An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

A canonical form for nonderogatory matrices under unitary similarity

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for (1) nonderogatory complex matrices up to unitary similarity, and (2) pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues. The types of these canonical forms are given by undirected and, respectively, directed graphs with no undirected cycles. (C) 2011 Elsevier Inc. All rights reserved.

Investigating the Nature of Noble Gas-Copper Bonds by the Quantum Theory of Atoms in Molecules

We investigated noble gas copper bonds in linear complexes represented by the NgCuX general formula in which Ng and X stand for a noble gas (neon, argon, krypton, or xenon) and a halogen (fluorine, chlorine or bromine), respectively, by coupled cluster methods and modified cc-pVQZ basis sets. The quantum theory of atoms in molecules (QTAIM) shows a linear relation between the dissociation energy or noble gas-copper bonds and the amount of electronic charge transferred mainly from the noble gas to copper during complexation. Large changes in the QTAIM quadrupole moments of copper and noble gases resulting from this bonding and a comparison between NgCuX and NgNaCl systems indicate that these noble gas-copper bonds should be better interpreted as predominantly covalent. Finally, QTAIM atomic dipoles of noble gases in NgNaCl systems agree satisfactorily with atomic dipoles given by a simple model for these NgNa van der Waals bonds.

Inflammation, oxidative stress, glomerular filtration rate, and albuminuria in elderly men : a cross-sectional study

BACKGROUND: The role of inflammation and oxidative stress in mild renal impairment in the elderly is not well studied. Accordingly, we aimed at investigating the associations between estimated glomerular filtration rate (eGFR), albumin/creatinine ratio (ACR), and markers of different inflammatory pathways and oxidative stress in a community based cohort of elderly men. FINDINGS: Cystatin C-based GFR, ACR, and biomarkers of cytokine-mediated inflammation (interleukin-6, high-sensitivity C-reactive protein[CRP], serum amyloid A[SAA]), cyclooxygenase-mediated inflammation (urinary prostaglandin F2alpha [PGF2alpha]), and oxidative stress (urinary F2 isoprostanes) were assessed in the Uppsala Longitudinal Study of Adult Men(n = 647, mean age 77 years). RESULTS: In linear regression models adjusting for age, BMI, smoking, blood pressure, LDL-cholesterol, HDL-cholesterol, triglycerides, and treatment with statins, ACE-inhibitors, ASA, and anti-inflammatory agents, eGFR was inversely associated with CRP, interleukin-6, and SAA (beta-coefficient -0.13 to -0.19, p < 0.001 for all), and positively associated with urinary F2-isoprostanes (beta-coefficient 0.09, p = 0.02). In line with this, ACR was positively associated with CRP, interleukin-6, and SAA (beta- coefficient 0.09-0.12, p < 0.02 for all), and negatively associated with urinary F2-isoprostanes (beta-coefficient -0.12, p = 0.002). The associations were similar but with lower regression coefficients in a sub-sample with normal eGFR (>60 ml/min/1.73 m2, n = 514), with the exception that F2-isoprostane and SAA were no longer associated with eGFR. CONCLUSION: Our data indicate that cytokine-mediated inflammation is involved in the early stages of impaired kidney function in the elderly, but that cyclooxygenase-mediated inflammation does not play a role at this stage. The unexpected association between higher eGFR/lower albuminuria and increased F2-isoprostanes in urine merits further studies.

Femur biometry, densitometry and chemical composition from Moxoto goats supplemented with concentrate in a semiarid region

The aim of study was to investigate if different intake levels of concentrate (supplementation levels) would have an influence on chemical composition, biometric aspects and bone mineral density (BMD) of femurs from Moxoto growing goats in the Brazilian semiarid region. Thirty-two castrated kids (15.69 +/- 0.78 kg initial BW) were used allocated randomly to one of the four levels of supplementation (SL) (treatments groups: 0: 5; 10 and 15 g/kg BW). When the animals of treatment group 15 g/kg BW reached 25 kg BW, the animals in the others treatments groups were also slaughtered. The increase SL resulted in linear increase (P<0.001) in the performance of animals as well as in fresh and dry weight of the femur and decrease of relative weight of the femur. The dry matter contents (g/kg) of femur increased linearly, however, the amounts of MM, ether extract, Ca, P. Mg, Na and K were not affected by the treatments. The values found in this study ranged from 134.84 to 155.90g of Ca, 48.14 to 55.95g of P. 1.69 to 1.87g of Mg, 2.87 to 3.24g of Na and 1.42 to 1.61 g of K/kg of bone in natura for animals with smaller and higher slaughter weight, respectively. The biometric and densitometric variables increased linearly with increasing treatments, except for the thickness of the sponge layer of the proximal and distal epiphysis and BMD measured in the distal epiphysis. The supplementation with concentrate did not affect the chemical composition of the femur, although it has positively influenced the structure and the bone mineral density. A BMD estimated via radiographic bone aluminum equivalent did not have correspondence with bone mineral content measured chemically. (C) 2011 Elsevier BM. All rights reserved.

Stabilizing a class of time delay systems using the Hermite-Biehler theorem

In this paper we use the Hermite-Biehler theorem to establish results for the design of fixed order controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. (C) 2003 Elsevier B.V. All rights reserved.

Polynomials generated by a three term recurrence relation: bounds for complex zeros

This paper deals with the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to find bounds, in terms of the coefficients of the recurrence relation, for the regions where the zeros are located. In most part, the zeros are explored through an Eigenvalue representation associated with a corresponding Hessenberg rnatrix. Applications to Szego polynomials, para-orthogonal polynomials and polynomials with non-zero complex coefficients are considered. (C) 2004 Elsevier B.V. All rights reserved.

CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evaluation of Ir and Pd(NO3)(2)/Mg(NO3)(2) as Modifiers for the Simultaneous Determination of Mn, Ni, Pb, and Sb in Fuel Ethanol by Graphite Furnace MS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Short term hydroelectric scheduling combining network flow and interior point approaches

In this paper, short term hydroelectric scheduling is formulated as a network flow optimization model and solved by interior point methods. The primal-dual and predictor-corrector versions of such interior point methods are developed and the resulting matrix structure is explored. This structure leads to very fast iterations since it avoids computation and factorization of impedance matrices. For each time interval, the linear algebra reduces to the solution of two linear systems, either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored off-line. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved, although its size is reduced to the number of generating units and is not a function of time intervals. These methods were applied to IEEE and Brazilian power systems, and numerical results were obtained using a MATLAB implementation. Both interior point methods proved to be robust and achieved fast convergence for all instances tested. (C) 2004 Elsevier Ltd. All rights reserved.

A controller design used in Lorenz synchronization chaotic system for secure communication based on LMI fuzzy control system

This paper describes a mathematical study about chaotic system and about the unified approach of chaos control via fuzzy control system based in Linear Matrix Inequality to design a controller which synchronizes the transmission/reception system. This system, that was based in Lorenz chaotic circuit, can be used for transmit signals in secure way.

Food intake and digestive efficiency in temperate wool and tropic semi-arid hair lambs fed different concentrate: forage ratio diets

This work was conducted to evaluate food intake and digestive efficiency of temperate wool and tropic semi-arid hair lambs, according to different concentrate: forage ratios in diet. Twenty-four lambs, averaging 90 +/- 1.8 days old and a mean body weight of 20 +/- 0.69 kg, 12 of them wool lambs, F, from Ideal x Ile de France crossing, and 12 others pure Santa Ines hair lambs, were distributed into a four replication 3 x 2 factorial arrangement consisting of three diets and two genotypes. Experimental diets consisted of: D1 = 60% concentrate mix (C) and 40% Cynodon sp. cv. Tifton-85 hay (F), D2 = 40% C and 60% F, and D3 = 20% C and 80% F. D1 was formulated for a daily gain of 300g per animal. Increasing forage levels in diets resulted in linear reductions (P < 0.01) in DM, OM, CP, TCH and metabolizable energy (ME) intake, and a linear increase (P < 0.01) in NDF ingestion. Tropic semi-arid hair lambs had higher DM, OM, NDF, CP, and TCH intake than temperate wool lambs. Although there were no genotype effects in OM and GE coefficient of digestibility, hair lambs showed more efficient (P < 0.05) digestibility of DM, CP, NDF and TCH. Increases in forage levels of diets corresponded to a negative linear effect (P < 0.01) in the apparent digestibility of DM, OM, CP, TCH and GE, while apparent digestibility of NDF increased linearly (P < 0.01). Total endogenous nitrogen (fecal plus urinary N) for F(1) Ideal x Ilede France wool and Santa Ines hair lambs were, respectively, 182 and 312 mg/kg(0.75) per day. Thus, Santa Ines tropic semi-arid hair lambs showed to be more responsive than F(1) Ideal x Ile de France temperate wool lambs to low quality fibrous diets. (C) 2004 Elsevier B.V. All rights reserved.

Construction and decoding of BCH codes over finite commutative rings

BCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, for these codes. The code construction and the decoding procedures are very similar to the BCH codes over finite integer rings. © 1999 Elsevier B.V. All rights reserved.

Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.