Some approximation properties of the Kantorovich variant of the Bleimann, Butzer and Hahn operators

summary:For some classes of functions $f$ locally integrable in the sense of Lebesgue or Denjoy-Perron on the interval $[0;\infty )$, the Kantorovich type modification of the Bleimann, Butzer and Hahn operators is considered. The rate of pointwise convergence of these operators at the Lebesgue or Lebesgue-Denjoy points of $f$ is estimated

La complejidad de las huellas de uso en puntas de proyectil de sílex – Una contribución para el debate

In this paper we describe an experiment designed to provide guidelines for a detailed classification of use-wear traces formed on flint projectile points, resulting from striking a range of organic and non-organic materials. We verify the existing findings, and pay particular attention to microscopic damage (retouches, polish and striations). The list of traces characteristic for projectile points is formed mainly on the basis of morphology (current microscopic observations) and only indirectly on functional classifications. In the course of our experiment 122 arrowhead replicas were used: 33 points, 31 arrowheads with bifacial surface retouch, 26 trapezes and 16 composite arrowheads (made of a lateral inset/barb and point inset each). Our classification in- cludes 22 diagnostic features, divided into 4 main groups: fractures, retouch, polish and striations. Among the fractures, the most characteristic were the complex splintered ones as well as certain types of fractures with retouch (especially those with spin-off spalls). Among the retouched ones and crush-outs the most abundant ones exhibited burin-like fractures and spin-off spalls, though retouches such as: toothed, splintered, post-impact and splintered from the shaft were considered as important too. Attention was also paid to slanting edge retouch, which is not found on other types of functional tools. Among the different types of polish special attention was given to those formed as a result of a tool’s rapid friction against a hard material at the point of impact. Prime importance was given to patch-like and linear polish; large significance was also given to specific types of ridge and edge polish. Linear traces were found to be of little use for the interpretation of a projectile weapon’s insets function. Our observations sug- gest that the identification of prehistoric projectile points may require a much more precise analysis than those hitherto conducted. Relying solely on the basic types of post-impact traces is inadequate. Traces of this type are in fact only present on a small percentage of the total number of insets. In addition, some kinds of them formed only in specific circumstances, in which both the type of arrowhead and the kind of target were of importance.En este artículo describimos un experimento programado para proporcionar pautas para una clasificación detallada de las huellas de uso generadas en las puntas de proyectil de sílex por golpeo sobre una variedad de materiales orgánicos y no orgánicos. Veri- ficamos los resultados existentes y prestamos especial atención al daño microscópico (retoques, pulido y estrías). La lista de trazas características de las puntas de proyectil se estableció principalmente sobre la base de la morfología (observaciones microscó- picas actuales) y solo indirectamente a partir de las clasificaciones funcionales. En el transcurso del experimento se utilizaron 122 réplicas de puntas de flecha: 33 puntas, 31 puntas de flecha con retoque bifacial, 26 trapecios y 16 puntas de flecha compuestas (realizada cada una mediante la inserción de una punta y una barba lateral). Nuestra clasificación incluye 22 rasgos de diagnóstico, divididos en 4 grupos principales: fracturas, retoque, pulido y estriaciones. Entre las fracturas, las más características fueron los astillamientos complejos, así como ciertos tipos de fracturas con retoque (especialmente las producidas con levantamiento de esquirlas). Entre los retocados y los aplastados, los más abundantes mostraban fracturas burilantes y negativos de esquirlas, aunque retoques denticulados, astillados postimpacto y astillados del astil se consideraron importantes. También se prestó atención a los retoques en el filo que no se encuentran en otros tipos de útiles funcionales. Entre los diferentes tipos de pulidos, se prestó especial atención a los producidos como resultado de la rápida fricción del útil contra un material duro en el punto de impacto. Se dio una gran im- portancia al pulido lineal y al extenso; también se consideraron significativos los tipos específicos de pulido en aristas y bordes. Se encontró que las huellas lineales son de poca utilidad para la interpretación de la función de las inserciones de los proyecti- les. Nuestras observaciones sugieren que la identificación de puntas de proyectiles prehistóricos puede requerir un análisis mucho más preciso que los realizados hasta ahora. Depender únicamente de los tipos básicos de estigmas posteriores al impacto es inadecuado. Las huellas de este tipo solo están presentes en un pequeño porcentaje del número total de inserciones. Además, algunos tipos de ellas se formaron solo en circunstancias específicas, en las que tanto el tipo de punta de flecha como el tipo de blanco tenían importancia

Periodic points of latitudinal maps of the m-dimensional sphere

Let f be a smooth self-map of the m-dimensional sphere Sm. Under the assumption that f preserves latitudinal foliations with the fibres S1, we estimate from below the number of fixed points of the iterates of f. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz

Shub’s conjecture for smooth longitudinal maps of Sm

Let f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f, reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m=2 and in a weak form for m=3

Some approximation properties of modified Szasz-Mirakyan-Kantorovich operators

In this paper we consider the modified Szasz-Mirakyan-Kantorovich operators for functions $f$ integrable in the sense of Denjoy-Perron. Moreover, we estimate the rate of pointwise convergence of $M_nf(x)$ at the Lebesgue-Denjoy points $x$ of $f$

The PSU/TCfA Search for Planets around Evolved Stars. Stellar parameters and activity indicators of targets

The main objective of the Penn State/Torun Centre for Astronomy Search for Planets around Evolved Stars is the detection of planetary systems around massive, evolved stars. We are also interested in the evolution of these systems on stellar evolution timescales. In this paper we present our approach to determine the basic physical parameters of our targets GK-giants. We also discuss the stellar activity indicators used in our survey: line bisector and curvature, and Halpha variability.Comment: 5 pages, to appear in ,,Exoplanets. Detection, Formation & Dynamics'' IAU Symposium 249, Cambridge University Press, 200