A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

Age-related difference on weight transfer during unconstrained standing

The ability to transfer weight from one lower limb to the other is essential for the execution of daily life activities and little is known about how weight transfer during unconstrained natural standing is affected by age. This study examined the weight transfer ability of elderly individuals during unconstrained standing (for 30 mill) in comparison to young adults. The subjects (19 healthy elderly adults, range 65-80 years, and 19 healthy young adults, range 18-30 years) stood with each foot on a separate force plate and were allowed to change their posture freely at any time. The limits of stability and base of support width during standing, measures of mobility (using the timed up and go and the preferred walking speed tests), and fear of falling were also measured. In comparison to the young adults, during unconstrained standing the elderly adults produced four times fewer weight transfers of large amplitude (greater than,half of their body weight). The limits of stability and base of support width were significantly smaller for the elderly adults but there were no significant differences in the measures of mobility and in the fear of falling score compared to young adults. The observed significant age-related decrease in the use of weight transfer during unconstrained standing, despite any difference in the measured mobility of the subjects, suggests that this task reveals unnoticed and subtle differences in postural control, which may help to better understand age related impairments in balance that the elderly population experiences. (C) 2010 Elsevier B.V. All rights reserved.

Topological instability, average electronegativity difference and glass forming ability of amorphous alloys

In this paper, we report the remarkable agreement of the glass forming ability of binary alloys with a new criterion that combines the topological instability parameter (lambda) and the average electronegativity difference among the elements of an alloy, assuming both exert a synergetic effect. The best glass forming compositions for Zr-Cu and Ti-Ni systems are well predicted by this new approach. Although the new criterion needs further refinement, it is concluded that the proposed approach is a promising and simple tool to guide and reduce the tedious and labour intensive work to find good glass former compositions in metallic systems. (C) 2008 Elsevier Ltd. All rights reserved.

Identification of Elastic, Dielectric, and Piezoelectric Constants in Piezoceramic Disks

Three-dimensional modeling of piezoelectric devices requires a precise knowledge of piezoelectric material parameters. The commonly used piezoelectric materials belong to the 6mm symmetry class, which have ten independent constants. In this work, a methodology to obtain precise material constants over a wide frequency band through finite element analysis of a piezoceramic disk is presented. Given an experimental electrical impedance curve and a first estimate for the piezoelectric material properties, the objective is to find the material properties that minimize the difference between the electrical impedance calculated by the finite element method and that obtained experimentally by an electrical impedance analyzer. The methodology consists of four basic steps: experimental measurement, identification of vibration modes and their sensitivity to material constants, a preliminary identification algorithm, and final refinement of the material constants using an optimization algorithm. The application of the methodology is exemplified using a hard lead zirconate titanate piezoceramic. The same methodology is applied to a soft piezoceramic. The errors in the identification of each parameter are statistically estimated in both cases, and are less than 0.6% for elastic constants, and less than 6.3% for dielectric and piezoelectric constants.

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R(0)) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R(0) cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations. (C) 2009 Elsevier B.V. All rights reserved.

Watershed scale temporal stability of soil water content

The recognition of temporally stable locations with respect to soil water content is of importance for soil water management decisions, especially in sloping land of watersheds. Neutron probe soil water content (0 to 0.8 m), evaluated at 20 dates during a year in the Loess Plateau of China, in a 20 ha watershed dominated by Ust-Sandiic Entisols and Aeolian sandy soils, were used to define their temporal stability through two indices: the standard deviation of relative difference (SDRD) and the mean absolute bias error (MABE). Specific concerns were (a) the relationship of temporal stability with soil depth, (b) the effects of soil texture and land use on temporal stability, and (c) the spatial pattern of the temporal stability. Results showed that temporal stability of soil water content at 0.2 m was significantly weaker than those at the soil depths of 0.6 and 0.8 m. Soil texture can significantly (P<0.05) affect the stability of soil water content except for the existence of an insignificant difference between sandy loam and silt loam textures, while temporal stability of areas covered by bunge needlegrass land was not significantly different from those covered by korshinsk peashrub. Geostatistical analysis showed that the temporal stability was spatially variable in an organized way as inferred by the degree of spatial dependence index. With increasing soil depth, the range of both temporal stability indices showed an increasing trend, being 65.8-120.5 m for SDRD and 148.8-214.1 m for MABE, respectively. This study provides a valuable support for soil water content measurements for soil water management and hydrological applications on sloping land areas. (C) 2010 Elsevier B.V. All rights reserved.

Using a New Criterion to Identify Sites for Mean Soil Water Storage Evaluation

Establishing a few sites in which measurements of soil water storage (SWS) are time stable significantly reduces the efforts involved in determining average values of SWS. This study aimed to apply a new criterion the mean absolute bias error (MABE)-to identify temporally stable sites for mean SWS evaluation. The performance of MABE was compared with that of the commonly used criterion, the standard deviation of relative difference (SDRD). From October 2004 to October 2008, SWS of four soil layers (0-1.0, 1.0-2.0,2.0-3.0, and 3.0-4.0 m) was measured, using a neutron probe, at 28 sites on a hillslope of the Loess Plateau, China. A total of 37 SWS data sets taken over time were divided into two subsets, the first consisting of 22 dates collected during the calibration period from October 2004 to September 2006, and the second with 15 dates collected during the validation period from October 2006 to October 2008. The results showed that if a critical value of 5% for MABE was defined, more than half the sites were temporally stable for both periods, and the number of temporally stable sires generally increased with soil depth. Compared with SDRD, MABE was more suitable for the identification of time-stable sites for mean SS prediction. Since the absolute prediction error of drier sites is more sensitive to changes in relative difference in terms of mean SWS prediction, the sites of wet sectors should be preferable for mean SWS prediction for the same changes in relative difference.

Genetic variation for anatomic traits and volume shrinkage and their correlation with wood basic density in an Eucalyptus camaldulensis Dehn base population

Eucalyptus camaldulensis has great importance in Brazil because of their phenotypic plasticity for different environmental conditions, as soils, altitudes and rainfall. This study is an investigation of a base population of E. camaldulensis from Australia through a progeny test implanted in Selviria, MS. The trial was established in a randomized block design, with 25 families and 60 replications of single tree plots. Genetic parameters for anatomic traits and volume shrinkage were estimated, as well as their correlations with wood basic density. No significant differences among progenies were observed for the traits studied. The additive genetic variation coefficient at individual and among progeny levels ranged from low (0.26%) to high (16.98%). The narrow sense heritability at individual and family means levels also ranged from low (0.01) to high (0.87). This indicates that some traits are under strong genetic control and can be improved by selection. In the present situation, in order to attain the highest genetic gains, the sequential selection among and within progeny would be recommended.

Classification of individuals with dyslipidaemia controlled by statins according to plasma biomarkers of oxidative stress using cluster analysis

Oxidative stress is a physiological condition that is associated with atherosclerosis. and it can be influenced by diet. Our objective was to group fifty-seven individuals with dyslipidaemia controlled by statins according to four oxidative biomarkers, and to evaluate the diet pattern and blood biochemistry differences between these groups. Blood samples were collected and the following parameters were evaluated: diet intake; plasma fatty acids; lipoprotein concentration; glucose; oxidised LDL (oxLDL); malondialdehyde (MDA): total antioxidant activity by 2,2-diphenyl-1-picrylhydrazyl (DPPH) and ferric reducing ability power assays. Individuals were separated into five groups by cluster analysis. All groups showed a difference with respect to at least one of the four oxidative stress biomarkers. The separation of individuals in the first axis was based upon their total antioxidant activity. Clusters located on the right side showed higher total antioxidant activity, higher myristic fatty acid and lower arachidonic fatty acid proportions than clusters located on the left side. A negative correlation was observed between DPPH and the peroxidability index. The second axis showed differences in oxidation status as measured by MDA and oxLDL concentrations. Clusters located on the Upper side showed higher oxidative status and lower HDL cholesterol concentration than clusters located on the lower side. There were no differences in diet among the five clusters. Therefore, fatty acid synthesis and HDL cholesterol concentration seem to exert a more significant effect on the oxidative conditions of the individuals with dyslipidaemia controlled by statins than does their food intake.

Comparative analysis of the gas-phase reactions of cylindrospermopsin and the difference in the alkali metal cation mobility

Cylindrospermopsin (CYN) belongs to a group of toxins produced by several strains of freshwater cyanobacteria. It is a compact zwitterionic molecule composed of a uracil section and a tricyclic guanidinium portion with a primarily hepatotoxic effect. Using low multi-stage and high-resolution mass spectrometry, the gas-phase reactions of this toxin have been investigated. Our data show that collision-induced dissociation (CID) spectra of CYN are dominated by neutral losses, and three major initial fragmentation pathways are clearly distinguishable. Interestingly, comparative analysis of protonated and cationizated molecules showed a significant difference in the balance of the SO(3) and terminal ring elimination. These data indicate that the differential ion mobility of H(+), Li(+), Na(+) and K(+) leads to different fragmentation pathways, giving rise to mass spectra with different profiles. Copyright (C) 2008 John Wiley & Sons, Ltd.

Evaluation of Some Biological Aspects of the Presence of Abrasive Silica and Thickening Silica in Basic Formulations of Dentifrices

The aim of this study was to evaluate some biological characteristics and toxicity of basic formulations of dentifrices containing such substances, and to compare them with two existing products in market which also contains silic in their formulations. In this way, it was evaluated some biological parameters: weight of the animals, oral toxicity, hematological parameters, urinary analysis, and histological evaluation. The thrombocytes were also statistically at normal levels. The glutamate-pyruvate transaminase (TGP) showed normal aspect in 5 of the tested groups, as in control. Meanwhile, the oxalacetic transaminase (AST) in one group had a small increase in the control group. Regarding urine, in exception the rats of one group, the rats of the 4 other experimental groups showed leukocytosis urinary statistically higher than the control group. The histological evaluation of the animals showed that specimens from liver, stomach, kidney and submandibular gland presented normal aspects for these organs, without significant characteristics related to inflammatory infiltrates in any of the 6 samples tested in their respective groups.