attempts prior to the Marquis of the Ensenada’s cadastre was la décima. It was devised as a direct tax but its manner of collection ultimately depended on the willingness of the local cabildos.Taxation, Spain, Madrid, Indirect/Direct Taxes, 18th Century Tax Collection, War Expenses, Jenkin’s Ear War, The “Décima”

Comercial Relations Between USA and Cuba in Times of Peace and War,1803-1807

Commercial regulations of the Hispanic monarchy gave great importance to the relations between the metropolis and its colonies. In times of war, Spain was not able to supply her colonies by its own means. Her incapacity of maintaining the imperial communications forced Spanish government to open ports to the neutrals. When the war against Great Britain start in December of 1804 the Anglo-Americans didn't waste the opportunity and start to trade as neutrals according to a royal order dictated by the king. Thanks to the handwritten Balances of the port of Havana from 1803 to 1807 we can reconstruct Cuban commerce at the beginning of the XIXth Century and compare the volume of merchandises exported and imported from Havana in times of peace and war. This source also shows the importance of the North-Americans as intermediary and re-exporter. Trade links were intensifying in war times. Anglo-American trade with Cuba have been multiplied almost three times. Anglo-Americans followed the routes and guidelines that the British and the French had been practicing for years, but with different interests in commercial relations with CubaCaribbean, Spanish Empire, America, Commerce, Neutrals, Import/Export, Havana, Agriculture, Colonies.

System dynamics modelling in systems biology and applications in pharmacology

El modelado matemático de sistemas biológicos complejos es uno de los temas clave en la Biología de Sistemas y varios métodos computacionales basados ​​en la simulación computarizada han sido aplicados hasta ahora para determinar el comportamiento de los sistemas no lineales. La Dinamica de Sistemas es una metodología de modelado intuitivo basada en el razonamiento cualitativo por el cual un modelo conceptual se puede describir como un conjunto de relaciones de causa y efecto entre las variables de un sistema. A partir de esta estructura, es posible obtener un conjunto de ecuaciones dinámicas que describan cuantitativamente el comportamiento del sistema. Centrándose en los sistemas farmacológicos, el modelado compartimental a menudo se utiliza para resolver un amplio espectro de problemas relacionados con la distribución de materiales en los sistemas vivos en la investigación, el diagnóstico y la terapia en todo el cuerpo, los órganos y los niveles celulares. En este artículo presentamos la metodología de modelado de Dinámica del Sistema y su aplicación al modelado de un modelo compartimental farmacocinético-farmacodinámico del efecto de profundidad anestésica en pacientes sometidos a intervenciones quirúrgicas, derivando un modelo de simulación en el entorno de simulación orientada a objetos OpenModelica. La Dinamica de Sistemas se puede ver como una herramienta educativa poderosa y fácil de usar y en la enseñanza de Biología de Sistemas.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Resistance to the SDHI fungicides boscalid and fluopyram in Podosphaera xanthii from commercial cucurbit fields in Spain

Powdery mildew elicited by Podosphaera xanthii is a devastating disease of cucurbits worldwide and one of the most important diseases affecting these crops in Spain. Application of fungicides is the main control practice for managing P. xanthii; however, isolates resistant to multiple classes of site-specific fungicides have been recently reported in the Spanish cucurbit powdery mildew population. Succinate dehydrogenase inhibitors (SDHIs) constitute a relatively novel class of fungicides registered for powdery mildew control representing new alternatives for cucurbit growers. In the present study, 30 P. xanthii isolates were used to determine the effective concentration that reduces mycelial growth by 50% (EC50) to boscalid and fluopyram. The present study was also conducted to obtain discriminatory doses to monitor SDHI fungicide resistance in 180 P. xanthii isolates collected from several commercial cucurbit fields in Spain during 2017-2018. Three SDHI resistance patterns were observed in our population, which include patterns I (resistance to boscalid), II (resistance to fluopyram), and III (resistance to boscalid and fluopyram). The amino acid changes associated with these resistance patterns in the Sdh protein were also examined. Based on our results, SDHI fungicides are good alternatives for cucurbit powdery mildew control, although they should be applied with caution.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec