128,647 research outputs found
Families of Dirac operators, boundaries and the B-calculus
No full textA version of the Atiyah-Patodi-Singer index theorem is proved for general families of Dirac operators on compact manifolds with boundary. The vanishing of the analytic index of the boundary family, in K-1 of the base, allows us to define, through an explicit trivialization, a smooth family of boundary conditions of generalized Atiyah-Patodi-Singer type. The calculus of b-pseudodifferential operators is then employed to establish the family index formula. A relative index formula, describing the effect of changing the choice of the trivialization, is also given. In case the boundary family is invertible the form of the index theorem obtained by Bismut and Cheeger is recovered
MR2741185 Talvila, Erik The regulated primitive integral. Illinois J. Math. 53 (2009), no. 4, 1187–1219. (Reviewer: Luisa Di Piazza) 46G12 (26A39 46E15 46F10)
No full textTalvila Erik, The regulated primitive integral. Illinois J. Math. 53 (2009), no. 4, 1187–1219, 46Gxx (26A39 46Exx) MR 2 741 185
A descriptive definition of an integral is a definition which provides a ``description'' of the space of primitives. The derivatives in some sense of the primitives are the integrands.
In this paper the author introduces a descriptive method of integrating distributions: the regulated primitive integral.
The set \textbf{B}_R= \{F: [-\infty,\infty]
\rightarrow {\bf R}
\ \ | \mbox{ F {\it is regulated and left continuous on }}\\
\ \ {\bf R},
\ \ F(-\infty)=0, \ \ F(\infty)\in {\bf R}\} is the family of primitives.
The derivative here is in the sense of the distributions (i.e. a distributional or weak derivative). Then the integrable distributions are those distributions (in the Schwartz's sense) that are the distributional derivative of a function in .
The regulated primitive integral is a proper extension of the integral of distribution defined by L. Schwartz [Théorie des distributions. (French) Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. IX-X. Hermann, Paris 1966 xiii+420, 46.40 (44.00), MR0209834 (35730)]. Moreover it is proved that the space of regulated integrable distributions is the completion of the space of signed Radon measures in the Alexiewicz norm, but it is not the completion in this norm of the Henstock-Kurzweil integrable functions. The functions of bounded variation constitute its dual space and also the space of multipliers. In the introduction a wide
panorama of descriptive and constructive integration methods is given.
Reviewed by (L. Di Piazza
Progetto di fattibilità tecnico economica per la riqualificazione architettonica impiantistica e commerciale del mercato di piazza Cavour
No full textLa piazza del mercato costituisce attualmente il limite nord della parte pedonalizzata di corso Cavour, e si trova nelle immediate prossimità dell’area pedonale di via del Prione, in posizione di cerniera tra il centro storico a sud-est e il Quartiere Umbertino a nord-ovest. Una peculiarità dell’area è rappresentata dal fatto che essa è attualmente una sorta di ibrido tra un mercato in sede propria e una piazza su cui si svolge il mercato, ossia tra un edificio con una caratterizzazione funzionale ben precisa e uno spazio pubblico aperto. Il progetto di riqualificazione dello spazio pubblico, quindi, si prefigge di caratterizzare in maniera chiara degli ambiti complementari, ma distinti: l’uno, al centro, lasciato libero e attrezzato come una vera piazza; gli altri, intorno, adibiti all’attività commerciale. Per l’ambito centrale è prevista la realizzazione di due piccoli edifici che delimitano lo spazio a nord e a sud; al loro interno sono previste attività di bar e ristorazione. Per quanto concerne il mercato, le coperture a onda vengono conservate; il nostro progetto, però, prevede su di esse un intervento di manutenzione straordinaria e di parziale trasformazione, nonché la realizzazione di box fissi e di chiusure perimetrali in tutti e quattro i padiglioni del mercato. I bordi esterni, quelli interni e le testate vengono trattati in modo diverso, a seconda dei differenti contesti con cui si relazionano
Variational measures in the theory of integration
No full text{Variational measures in the theory of integration}
{Luisa Di Piazza}
{Palermo , Italy}
We will present here some results concerning the variational measures associated to a real valued function, or, in a more general setting, to a vector valued function. Roughly speaking, given a function defined on an interval of the real line it is possible to construct, using suitable families of intervals, a measure which carries information about . If is a real valued function, then the -finiteness of the measure implies the a.e. differentiability of , while the absolute continuity of the measure characterizes the functions which are Henstock-Kurzweil primitives. The situation becomes more complicate if we consider functions taking values in an infinite dimensional Banach space. If the Banach space has the Radon-Nikod\'{y}m property, then it is possible to obtain properties similar to those of the real case. But it is surprising that by means of the variational measures it is possible to characterize the Banach space having the Radon-Nikod\'{y}m property.
\begin{thebibliography}{99}
\bibitem{bds1} B. Bongiorno, L. Di Piazza and V. Skvortsov,
\textit{ A new full descriptive characterization of Denjoy-Perron
integral}, Real Analysis Exchange, {\bf 21} (1995/96), 256--263.
\bibitem{bdm} B. Bongiorno, L. Di Piazza and K. Musial,
\textit{ A characterization of the
Radon-Nikod\'{y}m property by finitely additive interval
functions}, Illinois Journal of Mathematics. Volume 53, Number 1 (2009), 87-99.
\bibitem{db} D. Bongiorno, \textit{ Stepanoff's theorem in separable Banach
spaces}, Comment. Math. Univ. Ca\-ro\-linae, {\bf 39} (1998),
323--335.
\bibitem{ldp1} L. Di Piazza, \textit{ Varational measures in the theory of the
integration in }, Czechos. Math. Jour. 51(126) (2001), no. 1,
95--110.
\bibitem{vm} V. Marraffa, \textit{
A descriptive characterization of the
variational Henstock integral}, Proceedings of the International
Mathematics Conference (Manila, 1998), Matimy\'{a}s Mat. {\bf 22}
(1999), no. 2, 73--84
MR3191427 Naralenkov, Kirill M., A Lusin type measurability property for vector- valued functions. J. Math. Anal. Appl. 417 (2014), no. 1, 293307. 28A20
No full textIn the paper under review the author introduces the notion of Riemann measurability for vector-valued
functions, generalizing the classical Lusin condition, which is equivalent to the Lebesgue measurability
for real valued functions. Let X be a Banach space, let f : [a; b] ! X and let E be a measurable subset of [a; b]. The function
f is said to be Riemann measurable on E if for each " > 0 there exist a closed set F E with
(E n F) < 0 (where is the Lebesgue measure) and a positive number such that
k XK
k=1
ff(tk) ?? f(t0
k)g (Ik)k < "
whenever fIkgKk
=1 is a nite collection of pairwise non-overlapping intervals with max1 k K (Ik) <
and tk; t0
k 2 Ik
T
F.
The Riemann measurability is more relevant to Riemann type integration theory, such as those of
McShane and Henstock, rather than the classical notion of Bochner or scalar measurability. In par-
ticular the author studies the relationship between the Riemann measurability and the M and the H
integrals that are obtained if we assume that the gauge in the de nitions of McShane and Henstock
integral can be chosen Lebesgue measurable.
The main results are the following
If f : [a; b] ! X is H-integrable on a measurable subset E of [a; b], then f is Riemann measurable
on E.
If f : [a; b] ! X is both bounded and Riemann measurable on a measurable subset E of [a; b], then
f is M-integrable on E.
If f : [a; b] ! X is both Riemann measurable and McShane (Henstock) integrable on a measurable
subset E of [a; b], then f is M-integrable (H-integrable) on E.
Suppose X separable. If f : [a; b] ! X is McShane (Henstock) integrable, then f is M-integrable
(H-integrable.)
The author concludes the paper with the following open problem: for which families of non-separable
Banach spaces does the McShane (or even the Pettis) integrability imply Riemann measurability?
Reviewed by (L. Di Piazza
A pilot model of vaccination against hepatitis B virus suitable for mass vaccination campaigns in hyperendemic area.
No full textA hepatitis B vaccination campaign was carried out in a town of 60,000 inhabitants, Afragola, Campania, Italy, a hyperendemic area for hepatitis B where HBsAg prevalence was 13.4% and anti-HBc prevalence was 64.7%. This experimental pilot project aimed to reduce the incidence of both acute and asymptomatic viral hepatitis B and of related chronic liver complications. From 1983-1989, 8,400 subjects were vaccinated: 6,900 children up to 10 years of age and 1,500 subjects from 11-60 years of age. High seroconversion rates were observed: 99.0% in all children under one year of age, 96.0% in the older children, and 86.7% in adults. The rate of infection in Afragola has diminished from 63/100,000 in 1983 to 10/100,000 in 1989. Carriers of HBsAg decreased in the general population (7.3% compared to 13.4%), especially in children up to 10 years of age (1.0% compared to 9.0%). In babies who received hepatitis B vaccine at the same time as compulsory vaccinations compliance was 98% while it was 80% in babies who were vaccinated separately. In June 1991 the Italian Parliament promulgated a decree which imposes hepatitis B vaccination for all newborn babies at 3, 5, and 11 months of age, at the same times as the mandatory childhood vaccinations (diphtheria, tetanus, and polio) according to a new protocol (Piazza scheme) which has been in use since January 1987 in our pilot vaccination campaign in Afragola
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Sistemazione Piazza Goldoni, Trieste (I)
No full textprogetto per la riqualificazione di piazza goldoni a trieste [i]; pubblicazione e mostra
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
An index theorem for families of Dirac operators on odd-dimensional manifolds with boundary
No full textFor a family of Dirac operators, acting on Hermitian Clifford modules over the odd-dimensional compact manifolds with boundary which are the fibres of a fibration with compact base, we compute the Chern character of the index, in K-1 of the base. Although we assume a product decomposition near the boundary, we make no assumptions on invertibility of the boundary family and instead obtain a family of self-adjoint Fredholm operators by choice of an auxiliary family of projections respecting the Z(2) decomposition of bundles over the boundary. In case the boundary family is invertible, this projection can be taken to be the Atiyah-Patodi-Singer projection and the resulting formula is as conjectured by Bismut and Cheeger. The derivation of the index formula is effected by the combination of the superconnection formalism of Quillen and Bismut, the calculus of b-pseudodifferential operators and suspension
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