Dynamical system solutions for homogeneous linear functional equations of higher order

We present the solution of a large class of homogeneous linear functional equations of higher order by using ideas from dynamical systems. A particularly simple example from this class is the functional equation $$f(x) = \frac{1}{2}f \left(\frac{x}{2}\right) + \frac{1}{2}f \left(\frac{x+1}{2}\right), \quad 0 < x < 1.$$ Equations such as these have found important applications in wavelet theory by Hilberdink (Aequa Math 61(1–2):179–189, 2001) where they are called dilation equations and are usually solved by Fourier methods by Daubechies (Comm Pure Appl Math 41(7):909–996, 1988) or iteration methods of Daubechies (SIAM J Math Anal 22(5):1388–1410, 1991). A recent result of Góra (Ergod Theory Dyn Syst 29(5):1549–1583, 2009) allows us to represent the solution as an infinite series that is determined by the dynamics of a map that is defined by the functional equation. In this problem the interplay between dynamical systems and solutions of functional equations is brought into sharp focus.     

Syrian hamster embryo (SHE) assay (pH 6.7) coupled with infrared spectroscopy and chemometrics towards toxicological assessment

The Syrian hamster embryo (SHE) assay (pH 6.7) is an in vitro candidate to replace in vivo carcinogenicity tests. However, the conventional method of visual scoring of foci (non-transformed vs. transformed colonies) can be time-consuming and is open to subjectivity. Infrared (IR) spectroscopy has the potential to provide objective assessment of such SHE colonies with the added advantage of potentially providing mechanistic information. In this study, SHE cells were treated with one of eight different chemical regimens, allowed in culture to attach and form foci on IR-reflective glass slides; these were subsequently interrogated by attenuated total reflection (ATR) Fourier-transform IR (FTIR) spectroscopy. Derived mid-IR spectra (n = 13,406) were subjected to chemometric analysis focusing primarily on the extraction of biochemical information related to test agent treatment and/or morphological transformation. The use of ATR-FTIR spectroscopy with chemometrics to analyze the SHE assay is a novel approach to toxicological assessment.     

Endo[metallo] SWNT‐amino acid interactions: A theoretical study

We propose that an atom of calcium (Ca) which is an alkaline earth metal on encapsulation inside of a metallic armchair (5,5) (SWNT) species can have stronger amino acid interactions. From our calculations of various physical parameters we depict several configurations in which such an endo[metallo] SWNT can be modified by an internally placed Ca atom. Density functional theory (DFT) calculations reveal that the most favorable interactions of the SWNT system is with tryptophan, tyrosine, and phenylalanine that can be directly correlated to the backbone geometry of the amino acid species. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Development of non-invasive Raman spectroscopy for in vivo evaluation of bone graft osseointegration in a rat model

The use of bone structural allografts for reconstruction following tumor resection is widespread, although successful incorporation and regeneration remain uncertain. There are few non-invasive methods to fully assess the progress of graft incorporation. Computed tomography and MRI provide information on the morphology of the graft/host interface. Limited information is also available from DXA and ultrasound. Only few techniques can provide information on the metabolic status of the graft, such as the mineral and matrix composition of the regenerated tissue that may provide early indications of graft success or failure. To address this challenge, we discuss here the implementation of Raman spectroscopy for in vivo assessment of allograft implantation in a rat model. An array of optical fibers was developed to allow excitation and collection of Raman spectra through the skin of rat at various positions around the rat's tibia. The system is calibrated against locally constructed phantoms that mimic the morphology, optics and spectroscopy of the rat. The system was evaluated by carrying out transcutaneous Raman measurement on rat. Bone mineral and matrix Raman bands are successfully recovered. This new technology provides a non-invasive method for in vivo monitoring of bone graft osseointegration.     

Biodegradable biocompatible xyloglucan films for various applications

Polysaccharides are known for their film-forming properties which have been intensively investigated for food and non-food applications. Here we have developed a xyloglucan transparent film for various applications especially in controlled release of drugs and cosmetics. The present study evaluated the properties of the composite films of xyloglucan, chitosan and rice starch obtained by the casting/solvent evaporation method. Xyloglucan chitosan blend film shows better mechanical properties. Hydrophobicity and crystallinity of xyloglucan film was increased by blending with chitosan. This was confirmed by X-ray diffraction studies and contact angle measurements. Scanning electron microscopic observations indicated that the xyloglucan chitosan blend films were smooth and homogenous. Thermogravimetric and differential scannining calorimetric analysis showed a high thermal stability and melting temperature of xyloglucan chitosan film compared with others. The swelling properties of the xyloglucan chitosan blend film, studied as a function of pH showed that the sorption ability of the blend film was high at a pH 7.4. This indicates its controlled release property at that pH. Controlled drug release property of the film was studied by using streptomycin as a model drug.     

High-performance liquid chromatography with post-column 2,2′-diphenyl-1-picrylhydrazyl radical scavenging assay: Methodological considerations and application to complex samples

An improved post-column 2,2′-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging assay for the screening of antioxidants in complex matrices was developed. Experimental parameters believed to be influential to DPPH response were studied in a univariate approach. Optimum conditions were found to be: 5 × 10⁻⁵ M DPPH reagent prepared in a 75% methanol: 25% 40 mM citric acid-sodium citrate buffer (pH 6) solution, degassed with nitrogen; reaction coil of 2 m × 0.25 mm i.d. PEEK tubing; detection at 521 nm; analysis at room temperature. The analytical utility of this protocol was evaluated by screening for antioxidants in thyme and green tea, in comparison with two commonly employed methodologies.     

Supramolecular networks of polymethylphosphonic acid groups bonded to aromatic platforms: biphenyldiyl-2,2'-bis(methylphosphonic acid) and benzenetriyl-1,3,5-tris(methylphosphonic acid)

Biphenyldiyl-2,2'-bis(methylphosphonic acid) (BBMP) and benzenetriyl-1,3,5-tris(methylphosphonic acid) (BTMP) as ligands have been synthesized from diphenic acid and trimesic acid, respectively. Cu, Mn and Co complexes of BBMP have been prepared but similar complexes of BTMP did not crystallize. However, a copper compound with added 4,4'-bipyridyl was obtained. This copper complex is dimeric in which the dimers are linked into a supramolecular compound through the bipyridyl groups. Interestingly, the structure was solved in P1 with an unusual correlation between the ligand oxygen bond distances and the copper bond distances to water molecules. The Mn and Co BBMP complexes are isostructural in which the BBMP ligands phenyl groups rotate around each other to bridge the metal atoms forming 1:1 linear chains. There are four water molecules bonded to Co that can be removed reversibly. In the case of the Cu compound, one Cu is square planar bonded to four phosphonate oxygen atoms from two BBMP molecules. The second copper is six coordinate adding two water molecules in the axial positions. The two copper ions alternate forming a one dimensional chain but with ligands bonding the chain on both sides. The four coordinate copper atoms are chelated by two BBMP ligands utilizing one oxygen atom from the two phosphonate groups of each ligand and a second oxygen atom from these groups that bridge across the Cu atoms to bond to the six coordinate copper ion. A detailed synthetic procedure for each of the two ligands is supplied as ESI.     

A model of the holographic principle: Randomness and additional dimension

In recent years an idea has emerged that a system in a 3-dimensional space can be described from an information point of view by a system on its 2-dimensional boundary. This mysterious correspondence is called the Holographic Principle and has had profound effects in string theory and our perception of space-time. In this note we describe a purely mathematical model of the Holographic Principle using ideas from nonlinear dynamical systems theory. We show that a random map on the surface S² of a 3-dimensional open ball B has a natural counterpart in B, and the two maps acting in different dimensional spaces have the same entropy. We can reverse this construction if we start with a special 3-dimensional map in B called a skew product. The key idea is to use the randomness, as imbedded in the parameter of the 2-dimensional random map, to define a third dimension. The main result shows that if we start with an arbitrary dynamical system in B with entropy E we can construct a random map on S² whose entropy is arbitrarily close to E.     

Structural analysis of xCsCl(1−x)Ga2S3 glasses by means of DFT calculations and Raman spectroscopy

The alkali metal halide doping of gallium‐sulfide glasses yields improvements in the optical, thermal and glass forming properties. To understand these improvements, the short‐range order of xCsCl(1 − x)Ga₂S₃ glasses was probed by Raman spectroscopy. Raman spectra have been interpreted using density functional theory (DFT) harmonic frequency calculations on specific clusters of GaS₄H₄ and/or GaS₃H₃Cl tetrahedral subunits. The assignment of the observed vibrational bands confirms the main structural conclusions obtained with X‐ray and neutron diffraction experiments and gives some new insights into the gallium‐network present in the xCsCl(1 − x)Ga₂S₃ glasses. At the lowest concentration, the observed spectrum may be interpreted with small clusters such as dimers and trimers connected by corner‐sharing (CS) GaS₄H₄ tetrahedral subunits. The vibrational fingerprints of tri‐clusters with three‐fold coordinated sulfur atoms have also been identified; however, no Raman signature of chlorine‐doped subunits has been found to be caused by their insufficient intensity. For higher CsCl concentrations, distinct spectral features corresponding to chlorine‐doped clusters appear and are increasing in intensity with x. In other words, undoped and Cl‐doped tetrahedra coexist in the xCsCl(1 − x)Ga₂S₃ glasses. The added chlorine atoms induce a fragmentation of the glass network and replace the sulfur atoms in the CS tetrahedral environment. The comparison of the observed spectra with theoretical predictions and diffraction data favoured one‐fold coordinated chlorine atoms in the glass network. Copyright © 2009 John Wiley & Sons, Ltd.     

Non-invasive investigation of art paintings by terahertz imaging

Terahertz electromagnetic waves propose attractive features such as non-invasive and non-destructive analysis, transparency and good penetration depth through various materials, low scattering and broad spectral bandwidth. In this paper, we demonstrate the capability of terahertz imaging for the investigation of art paintings. The imaging system is able to reveal buried layer information such as a graphite handmade sketch covered by several layers of painting. In addition, taking advantage of the pulsed terahertz emission, we show that it is also possible to evaluate the variations of the painting thickness.