Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

Spatial and temporal variability of the concentration field from localized releases in a regular building array

Spatial and temporal fluctuations in the concentration field from an ensemble of continuous point-source releases in a regular building array are analyzed from data generated by direct numerical simulations. The release is of a passive scalar under conditions of neutral stability. Results are related to the underlying flow structure by contrasting data for an imposed wind direction of 0 deg and 45 deg relative to the buildings. Furthermore, the effects of distance from the source and vicinity to the plume centreline on the spatial and temporal variability are documented. The general picture that emerges is that this particular geometry splits the flow domain into segments (e.g. “streets” and “intersections”) in each of which the air is, to a first approximation, well mixed. Notable exceptions to this general rule include regions close to the source, near the plume edge, and in unobstructed channels when the flow is aligned. In the oblique (45 deg) case the strongly three-dimensional nature of the flow enhances mixing of a scalar within the canopy leading to reduced temporal and spatial concentration fluctuations within the plume core. These fluctuations are in general larger for the parallel flow (0 deg) case, especially so in the long unobstructed channels. Due to the more complex flow structure in the canyon-type streets behind buildings, fluctuations are lower than in the open channels, though still substantially larger than for oblique flow. These results are relevant to the formulation of simple models for dispersion in urban areas and to the quantification of the uncertainties in their predictions.

Physical and sensory properties of regular and reduced-fat pound cakes with added amaranth flour

The sum of wheat flour and corn starch was replaced by 10, 20, or 30% whole amaranth flour in both conventional (C) and reduced fat (RF) pound cakes. and the effects on physical and sensory properties of the cakes were investigated. RF presented 33% fat reduction. The increasing amaranth levels darkened crust and crumb of cakes, which decreased color acceptability. Fresh amaranth-containing cakes had similar texture characteristics to (he controls, evaluated both instrumentally and sensorially. Sensory evaluation revealed that replacement by 30% amaranth flour decreased C cakes overall acceptability scores, clue to its lower specific volume and darker color. Amaranth flour levels had no significant effect on overall acceptability of RF cakes. Hence, the sum of wheat flour and corn starch could be successfully replaced by up to 20% amaranth flour in C and up to 30% in RF pound cakes without negatively affecting sensory quality in fresh cakes. Moisture losses for all the cakes were similar, approximate to 1% per day during storage. After six days of storage, both C and RF amaranth-containing cakes had higher hardness and chewiness values than control cakes. Further experiments involving sensory evaluation during storage are necessary to determine the exact limit of amaranth flour replacement.

Dietary copper absorption and excretion in three semi-terrestrial grapsoid crabs with different levels of terrestrial adaptation

Three species of phylogenetically related semi-terrestrial crabs (Superfamily Grapsoidea - Sesarma rectum, Goniopsis cruentata and Neohelice granulata (formerly: Chasmagnathus granulatus) with different degrees of terrestriality were studied to quantify the accumulation of copper (Cu) in hemolymph, gills, hepatopancreas and antennal gland, and its excretion through the faeces. These crabs were fed for 15 days practical diets containing 0 (A), 0.5 (B), 1.0 (C), and 1.5% (D) of added CuCl2 (corresponding to 0, 0.2, 0.5 and 0.7% of Cu2+, respectively). The amount of food ingested was directly proportional to the degree of terrestriality: S. rectum, the most terrestrial species, ate around 2-3 times more than the other crabs, whereas G. cruentata ate 1.5-2 times more than N. granulata, the least terrestrial. The amount of Cu excreted in the feces was proportional to Cu ingestion, and was 76.8% and 64.2% higher for Sesarma fed diet D compared to G. cruentata and N. granulata, respectively. Sesarma also displayed higher Cu concentration in the haemolymph, gills and antennal glands, but not in the hepatopancreas. A detoxifying mechanism followed by elimination was probably present at this last organ, preventing Cu accumulation. More terrestrial crabs, such as Sesarma, may accumulate more Cu in hemolymph and tissues, showing a correlation between metal accumulation and increased terrestriality. In this aspect, contaminated feed sources with Cu may have more impact in conservation of terrestrial crabs. (C) 2008 Elsevier Inc. All rights reserved.

The importance of dietary calcium consumption in two species of semi-terrestrial grapsoid crabs

Calcium (Ca) is essential for crustaceans, due to calcium carbonate (CaCO(3)) deposition in the new exoskeleton to harden it. The purpose of this work was to study short term Ca balance in terms of dietary Ca ingestion in two phylogenetically related crabs (Superfamily Grapsoidea) showing different degrees of terrestrial adaptations: Sesarma rectum Randall, 1840 and Neohelice granulata (Dana, 1851). Dietary Ca ingestion was studied using purified diets with different Ca concentrations (0, 2.2 and 6.66% Ca), together with measurements of Ca excretion and Ca hemolymph levels. The results showed that both crabs had the same response to foods containing different levels of Ca, with both species eating more of the high Ca diet. However, S. rectum consumed more per mg body mass at all Ca concentrations (6 mg.g(-1) for S. rectum against 3 mg.g(-1) for N. granulata). Both species excreted/egested Ca differently: S. rectum excreted Ca proportionally to ingestion, whereas N. granulata maintained constant faecal Ca output at all dietary Ca levels. Moreover, Ca hemolymph levels for crabs fed the different diets were independent of dietary Ca. In conclusion, both S. rectum and N. granulata seem to regulate the consumption of diets containing more Ca, which suggests a fine balance for Ca intake.

Upregulation of gp91(phox) Subunit of NAD(P)H Oxidase Contributes to Erectile Dysfunction Caused by Long-term Nitric Oxide Inhibition in Rats: Reversion by Regular Physical Training

OBJECTIVES To test the hypothesis that glyco protein 91phox (gp91(phox)) subunit of nicotinamide adenine dinucleotide phosphate [NAD(P) H] oxidase is a fundamental target for physical activity to ameliorate erectile dysfunction (ED). Vascular risk factors are reported to contribute to ED. Regular physical exercise prevents cardiovascular diseases by increasing nitric oxide (NO) production and/or decreasing NO inactivation. METHODS Male Wistar rats received the NO synthesis inhibitor N(omega)-nitro-L-arginine methyl ester (L-NAME) for 4 weeks, after which animals were submitted to a run training program for another 4 weeks. Erectile functions were evaluated by in vitro cavernosal relaxations and intracavernous pressure measurements. Expressions of gp91(phox) subunit and neuronal nitric oxidase synthase in erectile tissue, as well as superoxide dismutase activity and nitrite/nitrate (NO(x)) levels were determined. RESULTS The in vitro acetylcholine-and electrical field stimulation-induced cavernosal relaxations, as well as the increases in intracavernous pressure were markedly reduced in sedentary rats treated with L-NAME. Run training significantly restored the impaired cavernosal relaxations. No alterations in the neuronal nitric oxidase synthase protein expression (and its variant penile neuronal nitric oxidase synthase) were detected. A reduction of NO(x) levels and superoxide dismutase activity was observed in L-NAME-treated animals, which was significantly reversed by physical training. Gene expression of subunit gp91(phox) was enhanced by approximately 2-fold in erectile tissue of L-NAME-treated rats, and that was restored to basal levels by run training. CONCLUSIONS Our study shows that ED seen after long-term L-NAME treatment is associated with gp91(phox) subunit upregulation and decreased NO bioavailability. Exercise training reverses the increased oxidative stress in NO-deficient rats, ameliorating the ED. UROLOGY 75: 961-967, 2010. (C) 2009 Elsevier Inc.

Donor bone marrow cells play a role in the prevention of accelerated graft rejection induced by semi-allogeneic spleen cells in transplantation

Spleen or spleen plus bone marrow cells from (BALB/c x C57Bl/6)F1 donors were transferred into BALB/c recipients 21 days before skin or cardiac transplantation. Prolonged graft survival was observed on recipients treated with the mixture of donor-derived cells as compared to those treated with spleen cells alone. We evaluated the expression of CD45RB and CD44 by splenic CD4(+) and CD8(+) T cells 7 and 21 days after donor cell transfer. The populations of CD8(+)CD45RB(low) and CD8(+)CD44(high) cells were significantly decreased in mice pre-treated with donor spleen and bone marrow cells as compared to animals treated with spleen cells only, although these cells expanded in both groups when compared to an earlier time-point. No differences were observed regarding CD4+ T cell population when recipients of donor-derived cells were compared. An enhanced production of IL-10 was observed seven days after transplantation in the supernatants of spleen cell cultures of mice treated with spleen and bone marrow cells. Taken together these data suggest that donor-derived bone marrow cells modulate the sensitization of the recipient by semi-allogeneic spleen cells in part by delaying the generation of activated/memory CD8(+) T cells leading to enhanced graft survival. (c) 2007 Elsevier B.V. All rights reserved.

Cyclic Maximal Ideals of Rings of Differential Operators over Power Series Rings

In [3], Bratti and Takagi conjectured that a first order differential operator S=11 +...+ nn+ with 1,..., n, {x1,..., xn} does not generate a cyclic maximal left (or right) ideal of the ring of differential operators. This is contrary to the case of the Weyl algebra, i.e., the ring of differential operators over the polynomial ring [x1,..., xn]. In this case, we know that such cyclic maximal ideals do exist. In this article, we prove several special cases of the conjecture of Bratti and Takagi.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Aerosol inorganic composition at a tropical site: Discrepancies between filter-based sampling and a semi-continuous method

The concentrations of the water-soluble inorganic aerosol species, ammonium (NH4+), nitrate (NO3-), chloride (Cl-), and sulfate (SO42-), were measured from September to November 2002 at a pasture site in the Amazon Basin (Rondnia, Brazil) (LBA-SMOCC). Measurements were conducted using a semi-continuous technique (Wet-annular denuder/Steam-Jet Aerosol Collector: WAD/SJAC) and three integrating filter-based methods, namely (1) a denuder-filter pack (DFP: Teflon and impregnated Whatman filters), (2) a stacked-filter unit (SFU: polycarbonate filters), and (3) a High Volume dichotomous sampler (HiVol: quartz fiber filters). Measurements covered the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). Analyses of the particles collected on filters were performed using ion chromatography (IC) and Particle-Induced X-ray Emission spectrometry (PIXE). Season-dependent discrepancies were observed between the WAD/SJAC system and the filter-based samplers. During the dry season, when PM2.5 (D-p <= 2.5 mu m) concentrations were similar to 100 mu g m(-3), aerosol NH4+ and SO42- measured by the filter-based samplers were on average two times higher than those determined by the WAD/SJAC. Concentrations of aerosol NO3- and Cl- measured with the HiVol during daytime, and with the DFP during day- and nighttime also exceeded those of the WAD/SJAC by a factor of two. In contrast, aerosol NO3- and Cl- measured with the SFU during the dry season were nearly two times lower than those measured by the WAD/SJAC. These differences declined markedly during the transition period and towards the cleaner conditions during the onset of the wet season (PM2.5 similar to 5 mu g m(-3)); when filter-based samplers measured on average 40-90% less than the WAD/SJAC. The differences were not due to consistent systematic biases of the analytical techniques, but were apparently a result of prevailing environmental conditions and different sampling procedures. For the transition period and wet season, the significance of our results is reduced by a low number of data points. We argue that the observed differences are mainly attributable to (a) positive and negative filter sampling artifacts, (b) presence of organic compounds and organosulfates on filter substrates, and (c) a SJAC sampling efficiency of less than 100%.

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.