On a Biparameter Maximal Multilinear Operator

It is well-known that estimates for maximal operators and questions of pointwise convergence are strongly connected. In recent years, convergence properties of so-called `non-conventional ergodic averages' have been studied by a number of authors, including Assani, Austin, Host, Kra, Tao, and so on. In particular, much is known regarding convergence in $L^2$ of these averages, but little is known about pointwise convergence. In this spirit, we consider the pointwise convergence of a particular ergodic average and study the corresponding maximal trilinear operator (over $\mathbb{R}$, thanks to a transference principle). Lacey and Demeter, Tao, and Thiele have studied maximal multilinear operators previously; however, the maximal operator we develop has a novel bi-parameter structure which has not been previously encountered and cannot be estimated using their techniques. We will carve this bi-parameter maximal multilinear operator using a certain Taylor series and produce non-trivial H\"{o}lder-type estimates for one of the two "main" terms by treating it as a singular integrals whose symbol's singular set is similar to that of the Biest operator studied by Muscalu, Tao, and Thiele.Comment: 32 pages, 1 figur

Tamizaje del cáncer de mama: certezas y controversias

El cáncer de mama es globalmente el de mayor incidencia en mujeres, con estimaciones de entre 1.7 y 2.4 millones de casos anuales según diferentes fuentes1, 2. También es globalmente la principal causa de muerte por cáncer con unas 523 000 muertes anuales2. Según información del Instituto Nacional del Cáncer de la Argentina, en el año 2012 (último dato disponible) se registraron alrededor de 20 000 nuevos casos de cáncer de mama (que representa el 32.2% de los cánceres en mujeres), mientras que en 2016 se registraron 5645 fallecimientos de mujeres (19.4% de las muertes por cáncer considerando solamente ese sexo) y 45 de hombres por esta enfermedad. Probablemente estas cifras se encuentren subestimadas. Se publicaron una serie de trabajos que pusieron en duda la conveniencia del tamizaje del cáncer de mama, fundamentalmente debido al sobrediagnóstico y el consecuente sobretratamiento (revisado en4). Si se impone esta política tan contraria al concepto de medicina preventiva, ¿no veremos aumentar nuevamente las tasas de mortalidad que se mantenían constantes, aunque la incidencia seguía incrementándose?Fil: Luthy, Isabel Alicia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; Argentin

Terapia hormonal de reemplazo

Hacia el 1900 la esperanza de vida era de alrededor de 54 años, mientras que en la actualidad una mujer vive en los países indus­tria­liza­dos un promedio de 83 años. Sin embargo, la edad de la menopausia se ha mantenido alrededor de los 50 años desde que se posee registro escri­to. El hecho que en la actualidad las mujeres vivan un tercio de su vida en menopausia ha esti­mu­lado numerosas investigaciones sobre cómo me­­jorar la calidad de vida. Muchas mujeres buscan tratamiento para aliviar los sínto­mas asociados a la menopausia, siendo los sofocos, que llegan a afec­tar se­gún algu­nas esti­ma­ciones al 93% de las mujeres, la principal causa de consulta. Un tercio de las mu­jeres califican a los sofocos que su­fren como severos. Además de es­te tras­torno, en muchas mujeres se produce sequedad vaginal y sínto­mas uri­na­­rios que disminuyen la calidad de vida (3). Con la disminución de estróge­nos también aumenta la reab­sorción del hueso, provocando co­mo conse­cuencia osteo­porosis. De acuerdo con un estudio clínico reciente de los Institutos Nacio­nales de la Salud de Estados Unidos, el 55% de las mujeres entre 50 y 59 años y entre el 69 y 88% de aquellas entre 60 y 69 años presentan densidad ósea reducida.Fil: Luthy, Isabel Alicia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; Argentin

Toward identification of larval sailfish (Istiophorus platypterus), white marlin (Tetrapturus albidus), and blue marlin (Makaira nigricans) in the western North Atlantic Ocean*

The identification of larval istiophorid billfishes from the western North Atlantic Ocean has long been problematic. In the present study, a molecular technique was used to positively identify 27 larval white marlin (Tetrapturus albidus), 96 larval blue marlin (Makaira nigricans), and 591 larval sailfish (Istiophorus platypterus) from the Straits of Florida and the Bahamas. Nine morphometric measurements were taken for a subset of larvae (species known), and lower jaw pigment patterns were recorded on a grid. Canonical variates analysis (CVA) was used to reveal the extent to which the combination of morphometric, pigment pattern, and month of capture information was diagnostic to species level. Linear regression revealed species-specific relationships between the ratio of snout length to eye orbit diameter and standard length (SL). Confidence limits about these relationships served as defining characters for sailfish >10 mm SL and for blue and white marlin >17 mm SL. Pigment pattern analysis indicated that 40% of the preflexion blue marlin examined possessed a characteristic lower jaw pigment pattern and that 62% of sailfish larvae were identifiable by lower jaw pigments alone. An identification key was constructed based on pigment patterns, month of capture, and relationships between SL and the ratio of snout length to eye orbit diameter. The key yielded identifications for 69.4% of 304 (blind sample) larvae used to test it; only one of these identifications was incorrect. Of the 93 larvae that could not be identified by the key, 71 (76.3%) were correctly identified with CVA. Although identif ication of certain larval specimens may always require molecular techniques, it is encouraging that the majority (92.4%) of istiophorid larvae examined were ultimately identifiable from external characteristics alone

Projections and Dyadic Parseval Frame MRA Wavelets

A classical theorem attributed to Naimark states that, given a Parseval frame $\mathcal{B}$ in a Hilbert space $\mathcal{H}$, one can embed $\mathcal{H}$ in a larger Hilbert space $\mathcal{K}$ so that the image of $\mathcal{B}$ is the projection of an orthonormal basis for $\mathcal{K}$. In the present work, we revisit the notion of Parseval frame MRA wavelets from two papers of Paluszy\'nski, \v{S}iki\'c, Weiss, and Xiao (PSWX) and produce an analog of Naimark's theorem for these wavelets at the level of their scaling functions. We aim to make this discussion as self-contained as possible and provide a different point of view on Parseval frame MRA wavelets than that of PSWX.Comment: 19 page

Functional Analysis and its Applications

Functional analysis is, in short, the study of vector spaces with arbitrary dimension. Developed in the early twentieth century, it is an extension and amalgamation of the fields of complex analysis and linear algebra. David Hilbert, Frigyes and Marcel Riesz, and Stefan Banach were some of the noteworthy mathematicians who pushed the early frontiers of the subject. Many of the ideas produced from their seminal work led to powerful ideas and applications in related subjects: operator theory and ideas of Hilbert spaces were applied to physics in the early part of the twentieth century, and are now of fundamental importance in the field of quantum mechanics, and the theory of partial differential equations would be nearly impossible without the aid of very general fixed-point theorems. The purpose of this paper is threefold. First, we wish to make clear to the reader the structural similarities and differences between finite- and infinite-dimensional vector spaces. In doing so, the reader with some knowledge of linear algebra and real or complex analysis should be comfortable with the generalizations and abstractions contained below. Second, we wish to explore in detail the mathematical ideas and techniques at the foundation of functional analysis. In other words, we shall develop a context of study and, in doing so, convey to the reader some sense of what one actually means by functional analysis. The proofs are often elegant, and the techniques used to solve problems are quite easily applied to other areas of functional analysis. These two points shall be the topic of the first three chapters. Third, we wish to impress upon the reader the power of functional analysis to solve pure and applied problems in other areas of mathematics. This will be done especially in Chapter 4, where we apply a very general fixed point theorem to a particular partial differential equation to establish existence and smoothness of generalized solutions. This latter work was completed during the author\u27s NSF-funded internship at Cornell University and credit should be also attributed to Phillip Whitman, Frances Hammock, and Alexander Meadows

ἌΦΕΣΙΣ in the New Testament and Its Suggested Links to the Biblical Jubilee

This study responds to the claims that the term ἄφεσις (usually translated “forgiveness”) should be understood in light of the biblical Jubilee. The study commences with a brief survey of the word's use in the Septuagint and Classical Greek literature, alongwith the related verb ἀφίημι. It then examines each use of ἄφεσις in the New Testament. Texts in Matthew, Mark, Luke-Acts, Paul's writings and Hebrews are examined, with a particular focus on Lucan texts (since these contain the majority of the occurrences of the word). The study concludes that the verb ἀφίημι was never explicitly connected to the Jubilee in the Septuagint, so there is no reason to view the word in this light in the New Testament. The study also concludes that even though the term ἄφεσις had Jubilee connotations at the time the Septuagint was written, there was significant semantic development such that by the time of the New Testament, the word had a distinct and unambiguous meaning, centred on the forgiveness of sins and unrelated to the Jubilee

Movements and spawning of white marlin (Tetrapturus albidus) and blue marlin (Makaira nigricans) off Punta Cana, Dominican Republic

With a focus on white marlin (Tetrapturus albidus), a concurrent electronic tagging and larval sampling effort was conducted in the vicinity of Mona Passage (off southeast Hispaniola), Dominican Republic, during April and May 2003. Objectives were 1) to characterize the horizontal and vertical movement of adults captured from the area by using pop-up satellite archival tags (PSATs); and 2) by means of larval sampling, to investigate whether fish were reproducing. Trolling from a sportfishing vessel yielded eight adult white marlin and one blue marlin (Makaira nigricans); PSAT tags were deployed on all but one of these individuals. The exception was a female white marlin that was unsuitable for tagging because of injury; the reproductive state of its ovaries was examined histologically. Seven of the PSATs reported data summaries for water depth, temperature, and light levels measured every minute for periods ranging from 28 to 40 days. Displacement of marlin from the location of release to the point of tag pop-up ranged from 3l.6 to 267.7 nautical miles (nmi) and a mean displacement was 3.4 nmi per day for white marlin. White and blue marlin mean daily displacements appeared constrained compared to the results of other marlin PSAT tagging studies. White marlin ovarian sections contained postovulatory follicles and final maturation-stage oocytes, which indicated recent and imminent spawning. Neuston tows (n=23) yielded 18 istiophorid larvae: eight were white marlin, four were blue marlin, and six could not be identified to species. We speculate that the constrained movement patterns of adults may be linked to reproductive activity for both marlin species, and, if true, these movement patterns may have several implications for management. Protection of the potentially important white marlin spawning ground near Mona Passage seems warranted, at least until further studies can be conducted on the temporal and spatial extent of reproduction and associated adult movement

A Study of a Possible Oral Hypoglycemic Factor in Albahaca Morada (Ocimum Sanctum L.)

Author Institution: 3328 Euclid Avenue, Cleveland 15, Ohio ; Havana, Cub