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.

Concretes and mortars recycled with water treatment sludge and construction and demolition rubble

There are about 7500 water treatment plants in Brazil. The wastes these plants generate in their decantation tanks and filters are discharged directly into the same brooks and rivers that supply water for treatment. Another serious environmental problem is the unregulated disposal of construction and demolition rubble, which increases the expenditure of public resources by degrading the urban environment and contributing to aggravate flooding and the proliferation of vectors harmful to public health. In this study, an evaluation was made of the possibility of recycling water treatment sludge in construction and demolition waste recycling plants. The axial compressive strength and water absorption of concretes and mortars produced with the exclusive and joint addition of these two types of waste was also determined. The ecoefficiency of this recycling was evaluated by determining the concentration of aluminum in the leached extract resulting from the solubilization of the recycled products. The production of concretes and mortars with the joint addition of water treatment sludge and recycled concrete rubble aggregates proved to be a viable recycling alternative from the standpoint of axial compression strength, modulus of elasticity, water absorption and tensile strength by the Brazilian test method. (C) 2008 Elsevier Ltd. All rights reserved.

Chemical composition of mixed construction and demolition recycled aggregates from the State of Sao Paulo

Construction and Demolition Waste (CDW) represents. about 50% of the total Brazilian municipal solid waste: thus, recycling represents huge benefits both in environmental and economic perspectives. Herein, the chemical characterization results of three samples from two different recycling plants from the State of Sao Paulo is prevented. The results demonstrated that the visual classification into grey and red is not related to the chemical composition but mostly to the grain size fraction. The chemical composition of the CDW varies according to the content of cement paste, natural aggregates (quartz sand or granite), red ceramic and clay. Furthermore, the production of recycled concrete aggregates requires two crushing stages to meet the technical standards. The sand fraction (below 4.8 mm) presents high grades of SiO(2), which indicates the liberation of cement paste to fines (< 0.15 mm). The fines have a great potential to be used in the cement industry.

On the classification of mixed construction and demolition waste aggregate by porosity and its impact on the mechanical performance of concrete

The properties of recycled aggregate produced from mixed (masonry and concrete) construction and demolition (C&D) waste are highly variable, and this restricts the use of such aggregate in structural concrete production. The development of classification techniques capable of reducing this variability is instrumental for quality control purposes and the production of high quality C&D aggregate. This paper investigates how the classification of C&D mixed coarse aggregate according to porosity influences the mechanical performance of concrete. Concretes using a variety of C&D aggregate porosity classes and different water/cement ratios were produced and the mechanical properties measured. For concretes produced with constant volume fractions of water, cement, natural sand and coarse aggregate from recycled mixed C&D waste, the compressive strength and Young modulus are direct exponential functions of the aggregate porosity. Sink and float technique is a simple laboratory density separation tool that facilitates the separation of cement particles with lower porosity, a difficult task when done only by visual sorting. For this experiment, separation using a 2.2 kg/dmA(3) suspension produced recycled aggregate (porosity less than 17%) which yielded good performance in concrete production. Industrial gravity separators may lead to the production of high quality recycled aggregate from mixed C&D waste for structural concrete applications.

Laboratory evaluation of recycled construction and demolition waste for pavements

The wide production of construction and demolition waste and its illegal deposition are serious current problems in Brazil. This research proposes to evaluate the feasibility of using aggregate from recycled construction and demolition waste (RCDW) in pavement applications. A laboratory program was conducted by geotechnical characterization, bearing capacity and repeated load triaxial tests. The results show that the composition and the compactive effort influence on the physical characteristics of the RCDW aggregate. The compaction process has promoted a partial crushing and breakage of RCDW particles, changing the grain-size distribution and increasing the percentage of cubic grains. This physical change contributes to a better densification of the RCDW aggregate and consequently an improvement in bearing capacity, resilient modulus and resistance to permanent deformation. The results have shown that the RCDW aggregate may be utilized as coarse base and sub-base layer for low-volume roads. (C) 2010 Elsevier Ltd. All rights reserved.

Construction and Evaluation of an Opto-Coupled Potentiostat with a PC/PDA Interface

The design, construction, and characterization of a portable opto-coupled potentiostat are presented. The potentiostat is battery-powered, managed by a microcontroller, which implements cyclic voltammetry (CV) using suitable sensor electrodes. Its opto-coupling permits a wide range of current measurements, varying from mA to nA. Two software interfaces were developed to perform the CV measurement: a virtual instrument for a personal computer (PC) and a C-base interface for personal digital assistant (PDA). The potentiostat has been evaluated by detection of potassium ferrocyanide in KCl medium, both with macro and microelectrodes. There was good agreement between the instrumental results and those from commercial equipment.

Interior under construction, Carpenter Hall house, Wilston, Brisbane

View to upper tower from lower section of house.

Interior under construction, Carpenter Hall house, Wilston, Brisbane

Triangular window openings to upper section of house.

Interior under construction, Carpenter Hall house, Wilston, Brisbane

Timber structure to upper floors, as seen from interior.

Under construction, PNG Coffee Industry Board Office and Warehouse, Goroka

View of post being hoisted into position during construction.

Northern entrance court under construction, Sunshine Coast University Library, Maroochydore

View to library entrance court under construction.