Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

Binding constant measurement by hyper-Rayleigh scattering: bilirubin-human serum albumin binding as a case study

In this paper, a new application of the hyper-Rayleigh scattering technique in determining multiple binding constants of a small molecule like bilirubin to a macromolecule like the protein human serum albumin has been demonstrated. Human serum albumin has two binding sites for bilirubin, and the binding constants have been measured by carrying out a second harmonic titration of the protein against bilirubin and vice versa. The measured binding constants K(1) = 1.5 +/- 0.43 x 10(7) M(-1) and K(2) = 1.01 +/- 0.16 x 10(6) M(-1) agree well with the reported values obtained by other methods.     

Adsorption Characteristics of Pb(II) and Cr(III) onto C‐4‐Methoxyphenylcalix[4]Resorcinarene in Batch and Fixed Bed Column Systems

A study on the adsorption characteristics of Pb(II) and Cr(III) cations onto C‐4‐methoxyphenylcalix‐[4]resorcinarene (CMPCR) in batch and fixed bed column systems has been conducted. CMPCR was produced by one step synthesis from resorcinol, 4‐methoxybenzaldehyde, and HCl. The synthesis was carried out at 78 °C for 24 hours and afforded the adsorbent in 85.7% as a 3:2 mixture of C_4ν:C_2ν isomer. Most parameters in batch and fixed bed column systems confirm that CMPCR is a good adsorbent for Pb(II) and Cr(III), though Pb(II) adsorption was more favorable than that of Cr(III). The adsorption kinetic of Pb(II) and Cr(III) adsorptions in batch and fixed bed column systems followed a pseudo 2ⁿ order kinetics model. The rate constant of Pb(II) was higher than that of Cr(III) in the batch system, but this result was contrary to the result obtained in a fixed bed column system. Desorption studies to recover the adsorbed Pb(II) and Cr(III) were performed sequentially with distilled water and HCl, and the results showed that the adsorption was dominated by chemisorption.     

A note on general solution of Stokes equations

Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).     

Catalytic behavior of decomposed molybdophosphoric acid supported on alumina for oxidative dehydrogenation of ethane to ethylene

Oxidative dehydrogenation of ethane (ODHE) to ethylene was investigated over a series of alumina supported molybdophosphoric acid (MPA) catalysts. The MPA was transformed into surface Mo oxides on Al₂O₃ when subjected to calcination at 600°C. The catalysts were characterized by N₂-adsorption, XRD, FT-IR spectroscopy and TPR techniques. The results showed that MPA loading and the source of Mo precursor had a clear influence on the catalytic performance. The evaluation of the catalysts for ODHE at temperatures between 450 and 550°C revealed superior ethane conversion (X～24%) and ethylene selectivity (S = ca. 65%) over 20 wt % MPA/Al₂O₃ catalyst. The transformation of MPA into finely dispersed Mo oxides on Al₂O₃ appeared to be responsible for this improved performance.     

Sol–gel synthesis and optical behavior of Mg–Ce–O nano-crystallites

The Mg–Ce–O powder are shown to contain periclase-type MgO and/or fluoride-type cerium oxide (CeO₂) depending upon the composition (x) defined by Ce/(Ce + Mg) atomic ratio. Lattice contraction of pariclase phase of MgO (average crystallite size ~8.8 nm) at Ce content of ‘x’ = 0.20 in comparison to pure MgO (crystallite size ~9.5 nm) has been realized due to oxygen vacancy formation. The optical band gap values of CeO₂ varies (3.0–3.2 eV) due to oxygen vacancy formation in CeO₂ phase, crystallite size and/or Ce³⁺/Ce⁴⁺ ratio. Further, the addition of Ce has shown to reduce the physisorption and chemisorption of water significantly as reflected by (1) suppression of related absorption peaks and (2) absence of magnesium hydroxide, Mg(OH)₂, bands in Fourier transform infrared spectra.     

Approaches for Mitigating Microbial Biofilm-Related Drug Resistance: A Focus on Micro- and Nanotechnologies

Biofilms play an essential role in chronic and healthcare-associated infections and are more resistant to antimicrobials compared to their planktonic counterparts due to their (1) physiological state, (2) cell density, (3) quorum sensing abilities, (4) presence of extracellular matrix, (5) upregulation of drug efflux pumps, (6) point mutation and overexpression of resistance genes, and (7) presence of persister cells. The genes involved and their implications in antimicrobial resistance are well defined for bacterial biofilms but are understudied in fungal biofilms. Potential therapeutics for biofilm mitigation that have been reported include (1) antimicrobial photodynamic therapy, (2) antimicrobial lock therapy, (3) antimicrobial peptides, (4) electrical methods, and (5) antimicrobial coatings. These approaches exhibit promising characteristics for addressing the impending crisis of antimicrobial resistance (AMR). Recently, advances in the micro- and nanotechnology field have propelled the development of novel biomaterials and approaches to combat biofilms either independently, in combination or as antimicrobial delivery systems. In this review, we will summarize the general principles of clinically important microbial biofilm formation with a focus on fungal biofilms. We will delve into the details of some novel micro- and nanotechnology approaches that have been developed to combat biofilms and the possibility of utilizing them in a clinical setting.