The polysaccharide extracts from the fungi Coprinus comatus and Coprinellus truncorum do exhibit AChE inhibitory activity

The polysaccharide (PSH) extracts from the edible mushroom species Coprinus comatus and Coprinellus truncorum were screened in liquid for their acetylcholinesterase inhibitory (AChE) activity. Both extracts were found to display inhibition of the aforementioned enzyme reaching similar IC₅₀ values of 0.62 ± 0.07 and 0.61 ± 0.03 mg/mL, respectively. According to the means of FTIR spectroscopy, these PSH extracts mostly contained β-glucans. However, the presence of some proteins and polyphenolics as minor ingredients were also detected. Compared with existing literature data for anti-AChE activity of the sugar samples, the findings within this study may be treated as a profound bioactivity. Consequently, this study puts some light on the possible use of the screened macrofungi in the palliative treatment of Alzheimer’s disease.     

Programmable Temperature Vaporizer (PTV) Applied to the Triglyceride Analysis of Milk Fat

The PTV (Programmable Temperature Vaporizer) is a split/splitless injector which allows the sample to be introduced at a relatively low temperature, thus affording accurate and reproducible sampling. After injection the PTV is rapidly heated to transfer the vaporized components into the capillary column. This type of injector has proved to be an efficient tool for the evaluation of fatty acids, essential oils, and pesticides in food analysis. In this work the suitability of PTV for the analysis of milk fat purity by the Official EU method was evaluated. This method is based on the gas chromatographic determination of triglycerides only according to their total number of carbon atoms followed by the application of formulae deriving from multiple linear regressions. The analysis is currently carried out with a packed column or a short capillary column and an on-column injection system. Several samples of pure milk fat and mixtures of milk fat with foreign fat were analyzed with the same capillary column and by using both PTV and on-column injection systems. The results show that the gas chromatographic profile obtained by PTV is comparable with that obtained by the on-column injector, while repeatability and reproducibility data meet the requirements indicated in the Official Method. Therefore, this study demonstrates that it is possible to use the PTV instead of the on-column injector to determine the purity of milk fat with this method.     

The signal-to-noise ratio as the measure for the quantification of lysophospholipids by matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry

The subject of this report is the determination of lysophospholipids; lysophosphatidylcholine, lysophosphatidylethanolamine, lysophosphatidylserine and lysophosphatidic acid, by matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI-TOF MS). The mean signal-to-noise ratio (S/N) was used for the first time as a measure of lysophospholipid concentration. Two different sample preparation procedures were applied, the 'standard' procedure and the 'premix' in order to check to what extent these methods influence the results of the lysophospholipid quantification. Results can be summarised as follows: (a) All classes of lysophospholipids can be easily and sensitively analysed by MALDI-TOF MS. The smallest detectable amount of lysophospholipids was 0.09 pmol on the sample plate. That is about two orders of magnitude lower than the amount detectable by standard chromatographic methods. (b) The mean S/N of all peaks detected in the positive ion mass spectra can be used as a measure of the lysophospholipid concentration. Whereas the S/N for neutral lysophospholipids correlated with the applied concentrations only when the samples were analysed as 'premix', the sample preparation and application procedure did not influence the quantification of acidic lysophospholipids. The standard deviations were not higher than 10% of the mean value. (c) All spectra were additionally analysed in the presence of CsCl. The addition of caesium ions makes the peak identification unambiguous in phospholipid mixtures, but the Cs adducts of lysophospholipids do not properly reflect their concentration and, therefore, they were not useful for quantification. (d) The applicability of the method was demonstrated on the organic extract of human neutrophils.     

Analysis of flammability and smoke emission of rigid polyurethane foams modified with nanoparticles and halogen-free fire retardants

Using one-step method, rigid polyurethane foams were made, modified with developed fire retardant systems containing halogen-free flame retardants and nanofillers in the form of multi-walled carbon nanotubes or nanoscale titanium dioxide. The materials were subjected to a test using a cone calorimeter and smoke-generating chamber, and selected samples were further analyzed via thermogravimetry and oxygen index. Moreover, the products of thermal degradation of selected samples were identified using gas chromatography with mass spectrometer. Conducted flammability tests confirmed the presence of a synergistic effect between the used nanofillers and halogen-free flame retardants. It has been observed that the carbonized layer, the formation of which favored the presence of nanoadditives, inhibits the combustion process. Furthermore, nanofillers influenced favorably reduction in the amount and the number of occurring products of thermal degradation.     

Equiconvergence in rational approximation of meromorphic functions

Generalizing the Walsh theorem, E. B. Saff, A. Sharma, and R. S. Varga showed that there is a close relation between the rational interpolants in roots of unity and Padé approximants of certain meromorphic functions. The purpose of this paper is to extend this result, replacing the Padé approximant with other rational functions so as to obtain a larger region of equiconvergence.     

Asymptotic Behavior of the Fourth Painlevé Transcendents in the Space of Initial Values

We study the asymptotic behavior of solutions of the fourth Painlevé equation as the independent variable goes to infinity in its space of (complex) initial values, which is a generalization of phase space described by Okamoto. We show that the limit set of each solution is compact and connected and, moreover, that any solution that is not rational has an infinite number of poles and infinite number of zeros.     

On the new fourth-order methods for the simultaneous approximation of polynomial zeros

A new iterative method of the fourth-order for the simultaneous determination of polynomial zeros is proposed. This method is based on a suitable zero-relation derived from the fourth-order method for a single zero belonging to the Schröder basic sequence. One of the most important problems in solving polynomial equations, the construction of initial conditions that enable both guaranteed and fast convergence, is studied in detail for the proposed method. These conditions are computationally verifiable since they depend only on initial approximations, the polynomial coefficients and the polynomial degree, which is of practical importance. The construction of improved methods in ordinary complex arithmetic and complex circular arithmetic is discussed. Finally, numerical examples and the comparison with existing fourth-order methods are given.     

Generalized matrix inversion is not harder than matrix multiplication

Starting from the Strassen method for rapid matrix multiplication and inversion as well as from the recursive Cholesky factorization algorithm, we introduced a completely block recursive algorithm for generalized Cholesky factorization of a given symmetric, positive semi-definite matrix A∈R^n×n$A\in {\mathbb{R}}^{n\times n}$. We used the Strassen method for matrix inversion together with the recursive generalized Cholesky factorization method, and established an algorithm for computing generalized {2,3}$\{2,3\}$ and {2,4}$\{2,4\}$ inverses. Introduced algorithms are not harder than the matrix–matrix multiplication.     

Scale transformations in phase space and stretched states of a harmonic oscillator

We consider scale transformations (q, p) → (λq, λp) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson–Schrödinger uncertainty relations for stretched states.     

The von Kármán theory for incompressible elastic shells

We rigorously derive the von Kármán shell theory for incompressible materials, starting from the 3D nonlinear elasticity. In case of thin plates, the Euler-Lagrange equations of the limiting energy functional reduce to the incompressible version of the classical von Kármán equations, obtained formally in the limit of Poisson’s ratio ν → 1/2. More generally, the midsurface of the shell to which our analysis applies, is only assumed to have the following approximation property: ${\mathcal C^3}$ first order infinitesimal isometries are dense in the space of all W ^2,2 infinitesimal isometries. The class of surfaces with this property includes: subsets of ${\mathbb R^2}$ , convex surfaces, developable surfaces and rotationally invariant surfaces. Our analysis relies on the methods and extends the results of Conti and Dolzmann (Calc Var PDE 34:531–551, 2009, Lewicka et al. (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX:253–295, 2010, Friesecke et al. (Comm. Pure. Appl. Math. 55, no. 2, 1461–1506, 2002).