Basis property of eigenfunctions of nonselfadjoint operator pencils generated by the equation of nonhomogeneous damped string

We consider a class of nonselfadjoint quadratic operator pencils generated by the equation, which governs the vibrations of a string with nonconstant bounded density subject to viscous damping with a nonconstant damping coefficient. These pencils depend on a complex parameterh, which enters the boundary conditions. Depending on the values ofh, the eigenvalues of the above pencils may describe the resonances in the scattering of elastic waves on an infinite string or the eingenmodes of a finite string. We obtain the 7asymptotic representations for these eigenvalues. Assuming that the proper multiplicity of each eigenvalue is equal to one, we prove that the eigenfunctions of these pencils form Riesz bases in the weightedL ²-space, whose weight function is exactly the density of the string. The general case of multiple eigenvalues will be treated in another paper, based on the results of the present work.     

Amperometric Glucose Determination by Means of Glucose Oxidase Immobilized on a Cellulose Acetate Film: Dependence on the Immobilization Procedures

Glucose microelectrodes were prepared by immobilizing glucose oxidase onto a cellulose acetate film coating a platinum wire. Hexamethylenediamine (HMDA) and Glutaraldehyde (GA) were employed as spacer and coupling agent, respectively. Sensitivities and linear response ranges were studied as a function of the relative amounts of HMDA and GA. The best sensitivity was found when HMDA and GA were 5% and 2.5% in aqueous solutions, respectively. Taking as a reference the functioning of this biosensor, the roles of HMDA and GA percentages appear to be opposed when the extension of the linear response range is considered. Indeed, an increase of one unit in HMDA percentage (from 5 to 6 %) induces an increase in the extension of the linear response range equal to that obtained with a decrease of one unit of GA percentage (from 2.5 to 1.5%).     

Intraresidue distribution of energy in proteins

Boltzmann-like distributions appear in many properties and energy-related quantities of proteins. A few examples are hydrophobicity, various types of side-chain/side-chain interactions, proline isomerization, hydrogen bonds, internal cavities, interactions at the level of specific atom types, and the propensity of the phi/'phi' ratio. Here, we conjecture that the Boltzmann hypothesis also holds for the intra-residue energy distribution. We confirm the conjecture by calculating the energies of 41,672 residues of the structures of highly resolved proteins, where at least 12 out of 20 naturally occurring amino acids follow Boltzmann's law. We further examine the entire set of all residue energies and find that the convolution of the individual distributions gives a Poisson function, which is followed by approximately 50% of individual proteins' structures.     

Determination of the enantiomeric composition of phenylalanine samples by chemometric analysis of the fluorescence spectra of cyclodextrin guest-host complexes

A novel strategy for determining the enantiomeric composition of phenylalanine samples that combines ordinary fluorescence spectroscopy, guest-host cyclodextrin chemistry, and multivariate regression modeling is investigated. Partial-least-squares regression (PLS-1) models were developed from fluorescence spectral data obtained with a series of samples containing cyclodextrin guest-host complexes of phenylalanine with different known enantiomeric compositions. The regression models were subsequently validated by determining the enantiomeric composition of a set of independently prepared phenylalanine samples. The ability of the models to correctly predict the enantiomeric compositions of future samples was evaluated in terms of the root-mean-square percent relative error (RMS%RE). The RMS%RE in the mol fraction of D-phenylalanine ranged from 1.3% to 3.0% when beta-cyclodextrin was used as the host molecule for different guest-host concentrations. The RMS%RE in the mol fraction of D-phenylalanine obtained in a similar validation study conducted with gamma-cyclodextrin ranged between 1.8% and 4.0% for different guest-host concentrations. Compared with previous studies done in absorption, fluorescence data were found to be more sensitive and the spectral differences observed as a function of enantiomeric composition were more uniformly spaced, making regression modeling more reliable. As a result, good regression models could be made at lower concentrations than were possible previously when absorption measurements were used.     

Elimination of chemical shift artifacts of thoracic spine with contrast-enhanced FLAIR imaging with fat suppression at 3.0 T

The purpose of this study was to assess the effect of chemical shift artifacts and fat suppression between contrast-enhanced T1-weighted fast spin-echo (FSE) sequence with fat suppression and contrast-enhanced T1-weighted fluid attenuated inversion recovery (FLAIR) sequence with fat suppression in magnetic resonance imaging (MRI) of the thoracic spine at 3.0T. Forty patients, who underwent MRI examination, were recruited and analyzed both qualitatively and quantitatively. Due to chemical shift artifacts in the T1-weighted FSE, 14 of the patients were found to be of non-diagnostic value. On the contrary, in 11 of those 14 patients, no chemical shift artifacts were observed in the T1-weighted FLAIR sequence. Regarding the efficiency of fat suppression, both sequences achieved successful fat suppression. Consequently, the use of T1-weighted FLAIR fat suppression after contrast administration sequence seems to eliminate or significantly reduce image quality deterioration stemming from chemical shift artifacts in thoracic spine examinations.     

Electronic structure of 4H-pyrido[1,2-a]pyrimidin-4-ones

The characteristic features of ir and uv spectra of 43 4H-pyrido[1,2-a]pyrimidin-4-one derivatives with electron donor or acceptor groups in position 3, and positions 6, 7, 8, or 9, respectively, have been systematically studied. On the basis of the spectra some conclusions have been drawn for the molecular structure. The negative solvent effect of the lowest-energy π → π* transition is investigated by the PPP method.     

Design and Implementation of a New Local Alignment Algorithm for Multilayer Networks

Network alignment (NA) is a popular research field that aims to develop algorithms for comparing networks. Applications of network alignment span many fields, from biology to social network analysis. NA comes in two forms: global network alignment (GNA), which aims to find a global similarity, and LNA, which aims to find local regions of similarity. Recently, there has been an increasing interest in introducing complex network models such as multilayer networks. Multilayer networks are common in many application scenarios, such as modelling of relations among people in a social network or representing the interplay of different molecules in a cell or different cells in the brain. Consequently, the need to introduce algorithms for the comparison of such multilayer networks, i.e., local network alignment, arises. Existing algorithms for LNA do not perform well on multilayer networks since they cannot consider inter-layer edges. Thus, we propose local alignment of multilayer networks (MultiLoAl), a novel algorithm for the local alignment of multilayer networks. We define the local alignment of multilayer networks and propose a heuristic for solving it. We present an extensive assessment indicating the strength of the algorithm. Furthermore, we implemented a synthetic multilayer network generator to build the data for the algorithm’s evaluation.     

Emerging Direct Targeting β-Catenin Agents

Aberrant accumulation of β-catenin in the cell nucleus as a result of deregulation of the Wnt/β-catenin pathway is found in various types of cancer. Direct β-catenin targeting agents are being researched despite obstacles; however, specific β-catenin drugs for clinical treatments have not been approved so far. We focused on direct β-catenin targeting of potential therapeutic value as anticancer agents. This review provides recent advances on small molecule β-catenin agents. Structure-activity relationships and biological activities of reported inhibitors are discussed. This work provides useful knowledge in the discovery of β-catenin agents.