A large deviations principle for stochastic flows of viscous fluids

We study the well-posedness of a stochastic differential equation on the two dimensional torus ${\mathbb{T}}^2$, driven by an infinite dimensional Wiener process with drift in the Sobolev space $L^2(0,T;H^1\left({\mathbb{T}}^2\right))$. The solution corresponds to a stochastic Lagrangian flow in the sense of DiPerna Lions. By taking into account that the motion of a viscous incompressible fluid on the torus can be described through a suitable stochastic differential equation of the previous type, we study the inviscid limit. By establishing a large deviations principle, we show that, as the viscosity goes to zero, the Lagrangian stochastic Navier–Stokes flow approaches the Euler deterministic Lagrangian flow with an exponential rate function.     

A general framework for ADMM acceleration

Numerical Algorithms - The Alternating Direction Multipliers Method (ADMM) is a very popular algorithm for computing the solution of convex constrained minimization problems. Such problems are...     

Algebraic reflexivity of sets of bounded operators on vector valued Lipschitz functions

In this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued Lipschitz functions. We also derive a representation for the generalized bi-circular projections on these spaces.     

Differential equations in Schatten classes of operators

We study a system of differential equations in Schatten classes of operators, ${\mathcal{C}_p(\mathcal{H})\,(1 \leq p < \infty}$ ), with ${\mathcal{H}}$ a separable complex Hilbert space. The systems considered are infinite dimensional generalizations of mathematical models of unsupervised learning. In this new setting, we address the usual questions of existence and uniqueness of solutions. Under some restrictions on the spectral properties of the initial conditions, we explicitly solve the system. We also discuss the long-term behavior of solutions.     

Transitive A 6-invariant k-arcs in PG(2, q)

For q = p ^r with a prime p ≥ 7 such that ${q \equiv 1}$ or 19 (mod 30), the desarguesian projective plane PG(2, q) of order q has a unique conjugacy class of projectivity groups isomorphic to the alternating group A ₆ of degree 6. For a projectivity group ${\Gamma \cong A_6}$ of PG(2, q), we investigate the geometric properties of the (unique) Γ-orbit ${\mathcal{O}}$ of size 90 such that the 1-point stabilizer of Γ in its action on ${\mathcal O}$ is a cyclic group of order 4. Here ${\mathcal O}$ lies either in PG(2, q) or in PG(2, q ²) according as 3 is a square or a non-square element in GF(q). We show that if q ≥ 349 and q ≠ 421, then ${\mathcal O}$ is a 90-arc, which turns out to be complete for q = 349, 409, 529, 601,661. Interestingly, ${\mathcal O}$ is the smallest known complete arc in PG(2,601) and in PG(2,661). Computations are carried out by MAGMA.     

Some Combinatorial Aspects of Constructing Bipartite-Graph Codes

We propose geometrical methods for constructing square 01-matrices with the same number n of units in every row and column, and such that any two rows of the matrix contain at most one unit in common. These matrices are equivalent to n-regular bipartite graphs without 4-cycles, and therefore can be used for the construction of efficient bipartite-graph codes such that both the classes of its vertices are associated with local constraints. We significantly extend the region of parameters m, n for which there exist an n-regular bipartite graph with 2m vertices and without 4-cycles. In that way we essentially increase the region of lengths and rates of the corresponding bipartite-graph codes. Many new matrices are either circulant or consist of circulant submatrices: this provides code parity-check matrices consisting of circulant submatrices, and hence quasi-cyclic bipartite-graph codes with simple implementation.     

Evaluation of the Mooney Viscosity of Natural Rubber by Near‐Infrared Spectroscopy

Abstract

The direct near‐infrared spectroscopic reflectance measurements of prevulcanized natural rubber (brown crepe) was employed for determination of its Mooney viscosity. NIR reflectance spectra were obtained for a total of 100 samples whose Mooney viscosity (VM in the range 68–95 units) have been determined by the standard reference procedure using a commercial computerized Mooney viscometer. These samples were employed as the raw material or were treated to achieve better homogenization. A Fourier transform near infrared (FT‐NIR) spectrophotometer was employed, and the reflectance spectra were obtained with resolution of 4 cm^?1 in the range 4000–10,000 cm^?1 as an average of 75 scans. The samples were split in a calibration set containing 70 samples and in an external validation set consisting of the remaining 30 samples. The calibration and validation spectra sets were treated to correct for baseline shift, further transformed by first derivative and finally modeled by partial least squares (PLS) employing four latent variables. The model was evaluated with the external sample test set, and a RMSEP of 3.6 and 3.9 units of Mooney viscosity were obtained for homogenized and nonhomogenized samples, respectively. The NIR method is capable of determining the Mooney viscosity in few minutes in the non‐pretreated sample with an error that is satisfactory for quality control of natural rubber destined for automobile tire manufacturing.     

Structural and Functional Consequences of the Weak Binding of Chlorin e6 to Bovine Rhodopsin

The chlorophyll‐derivative chlorin e6 (Ce6) identified in the retinas of deep‐sea ocean fish is proposed to play a functional role in red bioluminescence detection. Fluorescence and ¹H NMR spectroscopy studies with the bovine dim‐light photoreceptor, rhodopsin, indicate that Ce6 weakly binds to it with μm affinity. Absorbance spectra prove that red light sensitivity enhancement is not brought about by a shift in the absorbance maximum of rhodopsin. ¹⁹F NMR experiments with samples where ¹⁹F labels are either placed at the cytoplasmic binding site or incorporated as fluorinated retinal indicate that the cytoplasmic domain is highly perturbed by binding, while little to no changes are detected near the retinal. Binding of Ce6 also inhibits G‐protein activation. Chemical shift changes in ¹H‐¹⁵N NMR spectroscopy of ¹⁵N‐Trp labeled bovine rhodopsin reveal that Ce6 binding perturbs the entire structure. These results provide experimental evidence that Ce6 is an allosteric modulator of rhodopsin.     

Quantum parallelism as a tool for ensemble spin dynamics calculations

Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local." It resorts to a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.     

Microbiological control and antibacterial action of a propolis-containing mouthwash and control of dental plaque in humans

Propolis is a bee product with several biological properties. This study aimed at investigating a propolis-containing mouthwash, its organoleptic properties, microbial contamination and its antibacterial action in vitro. This mouthwash was assessed in vivo to control dental plaque in humans. The presence of microorganisms was analyzed and the minimum inhibitory concentration against Streptococcus mutans was determined. A comparative study was done in vivo using propolis, chlorhexidine, and propolis plus chlorhexidine in lower concentrations for 14 days. Dental plaque was analyzed by the Patient Hygiene Performance (PHP) index. The odontological product was yellow, cloudy, free of microbial contamination, and exerted an inhibitory action in vitro. Individuals who used a propolis-containing mouthwash for 14 consecutive days in combination or not to chlorhexidine showed a similar PHP index to chlorhexidine alone. The product exerted an antibacterial action in vitro and in vivo, exhibiting a positive action in the control of dental plaque.