Key polynomials for simple extensions of valued fields

Let $\iota:K\hookrightarrow L\cong K(x)$ be a simple transcendental extension of valued fields, where $K$ is equipped with a valuation $\nu$ of rank 1. That is, we assume given a rank 1 valuation $\nu$ of $K$ and its extension $\nu'$ to $L$. Let $(R_\nu,M_\nu,k_\nu)$ denote the valuation ring of $\nu$. The purpose of this paper is to present a refined version of MacLane's theory of key polynomials, similar to those considered by M. Vaqui\'e, and reminiscent of related objects studied by Abhyankar and Moh (approximate roots) and T.C. Kuo. Namely, we associate to $\iota$ a countable well ordered set $$\mathbf{Q}=\{Q_i\}_{i\in\Lambda}\subset K[x];$$ the $Q_i$ are called {\bf key polynomials}. Key polynomials $Q_i$ which have no immediate predecessor are called {\bf limit key polynomials}. Let $\beta_i=\nu'(Q_i)$. We give an explicit description of the limit key polynomials (which may be viewed as a generalization of the Artin--Schreier polynomials). We also give an upper bound on the order type of the set of key polynomials. Namely, we show that if $\operatorname{char}\ k_\nu=0$ then the set of key polynomials has order type at most $\omega$, while in the case $\operatorname{char}\ k_\nu=p>0$ this order type is bounded above by $\omega\times\omega$, where $\omega$ stands for the first infinite ordinal.Comment: arXiv admin note: substantial text overlap with arXiv:math/060519

Rank one discrete valuations of power series fields

In this paper we study the rank one discrete valuations of the field $k((X_1,..., X_n))$ whose center in k\lcor\X\rcor is the maximal ideal. In sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote section 2 to finding an element of value 1, that is, a parameter. The field of coefficients is the residue field of the valuation, and it is given in section 5. The constructions given in these sections are not effective in the general case, because we need either to use the Zorn's lemma or to know explicitly a section $\sigma$ of the natural homomorphism R_v\to\d between the ring and the residue field of the valuation $v$. However, as a consequence of this construction, in section 7, we prove that k((\X)) can be embedded into a field L((\Y)), where $L$ is an algebraic extension of $k$ and the {\em ``extended valuation'' is as close as possible to the usual order function}

The whole-brain pattern of magnetic susceptibility perturbations in Parkinson's disease

Although iron-mediated oxidative stress has been proposed as a potential pathomechanism in Parkinson's disease, the global distribution of iron accumulation in Parkinson's disease has not yet been elucidated. This study used a new magnetic resonance imaging contrast, quantitative susceptibility mapping, and state-of-the-art methods to map for the first time the whole-brain landscape of magnetostatic alterations as a surrogate for iron level changes in n = 25 patients with idiopathic Parkinson's disease versus n = 50 matched controls. In addition to whole-brain analysis, a regional study including sub-segmentation of the substantia nigra into dorsal and ventral regions and qualitative assessment of susceptibility maps in single subjects were also performed. The most remarkable basal ganglia effect was an apparent magnetic susceptibility increase-consistent with iron deposition-in the dorsal substantia nigra, though an effect was also observed in ventral regions. Increased bulk susceptibility, additionally, was detected in rostral pontine areas and in a cortical pattern tightly concordant with known Parkinson's disease distributions of α-synuclein pathology. In contrast, the normally iron-rich cerebellar dentate nucleus returned a susceptibility reduction suggesting decreased iron content. These results are in agreement with previous post-mortem studies in which iron content was evaluated in specific regions of interest; however, extensive neocortical and cerebellar changes constitute a far more complex pattern of iron dysregulation than was anticipated. Such findings also stand in stark contrast to the lack of statistically significant group change using conventional magnetic resonance imaging methods namely voxel-based morphometry, cortical thickness analysis, subcortical volumetry and tract-based diffusion tensor analysis; confirming the potential of whole-brain quantitative susceptibility mapping as an in vivo biomarker in Parkinson's disease

Influence of a Concurrent Exercise Training Intervention during Pregnancy on Maternal and Arterial and Venous Cord Serum Cytokines: The GESTAFIT Project

The aim of the present study was to analyze the influence of a supervised concurrent exercise-training program, from the 17th gestational week until delivery, on cytokines in maternal (at 17th and 35th gestational week, and at delivery) and arterial and venous cord serum. Fifty-eight Caucasian pregnant women (age: 33.5 +/- 4.7 years old, body mass index: 23.6 +/- 4.1kg/m(2)) from the GESTAFIT Project (exercise (n = 37) and control (n = 21) groups) participated in this quasi-experimental study (per-protocol basis). The exercise group followed a 60-min 3 days/week concurrent (aerobic-resistance) exercise-training from the 17th gestational week to delivery. Maternal and arterial and venous cord serum cytokines (fractalkine, interleukin (IL)-1 beta, IL-6, IL-8, IL-10, interferon (IFN)-gamma, and tumor necrosis factor (TNF)-alpha) were assessed using Luminex xMAP technology. In maternal serum (after adjusting for the baseline values of cytokines), the exercise group decreased TNF-alpha (from baseline to 35th week, p = 0.02), and increased less IL-1 beta (from baseline to delivery, p = 0.03) concentrations than controls. When adjusting for other potential confounders, these differences became non-significant. In cord blood, the exercise group showed reduced arterial IL-6 and venous TNF-alpha (p = 0.03 and p = 0.001, respectively) and higher concentrations of arterial IL-1 beta (p = 0.03) compared to controls. The application of concurrent exercise-training programs could be a strategy to modulate immune responses in pregnant women and their fetuses. However, future research is needed to better understand the origin and clearance of these cytokines, their role in the maternal-placental-fetus crosstalk, and the influence of exercise interventions on them

PATÓGENOS Y SÍNTOMAS ASOCIADOS A LA MARCHITEZ DEL TOMATE (Solanum lycopersicum L.) EN TEXCOCO MÉXICO

Se identificó a Phytophthora capsici, Rhizoctonia solani y Fusarium oxysporum como agentes causales de la marchitez del tomate en Texcoco, Edo. de México y, se evaluó la sintomatología e incidencia de la marchitez inducida por estos hongos con diferentes métodos de inoculación. Cultivos de cada hongo se inocularon en plantas de tomate con 4-5 hojas verdaderas. La inoculación de P. capsici por inmersión de raíces en solución de zoosporas fue más eficiente (96,7 % de incidencia) que la inoculación al cuello, a los 6 días después de la inoculación (ddi). Este hongo indujo marchitez, pudrición de raíz y cuello, y muerte de las plantas a los 4 ddi. R. solani, al inocularse por inmersión en solución de propágalos y a través de granos de trigo infectados con el hongo, no ocasionó la muerte de las plantas, sin embargo, la inoculación con granos de trigo provocó una incidencia de 100 %, que se manifestó en reducción de crecimiento (50 %) y en amarillamiento generalizado. F. oxysporum presentó una incidencia de 100 % a los 15 y 30 ddi, para la variedad Río Grande e híbrido Yaqui, respectivamente. Las plantas manifestaron clorosis, marchitez generalizada, necrosis de tejido vascular y finalmente la muerte

Expression Quantitative Trait Locus Analysis in Systemic Sclerosis Identifies New Candidate Genes Associated With Multiple Aspects of Disease Pathology

Objective: To identify the genetic variants that affect gene expression (expression quantitative trait loci [eQTLs]) in systemic sclerosis (SSc) and to investigate their role in the pathogenesis of the disease. Methods: We performed an eQTL analysis using whole-blood sequencing data from 333 SSc patients and 524 controls and integrated them with SSc genome-wide association study (GWAS) data. We integrated our findings from expression modeling, differential expression analysis, and transcription factor binding site enrichment with key clinical features of SSc. Results: We detected 49,123 validated cis-eQTLs from 4,539 SSc-associated single-nucleotide polymorphisms (SNPs) (PGWAS 0.05). As a result, 233 candidates were identified, 134 (58%) of them associated with hallmarks of SSc and 105 (45%) of them differentially expressed in the blood cells, skin, or lung tissue of SSc patients. Transcription factor binding site analysis revealed enriched motifs of 24 transcription factors (5%) among SSc eQTLs, 5 of which were found to be differentially regulated in the blood cells (ELF1 and MGA), skin (KLF4 and ID4), and lungs (TBX4) of SSc patients. Ten candidate genes (4%) can be targeted by approved medications for immune-mediated diseases, of which only 3 have been tested in clinical trials in patients with SSc. Conclusion: The findings of the present study indicate a new layer to the molecular complexity of SSc, contributing to a better understanding of the pathogenesis of the disease

Feasibility study of reinforced concrete reinforced concrete buildings for upper stratum apartments in the city of Bogotá. A methodology to maximize profit

En el marco de la gerencia de proyectos y su fase de planeación se concibió e implementó una metodología para determinar la utilidad máxima que se puede obtener cuando se piensa en construir un edificio destinado a vivienda en estrato alto en la ciudad de Bogotá. La metodología que permitió alcanzar este objetivo fue la ciencia de investigación de operaciones, a través de la técnica de programación lineal. Esta metodología comprende la definición, planteamiento y resolución de modelos matemáticos para encontrar soluciones óptimas a través de las matemáticas y computadoras con el propósito de mitigar riesgos y facilitar la toma de decisiones. Conforme a la metodología seleccionada se formuló matemáticamente la expresión de la utilidad máxima esperada, la cual conjuntamente con otras fórmulas y variables de carácter comercial, técnico, normativo, económico y financiero, relacionadas con las restricciones propias del modelo, permitieron con la aplicación del Programa Solver de Excel obtener la solución deseada. Finalmente y teniendo en cuenta el cambiante y dinámico escenario de la industria de la construcción en la ciudad capital, se realizó el análisis de sensibilidad, que sometió los resultados óptimos obtenidos a escenarios alternativos para validar rechazar la aplicación de los mismos.INTRODUCCIÓN 19 ANTECEDENTES 22 DEFINICION DEL PROBLEMA DE INVESTIGACION 27 JUSTIFICACION 29 OBJETIVOS GENERALES Y ESPECIFICOS 30 HIPOTESIS O SUPUESTOS 32 1. MARCO TEORICO 34 1.1 CONTEXTO DE LA INVESTIGACIÓN 34 1.2 ENTORNO URBANO 35 1.3 DEFINICIÓN DE LA UTILIDAD DEL PROYECTO 39 1.4 ESTUDIO DE FACTIBILIDAD DEL PROYECTO 41 1.4.1 Factibilidad comercial 41 1.4.2 Factibilidad normativa 46 1.4.2.1 Indice de ocupación 47 1.4.2.2 Indice de construcción 48 1.4.2.3 Número máximo de pisos 49 1.4.3 Factibilidad técnica 51 1.4.3.1 Los estudios geotécnicos 51 1.4.3.2 El diseño arquitectónico 52 1.4.3.3 El diseño estructural 55 1.4.3.4 El diseño de la cimentación 66 1.4.4 Factibilidad económica 73 1.4.4.1 El lote y su valor comercial 74 1.4.4.2 Costos directos 75 1.4.4.3 Costos Indirectos 95 1.4.5 Factibilidad financiera 106 1.4.5.1 Bondad financiera del Proyecto 107 1.5 GERENCIA DE VALOR 112 1.5.1 Valor Económico Agregado. EVA. 112 2. METODOLOGIA 120 2.1 INVESTIGACIÓN DE OPERACIONES 120 2.1.1 Problema de programación lineal 124 2.1.2 Problema de Programación Lineal. Uso del Programa Solver de Excel 127 3. RESULTADOS DE LA INVESTIGACION 134 3.1 FORMULACIÓN DEL PROBLEMA DE LA INVESTIGACIÓN 136 3.2 PLANTEAMIENTO Y DESCRIPCIÓN PROBLEMA DE INVESTIGACIÓN 138 3.3 IDENTIFICACIÓN DE LOS DATOS DEL PROBLEMA 139 3.3.1 Información Comercial 139 3.3.2 Información Normativa 139 3.3.3 Información Técnica 140 3.3.4 Información Económica 141 3.3.5 Información Financiera 141 3.4 IDENTIFICACIÓN DEL CRITERIO DE DECISIÓN 142 3.5 IDENTIFICACIÓN DE LAS VARIABLES DE DECISIÓN 142 3.6 IDENTIFICACIÓN DE LA FUNCIÓN OBJETIVO 143 3.7 IDENTIFICACIÓN DE RESTRICCIONES CONCEPTUALES Y LÓGICAS 144 3.7.1 Restricción Comercial 144 3.7.2 Restricción Normativa 145 3.7.3 Restricción Técnica 146 3.7.4 Restricción Económica 150 3.7.5 Restricción Financiera 154 3.7.6 Restricciones lógicas 155 3.8 EVALUACIÓN FINANCIERA DEL PROYECTO. E.V.A. 156 3.9 OBTENCIÓN DE LA SOLUCIÓN ÓPTIMA 157 3.10.DESCRIPCIÓN, INTERPRETACIÓN Y ANÁLISIS SOLUCIÓN ÓPTIMA 160 3.11. ANÁLISIS DE SENSIBILIDAD Y PARAMÉTRICOS 174 3.11.1 Análisis de sensibilidad. Caso 1. Comercial 174 3.11.2 Análisis de sensibilidad. Caso 2. Técnica- económica 176 3.11.3 Análisis de sensibilidad. Caso 3. Financiera 178 3.11.4 Análisis de sensibilidad. Caso 4. Normativa 180 4. CONCLUSIONES 182 5. RECOMENDACIONES 199 BIBLIOGRAFIA 204 ANEXOS 210MaestríaWithin the framework of project management and its planning phase, a methodology was conceived and implemented to determine the maximum profit that can be obtained when thinking of constructing a building for upper-tier housing in the city of Bogotá. The methodology that allowed to achieve this objective was the science of operations research, through the linear programming technique. This methodology includes the definition, approach and resolution of mathematical models to find optimal solutions through mathematics and computers in order to mitigate risks and facilitate decision-making. In accordance with the selected methodology, the expression of the maximum expected profit was formulated mathematically, which together with other formulas and variables of a commercial, technical, regulatory, economic and financial nature, related to the model's own restrictions, allowed with the application of the Program. Excel solver get the desired solution. Finally, and taking into account the changing and dynamic scenario of the construction industry in the capital city, a sensitivity analysis was carried out, which submitted the optimal results obtained to alternative scenarios to validate reject their application.Modalidad Presencia