Seasonal Changes in Essential Oil Constituents of Cystoseira compressa: First Report

Marine macroalgae are well known to release a wide spectrum of volatile organic components, the release of which is affected by environmental factors. This paper aimed to identify the essential oil (EO) compounds of the brown algae Cystoseira compressa collected in the Adriatic Sea monthly, from May until August. EOs were isolated by hydrodistillation using a Clavenger-type apparatus and analyzed by gas chromatography coupled with mass spectrometry (GC–MS). One hundred four compounds were identified in the volatile fraction of C. compressa, accounting for 84.37–89.43% of the total oil. Samples from May, June, and July were characterized by a high share of fatty acids (56, 69, and 34% respectively) with palmitic acid being the dominant one, while in the August sample, a high content of alcohols (mainly phytol and oleyl alcohol) was found. Changes in the other minor components, which could be important for the overall aroma and biological activities of the algal samples, have also been noted during the vegetation periods. The results of this paper contribute to studies of algal EOs and present the first report on C. compressa EOs.     

Syntheses,characterization of and studies on the electrochemical behaviour of ferrocenyl dithiophosphonates and 4-methoxyphenyl dithiophosphonates

Some 1,3-dithiadiphosphetane 2,4-disulfides (X₂P₂S₄, X: Fc, FcLR; X: CH₃O?C₆H₄?, LR) were allowed to react with alcohols to obtain dithiophosphonic acids (X(OR)PS₂H). These were converted to the corresponding ammonium salts. The salts were of the structures [Fc(OR)PS₂]^?[NH₄]⁺, R: 3-methyl-1-butyl- for I; 1-phenyl-1-propyl- for II; 3-pentyl- for III; 3-phenyl-1-propyl- for IV and [CH₃O?C₆H₄(OR)PS₂]^?[NH₄]⁺, R: 3-methyl-1-butyl- for V and 1-phenyl-1-propyl- for VI. To the best of our knowledge, all the compounds except V were prepared for the first time.

The compounds synthesized were characterized by elemental analysis, NMR (¹H, ¹³C, ³¹P), MS, FTIR, and Raman spectroscopies. Electrochemical behaviors of I–VI at disposable pencil graphite electrode (PGE) were investigated by using cyclic voltammetry (CV) and square-wave voltammetry (SWV). Adsorption and diffusion patterns of all the compounds on the PGE were also studied.

Two electroactive groups were identified in the compounds I–IV and only one in V and VI. The ferrocenyl groups of I-IV were oxidized at around 0.4 V. The same compounds display a second, more intense CV band at 0.8 V. The corresponding band for the compounds V–VI appears at around 0.6 V with a much weaker intensity. It is suggested that the ferrocenyl group introduced into the structures stabilizes the radical species formed as the product of the oxidation of the dithiophosphonato group.     

PCCP-Catalyzed Synthesis of Tetrasubstituted Allenes Bearing Heteroaromatic Sulfenyl Group**

We report a Brønsted acid-catalyzed synthesis of tetrasubstituted allenyl compounds decorated with heterocyclic sulfenyl group. The reaction proceeds readily from available propargylic alcohols in the presence of pentacarboxycyclopenatadienes (PCCPs) as organocatalysts. The developed strategy provides tetrasubstituted allene derivatives in high yields (from 55 to 98 %) and under mild reaction conditions.     

Reference frames in harmonic coordinates: geometric and physical aspects

This work is focused on the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates. Precisely, we express in relative form the harmonicity conditions and consider the so called ??spatially harmonicity?? of a reference frame in spherical symmetry. The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions.     

On the influence of a constant force on the appearance of period-doubling bifurcations and chaos in a harmonically excited pure cubic oscillator

A pure cubic oscillator with a constant and a harmonic force acting on it, which represents a nonlinear asymmetric system, is considered. Building on previous studies on the matter, analytical and numerical approaches are used to examine and illustrate its dynamics related to the phenomenon of period-doubling bifurcations and their development into chaos for different values of the constant force. The region of control parameters in which this scenario is possible is determined and discussed with a view to revisiting literature results and to giving novel and deeper insights into the phenomenon related to the influence of the magnitude of the constant force and certain resonances.     

The strengthened C.B.S. inequality constant for second order elliptic partial differential operator and for hierarchical bilinear finite element functions

We estimate the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for hierarchical bilinear finite element spaces and elliptic partial differential equations with coefficients corresponding to anisotropy (orthotropy). It is shown that there is a nontrivial universal estimate, which does not depend on anisotropy. Moreover, this estimate is sharp and the same as for hierarchical linear finite element spaces.This research was supported by the Grant Agency of Czech Republic under the contract No. 201/02/0595.     

About a class of nonlinear oscillators with amplitude-independent frequency

This work is concerned with nonlinear oscillators that have a fixed, amplitude-independent frequency. This characteristic, known as isochronicity/isochrony, is achieved by establishing the equivalence between the Lagrangian of the simple harmonic oscillator and the Lagrangian of conservative oscillators with a position-dependent coefficient of the kinetic energy, which can stem from their mass that changes with the displacement or the geometry of motion. Conditions under which such systems have an isochronous center in the origin are discussed. General expressions for the potential energy, equation of motion as well as solutions for a phase trajectory and time response are provided. A few illustrative examples accompanied with numerical verifications are also presented.     

Exact approaches for solving robust prize-collecting Steiner tree problems

In the Prize-Collecting Steiner Tree Problem (PCStT) we are given a set of customers with potential revenues and a set of possible links connecting these customers with fixed installation costs. The goal is to decide which customers to connect into a tree structure so that the sum of the link costs plus the revenues of the customers that are left out is minimized. The problem, as well as some of its variants, is used to model a wide range of applications in telecommunications, gas distribution networks, protein–protein interaction networks, or image segmentation.     

Bases of Feigin–Stoyanovsky’s type subspaces for $$C_\ell ^{(1)}$$

In this paper, we construct combinatorial bases of Feigin–Stoyanovsky’s type subspaces of standard modules for level k affine Lie algebra \(C_\ell ^{(1)}\). We prove spanning by using annihilating field \(x_\theta (z)^{k+1}\) of standard modules. In the proof of linear independence, we use simple currents and intertwining operators whose existence is given by fusion rules.