A Comment on Governing Equations of Envelope Surface Created by a Two-Dimensional Directional Wavepacket Centered around a Propagation Direction on an Elastic Plate

Plates are common structural elements of most engineering structures, including aerospace, automotive, and civil engineering structures. The study of plates from theoretical perspective as well as experimental viewpoint is fundamental to understanding of the behavior of such structures. The dynamic characteristics of plates, such as natural vibrations, transient responses for the external forces and so on, are especially of importance in actual environments. In this paper, we consider natural vibrations of an elastic plate and the propagation of a wavepacket on it. We derive the two-dimensional equations that govern the spatial and temporal evolution of the amplitude of a wavepacket and discuss its features. We especially consider a directional wavepacket on an elastic plate, which propagation direction is centered around a main direction, but which wavenumber and frequency are fixed by a certain value. The fact that its envelope becomes time-invariant and is governed by the Schrödinger–Nohara type equation is shown.     

Governing equations of envelopes created by nearly bichromatic waves on deep water

In this paper, the author derives the modified Schrödinger equation that governs the envelope created by nearly bichromatic waves, which are defined by the waves whose energy is almost concentrated in two closely approached wavenumbers. The stability of the solution of the modified Schrödinger equation for nearly bichromatic waves on deep water is discussed and the fact that the Benjamin–Feir instability occurs in a condition is shown. Moreover, the solutions of the modified Schrödinger equation for nearly bichromatic waves on deep water are obtained and, in a special case, the solution becomes the standing wave solution is shown.     

Three new nortriterpene glycosides and two new triterpene glycosides from the bulbs of Scilla scilloides

Three new norlanostane-type triterpene glycosides, scillanostasides A, B, and C, and two new lanostane-type triterpene glycosides, scillanostasides D and E, were isolated from the bulbs of Scilla scilloides Druce (Liliaceae) along with one known norlanostane-type triterpene heptaglycoside, scillascilloside G-1. Their chemical structures were determined on the basis of spectroscopic data as well as chemical evidence.     

Identification and characterization of component organic and glycosidic acids of crude resin glycoside fraction from Calystegia soldanella

Alkaline hydrolysis of the crude resin glycoside fraction of the leaves, stems, and roots of Calystegia soldanella ROEM. et SCHULT. (Convolvulaceae) gave four new glycosidic acids, named calysolic acids A, B, C, and D, along with one known glycosidic acid, soldanellic acid B, and three organic acids, 2S-methylbutyric, tiglic, and 2S,3S-nilic acids. The structures of the new glycosidic acids were characterized on the basis of spectroscopic data and chemical evidence.     

A novel synthesis of spiro[2.6]nonadienones by the reaction of magnesium cyclopropylidenes with naphtholates and phenolates

The sulfoxide-magnesium exchange reaction of aryl 1-chlorocyclopropyl sulfoxides with i-PrMgCl in THF at low temperature gave magnesium cyclopropylidenes. Treatment of the magnesium cyclopropylidenes with lithium naphtholates or phenolates resulted in the formation of spiro[2.6]nonadienones in up to 82% yield. The structure of the spiro[2.6]nonadienones was found to be dependent on the structure of the naphtholates and phenolates.     

Two labdane diterpene and megastigmane glycosides from Aquilegia hybrida

Two new labdane diterpene glycosides, named aquosides A and B, and a new megastigmane glycoside, named aquoside C, have been isolated from the air-dried aerial parts of Aquilegia hybrida together with three known compounds comprising a phenolic glycoside and two flavone C-glycosides. Their structures were determined on the basis of spectroscopic data and chemical evidence.     

Five new diterpenoids, viteagnusins A--E, from the fruit of Vitex agnus-castus

Two new halimane-type diterpenoids, viteagnusins A and B, and three new labdane-type diterpenoids, viteagnusins C, D, and E, were isolated from the fruit of Vitex agnus-castus L. (Chasteberry, Verbenaceae) along with two known diterpenoids. Their chemical structures were determined on the basis of spectroscopic data.     

Cucurbitane glycosides from unripe fruits of Siraitia grosvenori

Studies on the constituents of the unripe fruits of Siraitia grosvenori led to the isolation of three new cucurbitane triterpene glycosides, 11-oxomogroside III (10), 11-dehydroxymogroside III (11), and 11-oxomogroside IV A (12). Their structures were determined on the basis of detailed analyses of 1D, 2D-NMR spectroscopic methods. All of the compounds isolated from the unripe fruits of S. grosvenori were tested for cytotoxic activities against tumor cells, HCT-116 and SMMC-7721.     

Acyclic diterpene glycosides, capsianosides C, D, E, F and III, from the fruits of hot red pepper Capsicum annuum L. used in Kimchi and their revised structures

Acyclic diterpene glycosides, named capsianosides I', II, III (1), C (2), D (3), E (4) and F (5), have been isolated from the dried hot red pepper fruits of Capsicum annuum L. used in Kimchi. The structures of these compounds have been revised in the sugar connectivities by 1D- and 2D-NMR spectroscopic and chemical methods.