Maximal monotonicity, conjugation and the duality product

Recently, the authors studied the connection between each maximal monotone operator and a family of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities.

The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.

     

Padé approximation in time-domain boundary conditions of porous surfaces

Formulation and implementation of time-domain boundary conditions (TDBCs) at the surface of a reactive porous material are made challenging by the slow decay, complexity, or noncausal nature of many commonly used models of porous materials. In this paper, approaches are described that improve computational efficiency and enforce causality. One approach involves approximating the known TDBC for the modified Zwikker-Kosten impedance model as a summation of decaying exponential functions. A second approach, which can be applied to any impedance model, involves replacing the characteristic admittance with its Padé approximation. Then, approximating fractional derivatives with decaying exponentials, a causal and recursive TDBC is formulated.     

Distortion product otoacoustic emission suppression tuning and acoustic admittance in human infants: birth through 6 months

Previous work has reported non-adultlike distortion product otoacoustic emission (DPOAE) suppression in human newborns at f2=6000 Hz, indicating an immaturity in peripheral auditory function. In this study, DPOAE suppression tuning curves (STCs) were recorded as a measure of cochlear function and acoustic admittance/reflectance (YR) in the ear canal recorded as a measure of middle-ear function, in the same 20 infants at birth and through 6 months of age. DPOAE STCs changed little from birth through 6 months, showing excessively narrow and sharp tuning throughout the test period. In contrast, several middle-ear indices at corresponding frequencies shifted systematically with increasing age, although they also remained non-adultlike at 6 months. Linear correlations were conducted between YR and DPOAE suppression features. Only two correlations out of 76 were significant, and all but three YR variables accounted for <10% of the variance in DPOAE suppression tuning. The strongest correlation was noted between admittance phase at 5700 Hz and STC tip-to-tail (R=0.49). The association between middle-ear variables and DPOAE suppression may be stronger during other developmental time periods. Study of older infants and children is needed to fully define postnatal immaturity of human peripheral auditory function.     

In vivo magnetic resonance microscopy of Drosophilae at 9.4 T

In preclinical research, genetic studies have made considerable progress as a result of the development of transgenic animal models of human diseases. Consequently, there is now a need for higher resolution MRI to provide finer details for studies of small animals (rats, mice) or very small animals (insects). One way to address this issue is to work with high-magnetic-field spectrometers (dedicated to small animal imaging) with strong magnetic field gradients. It is also necessary to develop a complete methodology (transmit/receive coil, pulse sequence, fixing system, air supply, anesthesia capabilities, etc.). In this study, we developed noninvasive protocols, both in vitro and in vivo (from coil construction to image generation), for drosophila MRI at 9.4 T. The 10*10*80-μm resolution makes it possible to visualize whole drosophila (head, thorax, abdomen) and internal organs (ovaries, longitudinal and transverse muscles, bowel, proboscis, antennae and optical lobes). We also provide some results obtained with a Drosophila model of muscle degeneration. This opens the way for new applications of structural genetic modification studies using MRI of drosophila.     

Experimental NMR and MS study of benzoylguanidines. Investigation of E/Z isomerism

Molecules containing the guanidinic nuclei possess several pharmacological applications, and knowing the preferred isomers of a potential drug is important to understand the way it operates pharmacologically. Benzoylguanidines were synthesized in satisfactory to good yields and characterized by NMR, Electrospray Ionization Mass Spectrometry (ESI‐MS) and Fourrier Transform InfraRed Spectroscopy techniques (FTIR). E/Z isomerism of the guanidines was studied and confirmed by NMR analysis in solution (¹H‐¹³C Heteronuclear Single Quantum Coherence (HSQC) and Heteronuclear Multiple‐Bond Correlation (HMBC), ¹H‐¹⁵N HMBC, ¹H‐¹H Correlation Spectroscopy (COSY) and Nuclear Overhauser Effect Spectroscopy (NOESY) experiments) at low temperatures. Compounds with p‐Cl and p‐Br aniline moiety exist mainly as Z isomer with a small proportion of E isomer, whereas compounds with p‐NO2 moiety showed a decrease in proportion of isomer Z. The results are important for the application of these molecules as enzymatic inhibitors. Copyright © 2013 John Wiley & Sons, Ltd.     

Vibration analysis of quasi-symmetric structures

An efficient computational procedure is presented for the free vibration analysis of structures with unsymmetric geometry. The procedure is based on approximating the unsymmetric vibrational response of the structure by a linear combination of a few symmetric and antisymmetric modes (global approximation vectors), each obtained using approximately half the degrees of freedom of the original model. The three key elements of the procedure are: (a) use of mixed finite element models having independent shape functions for the internal forces (stress resultants) and generalized displacements, with the internal forces allowed to be discontinuous at interelement boundaries, (b) operator splitting, or additive decomposition of the different arrays in the governing finite element equations to delineate the contributions to the symmetric and antisymmetric response vectors, and (c) use of a reduction method through successive application of the finite element method and the classical Bubnov-Galerkin technique. The finite element method is first used to generate a few symmetric and antisymmetric global approximation response vectors. Then, the classical Bubnov-Galerkin technique is used to substantially reduce the size of the eigenvalue problem.

An initial set of global approximation vectors is selected to be a few symmetric and antisymmetric eigenvectors, and their various-order derivatives with respect to a tracing parameter identifying all the correction terms to the symmetric (and antisymmetric) eigenvectors. A modified (improved) set of approximation vectors is obtained by using the inverse iteration procedure. The effectiveness of the proposed procedure is demonstrated by means of a numerical example.     

Enhancing molecular formation in a Rb-MOT

In this paper, we report observation of an enhancement of the ground state molecule Rb₂ formation in a Rb magneto-optical trap due to a photoassociation laser. Such an enhancement effect is due to flux enhancement of atomic pairs at short internuclear distances. Our experimental observations consist in the measurement of the molecular formation rate constant due to a probe laser as a function of the trap laser intensity. The results are compared with a simple semi-classical model, showing good agreement. We conclude that the production of cold Rb₂ may be enhanced using appropriate laser parameters; this may be useful for future experiments involving production and trapping of ultracold ground state molecules.     

k—Very Ample Line Bundles on Del Pezzo Surfaces

A k-very ample line bundle L on a Del Pezzo Surface is numerically characterized, improving the results of Biancofiore— Ceresa in [7].     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998