Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Magnesium, insulin resistance and body composition in healthy postmenopausal women

Objective: This study was conducted to determine the association between magnesium (Mg), body composition and insulin resistance in 136 sedentary postmenopausal women, 50 to 77 years of age. Methods: Diabetics, hypertensives and women on hormonal replacement therapy were excluded and the remaining 74 were divided according to BMI≥25 (obese: OG) and BMI<25 kg/m2 (non-obese: NOG). Nutritional data disclosed that intakes were high for protein and saturated fat, low for carbohydrates, polyunsaturated fat and Mg and normal for the other nutrients, according to recommended dietary allowances (RDA). Mg values in red blood cells (RBC-Mg) and plasma (P-Mg), were determined, as were fasting glucose, and insulin levels, Homeostasis Model Assessment (HOMA), body mass index (BMI), body fat percent (BF %), abdominal fat (AF) and free fat mass (FFM). Results: RBC-Mg values were low in both groups when compared with normal values. There were significant differences in body composition parameters, HOMA and insulin levels, with higher basal insulin levels in OG. RBC-Mg was directly correlated with insulin, HOMA and FFM in both groups, according to Pearson correlations. HOMA in OG was also directly correlated with BMI, FFM and AF. In NOG, HOMA was only correlated with FFM. The low RBC-Mg levels observed were probably due to low Mg intake and to deregulation of factors that control Mg homeostasis during menopause. Conclusions: Both Mg deficit and obesity may independently lead to a higher risk for insulin resistance and cardiovascular disease.

The complete sequence of a 9000 bp fragment of the right arm of Saccharomyces cerevisiae chromosome VII contains four previously unknown open reading frames

We report the sequence of a 9000 bp fragment from the right arm of Saccharomyces cerevisiae chromosome VII. Analysis of the sequence revealed four complete previously unknown open reading frames, which were named G7587, G7589, G7591 and G7594 following standard rules for provisional nomenclature. Outstanding features of some of these proteins were the homology of the putative protein coded by G7589 with proteins involved in transcription regulation and the transmembrane domains predicted in the putative protein coded by G7591.

Determination of airborne nanoparticles in elderly care centres

According to numerous studies, airborne nanoparticles have a potential to produce serious adverse human health effects when deposited into the respiratory tract. The most important parts of the lung are the alveolar regions with their enormous surface areas and potential to transfer nanoparticles into the blood stream. These effects may be potentiated in case of the elderly, since this population is more susceptible to air pollutants in general and more to nanoparticles than larger particles. The main goal of this investigation was to determine the exposure of institutionalized elders to nanoparticles using Nanoparticle Surface Area Monitor (NSAM) equipment to calculate the deposited surface area (DSA) of nanoparticles into elderly lungs. In total, 193 institutionalized individuals over 65 yr of age were examined in four elderly care centers (ECC). The occupancy daily pattern was achieved by applying a questionnaire, and it was concluded that these subjects spent most of their time indoors, including the bedroom and living room, the indoor microenvironments with higher prevalence of elderly occupancy. The deposited surface area ranged from 10 to 46 mu m(2)/cm(3). The living rooms presented significantly higher levels compared with bedrooms. Comparing PM10 concentrations with nanoparticles deposited surface area in elderly lungs, it is conceivable that living rooms presented the highest concentration of PM10 and were similar to the highest average DSA. The temporal distribution of DSA was also assessed. While data showed a quantitative fluctuation in values in bedrooms, high peaks were detected in living rooms.

Emissions of nanoparticles during friction stir welding (FSW) of aluminium alloys

Friction stir welding (FSW) is now well established as a welding process capable of joining some different types of metallic materials, as it was (1) found to be a reliable and economical way of producing high quality welds, and (2) considered a "clean" welding process that does not involve fusion of metal, as is the case with other traditional welding processes. The aim of this study was to determine whether the emission of particles during FSW in the nanorange of the most commonly used aluminum (Al) alloys, AA 5083 and AA 6082, originated from the Al alloy itself due to friction of the welding tool against the item that was being welded. Another goal was to measure Al alloys in the alveolar deposited surface area during FSW. Nanoparticles dimensions were predominantly in the 40- and 70-nm range. This study demonstrated that microparticles were also emitted during FSW but due to tool wear. However, the biological relevance and toxic manifestations of these microparticles remain to be determined.

Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.

Determiation of airborne nanoparticles from welding operations

The aim of this study is to assess the levels of airborne ultrafine particles emitted in welding processes (tungsten inert gas [TIG], metal active gas [MAG] of carbon steel, and friction stir welding [FSW] of aluminum) in terms of deposited area in pulmonary alveolar tract using a nanoparticle surface area monitor (NSAM) analyzer. The obtained results showed the dependence of process parameters on emitted ultrafine particles and demonstrated the presence of ultrafine particles compared to background levels. Data indicated that the process that resulted in the lowest levels of alveolar deposited surface area (ADSA) was FSW, followed by TIG and MAG. However, all tested processes resulted in significant concentrations of ultrafine particles being deposited in humans lungs of exposed workers.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

Weakly spectrally complete pair of matrices

Let and be matrices over an algebraically closed field. Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and, respectively, such that has eigenvalues.