Synchronous states of slowly rotating pendula

Coupled systems that contain rotating elements are typical in physical, biological and engineering applications and for years have been the subject of intensive studies. One problem of scientific interest, which among others occurs in such systems is the phenomenon of synchronization of different rotating parts. Despite different initial conditions, after a sufficiently long transient, the rotating parts move in the same way — complete synchronization, or a permanent constant shift is established between their displacements, i.e., the angles of rotation — phase synchronization. Synchronization occurs due to dependence of the periods of rotating elements motion and the displacement of the base on which these elements are mounted.     

Principal eigenvalue of the fractional Laplacian with a large incompressible drift

We study the principal Dirichlet eigenvalue of the operator \({L_A=\Delta^{\alpha/2}+Ab(x)\cdot\nabla}\) , on a bounded C ^1,1 regular domain D. Here \({\alpha\in(1,2)}\) , \({\Delta^{\alpha/2}}\) is the fractional Laplacian, \({A\in\mathbb{R}}\) , and b is a bounded d-dimensional divergence-free vector field in the Sobolev space W ^1,2d/(d+α)(D). We prove that the eigenvalue remains bounded, as A→ + ∞, if and only if b has non-trivial first integrals in the domain of the quadratic form of \({\Delta^{\alpha/2}}\) for the Dirichlet condition.     

Magnetostructural transformations in Ni<Subscript>51</Subscript>Mn<Subscript>36</Subscript>Sn<Subscript>13</Subscript> Heusler alloy thin films

In this paper we report structural, magnetic and transport properties of strongly textured Ni₅₁Mn₃₆Sn₁₃ thin films. The off-stoichiometric Heusler alloy films with 200 nm thickness were sputter-deposited on a MgO(100) substrate at 500 K and after annealed at 1000 K in UHV conditions. The textured growth was confirmed by x-ray diffraction in Bragg-Brentano geometry. The temperature dependence of the magnetic properties was measured by VSM and FMR methods. The electron transport measurements were carried out in function of temperature in 0 Oe and 50 kOe fields. All measurements corroborate the existence of the martensitic transformation in the film. Furthermore, transport measurements reveal an influence of the magnetic field on the transition temperature.     

On a new class of functional equations satisfied by polynomial functions

Aequationes mathematicae - The classical result of L. Székelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known...     

Revealing the Bonding Pattern from the Molecular Electron Density Using Single Exponential Decay Detector: An Orbital‐Free Alternative to the Electron Localization Function

We introduce a new tool (single exponential decay detector: SEDD) to extract information about bonding and localization in atoms, molecules, or molecular assemblies. The practical evaluation of SEDD does not require any explicit information about the orbitals. The only quantity needed is the electron density (calculated or experimental) and its derivatives up to the second order.     

Application of HPLC-DAD for In Vitro Investigation of Acetylcholinesterase Inhibition Activity of Selected Isoquinoline Alkaloids from Sanguinaria canadensis Extracts

Isoquinoline alkaloids may have a wide range of pharmacological activities. Some of them have acetylcholinesterase activity inhibition. Nowadays, neurodegenerative disorders such as Alzheimer’s disease have become a serious public health problem. Searching for new effective compounds with inhibited acetylcholinesterase activity is one of the most significant challenges of modern scientific research. The aim of this study was the in vitro investigation of acetylcholinesterase activity inhibition of extracts obtained from Sanguinaria canadensis collected before, during and after flowering. The acetylcholinesterase activity inhibition of these extracts has not been previously tested. The aim was also to quantify selected alkaloids in the investigated extracts by high performance liquid chromatography (HPLC). The analyses of alkaloid content were performed using HPLC in reversed phase (RP) mode using Polar RP column and mobile phase containing acetonitrile, water and ionic liquid (IL). The acetylcholinesterase activity inhibition of the tested plant extracts and respective alkaloid standards were examined using high performance liquid chromatography with diode-array detector (HPLC-DAD) for the quantification of 5-thio-2-nitro-benzoic acid, which is the product of the reaction between the thiocholine (product of the hydrolysis of acetylthiocholine reaction) with Ellman reagent. The application of the HPLC method allowed for elimination of absorption of interfering components, for example, alkaloids such as sanguinarine and berberine. It is revealed that the HPLC method can be successfully used for the evaluation of the acetylcholinesterase inhibitory activity in samples such as plant extracts, especially those containing colored components adsorbing at wavelength in the range 405–412 nm. The acetylcholinesterase inhibition activity synergy of pairs of alkaloid standards and mixture of all investigated alkaloids was also determined. Most investigated alkaloids and all Sanguinaria canadensis extracts exhibited very high acetylcholinesterase activity inhibition. IC₅₀ values obtained for alkaloid standards were from 0.36 for berberine to 23.13 µg/mL for protopine and from 61.24 to 89.14 µg/mL for Sanguinaria canadensis extracts. Our investigations demonstrated that these plant extracts can be recommended for further in vivo experiments to confirm their acetylcholinesterase activity inhibition.     

Stability of some aryllithiums in the presence of cyano group: synthesis of biaromatic cyanoarylboronic acids and silanes

Lithium diisopropylamine (LDA)‐mediated deprotonation reactions of halogenated cyanobenzyloxy‐benzenes and cyanobiphenyls were investigated. The resultant organolithium derivatives were converted into the corresponding arylboronic acids or silanes. It was found that the stability of the obtained aryllithiums towards isomerization to the respective benzyllithiums depends strongly on the number of fluorine atoms in the phenyl ring and on the position of the cyano group. Halogenated cyanobiaryls were selectively deprotonated in the position flanked by two halogen atoms; however, the yield depended strongly on the reaction conditions. Addition of LDA to the cyano group was observed on the lithiation of 4‐cyano‐3′,5′‐dichlorobiphenyl rather than deprotonation. Copyright © 2012 John Wiley & Sons, Ltd.     

Reaching Milestones in the Oxygenation Chemistry of Magnesium Alkyls: towards Intimate States of O2 Activation and the First Monomeric Well-Defined Magnesium Alkylperoxide

Despite decades of extensive studies on the reactivity of magnesium alkyls towards O₂, the isolation and structural characterization of discrete products of these reactions still remains a challenge. Although the formation of the most frequently encountered magnesium alkoxides through unstable alkylperoxide intermediates has commonly been accepted, the latter species have been elusive for over 100 years. Probing the oxygenation of a seemingly simple well-defined neo-pentylmagnesium complex stabilized by a β-diketiminate ligand, (^dippBDI)MgCH₂CMe₃, we report on the isolation and structure characterization of both a dimeric magnesium alkoxide [(^dippBDI)Mg(μ-OCH₂CMe₃)]₂ and the first example of monomeric magnesium alkylperoxide [(^dippBDI)Mg(thf)OOCH₂CMe₃] (^dippBDI=[(ArNCMe)₂CH]⁻ and Ar=C₆H₃iPr₂-2,6). The formation of monomeric magnesium alkylperoxide demonstrates a crucial role of an additional Lewis base for stabilizing the most elusive oxygenation products likely due to increasing of the electron density on the metal centre. Moreover, the ¹H NMR studies at −80 °C revealed that the dissociation of a coordinated Lewis base from the solvated complex (^dippBDI)Mg(L)CH₂CMe₃ (where L=thf or 4-methylpyridine) is likely not required prior to the effective attack of an O₂ molecule on the metal centre and the four-coordinate alkylmagnesium complex reacts smoothly with O₂ under these conditions. The results can be expected to aid future engineering of various organomagnesium/O₂-based reaction systems.     

Obtaining Granules from Waste Tannery Shavings and Mineral Additives by Wet Pulp Granulation

This paper presents the results of research on the granulation process of leather industry waste, i.e., tanning shavings. It is economically justified to granulate this waste together with mineral additives that are useful in the processes of their further processing. Unfortunately, the granulation of raw, unsorted shavings does not obtain desired results due to their unusual properties. In this study, the possibilities of agglomeration of this waste were examined by a new method consisting of the production and then the granulation of wet pulp. During granulation, no additional binding liquid is added to the granulated bed. As part of this work, the specific surface of granulated shavings, the granulometric composition of the obtained agglomerates, and their strength parameters were determined. The use of a vibrating disc granulator, the addition of a water glass solution (in the pulp), dolomite, and gypsum made it possible to obtain durable, mechanically stable granules.