Synthesis of an Open‐Cage Structure POSS Containing Various Functional Groups and Their Effect on the Formation and Properties of Langmuir Monolayers

Recently, silsesquioxanes have been recognized as a new group of film‐forming materials. This study has been aimed at determining the effect of the kind of functional groups present in two different open‐cage structure POSS molecules on the possibility of the formation of Langmuir monolayers and their properties. To achieve this goal, two new POSS derivatives (of open‐cage structures) containing polyether and fluoroalkyl functional groups have been synthesized on the basis of a hydrosilylation process. An optimization of the process was performed, which makes it possible to obtain the above‐mentioned derivatives with high yields. In the next step, the Langmuir technique was applied to measurements of the surface pressure (π) ? the mean molecular area (A) isotherms during the compression of monolayers formed by molecules of the two POSS derivatives considered. Subsequently, the monolayers were transferred onto quartz plates according to the Langmuir–Blodgett technique. Both derivatives are able to form insoluble Langmuir films at the air–water interface, which can be transferred onto a solid substrate and effectively change its wetting properties.     

Versatile Method for the Simultaneous Synthesis of Two Ionic Liquids,Otherwise Difficult to Obtain,with High Atom Economy

A new synthetic approach and full spectral (NMR, IR, MS) and ion chromatographic characterization (IC) of nitrogen-based ionic liquids bearing allyl- or ethyl- substituent and triflate, tosylate, methyl sulfate or methanesulfonate anion has been presented. On a sample of 16 new ionic liquids, the versatility of the anion exchange method has been proven. In the metathesis reactions that have been carried out, the halide anion was exchanged in ionic liquid with an alkyl sulfonate based anion using alkylating agents. The results obtained using ion chromatographic analysis on the newly synthesized compounds have been discussed. Also, the utilization of a gaseous methyl halide by-product, obtained in the metathesis reaction and otherwise difficult to synthesize, has been presented. This approach ensured high atom economy of the overall process, which makes the proposed methodology sustainable and eco-friendly.     

Pyrylium sulfonate based ionic liquids

Pyrylium salts represent a new group of ionic liquids (ILs) containing a positive charge on the oxygen atom. The novel ILs were obtained starting with 4-pyrones from petroleum feedstock and renewable resources and sulfonic acids. The use of carboxylic acids instead of salts resulted in the formation of cocrystals. The synthesized pyrylium ionic liquids were stable in air and in contact with water and common organic solvents. The permanganate indices which are characteristic for prepared sulfonates were also investigated. The pyrylium ionic liquids were useful as immobilizers and dissolving agents in hydrosilylation reactions.     

Active control of vibration in small and medium amplitude range of elements in automotive systems

In this paper two different visco-elastic suspensions active system with pneumatic cylinder, and semi-active system with piezoceramics, are presented. The active suspension controls the vibration in medium-amplitude range and low frequency excitation. The semi-active suppression system controls the vibration in the audio frequency range and small amplitudes. The main aim of proposed solutions is to decrease the amplitude of vibration in resonance of conventional, passive suspensions. Both systems are worked out, especially for the better protection of the human body against harmful sounds and vibrations.     

Stationary Solutions and Connecting Orbits for <Emphasis Type="Italic">p</Emphasis>-Laplace Equation

We deal with one dimensional p-Laplace equation of the form

$$\begin{aligned} u_t = (|u_x|^{p-2} u_x )_x + f(x,u), \ x\in (0,l), \ t>0, \end{aligned}$$

under Dirichlet boundary condition, where \(p>2\) and \(f:[0,l]\times {\mathbb {R}}\rightarrow {\mathbb {R}}\) is a continuous function with \(f(x,0)=0\). We will prove that if there is at least one eigenvalue of the p-Laplace operator between \(\lim _{u\rightarrow 0} f(x,u)/|u|^{p-2}u\) and \(\lim _{|u|\rightarrow +\infty } f(x,u)/|u|^{p-2}u\), then there exists a nontrivial stationary solution. Moreover we show the existence of a connecting orbit between stationary solutions. The results are based on Conley index and detect stationary states even when those based on fixed point theory do not apply. In order to compute the Conley index for nonlinear semiflows deformation along p is used.

     

Artifacts in femtosecond transient absorption spectroscopy

The paper discusses three different artifacts related to two-photon absorption (TPA), stimulated Raman amplification (SRA) and cross-phase modulation (XPM), all intrinsic to transient absorption measurements with femtosecond time resolution. Certain properties of these signals are analysed and shown to superimpose onto measured transient absorption spectra. Ways of reducing the influence of the artifacts discussed are suggested. A simple correcting procedure based on the linear intensity dependence of the artifacts discussed is proposed. Received: 29 May 2001 / Final version: 15 October 2001 / Published online: 29 November 2001     

Global Properties of Kovalevskaya Exponents

This paper contains a collection of properties of Kovalevskaya exponents which are eigenvalues of a linearization matrix of weighted homogeneous nonlinear systems along certain straight-line particular solutions. Relations in the form of linear combinations of Kovalevskaya exponents with nonnegative integers related to the presence of first integrals of the weighted homogeneous nonlinear systems have been known for a long time. As a new result other nonlinear relations between Kovalevskaya exponents calculated on all straight-line particular solutions are presented. They were obtained by an application of the Euler–Jacobi–Kronecker formula specified to an appropriate n-form in a certain weighted homogeneous projective space.     

Correction to Generic polynomial vector fields are not integrable

In the paper Generic polynomial vector fields are not integrable [1], we study some generic aspects of polynomial vector fields or polynomial derivations with respect to their integration. Using direct sums of derivations together with our previous results we showed that, for all n ≥ 3 and s ≥ 2, the absence of polynomial first integrals, or even of Darboux polynomials, is generic for homogeneous polynomial vector fields of degree s in n variables. To achieve this task, we need an example of such vector fields of degree s ≥ 2 for any prime number n ≥ 3 of variables and also for n = 4. The purpose of this note is to correct a gap in our paper for n = 4 by completing the corresponding proof.