A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

A criterion for unitary similarity of upper triangular matrices in general position

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a(ij)] and B = [b(ij)] be upper triangular n x n matrices that are not similar to direct sums of square matrices of smaller sizes, or are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if parallel to h(A(k))parallel to = parallel to h(B(k))parallel to for all h is an element of C vertical bar x vertical bar and k = 1, ..., n, where A(k) := [a(ij)](i.j=1)(k) and B(k) := [b(ij)](i.j=1)(k) are the leading principal k x k submatrices of A and B, and parallel to . parallel to is the Frobenius norm. (C) 2011 Elsevier Inc. All rights reserved.

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

General morphology and ultrastructure of the venom apparatus and convoluted gland of the fire ant, Solenopsis saevissima

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Pressure field in a tube with a general and arbitrary time- and position-dependent gas source

In this article we present analytical and numerical results for a pressure profile along the axis of a tube with a general and arbitrary time- and position-dependent gas source. The model is able to determine the pressure values along the tube, once the pumping speed at each extremity and the gas sources are specified. The time evolution of the pressure along a tube is presented for situations commonly found in high-vacuum applications, such as particle accelerators, colliders, storage rings, and synchrotron light sources. (C) 2004 American Vacuum Society.

Bismuth as a general internal standard for lead in atomic absorption spectrometry

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A survey of the management of patients with temporomandibular disorders by general dental practitioners in southern Brazil

Purpose: Temporomandibular disorders (TMD) are recognized as one of the mostcontroversial topics in dentistry, despite the fact that both basic science and clinicalresearchers have currently reached some degree of consensus. This study aimed toconduct a questionnaire-based survey about the management of TMD patients bygeneral dental practitioners (GDPs).Materials and Methods: One hundred fifty-one GDPs with a private practice in a cityof southern Brazil were included, independent of school of origin, gender, graduationyear, and curriculum content. All participants were administered a questionnaire aboutthe management of patients with TMD, and the responses were analyzed by binomialand chi-square tests (α = 0.05).Results: Of the GDPs, 88.7% received TMD patients, who were primarily diagnosedon the basis of medical history (36.6%) or physical examination (30.4%). Of these,65.4% referred the patients elsewhere, primarily to specialists in occlusion (36.1%) ororthodontics (29.7%). Occlusal splinting was the most commonly used managementmodality (20.8%), followed by occlusal adjustment (18.1%) and pharmacotherapy(16.6%). Splints were fabricated in maximum habitual intercuspation or centric re-lation depending on individual patient (54.8%). The hard stabilization form was themost common type of appliance used (35.0%). Moreover, 73.8% of the GDPs didnot employ semi-adjustable articulators, and 69.5% adjusted the appliances at thetime of fixing. The duration of splint use and the frequency of follow-up were con-sidered patient dependent by 62.1% and 72.8%, respectively. GDPs considered thetwo major TMD etiologic categories as multifactorial (20.8%) and occlusion (19.9%).Multidisciplinary medical and dental treatment was considered necessary by 97.9%.Conclusions: The evaluated general dental practitioners manage TMD patients ac-cording to international guidelines.

Assessment of dry residual biomass potential for use as alternative energy source in the party of General Pueyrredon, Argentina

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

General characterization of Tityus fasciolatus scorpion venom. Molecular identification of toxins and localization of linear B-cell epitopes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Validity of alcohol screening instruments in general population gender studies: an analytical review

The present study is an analytical review of the methodology used in studies of efficacy of screening instruments to detect harmful use/ alcohol dependence according to the gender in population surveys. Systematic review of bibliography was done, using data from Web of Science, Pubmed and PsycInfo. Population studies were included without date range, in English, Spanish or Portuguese languages, with sample of adults, evaluating psychometric characteristics of any alcohol screening instrument, whereas studies in special population or under treatment as well as prevalence of alcohol consumption were excluded. Thirteen studies were selected to be included in the present review. According to the studies, the instruments that presented a better performance among men were AUDIT and its derivatives (6 studies) and CAGE (2 studies), whereas among women, AUDIT and its derivatives (7 studies), followed by CAGE (3 studies). The increase of consumption and problems related to alcohol use and its implications for public health indicate the need and urgency for adequacy of screening instruments to differences of gender in general population. The population surveys in the area are scarce. Furthermore, the found studies present heterogeneous methodology which makes accurate comparisons difficult.

Class Notes for Math 871: General Topology, Instructor Jamie Radcliffe

Topics include: Topological space and continuous functions (bases, the product topology, the box topology, the subspace topology, the quotient topology, the metric topology), connectedness (path connected, locally connected), compactness, completeness, countability, filters, and the fundamental group.