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.

CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the well-known methods and a newly proposed method for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions in terms of self-adjoint boundary conditions. The new method has the advantage that it does not require explicitly evaluating deficient subspaces and deficiency indices (these latter are determined in passing) and that boundary conditions are of explicit character irrespective of the singularity of a differential expression. General assertions and constructions are illustrated by examples of well-known quantum-mechanical operators like momentum and Hamiltonian.

A new proposal for the picture changing operators in the minimal pure spinor formalism

Using a new proposal for the ""picture lowering"" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the. Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the. Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green`s function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

Evaluation of dental pulp repair using low level laser therapy (688 nm and 785 nm) morphologic study in capuchin monkeys

The aim of this study was to evaluate the hypothesis that low-level laser therapy (LLLT) 688 nm and 785 nm accelerate dentin barrier formation and repair process after traumatic pulp exposure. The sample consisted of 45 premolars of capuchin monkeys (Cebus apella) with pulp exposure Class V cavities. All premolars were treated with calcium hydroxide (Ca(OH)(2)), divided in groups of 15 teeth each, and analyzed on 7(th), 25(th), and 60(th) day. Group GI - only Ca(OH)(2), GIF- laser 688 nm, and GIII - laser 785 nm. Laser beam was used in single and punctual dose with the parameters: continuous, 688 nm and 785 nm wavelength, tip`s area of 0.00785 cm(2), power 50 mW, application time 20 s, dose 255 J/cm(2), energy 2 J. Teeth were capped with Ca(OH)(2), Ca(OH)(2) cement and restored with amalgam. All groups presented pulp repair. On 25(th) day the thickness of the formed dentin barrier was different between the groups GI and GII (p < 0.05) and between groups GI and GIII (p < 0.01). On 60(th) day there was difference between GI and GIII (p < 0.01). It may be concluded that, LLLT 688 nm and 785 nm accelerated dentin barrier formation and consequently pulp repair process, with best results using infrared laser 785 nm. (c) 2009 by Astro Ltd. Published exclusively by WLLEY-VCH Verlag GmbH & Co. KGaA

Multilevel Training of Binary Morphological Operators

The design of binary morphological operators that are translation-invariant and locally defined by a finite neighborhood window corresponds to the problem of designing Boolean functions. As in any supervised classification problem, morphological operators designed from a training sample also suffer from overfitting. Large neighborhood tends to lead to performance degradation of the designed operator. This work proposes a multilevel design approach to deal with the issue of designing large neighborhood-based operators. The main idea is inspired by stacked generalization (a multilevel classifier design approach) and consists of, at each training level, combining the outcomes of the previous level operators. The final operator is a multilevel operator that ultimately depends on a larger neighborhood than of the individual operators that have been combined. Experimental results show that two-level operators obtained by combining operators designed on subwindows of a large window consistently outperform the single-level operators designed on the full window. They also show that iterating two-level operators is an effective multilevel approach to obtain better results.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

Platinum nanoparticle-modified electrodes, morphologic, and electrochemical studies concerning electroactive materials deposition

The present work describes the synthesis of platinum nanoparticles followed by their electrophoretic deposition onto transparent fluorine-doped tin oxide electrodes. The nano-Pt-modified electrodes were characterized by voltammetric studies in acidic solutions showing a great electrocatalytic behavior towards H(+) reduction being very interesting for fuel cell applications. Morphological characterization was performed by atomic force microscopy on different modified electrodes showing a very rough surface which can be tuned by means of time of deposition. Also, nickel hydroxide thin films were galvanostatically grown onto these electrodes showing an interesting electrochemical behavior as sharper peaks, indicating a faster ionic exchange from the electrolyte to the film.

Enhancing the distribution of Swedish tourism services on international markets : Possible export-ready criteria requisitioned by European tour operators

This paper identifies subjects which are relevant for Swedish suppliers of tourism services beforeapproaching foreign markets. Most suppliers are micro, small or medium sized companies anduse intermediaries, such as tour operators, for internationalization. The research considers theopinion of British and German tour operators, which require some criteria beforehand in orderto simplify both the initialization and the development of cooperation. Destination marketingorganizations (DMOs) are hereby the go-betweens since they not only represent small-scalesuppliers on international markets, but also initiate first encounters between suppliers and touroperators. Suppliers need to provide DMOs with accurate information in order to ensure thebest possible representation. After initializing collaboration, business relationships are sought todevelop in order to facilitate long-term cooperation. Proper preparation forms therefore the basefor strengthening the competitiveness of Swedish tourism prior approaching internationalmarkets. The enhancement of distributing Swedish tourism services on foreign markets appearedto be a profitable way to enable further growth, which is strongly limited on the domestic market.Increasing the export share therefore secures and further facilitates tourism’s valuablecontributions to the Swedish economy.

A user guide to simple monitoring and sustainable operation of PV-diesel hybrid systems : Handbook for system users and operators

This report contains a suggestion for a simple monitoring and evaluation guideline for PV-diesel hybrid systems. It offers system users a way to better understand if their system is operated in a way that will make it last for a long time. It also gives suggestions on how to act if there are signs of unfavourable use or failure. The application of the guide requires little technical equipment, but daily manual measurements. For the most part, it can be managed by pen and paper, by people with no earlier experience of power systems.The guide is structured and expressed in a way that targets PV-diesel hybrid system users with no, or limited, earlier experience of power engineering. It is less detailed in terms of motivations for certain choices and limitations, but rich in details concerning calculations, evaluation procedures and maintenance routines. A more scientific description of the guide can be found in a related journal article.

Performance and ruminal morphologic characteristics of Saanen kids fed ground, pelleted or extruded total ration

The aim of the present study was to determine feed intake and average weight gain and to evaluate the ruminal morphologic characteristics of Saanen kids slaughtered at 30, 45 and 60 days of age, according to a completely randomized design. Thirty-six non-castrated male Saanen kids were fed ground total ration, pelleted total ration, or extruded total ration. Feed intake and refusals were controlled daily and the animals were weighed at birth and then once a week. Newborn kids received a milk replacer and were weaned at 45 days. Immediately after slaughter, the animals were eviscerated, the entire digestive apparatus was removed from the carcass. The reticulo-rumen was separated, emptied, washed and weighed. Samples were collected from the dorsal sac, pillar area and ventral sac of the rumen, fixed for about 24h in Bouin's solution, dehydrated, embedded in Histosec and cut into 5 mu m sections. Results showed that dry matter intake (DMI) at weaning and post-weaning and weight gain were higher (P < 0.05) in animals that received the pelleted total ration. The weight of the reticulo-rumen accompanied body development and was heavier in these animals. Histologically, after weaning ruminal papillae were more developed in animals that received pelleted total ration. Length of papillae increased with increase of age. The ratio of papillary height to papillary width increased with age in the ventral sac and until weaning (P > 0.05). We conclude that the pelleting process of the total ration favored increased intake, with a 46.7% increase in weight gain and increase in rumen weight and papillae length, suggesting that best results are obtained with this processing. In general, no difference was observed between the results obtained with extruded and ground total ration, although animals fed extruded total ration showed an increase in rumen weight and papillae width. (c) 2004 Elsevier B.V All rights reserved.

Morphologic and morphometric analysis of Hepatozoon spp. (Apicomplexa, Hepatozoidae) of snakes

Hepatozoon species are the most abundant hemoparasites of snakes. Its identification has been based mainly on the morphologic characterization of the gamonts in the peripheral blood of the vertebrate host and also of the cysts found in the internal organs of the vertebrate and invertebrate hosts. Using a computerized image analysis system, we studied five species of Hepatozoon from recently captured snakes in Botucatu, State of São Paulo, Brazil, to evaluate the importance of the morphology and morphometry of the gamonts for the characterization of Hepatozoon species and to analyze the morphologic changes induced in the erythrocytes by the parasite. The studied species were H. terzii of Boa constrictor amarali, Hepatozoon sp. of Crotalus durissusterrificus, H. philodryasi of Philodryas patagoniensis, and H. migonei and H. cyclagrasi of Hydrodynastes gigas. We observed three different groups, one of them including the species H. terzii, H. philodryasi and Hepatozoon sp. of C. durissus terrificus; and the other two consisting of H. migonei and H. cyclagrasi. Degree of alterations in the erythrocytes was variable and it may be useful for characterization of Hepatozoon species.

Morphologic and molecular characterization of Myrciaria spp species

A jabuticabeira é considerada uma das fruteiras mais típicas do Brasil. Entretanto, há poucos estudos sobre esta planta na literatura, e mesmo sua classificação botânica é muito controvertida. Este trabalho faz comparações entre as espécies de jabuticabeiras, usando as técnicas de marcadores morfológicos (organografia) e moleculares RAPD. As características morfológicas das plantas, usadas como marcadores morfológicos, foram comparadas com espécimes presentes nos herbários dos Estados de São Paulo e Minas Gerais e com as descrições obtidas em revisão de literatura especializada. As diferenças moleculares entre as espécies foram determinadas por meio do uso de marcadores RAPD. O experimento foi realizado nas cidades de Piracicaba, Jaboticabal e Ituverava do Estado de São Paulo, Brasil. Diferenças morfológicas e moleculares entre as plantas estudadas foram identificadas, e quatro grupos distintos de espécies foram definidos: Myrciaria cauliflora (Mart.) O. Berg, M. coronata Mattos, M. jaboticaba (Vell.) O. Berg. e M. phytrantha (Kiaersk.) Mattos. A técnica de marcadores moleculares, aliada à técnica de marcadores morfológicos, mostrou ser uma ferramenta importante na identificação de espécies de jabuticabeiras.

Morphologic and morphometric analysis of testis of Pseudis limellum (Cope, 1862) (Anura, Hylidae) during the reproductive cycle in the Pantanal, Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sparse 1D discrete Dirac operators I: Quantum transport

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sparse one-dimensional discrete Dirac operators II: Spectral properties

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