Constant and Equivariant Cyclic Cohomology

In this note, we prove that the constant and equivariant cyclic cohomology of algebras coincide. This shows that constant cyclic cohomology is rich and computable.     

Development of colorimetric sensor array for discrimination of herbal medicine

Today, traditional systems of medicines (such as herbal distillates) become important resources for providing healthcare benefits. The ability to discriminate among closely similar herbal products is critical to ensure their efficacy. This article proposes a pattern-based recognition approach for the rapid discrimination of herbal distillates using a low-cost and sensitive colorimetric sensor array composed of 25 indicators. The color changes of the sensor exposed to the vapor of the herbal distillates can be monitored easily with an ordinary flatbed scanner. The digital representation of the array response was analyzed with hierarchical clustering analysis (HCA) and principal component analysis (PCA). Using new variable selection strategy, 6 indicators among the 25 employed indicators were selected as discriminant elements of the array. So, a complete discrimination (with 100% accuracy) of 46 herbal distillates was achieved. The proposed sensor represented a better resolution when analytes were placed in an oven at 85 °C for 45 min. This colorimetric sensor array demonstrates excellent potential for quality assurance/control applications of herbal distillates.     

Existence results to positive solutions of fractional BVP with $${\varvec{}}$$-derivatives

This paper investigates the existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem with fractional q-derivative

$$\begin{aligned}&D_{q}^{\alpha }u(t)+f(t,u(t))=0, \quad {0<t<1, ~3<\alpha \le 4,} \\&u(0)= D_{q}u(0)=D_{q}^{2}u(0)=0, \quad D_{q}^{2}u(1)=\beta D_{q}^{2}u(\eta ), \end{aligned}$$

where \(D_{q}^{\alpha }\) denotes the Riemann–Liouville q-derivative of order \(\alpha \), \(0<\eta <1\) and \(1-\beta \eta ^{\alpha -3}>0\). Our analysis relies a fixed point theorem in partially ordered sets. An example to illustrate our results is given.

     

A review of calixarene applications in nuclear industries

Calixarenes has been subject to extensive research in development of many extractants, transporters, stationary phases, electrode ionophores and optical and electrochemical sensors over the past four decades. In this paper, the nuclear applications of calixarenes are summarized in six fields including complexation studies, solvent extraction, membrane transport, chromatography, luminescent and colorimetric applications, and electroanalytical applications. In the first to fourth sections, the extractability, extraction equilibria and extraction constants of lanthanide, actinide and other nuclear waste cations ions, which were subjected to solvent extraction by the macrocyclic ligands, are reviewed. In two last sections, the analytical applications of calixarene complexes towards nuclear waste cations, including spectroscopic and electroanalytic sensors, are discussed. The examples described in this review illustrate the potential of calixarene derivatives in the rapidly growing field of cations recognition in nuclear wastes.     

Determination of amylose in Iranian rice by multivariate calibration of the surface plasmon resonance spectra of silver nanoparticles

A simple and non-separative analytical method for selective determination of amylose in Iranian rice has been developed. It was based on the reduction of silver ions by amylose and production of Ag nanoparticles, which exhibit surface plasmon resonance (SPR) spectra in the ultraviolet/visible region. The formation of Ag nanoparticles in the presence of amylose was monitored by transmission electron microscopy (TEM) and dynamic light scattering (DLS). The experimental conditions were optimized to obtain the highest yield for nanoparticle formation. Partial least square (PLS) regression as an efficient multivariate spectral calibration method was employed to make a connection between the SPR spectra of the generated Ag nanoparticles and the amylose content (AC) of the rice starch. The number of PLS latent variables was optimized by leave-one-out cross-validation utilizing prediction residual error sum of square (PRESS). The proposed model exhibited a high ability for prediction of amylose concentration in both standard starch samples and real rice samples prepared from different regions of Iran. The relative errors of prediction were almost lower than ±5% for different real samples and the detection limit was 3.23 weight percent of amylose in rice. In comparison to the reference method (Juliano method), the proposed method is simpler and does not need tedious sample preprocessing steps.     

Applications of Nano-Baskets of Calixarenes in Chromatography

Nano-baskets of calixarenes have been subject to extensive research in the construction of liquid chromatographic phases, extractants, transporters, electrode ionophores, and optical and electrochemical sensors over the past 4 decades. There has long been interest in calixarene-based liquid chromatographic phases. Owing to the recent rapid growth in the number of publications on calixarene-based liquid chromatographic phases, this review paper focuses on their different applications in the main fields of molecular and ionic species as well as liquid chromatographic mobile and stationary phases. Although the recent reports have focused on the optimization and application of one kind or a unique group of calixarenic mobile or stationary phases, this review is a collection and comparison of a variety of research data dealing with the synthesis, preparation and behavior of calixarene-based liquid chromatographic phases.     

Hopf cyclic cohomology and transverse characteristic classes

We refine the cyclic cohomological apparatus for computing the Hopf cyclic cohomology of the Hopf algebras associated to infinite primitive Cartan–Lie pseudogroups, and for the transfer of their characteristic classes to foliations. The main novel feature is the precise identification as a Hopf cyclic complex of the image of the canonical homomorphism from the Gelfand–Fuks complex to the Bott complex for equivariant cohomology. This provides a convenient new model for the Hopf cyclic cohomology of the geometric Hopf algebras, which allows for an efficient transport of the Hopf cyclic classes via characteristic homomorphisms. We illustrate the latter aspect by indicating how to realize the universal Hopf cyclic Chern classes in terms of explicit cocycles in the cyclic cohomology of étale foliation groupoids.     

Cyclicity of the adjoint of weighted composition operators on the hilbert space of analytic functions

In this paper, we discuss the hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator on a Hilbert space of analytic functions.     

Monsterwellen aus Licht

Seit Jahrhunderten berichten Seefahrer von gigantischen Wellen, die scheinbar aus dem Nichts und ohne Vorwarnung auftauchen. Erst Mitte der 1990er‐Jahre hat sich die Erkenntnis durchgesetzt, dass es sie wirklich gibt und sie für eine größere Zahl katastrophaler Schiffsunglücke verantwortlich waren. In Experimenten an der University of California in Los Angeles haben wir vor kurzem überraschenderweise in Lichtleitfasern Monsterwellen aus Licht nachgewiesen. Ursache hierfür ist eine Nichtlinearität der Faser.     

Diamond-hexagonal semiconductor nanocones with controllable apex angle

We report on the synthesis of nanostructured and crystalline tapered Si and Ge polyhedra via metal-catalyzed chemical vapor deposition. These Si and Ge nanocones (SiNCs, GeNCs) possess tips with near-atomic sharpness, micron-scaled bases, hexagonal cross-sections, and controllable apex angles. High-resolution transmission electron microscopy, selected-area electron diffraction and Raman scattering spectroscopy and analysis indicate that the SiNCs are of the diamond-hexagonal Si(IV) phase.