Normal form for generalized Hopf bifurcation with non-semisimple 1 ∶ 1 resonance

The primary result of this research is the derivation of an explicit formula for the Poincaré-Birkhoff normal form of the generalized Hopf bifurcation with non-semisimple 1:1 resonance. The classical nonuniqueness of the normal form is resolved by the choice of complementary space which yields a unique equivariant normal form. The 4 leading complex constants in the normal form are calculated in terms of the original coefficients of both the quadratic and cubic nonlinearities by two different algorithms. In addition, the universal unfolding of the degenerate linear operator is explicitly determined. The dominant normal forms are then obtained by rescaling the variables. Finally, the methods of averaging and normal forms are compared. It is shown that the dominant terms of the equivariant normal form are, indeed, the same as those of the averaged equations with a particular choice for the constant of integration.Partially supported by NSF through grant MSS 90-57437, AFOSR through grant 91-0041 and NSERC of Canada.     

Charged particles on surfaces: coexistence of dilute phases and periodic structures at interfaces

We consider a mixture of two immiscible oppositely charged molecules strongly adsorbed to an interface, with a neutral nonselective molecular background. We determine the coexistence between a high density ionic periodic phase and a dilute isotropic ionic phase. We use a strong segregation approach for the periodic phase and determine the one-loop free energy for the dilute phase. Lamellar and hexagonal patterns are calculated for different charge stoichiometries of the mixture. Molecular dynamics simulations exhibit the predicted phase behavior. The periodic length scale of the solid phase is found to scale as epsilon/(lB psi3/2), where psi is the effective charge density, lB is the Bjerrum length, and epsilon is the cohesive energy.     

Active Longitudinal Control of Wind-Induced Oscillations of a Suspended Cable

Abstract. Active control of oscillations of a suspended cable under transversal wind, described by a constant term and a fluctuating turbulent component, is dealt with. Control of transversal in-plane and out-of-plane oscillations is performed by imposing a longitudinal motion to one support; the control law depends, linearly or quadratically, on measures of displacement and velocity of a selected point. First, the steady-state oscillations around the planar static configuration, determined by the wind constant component, under sinusoidal in-plane and out-of-plane loading are studied, showing the nonlinear behaviour in the regions of primary and parametric resonance and the effects of the control action. Afterwards, attention is focused on the response of the cable to transversal wind turbulence, whose fluctuating component is described by a random process with an assigned spectral density. The effectiveness of longitudinal control is analysed by means of numerical investigations.Sommario. Si analizza il controllo attivo delle oscillazioni di un cavo sospeso, sottoposto all'azione di un vento agente in direzione ortogonale al piano del cavo e descritto mediante un termine di carico costante ed una componente variabile di turbolenza. Il controllo delle oscillazioni piane e spaziali viene realizzato mediante spostamento longitudinale di uno degli appoggi; la legge di controllo dipende linearmente o quadraticamente da misure di spostamento e velocità di un punto prescelto. In una prima fase, vengono studiate le oscillazioni stazionarie sotto carichi sinusoidali agenti rispettivamente nel piano e fuori del piano del cavo, intorno alla configurazione di equilibrio statico determinata dalla presenza della componente costante del vento, mostrando il comportamento nonlineare nelle regioni di risonanza primaria e parametrica e gli effetti dell'azione di controllo. Successivamente, si focalizza l'attenzione sulla risposta del cavo alla componente trasversale di turbolenza del vento, la quale è descritta da un processo stocastico a media nulla con densità spettrale assegnata. L'efficacia del controllo viene analizzata attraverso un'indagine numerica.     

Nonlinear Oscillations of a Nonresonant Cable under In-Plane Excitation with a Longitudinal Control

The nonlinear oscillations of a controlled suspended elastic cable under in-plane excitation are considered. Active control realized by longitudinal displacement of one support is introduced in order to reduce the transverse in-plane and out-of-plane vibrations. Linear and quadratic enhanced velocity feedback control laws are chosen and their effects on the cable motion are investigated using a two degree-of-freedom model. Perturbation analysis is performed to determine the in-plane steady-state solutions and their stability under an out-of-plane disturbance. The analysis is extended to the bifurcated two-mode steady-state oscillations in the region of parametric excitation. The dependence of the control effectiveness on the system parameters is investigated in the case of the first symmetric mode and the range of oscillation amplitudes in which the proposed control ensures a dissipation of energy is determined. Although control based only on in-plane response quantities is effective in reducing oscillations with a prevailing in-plane component, addition of out-of-plane measures has to be considered when the motion is characterized by two comparable components.     

Chemical composition and bioactivity of Citrus medica L. cv. Diamante essential oil obtained by hydrodistillation, cold-pressing and supercritical carbon dioxide extraction

The chemical composition of the essential oil of Citrus medica L. cv. Diamante peel obtained by hydrodistillation, cold-pressing and supercritical carbon dioxide extraction techniques was determined by GC/MS analysis. Forty-six components were fully characterised. Limonene and γ-terpinene were the major components of the oils obtained by hydrodistillation (HD) and cold-pressing (CP), while citropten was the major constituent in the oil obtained by supercritical carbon dioxide extraction (SFE). Acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) inhibitory activities were evaluated. The essential oil obtained by hydrodistillation exerted the highest inhibitory activity against BChE (IC?? value of 154.6 μg mL?1) and AChE (IC?? value of 171.3 μg mL?1. Interestingly, the oil obtained by cold-pressing exhibited a selective inhibitory activity against AChE. The essential oils have also been evaluated for the inhibition of NO production in LPS induced RAW 264.7 macrophages. The oil obtained by hydrodistillation exerted a significant inhibition of NO production with an IC?? value of 17 μg mL?1 (IC?? of positive control 53 μg mL?1).     

Metal-free direct arylations of indoles and pyrroles with diaryliodonium salts

Direct arylations of indoles and pyrroles with differently substituted diaryliodonium salts were shown to efficiently proceed in the absence of metal catalysts.     

Krull’s theory for the double gamma function

The Barnes’ G-function G(x) = 1/Γ₂, satisfies the functional equation logG(x + 1) − logG(x) = logΓ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma functions, a new expansion for the Gamma function and summation formulae with Polygamma functions.     

Quantitative impact of small angle forward scatter on whole blood oximetry using a Beer-Lambert absorbance model

It is well known that red blood cell scattering has an impact on whole blood oximetry as well as in vivo retinal oxygen saturation measurements. The goal of this study was to quantify the impact of small angle forward scatter on whole blood oximetry for scattering angles found in retinal oximetry light paths. Transmittance spectra of whole blood were measured in two different experimental setups: one that included small angle scatter in the transmitted signal and one that measured the transmitted signal only, at absorbance path lengths of 25, 50, 100, 250 and 500 μm. Oxygen saturation was determined by multiple linear regression in the 520-600 nm wavelength range and compared between path lengths and experimental setups. Mean calculated oxygen saturation differences between setups were greater than 10% at every absorbance path length. The deviations to the Beer-Lambert absorbance model had different spectral dependences between experimental setups, with the highest deviations found in the 520-540 nm range when scatter was added to the transmitted signal. These results are consistent with other models of forward scatter that predict different spectral dependences of the red blood cell scattering cross-section and haemoglobin extinction coefficients in this wavelength range.     

Intercompany Study to Evaluate the Robustness of Capillary Isoelectric Focusing Technology for the Analysis of Monoclonal Antibodies

Interlaboratory comparisons are essential to bringing emerging technologies into biopharmaceutical industry practice and regulatory acceptance. As a result, an international team including 12 laboratories from 10 independent biopharmaceutical companies in the United States and Switzerland was formed to evaluate the precision and robustness of capillary isoelectric focusing (CIEF) to assess the charge heterogeneity of monoclonal antibodies. The different laboratories determined the apparent pI and the relative distribution of the charge isoforms of a representative monoclonal antibody (rMAb) sample using the same CIEF method. Statistical evaluation of the data was performed to determine within and between-laboratory consistencies and outlying information. The apparent pI data generated for each charge variant peak showed very good precision between laboratories with percentage of RSD values of ??0.5%. Similarly, the percentage of RSD for the rMAb charge variants percent peak area values are ??4.4% across different laboratories with different analysts using different lots of ampholytes and multiple instruments. Taken together, these results validate the appropriate use of CIEF in the biopharmaceutical industry in support of regulatory submissions.     

Can human prolidase enzyme use different metals for full catalytic activity?

The catalytic hydrolysis of the Gly-Pro substrate by the bimetallic prolidase active site model cluster has been investigated at the DF/B3LYP level of theory, in order to provide fundamental insights into the still poorly understood mechanism of prolidase catalysis. To date, the majority of prolidases exhibits metal-dependent activity, requiring two divalent cations such as Zn(2+), Mn(2+), or Co(2+) for maximal activity. In addition, it has been shown recently that two different metal ions in the active site of human prolidase (Zn and Mn) can coexist, with the protein remaining partially active. With the purpose of identifying which is the most efficient dimetallic center for the prolidase catalyzed reaction, Zn(II), Co(II), and Mn(II) have been examined as potential catalytic metals for this enzyme. Furthermore, to better elucidate the exact roles played by the metals occupying the site 1 and site 2 positions, the hetero-bimetallic active site having Zn and Mn cations has been also investigated, considering the two derivatives Mn1-Zn2 and Zn1-Mn2. The rate-determining step of the hydrolysis reaction is always found to be the nucleophilic addition of the hydroxide ion on the carbonyl carbon of the scissile peptide bond, followed by the less energetically demanding proline-peptide C-N bond scission. The analysis of the involved energy barriers does not indicate clearly a preference for a particular metal by the prolidase enzyme. Instead, we may point out a slightly better behavior of the cobalt-containing cluster as far as both tetrahedral formation and its decomposition are concerned, due to a greater degree of ligands-to-metals charge transfer. The mixed Mn-Zn hetero-dimetallic clusters appear to be also able to perform the hydrolysis of the Pro-Gly substrate, with a slight preference for the Mn1-Zn2 configuration.