Long cycles and paths in distance graphs

For n∈N and D⊆N, the distance graph has vertex set {0,1,…,n−1} and edge set {ij∣0≤i,j≤n−1,|j−i|∈D}. Note that the important and very well-studied circulant graphs coincide with the regular distance graphs.A fundamental result concerning circulant graphs is that for these graphs, a simple greatest common divisor condition, their connectivity, and the existence of a Hamiltonian cycle are all equivalent. Our main result suitably extends this equivalence to distance graphs. We prove that for a finite set D of order at least 2, there is a constant c_D such that the greatest common divisor of the integers in D is 1 if and only if for every n, has a component of order at least n−c_D if and only if for every n≥c_D+3, has a cycle of order at least n−c_D. Furthermore, we discuss some consequences and variants of this result.     

Biomagnetic measurements utilising a superparamagnetic marker: a feasibility study

Summary A preliminary study is here reported on a new potential marker for biomagnetic measurements. The marker consists of superparamagnetic polymer microspheres which were detected in the presence of external steady magnetic fields by means of an r.f.-SQUID magnetometer. The particles were prepared in samples differing in the concentration value and immersed in a homogeneous magnetic field of variable intensity. A simple model was taken into account for the distribution of the microspheres in the samples, so that the theoretical values were compared to the marker field values measured by the biomagnetic sensor. The overall sensitivity of the experimental apparatus and the minimum concentration value of the marker were then estimated.     

Unprecedented Diastereoselective Arylogous Michael Addition of Unactivated Phthalides

The first highly enantioselective arylogous Michael reaction (AMR) of 3-unsubstituted phthalides has been described. This phase-transfer methodology, which uses catalytic amounts of KOH/18-crown-6 catalyst in mesitylene in the presence of N,O-bis(trimethylsilyl)acetamide (BSA), gives access to a broad range of 3-monosubstituted phthalides with high levels of syn diastereoselectivity and good yields, starting from 3-unsubstituted derivatives and diverse α,β-unsaturated carbonyl compounds. The reaction also applies to unactivated 3-alkyl phthalides to afford 3,3-dialkyl derivatives. A plausible mechanism has been suggested. DFT analysis of possible transition states gives a rationale of the high syn diastereoselectivity observed and its correlation with the solvent's dielectric constant.     

A Novel [OSSO]-Type Chromium(III) Complex as a Versatile Catalyst for Copolymerization of Carbon Dioxide with Epoxides

A new chromium(III) complex, bearing a bis-thioether-diphenolate [OSSO]-type ligand, was found to be an efficient catalyst in the copolymerization of CO₂ and epoxides to achieve poly(propylene carbonate), poly(cyclohexene carbonate), poly(hexene carbonate) and poly(styrene carbonate), as well as poly(propylene carbonate)(cyclohexene carbonate) and poly(propylene carbonate)(hexene carbonate) terpolymers.     

Production of vector and tensor mesons in proton-proton collisions at\sqrt s = 52.5 GeV

Inclusive production of ?⁰,f, andg ⁰ mesons and ofK _s ⁰ ,K ^*0 (892), ? andK ^*0(1430)mesons has been measured at <y>～2.6 and <p _T >～1.1 GeV/c in proton-proton interactions at \(\sqrt s = 52.5\) GeV. The negative particle from the two-body decays of these resonances were identified by a threshold Cerenkov counter and used for triggering. Starting from the measured differential cross section, total inclusive cross sections for the vector and tensor mesons were determined using various parametrizations for they andp _T dependence of the differential cross section. The experimental results are discussed in the framework of production models based on the parton picture. The strangeness suppresion factor λ=(0.30±0.10) due toSU(3) symmetry breaking of the quark sea is derived.     

Modified edge finite elements for photonic crystals

We consider Maxwell’s equations with periodic coefficients as it is usually done for the modeling of photonic crystals. Using Bloch/Floquet theory, the problem reduces in a standard way to a modification of the Maxwell cavity eigenproblem with periodic boundary conditions. Following [8], a modification of edge finite elements is considered for the approximation of the band gap. The method can be used with meshes of tetrahedrons or parallelepipeds. A rigorous analysis of convergence is presented, together with some preliminary numerical results in 2D, which fully confirm the robustness of the method. The analysis uses well established results on the discrete compactness for edge elements, together with new sharper interpolation estimates.     

Gompertz zero-inflated cure rate regression models applied to credit risk data

In the financial market, it is important to consider that there is a proportion of customers that have settled their debt in time zero, immediately recovering their ability to pay. In this context, in this paper, we propose a survival analysis methodology that allows the insertion of times equal to zero in scenarios where credit risk is observed. The proposed model addresses the survival analysis model of the zero-inflated cure rate which incorporates the heterogeneity of three subgroups (individuals having events in the initial time, and individuals not susceptible and susceptible to the event). In our proposal, all available survival data of customers are modeled considering that the number of competitive causes follows a Poisson distribution and the baseline risk function follows a Gompertz distribution. The model parameter estimation is obtained by the maximum likelihood estimation procedure and simulation studies are conducted to evaluate the estimators' performance. The studied methodology will be applied to a credit database provided by a financial institution in Brazil.     

Fluorescent Flavin/PVP-Coated Silver Nanoparticles: Design and Biological Performance

A red-emitting fluorescent Riboflavin (RF)/Polyvinylpyrrolidone (PVP)-coated silver nanoparticles system, λ_em?=?527 nm, Φ?=?0.242, with a diameter of the metallic core of 27.33 nm and a zeta potential of ? 25.05 mV was prepared and investigated regarding its biological activity. We found that PVP has a key role in RF adsorption around the SNPs surface leading to an enhancement of antioxidant properties (～70%), low cytotoxicity (> 90% cell viability, at 50 µL/mL, after 48 h of incubation) as well as to an efficient process of its cellular uptake (～ 60%, after 24 h of incubation) in L929 cells. The results are relevant concerning the involvement of RF and its coenzymes forms in SNPs - based systems, in cellular respiration as well as for future studies as antioxidant marker system on tumoral cells for viewing and monitoring them, by cellular imaging.

     

Crystallization kinetics of PEO-alkaline perchlorate solutions observed by energy dispersive x-ray diffraction

The crystallization kinetics of poly(ethylene oxide) doped with various alkaline perchlorate salts were measured at room temperature by means of the new energy dispersive x-ray diffraction method for the phase transition. The experimental points of the transformation coordinate were fitted using the phenomenological Liquori-Tripiciano law, the parameters of which were evaluated for each case. The influence of the concentration and of the cation dimensions on the crystallization rate is discussed. Further details about the application of this nonconventional diffractometric technique to polymers are also reported, as is an intuitive model for describing the method.