A Note on the Theory of Motion of an Articulated Truck

A mathematical model of an n-link vehicle is described. It is based on the D'Alembert–Lagrange equations and the use of the instantaneous velocity centers of isolated links resulted from the constraints imposed on the system. The model, consisting of typical elements, is comparatively simple and obvious. The reactions of holonomic and nonholonomic constraints are determined. Specific systems, including those with imperfect constraints, are considered as an example.     

Structure of a Bloch domain wall in a cubic crystal

Planar Bloch domain walls with different senses and paths of rotation of the magnetization vector are studied in a cubic crystal with a negative first constant of magnetic anisotropy.     

Essential self-adjointness of Dirichlet operators of Gibbs measures on infinite products of manifolds

We obtain the conditions of essential self-adjointness of Dirichlet operators of Gibbs measures with essential domains consisting of smooth cylindrical functions. It is proved that certain spaces of smooth functions are invariant under the action of the semigroup of the Dirichlet operator.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 4–11, January, 1995.This research was partially supported by the Ukrainian State Committee on Science and Technology.     

Fourier transform infrared spectroscopic characterisation of heavy metal-induced metabolic changes in the plant-associated soil bacterium Azospirillum brasilense Sp7

Structural and compositional features of whole cells of the plant-growth-promoting rhizobacterium Azospirillum brasilense Sp7 under standard and heavy metal-stressed conditions are analysed using Fourier transform infrared (FTIR) spectroscopy and compared with the FT-Raman spectroscopic data obtained previously [J. Mol. Struct. 563–564 (2001) 199]. The structural spectroscopic information is considered together with inductively coupled plasma-mass spectrometric (ICP-MS) analytical data on the content of the heavy metal cations (Co²⁺, Cu²⁺ and Zn²⁺) in the bacterial cells. As a bacterial response to heavy metal stress, all the three metals, being taken up by bacterial cells from the culture medium (0.2 mM) in significant amounts (ca. 0.12, 0.48 and 4.2 mg per gram of dry biomass for Co, Cu and Zn, respectively), are shown to induce essential metabolic changes in the bacterium revealed in the spectra, including the accumulation of polyester compounds in bacterial cells and their enhanced hydration affecting certain IR vibrational modes of functional groups involved.     

Central peak in polaronic crystals

A possibility of the central peak appearance in crystals with low concentration of small-radius polarons is pointed out. The intensity of the central peak increases sharply with the softening of the phonon mode $\text{(ω}{}_{\mathrm{<mtext>K</mtext><mtext>0</mtext>}}\text{→ 0)}$ in the vicinity of the structural phase transition . The peak width γ₀ is determined by the probability W of the polaron hopping between the sites γ₀ = K₀²a²W.     

Two‐step chromatography purification of IgGs possessing sialidase activity from human blood serum

Sialation of cell surface is known to be tightly connected with tumorigenicity, invasiveness, metastatic potential and clearance of aged cells, while sialation of immunoglobulin G (IgG) molecules determines their anti‐inflammatory properties. Recently, we have found for the first time IgG‐antibodies possessing sialidase‐like activity (sialylic abzyme) in blood serum of multiple myeloma and systemic lupus erythematosis patients. This abzyme was detected in a pool of IgGs purified by a typical procedure including immunoglobulin's precipitation with ammonium sulfate and following chromatography on protein G–Sepharose column. Here we describe a novel matrix for affinity purification of sialylic abzyme that is based on using bovine submandibular gland mucin conjugated to Sepharose matrix (mucin–Sepharose). This matrix preferentially binds sialidase‐like IgGs from a pool of sialidase‐active fraction of proteins precipitated with 50% ammonium sulfate from blood serum of the systemic lupus erythematosis patients. That allowed us to develop a new scheme of double‐step chromatography purification of sialidase‐like IgGs from human blood serum. Copyright © 2014 John Wiley & Sons, Ltd.     

Site selective bond breaking in random media

We show that strong light with the frequency slightly less then the ‘gap’ in electron spectrum of fused quartz cuts off macroscopic balls with fixed diameter 2 ± 0.2 μm and throws them out of the ablation crater. The reason for the phenomenon is the light driven electron bunching and generation of strong static electric field on the bunch boundaries resulting in effective photon absorption and bonds breaking in these regions while the main part of a sample is almost transparent for the photons.     

Periodic structure of spicular magnetic clusters in a magnetic liquid

The behavior of clusters formed by magnetic particles of magnetic liquid placed into a cylindrical capillary tube in magnetic field is described. Spicular clusters are formed from the sediment at the application of a magnetic field. They arrange themselves along the capillary repeating the direction of external magnetic field. Clusters distribute uniformly in the region of a magnetic field maximum. Such a state remains steady with respect to changes of the magnetic field gradient profile in definite limits. The structure of the uniformly ordered clusters is obtained experimentally. The capability of control of the structure period is shown. It is observed that increasing of magnetic field gradient up to the magnitude higher than a certain threshold value results in rearrangement of the clusters row into a multi-row hexagonal structure.