Lie derivatives of the shape operator of real hypersurfaces in the complex and complex hyperbolic quadrics

El título del preprint era "Lie derivatives of the shape operator of real hypersurfaces in the complex and complex hyperbolic quadrics" y posteriormente, siguiendo las indicaciones de los reviewers, fue modificado a Some Real Hypersurfaces in Complex and Complex Hyperbolic Quadrics.On a real hypersurface in the complex quadric or the complex hyperbolic quadric we can consider the Levi-Civita connection and, for any nonnull real number $k$, the $k$-th generalized Tanaka-Webster connection. We also have a differential operator of first order of Lie type associated to the $k$-th generalized Tanaka-Webster connection. We classify real hypersurfaces in the complex quadric and the complex hyperbolic quadric for which the Lie derivative and the Lie type differential operator coincide when they act on the shape operator of the real hypersurface either in the direction of the structure vector field or in any direction of the maximal holomorphic distribution.MINECO-FEDER Project MTM 2016-78807-C2-1-

Shunt series LC circuit for compact coplanar waveguide notch filter design

A shunt series LC resonant circuit based on an open version of an interconnected split ring resonator (OISRR) is proposed. This OISRR exhibits half the resonant frequency of the split ring resonator, allows a parallel connection with a coplanar waveguide (CPW) section and according to its frequency response is an attractive cell for compact CPW notch filter design. 3 dB stop-band bandwidth lower than 4.5% with more than 11 dB insertion loss in the stop-band can be achieved with a CPW loaded with a single OISRR. The experimental results have confirmed the possibilities of this OISRR, which can be easily connected to CPW antennas to reject undesirable signalsThe authors gratefully acknowledge Ministerio de Ciencias e Innovación of Spain and FEDER for the financial support of this work under the grant no.: TEC2010‐21520‐C04‐04/TCM

Double-sided open split ring resonator for compact microstrip band-pass filter design

A metamaterial structure, called the double-sided open split ring resonator (DOSRR), which combines two open split ring resonators (OSRRs) aligned over the opposite faces of the substrate in an inverted fashion is presented. A study of this resonator from full-wave electromagnetic and circuit simulations is performed. As with the OSRR cell, the DOSRR cell allows a series connection along a microstrip transmission line and it has a small electrical size. Moreover, the DOSRR cell has the ability to add a transmission zero in the out-of-band region without increasing its size. This DOSRR cell is used for the design of compact microstrip slow-wave type band-pass filters. Two strategies based on circular windows etched in the bottom plane instead of square windows and U-shape slots etched in the microstrip transmission line are designed to increase the stop band and to add extra zeros in order to suppress the spurious band. The experimental results have confirmed the possibilities of this electrically small resonator (DOSRR) and the efficiency of both strategies to improve the out-of-band rejection.The authors gratefully acknowledge Ministerio de Ciencias e Innovación of Spain for financial support of this work under the grant no.: TEC2010-21520-C04-04/TCM

Las Ilustraciones en la enseñanza-aprendizaje de las ciencias : análisis de libros de texto

Este trabajo centra su atención en la importancia que poseen las ilustraciones que utilizan los libros de texto de ciencias para la comprensión de su contenido. Para ello se parte de una fundamentación teórica en cuanto a los requisitos que deberían cumplir aquéllas para favorecer su adecuado procesamiento, así como la diferente morfología que suelen presentar en los libros de texto. A continuación se aborda un proceso de diseño y validación de una taxonomía para la categorización de las ilustraciones, la cual fue aplicada a los temas de mecánica de una muestra representativa de siete libros de educación secundaria obligatoria y a tres previos. Tras este análisis se discuten los resultados y se extraen unas conclusiones tendentes a la mejora en el uso de las ilustraciones.This paper focuses on how important the illustrations in science textbooks can be for understanding their content. To that end we start from a theoretical base of the requirements that those illustrations should accomplish to favour their appropriate processing, as well as from the different morphology that they normally show in textbooks. Then we approach a process of design and validation of a taxonomy to categorize the illustrations that was applied to the subject of Mechanics on a representative sample of seven textbooks of Obligatory Secondary Education (ESO) and three books from a system previous to ESO. After this analysis we discuss the results and draw conclusions aimed at improving the use of illustrations

New results on derivatives of the shape operator of a real hypersurface in a complex projective space

This work was supported by MINECO-FEDER Project MTM 2016-78807-C2-1-P.We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka-Webster connections. For any nonnull real number k and any symmetric tensor field of type (1,1) L on M we can define a tensor field of type (1,2) on M, L(k) F , related to both connections. We study symmetry and skewsymmetry of the tensor A(k) F associated to the shape operatorA of M.MINECO-FEDER Project MTM 2016-78807-C2-1-

New characterizations of ruled real hypersurfaces in complex projective space

We consider real hypersurfaces M in complex projective space equipped with both the Levi–Civita and generalized Tanaka–Webster connections. For any nonnull constant k and any symmetric tensor field of type (1, 1) L on M, we can define two tensor fields of type (1, 2) on M, LF(k) and LT(k) , related to both connections. We study the behaviour of the structure operator ϕ with respect to such tensor fields in the particular case of L= A , the shape operator of M, and obtain some new characterizations of ruled real hypersurfaces in complex projective space.MICINN Project PID 2020-116126GB-100Junta de Andalucía Project PY20-0139Universidad de Granada/CBU

Lie Derivatives of the Shape Operator of a Real Hypersurface in a Complex Projective Space

This work was supported by MINECO-FEDER Project MTM 2016-78807-C2-1-P.We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka–Webster connections. Associated with the generalized Tanaka–Webster connection we can define a differential operator of first order. For any nonnull real number k and any symmetric tensor field of type (1,1) B on M, we can define a tensor field of type (1,2) on M, B(k) T , related to Lie derivative and such a differential operator. We study symmetry and skew symmetry of the tensor A(k) T associated with the shape operator A of M.MINECO-FEDER Project MTM 2016-78807-C2-1-

Horizontal Inequity in Access to Healthcare Services and Educational Level in Spain

The aim of this study is to measure horizontal equity in the use of healthcare services in Spain, proposing two methodological innovations. First by defending it as equality of access for equal need, irrespective of educational level, unlike the prevailing methodological approach to horizontal equity which relates it to income. Second, by estimating it by means of the slope index of the inequality of characteristics, analagous to the inequity index proposed by Kakwani, Wagstaff and van Doorslaer (1997; HIWV) but presenting some methodological advantages, the greater robustness of the data available on educational level than of those on income, and the possibility of isolating the net effect of the educational level on the use of healthcare by controlling for other variables. The methodology is designed in three parts: (1) estimation of the relationship between the educational level and the use of healthcare services by means of a model of the likelihood of demand for healthcare services, commonly used in the literature; (2) estimation of the relationship between educational level and health by approximating a production function of individuals' health according to their personal characteristics and other factors conditioning health; and (3) estimation of the slope index of inequality as a measure of horizontal inequity, using educational level instead of income as the criterion for ranking individuals. The data base used was a sample of 55,598 observations from the Survey of disabilities, handicaps and state of health of 1999, carried out in Spain. No significant statistical association was found between educational level and use of healthcare services. On the other hand, the relationship between educational level and health, with the three proxy variables used (perception of health, days of limitation and number of chronic illnesses) shows a positive correlation, i.e. an increase in educational level is associated with a greater probability of enjoying better health. Horizontal inequity, measured by the proposed slope index of inequality, gives a range of statistically significant values between 13.91% and 9.40%, depending on cases, i.e. the significant inverse relationship between state of health and educational level is not reflected proportionally in healthcare use, implying that, with greater need, the access of individuals with a lower educational level to public healthcare services is the same as for the rest. These results suggest that the educational level may be a variable to consider when characterizing the healthcare needs of a population in a defined geographical area, at least from the normative characterization of horizontal equity proposedEducation and health; Healthcare needs; Horizontal Inequity; Logistic regression ; Ordinal regression; Regional funding

Some Conditions Concerning the Shape Operator of a Real Hypersurface in Complex Projective Space

Funding for open access publishing: Universidad de Granada/CBUA Funding for open access charge: Universidad de Granada/CBUA.Let M be a real hypersurface of a complex projective space. For any operator B on M and any nonnull real number k, we can define two tensor fields of type (1,2) on M, BF(k) and BT(k) . We will classify real hypersurfaces in complex projective space for which BF(k) and BT(k) either take values in the maximal holomorphic distribution D or are parallel to the structure vector field ξ , in the particular case of B= A , where A denotes the shape operator of M. We also introduce the concept of AF(k) and AT(k) being D -recurrent and classify real hypersurfaces such that either AF(k) or AT(k) are D -recurrent.MICINN: PID 2020-116126GB-I00Universidad de Granada/CBU