Some Schroeder-Bernstein type theorems for Banach spaces

We first introduce the notion of (p, q, r)-complemented subspaces in Banach spaces, where p, q, r is an element of N. Then, given a couple of triples {(p, q, r), (s, t, u)} in N and putting Lambda = (q + r - p)(t + u - s) - ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p, q, r)-complemented in Y and Y is (s, t, u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds: (a) Lambda not equal 0, Lambda divides p - q and s - t, p = 1 or q = 1 or s = 1 or t = 1. (b) p = q = s = t = 1 and gcd(r, u) = 1. The case {(2, 1, 1), (2, 1,1)} is the well-known Pelczynski`s decomposition method. Our result leads naturally to some generalizations of the Schroeder-B em stein problem for Banach spaces solved by W.T. Gowers in 1996. (C) 2007 Elsevier Inc. All rights reserved.

Landau and Kolmogoroff type polynomial inequalities

Let 0type inequalitiesparallel to f((f))parallel to(2) less than or equal to A parallel to f(m)parallel to + B parallel to f parallel to/ A theta(k) + B mu(k),with certain constants theta(k)e mu(k), which hold for every f is an element of pi(n) (pi(n) denotes the space of real algebraic polynomials of degree not exceeding n).For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities parallel to f'parallel to less than or equal toA parallel to f parallel to + B parallel to f parallel to/ A theta(k) + B mu(k)hold. In each case we determine the corresponding extremal polynomials for which equalities are attained.

Search for heavy lepton partners of neutrinos in proton-proton collisions in the context of the type III seesaw mechanism

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Search for pair produced fourth-generation up-type quarks in pp collisions at root s=7 TeV with a lepton in the final state

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Genotyping of Epstein-Barr virus in Brazilian Burkitt's lymphoma and reactive lymphoid tissue - Type A with a high prevalence of deletions within the latent membrane protein gene

Both Epstein-Barr virus (EBV) types A and B are found in endemic Burkitt's lymphoma (BL) occurring in equatorial Africa. We studied 17 cases of Brazilian BL previously demonstrated to be EBV-positive to determine the EBV type as well as the presence of a characteristic 30 bp deletion within the 3' end of the latent membrane protein-1 (LMP-1) gene that may be important to the pathogenesis of several EBV-associated neoplasms. All case in which the age was known were children. We found type A EBV in 13 of 14 (93%) evaluable cases, and type B in one case. The LMP-1 deletion was found in 12 of 15 (80%) evaluable cases, including the one case of type B EBV, and a similar high prevalence (59%) of the deletion was detected in EBV-positive normal and reactive lymphoid tissues from individuals from the same geographic region. The high proportion of cases associated with type A EBV suggests that immunodeficiency is not an important factor in the pathogenesis of Brazilian BL, in contrast to endemic African BL. The presence of the LMP-1 deletion in a high prevalence in the normal population in this region is unexplained.

Landau and Kolmogoroff type polynomial inequalities II

Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.

Changes and inequality in Latin American families

Includes bibliography

Propriedades e aspectos geométricos de estimadores tipo James-Stein e do estimador de Hartigan

The James-Stein estimator is a biased shrinkage estimator with uniformly smaller risk than the risk of the sample mean estimator for the mean of multivariate normal distribution, except in the one-dimensional or two-dimensional cases. In this work we have used more heuristic arguments and intensified the geometric treatment of the theory of James-Stein estimator. New type James-Stein shrinking estimators are proposed and the Mahalanobis metric used to address the James-Stein estimator. . To evaluate the performance of the estimator proposed, in relation to the sample mean estimator, we used the computer simulation by the Monte Carlo method by calculating the mean square error. The result indicates that the new estimator has better performance relative to the sample mean estimator.

The location of the primary entry tear in acute type B aortic dissection affects early outcome

The goal of the retrospective study was to relate the site of the primary entry tear in acute type B aortic dissections to the presence or development of complications.

Repair of stent graft-induced retrograde type A aortic dissection using the E-vita open prosthesis

Stent graft-induced retrograde type A dissection is a life-threatening complication after endovascular treatment of acute aortic type B dissections.

Minimal assumption derivation of a weak Clauser-Horne inequality

According to Bell's theorem a large class of hidden-variable models obeying Bell's notion of local causality (LC) conflict with the predictions of quantum mechanics. Recently, a Bell-type theorem has been proven using a weaker notion of LC, yet assuming the existence of perfectly correlated event types. Here we present a similar Bell-type theorem without this latter assumption. The derived inequality differs from the Clauser-Horne inequality by some small correction terms, which render it less constraining.

Liraglutide once a day versus exenatide twice a day for type 2 diabetes: a 26-week randomised, parallel-group, multinational, open-label trial (LEAD-6)

BACKGROUND: Unlike most antihyperglycaemic drugs, glucagon-like peptide-1 (GLP-1) receptor agonists have a glucose-dependent action and promote weight loss. We compared the efficacy and safety of liraglutide, a human GLP-1 analogue, with exenatide, an exendin-based GLP-1 receptor agonist. METHODS: Adults with inadequately controlled type 2 diabetes on maximally tolerated doses of metformin, sulphonylurea, or both, were stratified by previous oral antidiabetic therapy and randomly assigned to receive additional liraglutide 1.8 mg once a day (n=233) or exenatide 10 microg twice a day (n=231) in a 26-week open-label, parallel-group, multinational (15 countries) study. The primary outcome was change in glycosylated haemoglobin (HbA(1c)). Efficacy analyses were by intention to treat. The trial is registered with ClinicalTrials.gov, number NCT00518882. FINDINGS: Mean baseline HbA(1c) for the study population was 8.2%. Liraglutide reduced mean HbA(1c) significantly more than did exenatide (-1.12% [SE 0.08] vs -0.79% [0.08]; estimated treatment difference -0.33; 95% CI -0.47 to -0.18; p<0.0001) and more patients achieved a HbA(1c) value of less than 7% (54%vs 43%, respectively; odds ratio 2.02; 95% CI 1.31 to 3.11; p=0.0015). Liraglutide reduced mean fasting plasma glucose more than did exenatide (-1.61 mmol/L [SE 0.20] vs -0.60 mmol/L [0.20]; estimated treatment difference -1.01 mmol/L; 95% CI -1.37 to -0.65; p<0.0001) but postprandial glucose control was less effective after breakfast and dinner. Both drugs promoted similar weight losses (liraglutide -3.24 kg vs exenatide -2.87 kg). Both drugs were well tolerated, but nausea was less persistent (estimated treatment rate ratio 0.448, p<0.0001) and minor hypoglycaemia less frequent with liraglutide than with exenatide (1.93 vs 2.60 events per patient per year; rate ratio 0.55; 95% CI 0.34 to 0.88; p=0.0131; 25.5%vs 33.6% had minor hypoglycaemia). Two patients taking both exenatide and a sulphonylurea had a major hypoglycaemic episode. INTERPRETATION: Liraglutide once a day provided significantly greater improvements in glycaemic control than did exenatide twice a day, and was generally better tolerated. The results suggest that liraglutide might be a treatment option for type 2 diabetes, especially when weight loss and risk of hypoglycaemia are major considerations.

Gruss aus Bayreuth! : Ein' Becher mit Leisten, ein' Becher mit Stein

kaum hör' ich die Glöcklein noch läuten / Und immer noch sitz ich und schenke mir ein, / Ich weiss nicht was soll es bedeuten!

Some Mean-Value Theorems of the Cauchy Type

2000 Mathematics Subject Classification: Primary 26A24, 26D15; Secondary 41A05