Remarks on some fixed point results in <Emphasis Type="Italic">b</Emphasis>-metric spaces

The main purpose of this paper is to generalize, improve and complement several famous results in b-metric spaces. Moreover, an essential estimation of b-quasi-contraction in b-metric spaces is given. We also establish some new results for multi-valued mappings in the metric and b-metric concept. We explore some different proof techniques which provide short proofs of the results.     

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized gquasi-contractions with the spectral radius r(λ) of the g-quasi-contractive constant vector λ satisfying r(λ) ∈ [0,1/s) in the setting of cone b-metric spaces over Banach algebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.     

Simulation of Two-Dimensional Fractional Gaussian Noise

Fractional Brownian surfaces have frequently been used to model various physical processes and to generate artificial landscapes. We study a closely related process, called two-dimensional fractional Gaussian noise. We devise a method for generating realizations of this process using an approximate conditioning approach, motivated by results from the corresponding one-dimensional process applied in teletraffic modeling.     

Salting-Out Thin-Layer Chromatography of Several Myorelaxants

JPC – Journal of Planar Chromatography – Modern TLC - The chromatographic behavior of five myorelaxant drugs has been studied under the conditions used for salting-out thin-layer...     

On different aspects of the optical rogue waves nature

Rogue waves are giant nonlinear waves that suddenly appear and disappear in oceans and optics. We discuss the facts and fictions related to their strange nature, dynamic generation, ingrained instability, and potential applications. We present rogue wave solutions to the standard cubic nonlinear Schrödinger equation that models many propagation phenomena in nonlinear optics. We propose the method of mode pruning for suppressing the modulation instability of rogue waves. We demonstrate how to produce stable Talbot carpets—recurrent images of light and plasma waves—by rogue waves, for possible use in nanolithography. We point to instances when rogue waves appear as numerical artefacts, due to an inadequate numerical treatment of modulation instability and homoclinic chaos of rogue waves. Finally, we display how statistical analysis based on different numerical procedures can lead to misleading conclusions on the nature of rogue waves.

     

INVESTIGATION OF THE REACTIVITY OF THIOAMIDES OF SOME SUBSTITUTED AROMATIC AND HETEROCYCLIC ACIDS

Abstract

Thioamides of some substituted aromatic and heterocyclic acids have been synthesized and the reactivity of the thioamide group has been tested.     

On the need of nonlinear control for efficient model-based wake stabilization

The mitigation of oscillatory vortex shedding behind a cylinder is chosen as a well-investigated benchmark problem to compare model-based feedback flow control approaches. The flow is sensed by a single velocity signal in the wake and is manipulated via a single volume force actuator. A low-dimensional proper orthogonal decomposition Galerkin model is adopted as a control-oriented fluid flow representation. An extended Kalman filter is used as an effective means for online dynamic state estimation. Investigated strategies of linear and nonlinear controller design include pole placement, linear parameter-varying, input–output linearization, Lyapunov-based backstepping, and nonlinear model predictive control. These strategies are applicable to a large class of flows with oscillatory dynamics and to experimental conditions, where variants have already been used. Controllers are evaluated and compared based on their application to the full plant, that is, to the direct numerical simulation of the wake, emulating an experiment with a single hot-wire sensor. Overall, nonlinear closed-loop control is shown to be distinctly superior to linear approaches. As is often the case, physics dictates a similarity of successful control commands, irrespective of the design approach, and differentiates these controllers, as a group, from less successful approaches.     

Syntheses of Novel Dipyrrylmethene-BF2 Dyes and Their Performance as Labels in Two-Photon Excited Fluoroimmunoassay

Two-photon excitation of fluorescence (TPE) has been found a powerful tool in the field of microscopy imaging and recently also in the field of bioanalytics. The recently introduced bioaffinity assay technology, ArcDia TPX, enables separation-free ultra-sensitive immunoassays from microvolumes. This assay technique is based on the use of microspheres as a solid reaction carriers and two-photon excited fluorescence detection. In the ArcDia TPX-technology, the individual microparticles are observed and the number of bound biomolecules on the microparticle surface is quantified by two-photon excited fluorescence. Here we present synthesis and use of a novel dipyrrylmethene-BF2 fluorophore that has been designed to be used as label in ArcDia TPX assay technique. The absorption and emission wavelengths of the label are tuned to allow excitation with a 1064 nm microchip laser. The label contains two-carboxylic residues, one of which is activated as N-hydroxysuccinimide ester to enable labeling of amino residues of biomolecules. The other carboxylic group is in free form to increase solubility in aqueous solutions. This new fluorescent label is tested in a separation-free immunoassay using ArcDia TPX assay technique. The performance of the new label is compared to that of one of the brightest fluorophores available, R-phycoerythrin (RPE). According to the results, the dipyrrylmethene-BF2 label provides significantly better signal-to-background ratio, leading to higher assay sensitivity and broader dynamic range compared to that of RPE. Good solubility to aqueous solutions and high fluorescence quantum efficiency, suggests the dipyrrylmethene-BF2 label is applicable also in other fluorescence-based applications.     

Dipyrrylmetheneboron Difluorides as Labels in Two-Photon Excited Fluorometry. Part I-Immunometric Assays

Seven different two-photon excitable dipyrrylmetheneboron difluoride labels (dipyrrylmethene-BF₂ labels) and a frequently used TAMRA label were conjugated to mouse IgG against α-fetoprotein in variable substitution degrees. Altogether 40 IgG conjugates were prepared, and studied with respect to one-photon absorption and emission properties, and two-photon fluorescence efficiency using 1064 nm laser as illumination source. Performance of the IgG conjugates as tracers in a separation-free immunometric assay of α-fetoprotein was evaluated using two-photon excitation assay technology, ArcDia^TM TPX. The results show that the dipyrrylmethene-BF₂ labels provide subpicomolar sensitivity, which is an order of magnitude better than that of TAMRA label. The effect of chromophore structure and substitution degree of IgG-label conjugates on the assay performance is discussed.