A pointwise constrained version of the Liapunov convexity theorem for single integrals

Given any AC solution ${\overline{x} : [a,b] \rightarrow \mathbb{R}^{n}}$ to the convex ordinary differential inclusion $$x^{\prime} ( t) \in co\{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e. on [ a,b], \qquad \qquad (^{*})$$ we aim at solving the associated nonconvex inclusion $$x^{\prime} ( t) \in \{v^{1} ( t), \ldots, v^{m} ( t)\} \qquad a.e.,x( a) = \overline{x} ( a), x( b) = \overline{x} ( b), \qquad \qquad (^{**})$$ under an extra pointwise constraint (e.g. on the first coordinate): $$x_{1} ( t) \leq \overline{x}_{1} ( t) \qquad \forall t \in [ a,b]. \qquad \qquad \qquad (^{***})$$ While the unconstrained inclusion (**) had been solved already in 1940 by Liapunov, its constrained version, with (***), was solved in 1994 by Amar and Cellina in the scalar n = 1 case. In this paper we add an extra geometrical hypothesis which is necessary and sufficient, in the vector n > 1 case, for it existence of solution to the constrained inclusion (**) and (***). We also present many examples and counterexamples to the 2 × 2 case.     

Travelling Waves in a SI Endemic Model

In this paper we consider an endemic SI model with standard incidence and prove the existence of monotone and unimodal travelling waves with large velocity. The birth and death rates can be quite general. When the birth rate is constant we prove the existence of two kinds of travelling waves and give the minimal velocity of one of the types.     

Experimental and theoretical investigation of the micellar-assisted solubilization of ibuprofen in aqueous media

Surfactants can be used to increase the solubility of poorly soluble drugs in water and to increase drug bioavailability. In this article, the aqueous solubilization of the nonsteroidal, antiinflammatory drug ibuprofen is studied experimentally and theoretically in micellar solutions of anionic (sodium dodecyl sulfate, SDS), cationic (dodecyltrimethylammonium bromide, DTAB), and nonionic (dodecyl octa(ethylene oxide), C12E8) surfactants possessing the same hydrocarbon "tail" length but differing in their hydrophilic headgroups. We find that, for these three surfactants, the aqueous solubility of ibuprofen increases linearly with increasing surfactant concentration. In particular, we observed a 16-fold increase in the solubility of ibuprofen relative to that in the aqueous buffer upon the addition of 80 mM DTAB and 80 mM C12E8 but only a 5.5-fold solubility increase upon the addition of 80 mM SDS. The highest value of the molar solubilization capacity (chi) was obtained for DTAB (chi = 0.97), followed by C12E8 (chi = 0.72) and finally by SDS (chi = 0.23). A recently developed computer simulation/molecular-thermodynamic modeling approach was extended to predict theoretically the solubilization behavior of the three ibuprofen/surfactant mixtures considered. In this modeling approach, molecular-dynamics (MD) simulations were used to identify which portions of ibuprofen are exposed to water (hydrated) in a micellar environment by simulating a single ibuprofen molecule at an oil/water interface (modeling the micelle core/water interface). On the basis of this input, molecular-thermodynamic modeling was then implemented to predict (i) the micellar composition as a function of surfactant concentration, (ii) the aqueous solubility of ibuprofen as a function of surfactant concentration, and (iii) the molar solubilization capacity (chi). Our theoretical results on the solubility of ibuprofen in aqueous SDS and C12E8 surfactant solutions are in good agreement with the experimental data. The ibuprofen solubility in aqueous DTAB solutions was somewhat overpredicted because of challenges associated with accurately modeling the strong electrostatic interactions between the anionic ibuprofen and the cationic DTAB. Our results indicate that computer simulations of ibuprofen at a flat oil/water interface can be used to obtain accurate information about the hydrated and the unhydrated portions of ibuprofen in a micellar environment. This information can then be used as input to a molecular-thermodynamic model of self-assembly to successfully predict the aqueous solubilization behavior of ibuprofen in the three surfactant systems studied.     

Tunable, passively Q-switched single-longitudinal-mode Nd:YVO4 laser using a chirped volume Bragg grating

A Nd:YVO₄ laser was locked with a chirped volume Bragg grating to achieve single-longitudinal-mode output. Tuning was performed from 1,063 to 1,065?nm by translating the grating and a maximum output power of 4?W was obtained. With a Cr⁴⁺:YAG saturable absorber, Q-switched pulses with 4?ns and a pulse energy of 5.7???J were achieved which could be frequency doubled in PPKTP with a conversion efficiency exceeding 50?%.     

Long-time behaviour of a one-dimensional BGK model: convergence to macroscopic rarefaction waves

For one-dimensional kinetic BGK models, regarded as relaxation models for scalar conservation laws with genuinely nonlinear fluxes, we prove that the macroscopic density converges to the rarefaction wave solution of the corresponding scalar conservation law in the long time limit, and that the phase space density approaches an equilibrium distribution with the rarefaction wave as macroscopic density. The proof requires a smallness assumption on the amplitude of the rarefaction waves and uses a micro-macro decomposition of the perturbation equation.     

Three-dimensional structure determination of N-(p-Tolyl)-dodecylsulfonamide from powder diffraction data and validation of structure using solid-state NMR spectroscopy

The three-dimensional structure, conformation, and packing of molecules in the solid state are crucial components used in the optimization of many technologically useful materials properties. Single-crystal X-ray diffraction is the traditional and most effective method of determining 3-D structures in the solid state. Obtaining single crystals that are sufficiently large and free of imperfections is often laborious, time-consuming, and, occasionally, impossible. The feasibility of an integrated approach to the determination and verification of a complete three-dimensional structure for a medium-sized organic molecule without using single crystals is demonstrated for the case of an organic stabilizer compound N-(p-tolyl)-dodecylsulfonamide. The approach uses a combination of powder XRD data, several computational packages involving Monte Carlo simulations and ab initio quantum mechanical calculations, and experimental solid-state NMR chemical shifts. Structure elucidation of N-(p-tolyl)-dodecylsulfonamide revealed that the Bravais lattice is monoclinic, with cell dimensions of a = 38.773 A, b = 5.507 A, c = 9.509 A, and beta = 86.35 degrees, and a space group of P21/c.     

Intra-cavity frequency-doubled Yb:KYW laser using periodically poled Rb-doped KTP with a volume Bragg grating input coupler

An Yb:KYW laser intra-cavity frequency doubled to the green at 514.7 nm using a periodically poled Rb:KTP crystal with an output power exceeding 1 W is presented. Spectral narrowing and locking at the fundamental wavelength has been achieved by using a volume Bragg grating as the input coupler.     

Fluorescence spectroscopy evaluation of fibrinogen-beta-estradiol binding

Fluorescence spectroscopy experiments were performed in order to study conformational changes induced by the binding of beta-estradiol to fibrinogen at different ligand concentrations. The association constant (Ka) obtained for the fibrinogen-beta-estradiol binding was 6.47x10(6)M(-1), indicating a high affinity interaction. Fluorescence quenching experiments showed that approximately 30% of the tryptophan residues in the protein quaternary structure are accessible to ionic quenchers. The extent of quenching in the absence and presence of beta-estradiol was maximum for cesium ions and minimum for iodide, suggesting the presence of negatively charged residues in the vicinity of the tryptophan residues. The quenching parameters obtained at different beta-estradiol concentrations show alterations that confirm a conformational change, possibly due to a discrete reorganization of tryptophan residues during fibrinogen-beta-estradiol binding. This binding may be responsible for the effects of beta-estradiol on the decrease of erythrocyte aggregation and on cardiovascular risk reduction.