21,142 research outputs found

    C1,ω extension formulas for 1-jets on Hilbert spaces

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    Funding Information: D. Azagra and C. Mudarra were partially supported by Grant PGC2018-097286-B-I00 , Ministerio de Ciencia e Innovación , Spain. C. Mudarra also acknowledges financial support from the Academy of Finland . Funding Information: D. Azagra and C. Mudarra were partially supported by Grant PGC2018-097286-B-I00, Ministerio de Ciencia e Innovaci?n, Spain. C. Mudarra also acknowledges financial support from the Academy of Finland. Publisher Copyright: © 2021 The Author(s)We provide necessary and sufficient conditions for a 1-jet (f,G):E→R×X to admit an extension (F,∇F) for some F∈C1,ω(X). Here E stands for an arbitrary subset of a Hilbert space X and ω is a modulus of continuity. As a corollary, in the particular case X=Rn, we obtain an extension (nonlinear) operator whose norm does not depend on the dimension n. Furthermore, we construct extensions (F,∇F) in such a way that: (1) the (nonlinear) operator (f,G)↦(F,∇F) is bounded with respect to a natural seminorm arising from the constants in the given condition for extension (and the bounds we obtain are almost sharp); (2) F is given by an explicit formula; (3) (F,∇F) depend continuously on the given data (f,G); (4) if f is bounded (resp. if G is bounded) then so is F (resp. F is Lipschitz). We also provide similar results on superreflexive Banach spaces.Peer reviewe

    La educación bilingüe y la interculturalidad en los estudiantes del Instituto Superior Pedagógico Fray Ángel José Azagra Murillo del Distrito de Puerto Bermúdez Oxapampa – 2022

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    El objetivo de este trabajo de investigación fue determinar la relación entre la educación bilingüe y la interculturalidad en los estudiantes de la Escuela Superior Pedagógico “Fray Ángel José Azagra Murillo” de Puerto Bermúdez de Oxapampa en el año 2022. Debido a la naturaleza cualitativa de la información de los datos; el estudio se describe como una investigación fundamental debido a la profundidad de su relevancia. La población de investigación estuvo conformada por 160 estudiantes, la muestra de investigación fue probabilística, con muestreo sistemático, un total de 60 estudiantes, el cuestionario contó con 20 preguntas, denominado educación bilingüe, y el segundo instrumento contó con 20 ítems transculturales. Los resultados de la variable educación bilingüe muestran que el 30% de los estudiantes nivel regular, 27 estudiantes, el 45%, están en el nivel normal,15 estudiantes, el 25% están en el nivel malo, 15 estudiantes, el 25%, se desempeñan bien en la variable intercultural, hay son 28 alumnos de la clase general, que representa el 46,7%, y 17 personas de la clase pobre que representa el 28,3%. El análisis inferencial arrojó un p-valor de 0.000, por debajo del nivel de significancia de 0.05, rechazando así la hipótesis nula y concluyendo que existe una relación significativa entre la educación bilingüe y la interculturalidad de los estudiantes del Instituto Superior Pedagógico “Fray Ángel José Azagra Murillo” de Puerto Bermúdez de Oxapampa.Tesi

    Report on Meteorological Research March 1, 1935 (m-1)

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    The object of the report was to elucidate in detail the various features of the research program in meteorology being carried on at the Daniel Guggenheim Airship Institute in Akron, Ohio. Mr. L. J. Fangman, of the U.S. Weather Bureau, was collaborating with the author in carrying out work such as a study of autographic records of the various meteorological elements during frontal passages with a view to the possible prediction of the intensity of the accompanying disturbance as it may affect the operation of aircraft and a study of atmospheric gustiness with a view to finding the dependence between frequency end amplitude of velocity fluctuations and the vertical temperature and velocity gradients

    (Fourth) Report on Meteorological Activities at the DGAI (8-1-36)(Weather Bureau Copy)

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    This report is on the investigations of frontal phenomena at the Daniel Guggenheim Airship Institute in Akron, Ohio from January 1, 1935 through August 1, 1936. The investigation was carried out with the cooperation of the U.S. Bureau of Aeronautics, the U.S. Weather Bureau, the California Institute of Technology, and the Guggenheim Airship Institute. Mr. R.C. Robinson of the Weather Bureau cooperated with the author in carrying out the investigation. The object of the investigation was to determine the intensity of the atmospheric disturbances (i.e. rapidity of wind shift and gustiness) accompanying the passage of cold fronts, along with a study of the characteristics of the air masses involved and other features which might affect the intensity of the disturbance. The report treated thirty cold fronts which passed the station during 1935 to 1936

    Aproximación y extensión diferenciable de funciones convexas

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    Tesis de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Departamento de Análisis Matemáticos, leída el 07-09-2018Las funciones convexas y, en particular, las funciones convexas diferenciables juegan un papel fundamental dentro del Análisis Matemático y tienen una gran cantidad de aplicaciones en otras disciplinas como la Geometría Diferencial, la teoría de EDP’S (por ejemplo, las ecuaciones de Monge-Ampère), las Dinámicas No Nineales, la Computación Cuántica o la Economía. Por tanto, es sin duda útil cualquier herramienta que permita aproximar o extender por funciones convexas diferenciables en distintos espacios de Banach. Si tenemos una función convexa y acotada en conjuntos acotados definida en un espacio de Banach con dual LUR, se sabe por los resultados de D. Azagra que esta función puede aproximarse por funciones convexas diferenciables uniformemente en todo el espacio. Sin embargo, puesto que existen ejemplos defunciones convexas continuas no acotadas en conjuntos acotados, es deseable eliminar esta restricción de la función que deseamos aproximar. En esta tesis se elimina esta restricción y se demuestra que las funciones convexas y continuas definidas en abiertos convexos de espacios de Banach con dual LUR, pueden aproximarse uniformemente por funciones convexas diferenciables uniformemente en todo el espacio. Esto es consecuencia de un resultado más general que muestra que el problema de aproximación uniforme de funciones convexas por funciones convexas de una cierta clase de diferenciabilidad puede reducirse al caso en el que las funciones a aproximar son, además, Lipschitzianas...The class of convex functions and, in particular, the class of differentiable convex functions play a very important role in the field of Mathematical Analysis and they have plenty of applications in other disciplines such as Differential Geometry, PDE theory (for instance, Monge-Ampère equations), Non linear Dynamics, Quantum Computing or Economics. Therefore, it is no doubt useful to be able to approximate or to extend by differentiable convex functions in various Banach spaces. If we are given a convex function bounded on bounded sets defined on a Banach space whose dual norm is LUR, recent results by D. Azagra ensure that this function can be approximated by differentiable convex functions uniformly on the whole space. However, since there are example of continuous convex functions which are not bounded on bounded subsets, it is desirable to improve these results in such away that this restriction on the function to be approximated can be removed. In this thesis, we drop this assumption and show that every continuous convex function (not necessarily bounded on bounded subsets) defined on an open convex subset of a Banach space whose dual norm is LUR, can be uniformly approximated by differentiable convex functions. This result is a consequence of a more general result which shows that the problem of approximating continuous convex functions uniformly by convex functions of a certain differentiability class can be reduced to the case when the original functions are, in addition, Lipschitz...Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEunpu

    Daniel Akech

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    abstract: Daniel was a little boy when the war came to his village. He witnessed people being shot and running for shelter. There was no food or water so he drank urine and ate tree leaves. “Lost Boys Found” is an ongoing, interdisciplinary project that is collecting, recording and archiving the oral histories of the Lost Boys/Girls of Sudan. The collection is a work-in-progress, seeking to record the oral history of as many Lost Boys/Girls as are willing, and will be used in a future book.Age: 24Region: Upper NileThis picture and bio was donated to the "Lost Boys Found" oral history project from The Arizona Lost Boys Cente

    Daniel Emmett postcard

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    Postcard of Daniel Emmett and his home in Mount Vernon, Ohio. Emmett is considered to be the author of the antebellum song "Dixie," written in 1859, which became the unofficial song of the Confederate soldiers during the American Civil War. He was born in Mount Vernon in 1815 and taught himself the fiddle, and later became associated with minstrel shows and helped to define that genre. Minstrel shows traveled around the United States, presenting skits and musical performances. Emmett also composed many other songs, including "Old Dan Tucker," "Turkey in the Straw," and "The Blue Tail Fly." He died in 1904

    Daniel Jau Maper

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    abstract: Daniel Jau Maper was herding cattle when Arabs attacked his village. “Lost Boys Found” is an ongoing, interdisciplinary project that is collecting, recording and archiving the oral histories of the Lost Boys/Girls of Sudan. The collection is a work-in-progress, seeking to record the oral history of as many Lost Boys/Girls as are willing, and will be used in a future book.Age: 27Region: Upper NileThis picture and bio was donated to the "Lost Boys Found" oral history project from The Arizona Lost Boys Cente

    Daniel A. Ngor

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    When Daniel was five years old Arab soldiers attacked his village. “Lost Boys Found” is an ongoing, interdisciplinary project that is collecting, recording and archiving the oral histories of the Lost Boys/Girls of Sudan. The collection is a work-in-progress, seeking to record the oral history of as many Lost Boys/Girls as are willing, and will be used in a future book.Age : 23Region: Upper NileThis picture and bio was donated to the "Lost Boys Found" oral history project from The Arizona Lost Boys Cente
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