Bahrain's Formula-1 racing circuit: energy and environmental considerations

The Bahrain International Circuit (BIC) and complex, at latitude 26.00N and longitude 51.54E, was built in 483 days and cost 150 million US$. The circuit consists of six different individual tracks with a 3.66 km outer track (involving 10 turns) and a 2.55 km inner track (having six turns). The complex has been designed to host a variety of other sporting activities. Fifty thousand spectators, including 10,500 in the main grandstand, can be accommodated simultaneously. State-of-the art on-site media and broadcast facilities are available. The noise level emitted from vehicles on the circuit during the Formula-1 event, on April 4th 2004, was acceptable and caused no physical disturbance to the fans in the VIP lounges or to scholars studying at the University of Bahrain's Shakeir Campus, which is only 1.5 km away from the circuit. The sound-intensity level (SIL) recorded on the balcony of the VIP lounge was 128 dB(A) and was 80 dB(A) inside the lounge. The calculated SIL immediately outside the lecture halls of the University of Bahrain was 70 dB(A) and 65 dB(A) within them. Thus racing at BIC can proceed without significantly disturbing the academic-learning process. The purchased electricity demand by the BIC complex peaked (at 4.5 MW) during the first Formula-1 event on April 4th 2004. The reverse-osmosis (RO) plant at the BIC provides 1000 m(3) of desalinated water per day for landscape irrigation. Renewable-energy inputs, (i.e., via solar and wind power), at the BIC could be harnessed to generate electricity for water desalination, air conditioning, lighting as well as for irrigation. If the covering of the BIC complex was covered by adhesively fixed modern photovoltaic cells, then similar to 1.2 MW of solar electricity could be generated. If two horizontal-axis, at 150 m height above the ground, three 75m bladed, wind turbines were to be installed at the BIC, then the output could reach 4 MW. Furthermore, if 10,000 Jojoba trees (a species renowned for having a low demand for water, needing only five irrigations per year in Bahrain and which remain green throughout the year) are planted near the circuit, then the local micro-climate would be improved with respect to human comfort as well as the local environment becoming cleaner.

Examination of faecal Bifidobacterium populations in breast- and formula-fed infants during the first 18 months of life.

Bifidobacteria in the infant faecal microbiota have been the focus of much interest, especially during the exclusive milk-feeding period and in relation to the fortification of infant formulae to better mimic breast milk. However, longitudinal studies examining the diversity and dynamics of the Bifidobacterium population of infants are lacking, particularly in relation to the effects of weaning. Using a polyphasic strategy, the Bifidobacterium populations of breast- and formula-fed infants were examined during the first 18 months of life. Bifidobacterium-specific denaturing gradient gel electrophoresis demonstrated that breast-fed infants harboured greater diversity than formula-fed infants and the diversity of the infants' Bifidobacterium populations increased with weaning. Twenty-seven distinctive banding profiles were observed from ∼1100 infant isolates using ribosomal intergenic spacer analysis, 14 biotypes of which were confirmed to be members of the genus Bifidobacterium. Two profiles (H, Bifidobacterium longum subsp. infantis; and I, Bifidobacterium bifidum) were common culturable biotypes, seen in 9/10 infants, while profile E (Bifidobacterium breve) was common among breast-fed infants. Overall, inter- and intra-individual differences were observed in the Bifidobacterium populations of infants between 1 and 18 months of age, although weaning was associated with increased diversity of the infant Bifidobacterium populations. Breast-fed infants generally harboured a more complex Bifidobacterium microbiota than formula-fed infants.

A unified titration formula

In a number of standard titrations, a volume of a monoprotic base MOH at a specific concentration is added to a volume of a monoprotic acid HA at a specific concentrations. Four different types of titration are possible, depending on whether the acid and base are strong or weak. A single unifying formula covering all four cases has been determined.

A review of vertebroplasty for osteoporotic and malignant vertebral compression fractures

Vertebral compression fractures are a common clinical problem and the incidence of them will increase with the ageing population. Traditionally management has been conservative; however, there has been a growing trend towards vertebroplasty as an alternative therapy in patients with persisting severe pain. NICE produced guidance in 2003 recommending the procedure after 4 weeks of conservative management. Recent high-quality studies have been contradictory and there is currently a debate surrounding the role of the procedure with no agreement in the literature. We examine the evidence in both osteoporotic and malignant vertebral compression fractures; we also describe the benefits and side effects, alternative treatment options and the cost of the procedure. Finally, we recommend when vertebroplasty is most appropriately used based on the best available evidence.

On a stochastic Trotter formula with application to spontaneous localization models

We consider the relation between so called continuous localization models—i.e. non-linear stochastic Schrödinger evolutions—and the discrete GRW-model of wave function collapse. The former can be understood as scaling limit of the GRW process. The proof relies on a stochastic Trotter formula, which is of interest in its own right. Our Trotter formula also allows to complement results on existence theory of stochastic Schrödinger evolutions by Holevo and Mora/Rebolledo.

A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

Prevalence and risk factors of radiographic vertebral fracture in Brazilian community-dwelling elderly

The prevalence and risk factors of radiographic vertebral fracture were determined among Brazilian community-dwelling elderly. Vertebral fractures were a common condition in this elderly population, and lower hip bone mineral density was a significant risk factor for vertebral fractures in both genders. The aim of the study was to estimate the prevalence of radiographic vertebral fracture and investigate factors associated with this condition in Brazilian community-dwelling elderly. This cross-sectional study included 943 elderly subjects (561 women and 382 men) living in So Paulo, Brazil. Thoracic and lumbar spine radiographs were obtained, and vertebral fractures were evaluated using Genant`s semiquantitative method. Bone mineral density (BMD) was measured by dual X-ray absorptiometry, and bone biochemical markers were also evaluated. Female and male subjects were analyzed independently, and each gender was divided into two groups based on whether vertebral fractures were present. The prevalence of vertebral fracture was 27.5% (95% CI 23.8-31.1) in women and 31.8% in men (95% CI 27.1-36.5) (P = 0.116). Cox regression analyses using variables that were significant in the univariate analysis showed that age (prevalence ratio = 1.03, 95% CI 1.01-1.06; p = 0.019) and total femur BMD (PR = 0.27, 95% CI 0.08-0.98; p = 0.048) were independent factors in predicting vertebral fracture for the female group. In the male group, Cox regression analyses demonstrated that femoral neck BMD (PR = 0.26, 95% CI 0.07-0.98; p = 0.046) was an independent parameter in predicting vertebral fractures. Our results suggest that radiographic vertebral fractures are common in Brazilian community-dwelling elderly and that a low hip BMD was an important risk factor for this condition in both genders. Age was also significantly correlated with the presence of vertebral fractures in women.

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.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+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 G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting 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 D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

THE CRYSTAL STRUCTURE OF A MICROLITE-GROUP MINERAL WITH A FORMULA NEAR NaCaTa(2)O(6)F FROM THE MORRO REDONDO MINE, CORONEL MURTA, MINAS GERAIS, BRAZIL

We present electron-microprobe and single-crystal X-ray-diffraction data for a microlite-group mineral with a formula near NaCaTa(2)O(6)F from the Morro Redondo mine, Coronel Murta, Minas Gerais, Brazil. On the basis of these data, the formula is A(Na(0.88)Ca(0.88)Pb(0.02)square(0.22))(Sigma 2.00) (B)(Ta(1.70)Nb(0.14)Si(0.12)As(0.04))(Sigma 2.00) (X)[(O(5.75)(OH)(0.25)](Sigma 6.00) (Y)(F(0.73)square(0.27))(Sigma 1.00). According to the new nomenclature for the pyrochlore-supergroup minerals, it is intermediate between fluornatromicrolite and "" fluorcalciomicrolite"". The crystal structure, F (d3) over barm, a = 10.4396(12) angstrom, has been refined to an R(1) value of 0.0258 (wR(2) = 0.0715) for 107 reflections (MoK alpha radiation). There is a scarcity of crystal-chemical data for pyrochlore-supergroup minerals in the literature. A compilation of these data is presented here.

On a product formula for the Conley-Zelmder index of symplectic paths and its applications

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley-Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.