Kurzweil integral for Riesz space-valued functions: Uniform convergence theorem

Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.

Prediction of retail beef yield, trim fat and proportion of high-valued cuts in Nellore cattle using ultrasound live measurements

The objective of this study was to develop equations to predict retail product and fat trim (weights and percentages) for Nellore (Bos indicus) cattle. Live ultrasound measurements of the longissimus muscle area, backfat thickness at the 12th rib and rump fat depth and shrunk body weight were obtained from 218 Nellore steers to predict weights and percentages of carcass retail product, pistola retail product and fat trimmings. After slaughter, carcasses were deboned and weighed and percentages of retail cuts were obtained directly. Measurements taken directly in the carcasses explained 97% and 36% of variation in carcass retail product weight and percentage, and 94% and 36% of variation in pistola retail weight and percentage, respectively. Live measurements explained 93% of carcass retail product weight and 39% of carcass retail product percentage. Lower accuracies were observed for pistola retail product weight (R-2=0.87) and percentage (R-2=0.33). Accuracies for fat trimmings weight and percentage were 79% and 55%, respectively. Ultrasound rump fat thickness showed greater correlations with retail product and fat trimmings (weights and percentages) when compared with ultrasound backfat thickness. The weight and percentage of retail products and of trimmable fat can be estimated in Nellore steers from live animal measurements, with similar accuracy to equations developed based on carcass measurements obtained at slaughter.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

EQUIVALENCE OF REAL MILNOR FIBRATIONS FOR QUASI-HOMOGENEOUS SINGULARITIES

We show that for real quasi-homogeneous singularities f : (R-m, 0) -> (R-2, 0) with isolated singular point at the origin, the projection map of the Milnor fibration S-epsilon(m-1) \ K-epsilon -> S-1 is given by f/parallel to f parallel to. Moreover, for these singularities the two versions of the Milnor fibration, on the sphere and on a Milnor tube, are equivalent. In order to prove this, we show that the flow of the Euler vector field plays and important role. In addition, we present, in an easy way, a characterization of the critical points of the projection (f/parallel to f parallel to) : S-epsilon(m-1) \ K-epsilon -> S-1.

Identification of novel components of NAD-utilizing metabolic pathways and prediction of their biochemical functions

Nicotinamide adenine dinucleotide (NAD) is a ubiquitous cofactor participating in numerous redox reactions. It is also a substrate for regulatory modifications of proteins and nucleic acids via the addition of ADP-ribose moieties or removal of acyl groups by transfer to ADP-ribose. In this study, we use in-depth sequence, structure and genomic context analysis to uncover new enzymes and substrate-binding proteins in NAD-utilizing metabolic and macromolecular modification systems. We predict that Escherichia coli YbiA and related families of domains from diverse bacteria, eukaryotes, large DNA viruses and single strand RNA viruses are previously unrecognized components of NAD-utilizing pathways that probably operate on ADP-ribose derivatives. Using contextual analysis we show that some of these proteins potentially act in RNA repair, where NAD is used to remove 2'-3' cyclic phosphodiester linkages. Likewise, we predict that another family of YbiA-related enzymes is likely to comprise a novel NAD-dependent ADP-ribosylation system for proteins, in conjunction with a previously unrecognized ADP-ribosyltransferase. A similar ADP-ribosyltransferase is also coupled with MACRO or ADP-ribosylglycohydrolase domain proteins in other related systems, suggesting that all these novel systems are likely to comprise pairs of ADP-ribosylation and ribosylglycohydrolase enzymes analogous to the DraG-DraT system, and a novel group of bacterial polymorphic toxins. We present evidence that some of these coupled ADP-ribosyltransferases/ribosylglycohydrolases are likely to regulate certain restriction modification enzymes in bacteria. The ADP-ribosyltransferases found in these, the bacterial polymorphic toxin and host-directed toxin systems of bacteria such as Waddlia also throw light on the evolution of this fold and the origin of eukaryotic polyADP-ribosyltransferases and NEURL4-like ARTs, which might be involved in centrosomal assembly. We also infer a novel biosynthetic pathway that might be involved in the synthesis of a nicotinate-derived compound in conjunction with an asparagine synthetase and AMPylating peptide ligase. We use the data derived from this analysis to understand the origin and early evolutionary trajectories of key NAD-utilizing enzymes and present targets for future biochemical investigations.

Repeated inhalation of crack-cocaine affects spermatogenesis in young and adult mice

To investigate the effects of repeated crack-cocaine inhalation on spermatogenesis of pubertal and mature Balb/c mice, ten young (Y-ex) and ten adult (A(ex)) Balb/c mice were exposed to the smoke from 5 g of crack with 57.7% of pure cocaine in an inhalation chamber, 5 days/week for 2 months. The young (Y-c) and adult (A(c)) control animals (n = 10) were kept in a specially built and controlled animal house facility. The morphologic analysis of both testes of all animals included the analysis of quantitative and qualitative histologic parameters to assess the effect of crack-cocaine on spermatogenesis and Leydig cells. Apoptosis was determined by immunolabeling with caspase-3 antibodies. Compared to the Y-c animals, Y-ex animals showed a significant reduction in the number of stage VII tubules per testis (p = 0.02), Sertoli cells (p < 0.001) and elongated spermatids (p = 0.001). Comparisons between the Y-ex and A(ex) groups identified a significant reduction in the number of Sertoli cells (p < 0.001) and round spermatids (p < 0.001) in the Y-ex group and a significant increase in apoptotic Leydig cells (p = 0.04) in the A(ex) group. The experimental results indicate that crack-cocaine smoke inhalation induced spermatogenesis disruption in chronically exposed mice, particularly in pubertal mice.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

GEOMETRIC RELATIONS BETWEEN SPACES OF NUCLEAR OPERATORS AND SPACES OF COMPACT OPERATORS

We extend and provide a vector-valued version of some results of C. Samuel about the geometric relations between the spaces of nuclear operators N(E, F) and spaces of compact operators K(E, F), where E and F are Banach spaces C(K) of all continuous functions defined on the countable compact metric spaces K equipped with the supremum norm. First we continue Samuel's work by proving that N(C(K-1), C(K-2)) contains no subspace isomorphic to K(C(K-3), C(K-4)) whenever K-1, K-2, K-3 and K-4 are arbitrary infinite countable compact metric spaces. Then we show that it is relatively consistent with ZFC that the above result and the main results of Samuel can be extended to C(K-1, X), C(K-2,Y), C(K-3, X) and C(K-4, Y) spaces, where K-1, K-2, K-3 and K-4 are arbitrary infinite totally ordered compact spaces; X comprises certain Banach spaces such that X* are isomorphic to subspaces of l(1); and Y comprises arbitrary subspaces of l(p), with 1 < p < infinity. Our results cover the cases of some non-classical Banach spaces X constructed by Alspach, by Alspach and Benyamini, by Benyamini and Lindenstrauss, by Bourgain and Delbaen and also by Argyros and Haydon.

Kleiner's theorem for unitary representations of posets

A subspace representation of a poset S = {s(1), ..., S-t} is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. All rights reserved.

Electronic Properties of Water in Liquid Environment. A Sequential QM/MM Study Using the Free Energy Gradient Method

There is a continuous search for theoretical methods that are able to describe the effects of the liquid environment on molecular systems. Different methods emphasize different aspects, and the treatment of both the local and bulk properties is still a great challenge. In this work, the electronic properties of a water molecule in liquid environment is studied by performing a relaxation of the geometry and electronic distribution using the free energy gradient method. This is made using a series of steps in each of which we run a purely molecular mechanical (MM) Monte Carlo Metropolis simulation of liquid water and subsequently perform a quantum mechanical/molecular mechanical (QM/MM) calculation of the ensemble averages of the charge distribution, atomic forces, and second derivatives. The MP2/aug-cc-pV5Z level is used to describe the electronic properties of the QM water. B3LYP with specially designed basis functions are used for the magnetic properties. Very good agreement is found for the local properties of water, such as geometry, vibrational frequencies, dipole moment, dipole polarizability, chemical shift, and spin-spin coupling constants. The very good performance of the free energy method combined with a QM/MM approach along with the possible limitations are briefly discussed.

The COP9 signalosome counteracts the accumulation of cullin SCF ubiquitin E3 RING ligases during fungal development

Defects in the COP9 signalosome (CSN) impair multicellular development, including embryonic plant or animal death or a block in sexual development of the fungus Aspergillus nidulans. CSN deneddylates cullin-RING ligases (CRLs), which are activated by covalent linkage to ubiquitin-like NEDD8. Deneddylation allows CRL disassembly for subsequent reassembly. An attractive hypothesis is a consecutive order of CRLs for development, which demands repeated cycles of neddylation and deneddylation for reassembling CRLs. Interruption of these cycles could explain developmental blocks caused by csn mutations. This predicts an accumulation of neddylated CRLs exhibiting developmental functions when CSN is dysfunctional. We tested this hypothesis in A. nidulans, which tolerates reduced levels of neddylation for growth. We show that only genes for CRL subunits or neddylation are essential, whereas CSN is primarily required for development. We used functional tagged NEDD8, recruiting all three fungal cullins. Cullins are associated with the CSN1/CsnA subunit when deneddylation is defective. Two CRLs were identified which are specifically involved in differentiation and accumulate during the developmental block. This suggests that an active CSN complex is required to counteract the accumulation of specific CRLs during development.

Study of postures in sugarcane cutters in the Pontal of Paranapanema-SP, Brazil

The expansion of sugarcane monoculture in Brazil in the last decades has pointed out to the necessity of considering the question of sugarcane cutters occupational health. In this work we present a cross-sectional study aiming to examine the occupational posture of a group of sugarcane cutters, which work in a cane field located in the region of Pontal do Paranapanema-SP, Brazil. The study was made using the Ergonomic Analysis of Work - EAW methodology and the postural analysis method by Win-OWAS. Through the obtained records of postures, it was observed that during a workday the sugarcane cutters remain standing erect on two legs or in one leg 66% of the time and that their trunk remain tilted and in rotation, according to 63% of the positions categorized. It was also observed that the sugarcane cutter trunk performs repetitive and boundless movements during his routine of work, which can expose this individual to additional wear of their musculoskeletal functions. The activities in which the individual engages have favorable or adverse influence on his posture. The repetitive movements involved in specialized occupations are equivalent to repeated exercises, thus may be responsible for the excessive development of certain muscle groups. The study suggests that the postures adopted by sugarcane cutters can overload their musculoskeletal system and predispose the cutters to work-related musculoskeletal diseases.