Heat and Poisson semigroups for Fourier-Neumann expansions

Given $\alpha > -1$, consider the second order differential operator in $(0,\infty)$, $$L_\alpha f \equiv (x^2 \frac{d^2}{dx^2} + (2\alpha+3)x \frac{d}{dx} + x^2 + (\alpha+1)^2)(f),$$ which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking $L_\alpha$ as the analogue to the classical Laplacian. Namely we study the boundedness properties of the heat and Poisson semigroups. These boundedness properties allow us to obtain some convergence results that can be used to solve the Cauchy problem for the corresponding heat and Poisson equations.Comment: 16 page

CAR T cells for T-cell leukemias: Insights from mathematical models

Immunotherapy has the potential to change the way all cancer types are treated and cured. Cancer immunotherapies use elements of the patient immune system to attack tumor cells. One of the most successful types of immunotherapy is CAR-T cells. This treatment works by extracting patient's T-cells and adding to them an antigen receptor allowing tumor cells to be recognized and targeted. These new cells are called CAR-T cells and are re-infused back into the patient after expansion in-vitro. This approach has been successfully used to treat B-cell malignancies (B-cell leukemias and lymphomas). However, its application to the treatment of T-cell leukemias faces several problems. One of these is fratricide, since the CAR-T cells target both tumor and other CAR-T cells. This leads to nonlinear dynamical phenomena amenable to mathematical modeling. In this paper we construct a mathematical model describing the competition of CAR-T, tumor and normal T-cells and studied some basic properties of the model and its practical implications. Specifically, we found that the model reproduced the observed difficulties for in-vitro expansion of the therapeutic cells found in the laboratory. The mathematical model predicted that CAR-T cell expansion in the patient would be possible due to the initial presence of a large number of targets. We also show that, in the context of our mathematical approach, CAR-T cells could control tumor growth but not eradicate the disease

El sol y la piel

ResumenLa alta incidencia de patologías relacionadas con la exposición al sol, en los últimos tiempos ha centrado nuestro interés en el estudio de los diferentes tipos de piel y cómo los UVR afectan su constitución normal. En esta revisión se clasifican los tipos de piel y se mencionan los diferentes mecanismos de respuesta del organismo ante los rayos UVR, así como también las alternativas farmacológicas que previenen el desarrollo de enfermedades de la piel.[MedUNAB 2002; 5(13):44-50].Palabras clave: Radiación ultravioleta, fotodaño, fotoprotección

The interactions that arise in the work for corners in Infantile Education

Este artículo forma parte de una investigación más amplia que aborda el conocimiento y la utilización de los rincones como recurso metodológico y didáctico en las aulas de Educación Infantil. Nos centraremos concretamente, en las interacciones que se producen entre el alumnado en dichos rincones a partir de la interpretación que hace el docente. La muestra considerada la ha formado 15 profesores de centros educativos (11 colegios públicos y 4 colegios concertados) de un ámbito urbano (ciudad mediana) y de un ámbito rural. La muestra participante ha sido de 74 docentes de dichos centros. La metodología que hemos utilizado ha sido cuantitativa, tomando como fuente de recogida de datos un cuestionario. Los resultados obtenidos muestran que el trabajo por rincones en las aulas de Educación Infantil tiene importantes beneficios para los niños de estas edades tanto para las interacciones sociales como las afectivasThis article is part of an investigation wider that tackles the knowledge and the use of the corners as methodological and didactic resource in the classroom of Infantile Education. We will center specifically, in the interactions that take place between the pupils in the above mentioned corners from the interpretation that the teacher does. The considered sample there have been teachers of 15 educational school (11 public schools and 4 compound schools) of an urban ambience(medium-sized city) and of a rural ambience,74 teachers of the above mentioned schools have been the taking part sample. The methodology that we have been quantitative using like data source a questionnaire. The obtained results show that the work of corners in the classrooms of Infantile Education has important benefits for the children of this age so much for the social interactions like the affective ones

Molecular prototypes for spin-based CNOT quantum gates

We show that a chemically engineered structural asymmetry in [Tb2] molecular clusters renders the two weakly coupled Tb3+ spin qubits magnetically inequivalent. The magnetic energy level spectrum of these molecules meets then all conditions needed to realize a universal CNOT quantum gate.Comment: 4 pages, 4 figure

Combining microfluidic paper-based platform and metal–organic frameworks in a single device for phenolic content assessment in fruits

A microfluidic paper-based device (µPAD) has been combined with metal–organic frameworks (MOFs) for total phenolic compounds (TPC) quantification in fruit samples for the first time. The performance of the µPAD, based upon the vertical flow approach, was enhanced in order to determine the TPC content with high accuracy in fruit samples. The method was based on the traditional Folin-Ciocalteu Index using gallic acid or oenotannin as reference phenolic compounds. This novel design and construction of the device are in agreement with the principles of Green Chemistry avoiding wax technology (lower toxicity). The analytical parameters that affect the colorimetric method (using digital imaging of the colored zone) performance were optimized including design, sample volume, and MOF amount. Then, the analytical features of the developed method were investigated such as dynamic range (1.6–30 mg L−1), limit of detection (0.5 mg L−1), and precision (RSD < 9%). Besides, the in-field analysis is achievable with a color stability up to 6 h after the loading process of the sample and storage stability for at least 15 days without performance losses (under vacuum at − 20 °C). Furthermore, the MOF ZIF-8@paper was characterized to study its composition and the successful combination. The feasibility of the proposed method was demonstrated by determining the TPC in 5 fruit samples using oenotannin as reference solute. The accuracy was validated by comparison of the data with the results obtained with the recommended protocol proposed by the International Organisation of Vine and Wine (OIV).info:eu-repo/semantics/publishedVersio

Extending Graph (Discrete) Derivative Descriptors to N-Tuple Atom-Relations

In the present manuscript, an extension of the previously defined Graph Derivative Indices (GDIs) is discussed. To achieve this objective, the concept of a hypermatrix, conceived from the calculation of the frequencies of triple and quadruple atom relations in a set of connected sub-graphs, is introduced. This set of subgraphs is generated following a predefined criterion, known as the event (S), being in this particular case the connectivity among atoms. The triple and quadruple relations frequency matrices serve as a basis for the computation of triple and quadruple discrete derivative indices, respectively. The GDIs are implemented in a computational program denominated DIVATI (acronym for DIscrete DeriVAtive Type Indices), a module of TOMOCOMD-CARDD program. Shannon‟s entropy-based variability analysis demonstrates that the GDIs show major variability than others indices used in QSAR/QSPR researches. In addition, it can be appreciated when the indices are extended over n-elements from the graph, its quality increases, principally when they are used in a combined way. QSPR modeling of the physicochemical properties Log P and Log K of the 2-furylethylenes derivatives reveals that the GDIs obtained using the tripleand quadruple matrix approaches yield superior performance to the duplex matrix approach. Moreover, the statistical parameters for models obtained with the GDI method are superior to those reported in the literature by using other methods. It can therefore be suggested that the GDI method, seem to be a promissory tool to reckon on in QSAR/QSPR studies, virtual screening of compound datasets and similarity/dissimilarity evaluations

Ecological niche modeling to calculate ideal sites to introduce a natural enemy: the case of apanteles opuntiarum (hymenoptera: Braconidae) to control cactoblastis cactorum (lepidoptera: Pyralidae) in North America

The cactus moth, Cactoblastis cactorum (Berg) (Lepidoptera: Pyralidae), is an invasive species in North America where it threatens Opuntia native populations. The insect is expanding its distribution along the United States Gulf Coast. In the search for alternative strategies to reduce its impact, the introduction of a natural enemy, Apanteles opuntiarum Martínez and Berta (Hymenoptera: Braconidae), is being pursued as a biological control option. To identify promising areas to intentionally introduce A. opuntiarum for the control of C. cactorum, we estimated the overlap of fundamental ecological niches of the two species to predict their common geographic distributions using the BAM diagram. Models were based on native distributional data for both species, 19 bioclimatic variables, and the Maxent algorithm to calculate the environmental suitability of both species in North America. The environmental suitability of C. cactorum in North America was projected from Florida to Texas (United States) along the Gulf coastal areas, reaching Mexico in northern regions. Apanteles opuntiarum environmental suitability showed a substantial similarity with the calculations for C. cactorum in the United States. Intentional introductions of A. opuntiarum in the actual distribution areas of the cactus moth are predicted to be successful; A. opuntiarum will find its host in an environment conducive to its survival and dispersal.Fil: Pérez De la O, Nidia Bélgica. Universidad Autónoma de Chiapas. Facultad de Ciencias Agrícolas; MéxicoFil: Espinosa Zaragoza, Saúl. Universidad Autónoma de Chiapas. Facultad de Ciencias Agrícolas; MéxicoFil: López Martínez, Víctor. Universidad Autónoma del Estado de Morelos; MéxicoFil: Hight, Stephen D.. US Department of Agriculture. Agricultural Research Service; Estados UnidosFil: Varone, Laura. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Fundación para el Estudio de Especies Invasivas; Argentin

Swinging Atwood's Machine: Experimental and Theoretical Studies

A Swinging Atwood Machine (SAM) is built and some experimental results concerning its dynamic behaviour are presented. Experiments clearly show that pulleys play a role in the motion of the pendulum, since they can rotate and have non-negligible radii and masses. Equations of motion must therefore take into account the inertial momentum of the pulleys, as well as the winding of the rope around them. Their influence is compared to previous studies. A preliminary discussion of the role of dissipation is included. The theoretical behaviour of the system with pulleys is illustrated numerically, and the relevance of different parameters is highlighted. Finally, the integrability of the dynamic system is studied, the main result being that the Machine with pulleys is non-integrable. The status of the results on integrability of the pulley-less Machine is also recalled.Comment: 37 page