Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.

A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.

GEVREY SOLVABILITY AND GEVREY REGULARITY IN DIFFERENTIAL COMPLEXES ASSOCIATED TO LOCALLY INTEGRABLE STRUCTURES

In this work we study some properties of the differential complex associated to a locally integrable (involutive) structure acting on forms with Gevrey coefficients. Among other results we prove that, for such complexes, Gevrey solvability follows from smooth solvability under the sole assumption of a regularity condition. As a consequence we obtain the proof of the Gevrey solvability for a first order linear PDE with real-analytic coefficients satisfying the Nirenberg-Treves condition (P).

On the loss of regularity for a class of weakly hyperbolic operators

In this paper we determine bounds for the optimal loss of regularity in the Sobolev scale for a class of weakly hyperbolic operators. (C) 2009 Elsevier Inc. All rights reserved.

Green's relations, regularity and abundancy for semigroups of quasi-onto transformations

Let V be an infinite-dimensional vector space and for every infinite cardinal n such that n≤dimV, let AE(V,n) denote the semigroup of all linear transformations of V whose defect is less than n. In 2009, Mendes-Gonçalves and Sullivan studied the ideal structure of AE(V,n). Here, we consider a similarly-defined semigroup AE(X,q) of transformations defined on an infinite set X. Quite surprisingly, the results obtained for sets differ substantially from the results obtained in the linear setting.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

Prescription footwear for severe injuries of foot and ankle: effect on regularity and symmetry of the gait assessed by trunk accelerometry.

After foot and/or ankle fracture, the restoration of optimal gait symmetry is one of the criteria of recovery. Orthotic insoles and orthopaedic shoes improve gait symmetry and regularity by controlling joint motion and improving alignment. The aim of the present study was to assess the effect of prescription footwear on gait quality by using accelerometers attached to the lower back. Sixteen adult patients with persistent disability after ankle and/or foot fractures performed two 30-s walking trials with and without prescription footwear (insoles and stabilizing shoes). Sixteen control subjects were also tested for comparison. The autocorrelation function was computed from the acceleration signal and the first two dominant periods were assessed (d1 and d2). Two parameters were used: (1) Stride Regularity (SR) which expresses the similarity between strides over time (d2), and (2) Stride Symmetry (SS) a ratio (d1/d2) which expresses the left/right similarity of gait independently of repeatability in the successive movements of each limb. In control subjects, SR and SS were 0.86+/-0.05 (correlation coefficient) and 81+/-10%, respectively. In the patient group, the effect of footwear was significant (SR: 0.88+/-0.06 vs. 0.90+/-0.05, SS: 38+/-23% vs. 46+/-27%). Pain was also significantly reduced (-34%). By using a rapid and low-cost method, we objectively quantified gait quality improvement after footwear intervention, concomitant to pain reduction. Substantial inter-patient variability in the footwear outcome was observed. In conclusion, we believe that trunk accelerometry can be a useful tool in the field of gait rehabilitation.

On the existence of doubling measures with certain regularity properties

Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the pseudo-metric. Then we construct a doubling measure for which the measure of a dilated ball is closely related to these dimensions.

Cell wall thickness and tangential and radial cell diameter of fertilized and irrigated Norway spruce

Abstract

Tangential migration of neuronal precursors of glutamatergic neurons in the adult mammalian brain.

In a classic model of mammalian brain formation, precursors of principal glutamatergic neurons migrate radially along radial glia fibers whereas GABAergic interneuron precursors migrate tangentially. These migration modes have significant implications for brain function. Here we used clonal lineage tracing of active radial glia-like neural stem cells in the adult mouse dentate gyrus and made the surprising discovery that proliferating neuronal precursors of glutamatergic granule neurons exhibit significant tangential migration along blood vessels, followed by limited radial migration. Genetic birthdating and morphological and molecular analyses pinpointed the neuroblast stage as the main developmental window when tangential migration occurs. We also developed a partial "whole-mount" dentate gyrus preparation and observed a dense plexus of capillaries, with which only neuroblasts, among the entire population of progenitors, are directly associated. Together, these results provide insight into neuronal migration in the adult mammalian nervous system.

Regularity and counterfactuality in Hume's treatment of causation

Of the several theories of causation current in our days, Hume is said to be the inspiration of two of the most influential and accepted: the regularity theory, first clearly formulated by Thomas Brown in 1822, and the counterfactual theory, proposed by David Lewis in 1973. After a brief outline of the comparative merits and difficulties of these two views, I proceed to examine whether Hume's own treatment of causation actually corresponds to any of them. I will show that his first definition of cause, coupled with his rules by which to judge about causes and effects, contains elements that, properly developed, allow us to address successfully some traditional difficulties of the regularity view of causation, without resorting to the conceptual resources employed in the counterfactual approach. Therefore, we can properly classify Hume as an advocate of the conception of causation as regularity, noting however that his primary goal in his research and definitions of the concept was to provide not so much an analysis of causation as such, but of causation as we apprehend it, in the form of our ability to make causal inferences and refine them to reach the more sophisticated causal reasonings that are required in the theoretical and practical issues of life.

Tangential microfiltration of orange juice in bench pilot

The aim of this study was to introduce the tangential microfiltration (TMF) technique on the production of orange juice (TMFJ), and compare it with pasteurised juice (control) as regards chemical composition and sensorial characteristics. We used a TMF pilot equipped with four monotubular ceramic membranes (0.1, 0.2, 0.8 and 1.4mm) arranged in series with a filtering area of 0.005 m² each. Commercial flash-pasteurised orange juice was used as the initial product. Experiments were divided into three parts: a) the characterisation of the TMF pilot; b) optimisation of operational conditions; c) production of the TMFJ. In the second part, membrane with 0.8-mm pores presented best flux followed by those with 1.4-, 0.1-, and 0.2-mm pores. However, to guarantee permeate sterility, we chose the membrane with 0.1-mm pores for TMFJ production. Initially, the orange juice was sieved in order to separate part of the pulp, being subsequently submitted to TMF. A mixture of retentate and pulp was made, and was subsequently pasteurised. We obtained the TMFJ by adding the permeate to the mixture. TMFJ presented soluble solids content (°Brix), pulp, pH, and titrable acidity similar to the initial pasteurised juice (control). Nevertheless, 28% of vitamin C was lost during the TMFJ production. According to the juice taster panel, the control juice presented best sensorial characteristics (greater aroma intensity and fruity flavour) when compared with the TMJF.

Steady periodic water waves with constant vorticity: regularity and local bifurcation

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.