Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Extended Maximum Principles

2000 Mathematics Subject Classification: 35B50, 35L15.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.

Biological evolution of replicator systems: towards a quantitative approach

The aim of this work is to study the features of a simple replicator chemical model of the relation between kinetic stability and entropy production under the action of external perturbations. We quantitatively explore the different paths leading to evolution in a toy model where two independent replicators compete for the same substrate. To do that, the same scenario described originally by Pross (J Phys Org Chem 17:312–316, 2004) is revised and new criteria to define the kinetic stability are proposed. Our results suggest that fast replicator populations are continually favored by the effects of strong stochastic environmental fluctuations capable to determine the global population, the former assumed to be the only acting evolution force. We demonstrate that the process is continually driven by strong perturbations only, and that population crashes may be useful proxies for these catastrophic environmental fluctuations. As expected, such behavior is particularly enhanced under very large scale perturbations, suggesting a likely dynamical footprint in the recovery patterns of new species after mass extinction events in the Earth’s geological past. Furthermore, the hypothesis that natural selection always favors the faster processes may give theoretical support to different studies that claim the applicability of maximum principles like the Maximum Metabolic Flux (MMF) or Maximum Entropy Productions Principle (MEPP), seen as the main goal of biological evolution.

Uniqueness for boundary value problems for second order finite difference equations

We establish maximum principles for second order difference equations and apply them to obtain uniqueness for solutions of some boundary value problems.

On the existence of solutions to boundary value problems on time scales

This work formulates existence theorems for solutions to two-point boundary value problems on time scales. The methods used include maximum principles, a priori bounds and topological degree theory.

Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

Applying the principles of life cycle assessment and costing in process modeling to examine profit-making capability

Static process simulation has traditionally been used to model complex processes for various purposes. However, the use of static processsimulators for the preparation of holistic examinations aiming at improving profit-making capability requires a lot of work because the production of results requires the assessment of the applicability of detailed data which may be irrelevant to the objective. The relevant data for the total assessment gets buried byirrelevant data. Furthermore, the models do not include an examination of the maintenance or risk management, and economic examination is often an extra property added to them which can be performed with a spreadsheet program. A process model applicable to holistic economic examinations has been developed in this work. The model is based on the life cycle profit philosophy developed by Hagberg and Henriksson in 1996. The construction of the model has utilized life cycle assessment and life cycle costing methodologies with a view to developing, above all, a model which would be applicable to the economic examinations of complete wholes and which would require the need for information focusing on aspects essential to the objectives. Life cycle assessment and costing differ from each other in terms of the modeling principles, but the features of bothmethodologies can be used in the development of economic process modeling. Methods applicable to the modeling of complex processes can be examined from the viewpoint of life cycle methodologies, because they involve the collection and management of large corpuses of information and the production of information for the needs of decision-makers as well. The results of the study shows that on the basis of the principles of life cycle modeling, a process model can be created which may be used to produce holistic efficiency examinations on the profit-making capability of the production line, with fewer resources thanwith traditional methods. The calculations of the model are based to the maximum extent on the information system of the factory, which means that the accuracyof the results can be improved by developing information systems so that they can provide the best information for this kind of examinations.

First-principles simulation of elastic constants and electronic properties of GaN

The electronic and structural properties and elastic constants of the wurtzite phase of GaN, was investigated by computer simulation at Density Functional Theory level, with B3LYP and B3PW hybrid functional. The electronic properties were investigated through the analysis of the band structures and density of states, and the mechanical properties were studied through the calculus of the elastic constants: C11, C33, C44, C12, and C13. The results show that the maximum of the valence band and the minimum of the conduction band are both located at the Γ point, indicating that GaN is a direct band gap semiconductor. The following constants were obtained for B3LYP and B3PW (in brackets): C11 = 366.9 [372.4], C33 = 390.9 [393.4], C44 = 99.1 [96.9], C12 = 143.6 [155.2], and C13 = 107.6 [121.4].

Recommendations for sex/gender neuroimaging research: Key principles and implications for research design, analysis and interpretation

Neuroimaging (NI) technologies are having increasing impact in the study of complex cognitive and social processes. In this emerging field of social cognitive neuroscience, a central goal should be to increase the understanding of the interaction between the neurobiology of the individual and the environment in which humans develop and function. The study of sex/gender is often a focus for NI research, and may be motivated by a desire to better understand general developmental principles, mental health problems that show female-male disparities, and gendered differences in society. In order to ensure the maximum possible contribution of NI research to these goals, we draw attention to four key principles—overlap, mosaicism, contingency and entanglement—that have emerged from sex/gender research and that should inform NI research design, analysis and interpretation. We discuss the implications of these principles in the form of constructive guidelines and suggestions for researchers, editors, reviewers and science communicators.

Photovoltaic application of O-doped Wittichenite-Cu 3 BiS 3: from microscopic properties to maximum efficiencies

The electronic properties and the low environmental impact of Cu 3 BiS 3 make this compound a promising material for low-cost thin film solar cell technology. From the first principles, the electronic properties of the isoelectronic substitution of S by O in Cu 3 BiS 3 have been obtained using two different exchange-correlation potentials. This compound has an acceptor level below the conduction band, which modifies the opto-electronic properties with respect to the host semiconductor. In order to analyze a possible efficiency increment with respect to the host semiconductor, we have calculated the maximum efficiency of this photovoltaic absorber material.

Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm

This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method. There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI)method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail. The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters.