Designs for generalized linear models with several variables and model uncertainty

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.

Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

Cauchy Problem for Differential Equation with Caputo Derivative

The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.

An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel

Mathematics Subject Classification: 44A40, 45B05

On a Differential Equation with Left and Right Fractional Derivatives

Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05

On a Stochastic Partial Differential Equation with a Noisy Term

2000 Mathematics Subject Classification: 60H15, 60H40

Hemodynamic Changes With Two Lipid Emulsions For Treatment Of Bupivacaine Toxicity In Swines.

To compare the hemodynamic changes following two different lipid emulsion therapies after bupivacaine intoxication in swines. Large White pigs were anesthetized with thiopental, tracheal intubation performed and mechanical ventilation instituted. Hemodynamic variables were recorded with invasive pressure monitoring and pulmonary artery catheterization (Swan-Ganz catheter). After a 30-minute resting period, 5 mg.kg-1 of bupivacaine by intravenous injection was administered and new hemodynamic measures were performed 1 minute later; the animals were than randomly divided into three groups and received 4 ml.kg-1 of one of the two different lipid emulsion with standard long-chaim triglyceride, or mixture of long and medium-chain triglyceride, or saline solution. Hemodynamic changes were then re-evaluated at 5, 10, 15, 20 and 30 minutes. Bupivacaine intoxication caused fall in arterial blood pressure, cardiac index, ventricular systolic work index mainly and no important changes in vascular resistances. Both emulsion improved arterial blood pressure mainly increasing vascular resistance since the cardiac index had no significant improvement. On the systemic circulation the hemodynamic results were similar with both lipid emulsions. Both lipid emulsions were efficient and similar options to reverse hypotension in cases of bupivacaine toxicity.

Comparison of agglutinating and neutralizing antibodies to serovar hardjo in sows immunized with two commercial whole culture polivalent anti-leptospira bacterins

It was performed the comparison of the intensity and duration of agglutinating and neutralizing antibodies to serovar Hardjo in swines vaccinated with two commercial anti-leptospira bacterins. Sows no reactive to 24 Leptospira sp serovars in the microscopic agglutination test (MAT) were divided in three groups: Group A (n=08): received two vaccine A doses with 30 days interval, Group B (n=08) two vaccine B doses with 30 days interval and Group C (n=08): control no vaccinated against leptospirosis.Blood samples were collected each 30 days during six months following the first vaccination. The sera were tested by MAT and growth inhibition test (GIT) to serovar Hardjo in order to evaluate respectively agglutinating and neutralizing antibodies. It was found that neutralizing antibodies persisted for a longer time than the agglutinating ones and that the absence of agglutinating antibodies does not means in the absence of the neutralizing. The peaks of agglutinating antibodies was obtained at least 30 days earlier than that produced by neutralizing. The duration of both kinds of antibodies measured differed between the two bacterines tested. The period for inducing neutralizing antibodies against serovar Hardjo indicated that gilts must be immunized with two doses of whole culture anti-leptospira bacterines applied 30 days each other at least 90 days before the first mating. For the maintenance of hight levels of neutralizing antibodies the revaccinations must be performed every six months after the first vaccination.

Time correlation function in systems with two coexisting biological species

We study a stochastic lattice model describing the dynamics of coexistence of two interacting biological species. The model comprehends the local processes of birth, death, and diffusion of individuals of each species and is grounded on interaction of the predator-prey type. The species coexistence can be of two types: With self-sustained coupled time oscillations of population densities and without oscillations. We perform numerical simulations of the model on a square lattice and analyze the temporal behavior of each species by computing the time correlation functions as well as the spectral densities. This analysis provides an appropriate characterization of the different types of coexistence. It is also used to examine linked population cycles in nature and in experiment.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Diketopiperazines produced by endophytic fungi found in association with two Asteraceae species

Diketopiperazine (DKP) derivatives, named colletopiperazine, fusaperazine C and E as well as four known DKPs were isolated from cultures of Colletotrichum gloeosporioides, Penicillium crustosum, both endophytic fungi isolated from Viguiera robusta, and a Fusarium spp., an endophyte of Viguiera arenaria, respectively. Their structures were established on the basis of their spectroscopic data. Conformational analysis of two known DKPs showed that folded conformations were as energetically stable as the extended one. (C) 2010 Elsevier Ltd. All rights reserved.

On a semilinear Schrodinger equation with critical Sobolev exponent

We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an element of W-1,W-2 (R-N), where N greater than or equal to4, V, K, g are periodic in x(j) for 1 less than or equal toj less than or equal toN, K>0, g is of subcritical growth and 0 is in a gap of the spectrum of -Delta +V. We show that under suitable hypotheses this equation has a solution u not equal 0. In particular, such a solution exists if K equivalent to 1 and g equivalent to 0.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Metal-directed synthesis routes to a 16-membered tetraazamacrocycle with two pendant primary amine groups

The reaction of the bis(propane-1,3-diamine)copper(II) ion with paraformaldehyde and nitroethane in dry methanol under basic conditions produces a macrocyclic product, (cis-3,11-dimethyl-3,11-dinitro-1,5,9,13-tetraazacyclohexadecane)copper(II) perchlorate, in low yield, compared with the good yield obtained in the parallel chemistry possible even under aqueous conditions using palladium(II) as a template. The palladium complex was reduced with zinc amalgam in dilute aqueous acid to yield the metal-free 16-membered macrocyclic hexaamine, in this case re-complexed and characterised by an X-ray crystal structure as the (cis-3,11-dimethyl-1,5,9,13-tetraazacyclohexadecane-3,11-diamine)copper(II) perchlorate. The copper ion is found in a tetragonally elongated and trigonally-distorted octahedral environment, with all six of the ligand nitrogens coordinated, the two primary amine pendant groups occupying cis sites. (C) 2000 Elsevier Science S.A. All rights reserved.