On the diameter of planar curves and Fourier coefficients

Summary LetF denote a complex valued function on , which is absolutely continuous and periodic with a period 2. Its complex Fourier coefficientsc _n satisfy the inequality 2|c _n |d,n0, whered denotes the diameter of the closed planar curve defined byF. In this paper those functionsF are considered, which give equality for a specificn.

---

Zusammenfassung Es seiF eine komplexwertige Funktion auf , die absolut stetig und periodisch ist mit einer Periode 2. Sie definiert eine geschlossene ebene Kurve. Zwischen ihrem Durchmesserd und den komplexen Fourierkoeffizientenc _n besteht die Ungleichung 2|c _n |d fürn0. Es werden jene FunktionenF betrachtet, für die in dieser Ungleichung, für ein gegebenesn, Gleichheit besteht.

---

---

Dedicated to my colleague for many years, Professor Eduard Stiefel

---

This research was supported in part by the National Research Council of Canada A-7339     

Mathematical theory of reduction of physical parameters and similarity analysis

The method of similarity analysis in the study of differential equations is extended to study the variability of parameters in a physical system. The analysis provides an insight into the meaning of physical similarity, which usually means the possibility of a reduction in the number of physical parameters characterizing the system. Theorems relating similarities to groups of invariant transformations are proved and employed to show how the number of parameters can be reduced.     

Effect of annealing on the conduction mechanism in amorphous silicon

This paper reports the effect of annealing on conduction mechanisms in amorphous silicon films. High field transport is mainly by the Poole-Frenkel mechanism in unannealed films of amorphous silicon. As they are annealed, the conduction meachnism changes from Poole-Frenkel to space charge conduction. The films are fully annealed at 120°C for 15 h and any more annealing for longer periods does not change the I–V characteristics. From the measured values of threshold voltage at which space charge conduction sets in, the density of localized states around the Fermi level is calculated to be about 10¹⁷–10¹⁸/eV · cm³ which agrees very well with our results from other experimental techniques.     

The Extracts of Polygonum cuspidatum Root and Rhizome Block the Entry of SARS-CoV-2 Wild-Type and Omicron Pseudotyped Viruses via Inhibition of the S-Protein and 3CL Protease

COVID-19, resulting from infection by the SARS-CoV-2 virus, caused a contagious pandemic. Even with the current vaccines, there is still an urgent need to develop effective pharmacological treatments against this deadly disease. Here, we show that the water and ethanol extracts of the root and rhizome of Polygonum cuspidatum (Polygoni Cuspidati Rhizoma et Radix), a common Chinese herbal medicine, blocked the entry of wild-type and the omicron variant of the SARS-CoV-2 pseudotyped virus into fibroblasts or zebrafish larvae, with IC₅₀ values ranging from 0.015 to 0.04 mg/mL. The extracts were shown to inhibit various aspects of the pseudovirus entry, including the interaction between the spike protein (S-protein) and the angiotensin-converting enzyme II (ACE2) receptor, and the 3CL protease activity. Out of the chemical compounds tested in this report, gallic acid, a phytochemical in P. cuspidatum, was shown to have a significant anti-viral effect. Therefore, this might be responsible, at least in part, for the anti-viral efficacy of the herbal extract. Together, our data suggest that the extracts of P. cuspidatum inhibit the entry of wild-type and the omicron variant of SARS-CoV-2, and so they could be considered as potent treatments against COVID-19.     

Theragnostic Applications of Mammal and Plant-Derived Extracellular Vesicles: Latest Findings,Current Technologies,and Prospects

The way cells communicate is not fully understood. However, it is well-known that extracellular vesicles (EVs) are involved. Researchers initially thought that EVs were used by cells to remove cellular waste. It is now clear that EVs function as signaling molecules released by cells to communicate with one another, carrying a cargo representing the mother cell. Furthermore, these EVs can be found in all biological fluids, making them the perfect non-invasive diagnostic tool, as their cargo causes functional changes in the cells upon receiving, unlike synthetic drug carriers. EVs last longer in circulation and instigate minor immune responses, making them the perfect drug carrier. This review sheds light on the latest development in EVs isolation, characterization and, application as therapeutic cargo, novel drug loading techniques, and diagnostic tools. We also address the advancement in plant-derived EVs, their characteristics, and applications; since plant-derived EVs only recently gained focus, we listed the latest findings. Although there is much more to learn about, EV is a wide field of research; what scientists have discovered so far is fascinating. This paper is suitable for those new to the field seeking to understand EVs and those already familiar with it but wanting to review the latest findings.     

Solution of Some Structural Analysis Problems by Orthogonal Collocation

Abstract

Application of the method of orthogonal collocation to boundary value problems in structural and applied mechanics is investigated. Typical boundary value problems, such as the torsion of rectangular bars and the bending of plates, are employed as illustrative examples. Simplicity in application and good accuracy of orthogonal collocation are demonstrated by the solution of such complex problems as the large deflection analysis of rectangular isotropic, orthotropic, and sandwich plates. Results are compared wherever possible with existing solutions based on much more laborious and lengthy methods of computation. Excellent agreements are obtained.     

Relaxation dynamics of stretched polymer chains traced by shear induced Shish‐Kebab structure

We have developed a morphologic method to investigate the relaxation processing of the stretched polymer chains in melts, in which an atomic force microscope probe was used to shear the surface of an isotactic polypropylene melt to obtain the isolated shish‐kebab structure. We present the results of the time dependence of length of the isolated shish‐kebab structure and the stress dependence of the kebab density along the direction of shish in this paper. Our results demonstrate that the shear‐oriented polymer melts show the relaxation dynamics of worm‐like chain where the length deficit of the isolated shish‐kebab structure is scaled with the relaxation time as a power of 1/3. The melting behavior of shish‐kebab structure was also investigated. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 907–914     

Regiospecific synthesis of cepanolide,a cancer chemoprotective micronutrient found in green onions

The naturally occurring γ-hydroxy-β-sulfanylbutenolide cepanolide and a range of new analogues were synthesized in concise, regiospecific manner through the combined use of 2-silyloxyfuran oxyfunctionalization and tandem thio-Michael addition/elimination.     

Mitigation of signal suppression caused by the use of trifluoroacetic acid in liquid chromatography mobile phases during liquid chromatography/mass spectrometry analysis via post‐column addition of ammonium hydroxide

A method has been developed to reduce the mass spectrometric ion signal suppression associated with the use of TFA as an additive in LC mobile phases. Through post‐column infusion of diluted NH₄OH solution to LC eluents, the ammonium ion introduced causes the neutral analyte‐TFA ion pair to dissociate which consequently releases the protonated analyte as free ions into the gas phase (through regular electrospray ionization mechanisms). An ion signal improvement from 1.2 to 20 times for a variety of compounds had been achieved through the application of this method. The molar ratios of NH₄OH:TFA which result in a reduction of signal suppression were determined to be between 0.5:1 and 50:1. In addition, it was shown that this NH₄OH infusion method could reduce the level of doubly‐charged species and the product ions formed via in‐source collision. The use of diluted NH₄OH solution is favorable since it is compatible with mass spectrometry analysis, and it is applicable in both positive and negative‐ion generation mode. Copyright © 2012 John Wiley & Sons, Ltd.