Репозиторий Университета

Recently, zinc and its alloys have been proposed as promising candidates for biodegradable metals (BMs), owning to their preferable corrosion behavior and acceptable biocompatibility in cardiovascular, bone and gastrointestinal environments, together with Mg-based and Fe-based BMs. However, there is the desire for surface treatment for Zn-based BMs to better control their biodegradation behavior. Firstly, the implantation of some Zn-based BMs in cardiovascular environment exhibited intimal activation with mild inflammation. Secondly, for orthopedic applications, the biodegradation rates of Zn-based BMs are relatively slow, resulting in a long-term retention after fulfilling their mission. Meanwhile, excessive Zn2+ release during degradation will cause in vitro cytotoxicity and in vivo delayed osseointegration. In this review, we firstly summarized the current surface modification methods of Zn-based alloys for the industrial applications. Then we comprehensively summarized the recent progress of biomedical bulk Zn-based BMs as well as the corresponding surface modification strategies. Last but not least, the future perspectives towards the design of surface bio-functionalized coatings on Zn-based BMs for orthopedic and cardiovascular applications were also briefly proposed.

Recently, zinc and its alloys have been proposed as promising candidates for biodegradable metals (BMs), owning to their preferable corrosion behavior and acceptable biocompatibility in cardiovascular, bone and gastrointestinal environments, together with Mg-based and Fe-based BMs. However, there is the desire for surface treatment for Zn-based BMs to better control their biodegradation behavior. Firstly, the implantation of some Zn-based BMs in cardiovascular environment exhibited intimal activation with mild inflammation. Secondly, for orthopedic applications, the biodegradation rates of Zn-based BMs are relatively slow, resulting in a long-term retention after fulfilling their mission. Meanwhile, excessive Zn2+ release during degradation will cause in vitro cytotoxicity and in vivo delayed osseointegration. In this review, we firstly summarized the current surface modification methods of Zn-based alloys for the industrial applications. Then we comprehensively summarized the recent progress of biomedical bulk Zn-based BMs as well as the corresponding surface modification strategies. Last but not least, the future perspectives towards the design of surface bio-functionalized coatings on Zn-based BMs for orthopedic and cardiovascular applications were also briefly proposed.

© 2020 Purpose: To evaluate the density and distribution of conjunctival goblet cells in mice without clinical evidence of ocular surface diseases. Methods: Immediately after euthanasia of C57BL/6 wild-type mice, the eyes including eyelids were removed and fixed in paraformaldehyde. Entire eyeballs and eyelids were cut in series along the sagittal axis from nasal to temporal on a microtome and then stained with Periodic Acid-Schiff acid to visualize the goblet cells. At each section stained in this way, the conjunctival goblet cells of the entire upper and lower lid conjunctiva were counted by light microscopy. Additional (transmission electron microscopy) (TEM)-Analysis on ultrathin sections was performed to evaluate morphological differences. Results: The total number of conjunctival goblet cells differs markedly between individual animals. Categorisation into upper eyelid (UL) and lower eyelid (LL) and into regions (nasal, middle, temporal) revealed a significant increase of goblet cells from nasal to temporal in the UL and a significant decrease in the LL. Conclusion: The distribution of conjunctival goblet cells in mice differs considerably from humans and between individual animals. Therefore, precise selection of sampling and methods are needed to obtain comparable data. We recommend to use the middle region of the conjunctiva of UL/LL for goblet cell studies in mice. These findings are of particular interest for dry eye mouse models as well as pharmacological studies on mice with influence on their goblet cells.

© 2020 Elsevier B.V. Fe/Fe3O4 nanoparticles have been deposited on the surfaces of ultrathin CoFeB film and CoFeB/Ta/CoFeB hetero-structure to be detected due to the stray field generated by one particle or a cluster of particles. Exchange biased Fe/Fe3O4 core-shell nanoparticles have been used to stabilize the particles magnetization. Comparison between the Atomic Force and Magnetic Force Microscope images and subtraction of corresponding phase contrasts allows visualization of the film magnetization affected by the particles. Spectra of Ferromagnetic Resonance of the ultrathin films with deposited particles allow one to estimate particle/film dipolar interaction. The results will be useful for the development of lab-on-chip sensors of magnetically labeled cells. Estimation of particles number by magnetic response of the CoFeB heterostructure is demonstrated.

© 2020 Background: Miramistin is a widely used antiseptic, disinfectant and preservative, and one of the most popular antimicrobial agents on pharmaceutical market of the Russian Federation (http://www.dsm.ru/en/news/385/). However, there is a lack of reported systematic data on antibacterial efficacy of this agent obtained in accordance with the international standards. Aim: This paper represents a systematic study of antibacterial properties of miramistin. Another objective of this work is to evaluate and compare the exploratory performance of in vitro and in vivo protocols of antiseptics’ efficacy testing using miramistin as the reference antiseptic. Methods: Antibacterial activity of 0.1% and 0.2% aqueous solutions of miramistin against two museum strains of S. aureus (ATCC 209p) and E. coli (CDC F-50) was studied. Three standard in vitro laboratory tests (microdilution test, suspension test, and metal surface test), and one in vivo test (on rat's skin) were used. The study was conducted in accordance with the international regulatory documents. Results: Miramistin showed high bactericidal activity against the studied bacterial pathogens in the standard in vitro tests. Thus, in the microdilution test it showed expressed activity against S. aureus (MIC 8 μg/ml, MBC 16 μg/ml) and E. coli (MIC 32 μg/ml, MBC 128 μg/ml). In the suspension test, miramistin decreased the amount of colony forming units by at least 6 log10 units for S. aureus, and by at least 4.5 log10 units for E. coli. Transition to the metal surface test led to significant decrease of antibacterial activity by 1–3 log10 units as compared to the suspension test. Further dramatic reduction of antiseptic activity (by 3–4 log10 units) was observed in in vivo rat skin test. Addition of a protein contaminant (bovine serum albumin) led to a general decrease in the effectiveness of miramistin against the test pathogens (typically, by 1–2 log10 units). An interesting effect of exposure time-dependent reversal of miramistin's specificity to the studied Gram-positive S. aureus and the Gram-negative E. coli organisms was observed in the metal surface test. Conclusions: The results of this work provide systematic data on antibacterial efficacy of miramistin. They also underscore the need in relevant in vivo models for evaluation of antiseptics' efficacy. While the existing in vitro methods can be successfully applied at the discovery stages, it is necessary to use more realistic in vivo models at more advanced development stages. The observed selectivity reversal effect should be taken into account when carrying out the antiseptics’ efficacy testing and surface disinfection procedures.

© 2020 Background: Miramistin is a widely used antiseptic, disinfectant and preservative, and one of the most popular antimicrobial agents on pharmaceutical market of the Russian Federation (http://www.dsm.ru/en/news/385/). However, there is a lack of reported systematic data on antibacterial efficacy of this agent obtained in accordance with the international standards. Aim: This paper represents a systematic study of antibacterial properties of miramistin. Another objective of this work is to evaluate and compare the exploratory performance of in vitro and in vivo protocols of antiseptics’ efficacy testing using miramistin as the reference antiseptic. Methods: Antibacterial activity of 0.1% and 0.2% aqueous solutions of miramistin against two museum strains of S. aureus (ATCC 209p) and E. coli (CDC F-50) was studied. Three standard in vitro laboratory tests (microdilution test, suspension test, and metal surface test), and one in vivo test (on rat's skin) were used. The study was conducted in accordance with the international regulatory documents. Results: Miramistin showed high bactericidal activity against the studied bacterial pathogens in the standard in vitro tests. Thus, in the microdilution test it showed expressed activity against S. aureus (MIC 8 μg/ml, MBC 16 μg/ml) and E. coli (MIC 32 μg/ml, MBC 128 μg/ml). In the suspension test, miramistin decreased the amount of colony forming units by at least 6 log10 units for S. aureus, and by at least 4.5 log10 units for E. coli. Transition to the metal surface test led to significant decrease of antibacterial activity by 1–3 log10 units as compared to the suspension test. Further dramatic reduction of antiseptic activity (by 3–4 log10 units) was observed in in vivo rat skin test. Addition of a protein contaminant (bovine serum albumin) led to a general decrease in the effectiveness of miramistin against the test pathogens (typically, by 1–2 log10 units). An interesting effect of exposure time-dependent reversal of miramistin's specificity to the studied Gram-positive S. aureus and the Gram-negative E. coli organisms was observed in the metal surface test. Conclusions: The results of this work provide systematic data on antibacterial efficacy of miramistin. They also underscore the need in relevant in vivo models for evaluation of antiseptics' efficacy. While the existing in vitro methods can be successfully applied at the discovery stages, it is necessary to use more realistic in vivo models at more advanced development stages. The observed selectivity reversal effect should be taken into account when carrying out the antiseptics’ efficacy testing and surface disinfection procedures.

© 2020 Background: Miramistin is a widely used antiseptic, disinfectant and preservative, and one of the most popular antimicrobial agents on pharmaceutical market of the Russian Federation (http://www.dsm.ru/en/news/385/). However, there is a lack of reported systematic data on antibacterial efficacy of this agent obtained in accordance with the international standards. Aim: This paper represents a systematic study of antibacterial properties of miramistin. Another objective of this work is to evaluate and compare the exploratory performance of in vitro and in vivo protocols of antiseptics’ efficacy testing using miramistin as the reference antiseptic. Methods: Antibacterial activity of 0.1% and 0.2% aqueous solutions of miramistin against two museum strains of S. aureus (ATCC 209p) and E. coli (CDC F-50) was studied. Three standard in vitro laboratory tests (microdilution test, suspension test, and metal surface test), and one in vivo test (on rat's skin) were used. The study was conducted in accordance with the international regulatory documents. Results: Miramistin showed high bactericidal activity against the studied bacterial pathogens in the standard in vitro tests. Thus, in the microdilution test it showed expressed activity against S. aureus (MIC 8 μg/ml, MBC 16 μg/ml) and E. coli (MIC 32 μg/ml, MBC 128 μg/ml). In the suspension test, miramistin decreased the amount of colony forming units by at least 6 log10 units for S. aureus, and by at least 4.5 log10 units for E. coli. Transition to the metal surface test led to significant decrease of antibacterial activity by 1–3 log10 units as compared to the suspension test. Further dramatic reduction of antiseptic activity (by 3–4 log10 units) was observed in in vivo rat skin test. Addition of a protein contaminant (bovine serum albumin) led to a general decrease in the effectiveness of miramistin against the test pathogens (typically, by 1–2 log10 units). An interesting effect of exposure time-dependent reversal of miramistin's specificity to the studied Gram-positive S. aureus and the Gram-negative E. coli organisms was observed in the metal surface test. Conclusions: The results of this work provide systematic data on antibacterial efficacy of miramistin. They also underscore the need in relevant in vivo models for evaluation of antiseptics' efficacy. While the existing in vitro methods can be successfully applied at the discovery stages, it is necessary to use more realistic in vivo models at more advanced development stages. The observed selectivity reversal effect should be taken into account when carrying out the antiseptics’ efficacy testing and surface disinfection procedures.

© 2019 Wiley Periodicals, Inc. Control over biomaterials surface characteristics through surface modification or deposition of coatings is one of the key aspects of tissue engineering. This work was aimed to evaluate an effectiveness of various methods of chitosan-coating formations onto polylactide films using a number of techniques, such as vacuum deposition by electron-beam sputtering, chemical entrapment method, and electrospray procedure. Differently coated films were studied in terms of surface morphology (scanning electron and atomic-force microscopy), chemical structure (FTIR and X-ray photoelectron spectroscopy), and hydrophilic/hydrophobic balance (goniometry). The effect of coating technique on homogeneity of chitosan distribution over the substrate surface was evaluated using genipin and fluorescein isothiocyanate labeling as well as FTIR-microscopy. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48287.

© 2019 The Author(s) A method of 4-fluoro-3-(morpholinosulfonyl)benzo[b]thiophene-2-carboxylate synthesis has been developed and the electronic and spatial structure of a new biologically active molecule has been studied both theoretically and experimentally. The title compound was crystallized from acetonitrile and the single crystal X-ray analysis has revealed that it exists in a monoclinic P21/c space group, with one molecule in the asymmetric part of the unit cell. Hirshfeld surface analysis was used to study intermolecular interactions in the crystal. Molecular docking study evaluates the investigated compound as a new potential inhibitor of hepatitis B. Testing for anti-hepatitis B virus activity has shown that this substance demonstrates in vitro nanomolar inhibitory activity against HBV. Organic chemistry; Theoretical chemistry; Pharmaceutical chemistry, Hepatitis B; HBV; Pharmaceutical crystals; 4-Fluoro-3-(morpholinosulfonyl)benzo[b]thiophene-2-carboxylate; Benzothiophene; Hydrogen bond; Hirshfeld surface analysis; Molecular docking study

© 2018 by the authors. Computer-aided design (CAD) and additive manufacturing (AM) have shown promise in facilitating the fabrication of custom trays. Due to the clinical requirements, custom tray materials should achieve good bonding to the impression/adhesive systems. This study evaluated the retention of three fused deposition modeling (FDM) custom tray materials to a silicone impression/adhesive system before and after gritblasting (GB) by peel-off test. CAD-designed experimental test blocks were printed by FDM using acrylonitrile butadiene styrene (ABS), polyethylene terephthalate glycol copolyester (PETG), and high impact polystyrene (HIPS), and the reference test blocks were made of a conventional light-curing resin (n = 11). Before and after GB, the surface topography of all tray materials was analysed, and the maximum strength of the test block peeled off from a silicone impression/adhesive system was measured. After GB, the arithmetic mean height (Sa) and the valley fluid retention index (Svi) of the four material groups declined (p < 0.05). The peel-off strength of each of the four material groups significantly decreased by GB (p < 0.05), but no statistical difference could be found among them before or after GB. In all peel-off tests, adhesive failure occurred at the adhesive-impression material interface. The results indicated ABS, HIPS, and PETG could provide sufficient adhesion to the adhesive as the conventional light-curing resin, and GB could reduce the roughness generated by FDM and weaken the bonding between the adhesive and the silicone impression.

Copyright © 2018 American Chemical Society. Upconversion nanoparticles (UCNPs) coated with polyethylenimine (PEI) are popular background-free optical contrast probes and efficient drug and gene delivery agents attracting attention in science, industry, and medicine. Their unique optical properties are especially useful for subsurface nanotheranostics applications, in particular, in skin. However, high cytotoxicity of PEI limits safe use of UCNP@PEI, and this represents a major barrier for clinical translation of UCNP@PEI-based technologies. Our study aims to address this problem by exploring additional surface modifications to UCNP@PEI to create less toxic and functional nanotheranostic materials. We designed and synthesized six types of layered polymer coatings that envelop the original UCNP@PEI surface, five of which reduced the cytotoxicity to human skin keratinocytes under acute (24 h) and subacute (120 h) exposure. In parallel, we examined the photoluminescence spectra and lifetime of the surface-modified UCNP@PEI. To quantify their brightness, we developed original methodology to precisely measure the colloidal concentration to normalize the photoluminescence signal using a nondigesting mass spectrometry protocol. Our results, specified for the individual coatings, show that, despite decreasing the cytotoxicity, the external polymer coatings of UCNP@PEI quench the upconversion photoluminescence in biologically relevant aqueous environments. This trade-off between cytotoxicity and brightness for surface-coated UCNPs emphasizes the need for the combined assessment of the viability of normal cells exposed to the nanoparticles and the photophysical properties of postmodification UCNPs. We present an optimized methodology for rational surface design of UCNP@PEI in biologically relevant conditions, which is essential to facilitate the translation of such nanoparticles to the clinical applications.

© 2018 IEEE. Shown the efficiency of the LAS method in creating mechanically induced scaffolds with a multilayer biointerface.

© 2018 American Society for Microbiology. The tick-borne pathogen Borrelia burgdorferi is responsible for approximately 300,000 Lyme disease (LD) cases per year in the United States. Recent increases in the number of LD cases, in addition to the spread of the tick vector and a lack of a vaccine, highlight an urgent need for designing and developing an efficacious LD vaccine. Identification of protective epitopes that could be used to develop a second-generation (subunit) vaccine is therefore imperative. Despite the antigenicity of several lipoproteins and integral outer membrane proteins (OMPs) on the B. burgdorferi surface, the spirochetes successfully evade antibodies primarily due to the VlsE-mediated antigenic variation. VlsE is thought to sterically block antibody access to protective epitopes of B. burgdorferi. However, it is highly unlikely that VlsE shields the entire surface epitome. Thus, identification of subdominant epitope targets that induce protection when they are made dominant is necessary to generate an efficacious vaccine. Toward the identification, we repeatedly immunized immunocompetent mice with live-attenuated VlsE-deleted B. burgdorferi and then challenged the animals with the VlsE-expressing (host-adapted) wild type. Passive immunization and Western blotting data suggested that the protection of 50% of repeatedly immunized animals against the highly immune-evasive B. burgdorferi was antibody mediated. Comparison of serum antibody repertoires identified in protected and nonprotected animals permitted the identification of several putative epitopes significantly associated with the protection. Most linear putative epitopes were conserved between the main pathogenic Borrelia genospecies and found within known subdominant regions of OMPs. Currently, we are performing immunization studies to test whether the identified protection-associated epitopes are protective for mice.

© 2018 WILEY-VCH Verlag GmbH  &  Co. KGaA, Weinheim Nature has long inspired scientists and engineers. As one ubiquitous example of this, nature has provided all with several clever methods to absorb, repel, and/or allow both sunlight and water to pass through surfaces. Moth's eyes (highly antireflective) and lotus leaves (highly hydrophobic and self-cleaning) represent durable natural surfaces which exhibit nearly ideal physical and optical properties. Man-made transparent surfaces must also be able to cope with water and dust while reaching the maximum possible light transmission for solar collectors, displays, and other optical devices. To explore the link between these – particularly for transparent surfaces – this review puts the physics, progress, and limitations of synthetic materials in context with natural materials. This perspective reveals that there is still much more to learn (and implement) if it is hoped to match the multifunctionality and resilience of natural materials.

© 2018 IOP Publishing Ltd. This study was aimed to design and characterise hybrid tissue-engineered constructs composed of osteoinducing polylactide-based scaffolds with multi-layered cellular biointerface for bone tissue reconstruction. Three-dimensional scaffolds with improved hydrophilic and osteoinducing properties were produced using the surface-selective laser sintering (SSLS) method. The designed scaffold pattern had dimensions of 8 ×8 ×2.5 mm and ladder-like pores (∼700 μm in width). Hyaluronic acid-coated polylactide microparticles (∼100 μm in diameter) were used as building blocks and water was used as the photosensitizer for SSLS followed by photocross-linking with Irgacure 2959 photoinitiator. Resulting scaffolds provided successful adhesion and expansion of human bone marrow mesenchymal stromal cells from a single-cell suspension. Induced calcium deposition by the cells associated with osteogenic differentiation was detected in 7-21 days of culturing in basal medium. The values were up to 60% higher on scaffolds produced at a higher prototyping speed under the experimental conditions. Innovative approach to graft the scaffolds with multi-layered cell sheets was proposed aiming to facilitate host tissue-implant integration. The sheets of murine MS-5 stromal cell line exhibited contiguous morphology and high viability in a modelled construct. Thus, the SSLS method proved to be effective in designing osteoinducing scaffolds suitable for the delivery of cell sheets.

© 2018 National Academy of Sciences. All rights reserved. Hemispheric asymmetry is a cardinal feature of human brain organization. Altered brain asymmetry has also been linked to some cognitive and neuropsychiatric disorders. Here, the ENIGMA (Enhancing NeuroImaging Genetics through Meta-Analysis) Consortium presents the largest-ever analysis of cerebral cortical asymmetry and its variability across individuals. Cortical thickness and surface area were assessed in MRI scans of 17,141 healthy individuals from 99 datasets worldwide. Results revealed widespread asymmetries at both hemispheric and regional levels, with a generally thicker cortex but smaller surface area in the left hemisphere relative to the right. Regionally, asymmetries of cortical thickness and/or surface area were found in the inferior frontal gyrus, transverse temporal gyrus, parahippocampal gyrus, and entorhinal cortex. These regions are involved in lateralized functions, including language and visuospatial processing. In addition to population-level asymmetries, variability in brain asymmetry was related to sex, age, and intracranial volume. Interestingly, we did not find significant associations between asymmetries and handedness. Finally, with two independent pedigree datasets (n = 1,443 and 1,113, respectively), we found several asymmetries showing significant, replicable heritability. The structural asymmetries identified and their variabilities and heritability provide a reference resource for future studies on the genetic basis of brain asymmetry and altered laterality in cognitive, neurological, and psychiatric disorders.

© 2018 Walter de Gruyter GmbH, Berlin/Boston 2018. The paper proposes a stable time-splitting method for the numerical simulation of free-surface viscous flows. The key features of the method are a semi-Lagrangian scheme for the level-set function transport improved with MacCormack predictor-corrector step with limiting strategy and an adaptive volume-correction procedure. The spatial discretization is done by a hybrid finite volume/finite difference method on dynamically adaptive hexahedral meshes. Numerical verification is done by comparing full-scale 3D numerical simulations of the sloshing tank and the coastal wave run-up with other numerical and experimental results known from the literature.

© 2018 Stolichnaya Izdatelskaya Kompaniya. The metabolic syndrome is a highly prevalent condition associated with increased cardiovascular risk in the population. Microvasculature is the terminal part of the cardiovascular system which primarily reacts to the increased secretion of the pro inflammatory adipokines typical for the metabolic syndrome. Microcirculation and blood cell abnormalities are the leading mechanisms of cardiovascular events development in this condition. Prevalence of microcirculation abnormalities and red blood cell dysfunction in metabolic syndrome and their role in the increased blood viscosity and cardiovascular events development are covered by the paper. The microcirculation abnormalities with a special focus on red blood cell dysfunction (impaired aggregation, stiffness) seen in metabolic syndrome and associated conditions are discussed in detail. The impact of abnormal red blood cell deformability (secondary to cholesterol accumulation in the cellular membranes) on the hemorheological abnormalities is revealed. Abnormal red blood cell surface charge due to proinflammatory changes associated with insulin resistance in diabetes mellitus is highlighted. These abnormalities lead to increased red blood cell aggregation and plasma viscosity that are the essential components of cardiovascular events pathogenesis. Their timely diagnosis is crucial for effective cardiovascular prevention.

© 2018 Media Sfera. All rights reserved. Purpose. To study the effects of long-term instillation of 0.18% sodium hyaluronate artificial tears VISMED multi on ocular surface in glaucomatous patients with long-term instillation of preserved anti-glaucoma drops. Material and methods. The study included 79 patients (40 female and 39 male; 79 eyes in total) with primary open-angle glaucoma (POAG) divided into 3 groups according to disease stage: mild or early (stage I) glaucoma - 15 patients (15 eyes), moderate (stage II) glaucoma - 30 patients (30 eyes), advanced or severe (stage III) glaucoma - 34 patients (34 eyes). Conjunctival and corneal changes were assessed with Norn's test, Schirmer I test and corneal fluorescein staining test. All patients completed Ocular Surface Disease Index (OSDI) questionnaire. Corneal compensated intraocular pressure (IOPcc) was measured using Ocular Response Analyzer (ORA) (Reichert Optics Inc., USA). In addition to hypotensive therapy, all patients received instillations of 0.18% sodium hyaluronate (VISMED multi) three times every day. After 14 days, all examinations were repeated. Results. The condition of eye surface in patients with moderate and advanced (stage II and III) glaucoma depends on the degree of IOPcc compensation. As glaucoma increases in severity, the pathological changes in the ocular surface progress. Instillations of 0.18% sodium hyaluronate solution lead to significant improvement of the test results in all groups, and in early glaucoma patients it restores all objective indicators to normal values. Conclusion. Treatment with 0.18% sodium hyaluronate solution (VISMED multi) leads to statistically significant (p<0.05) improvement of ocular surface condition in glaucoma patients with long-term instillation of preserved antiglaucoma eye drops.

© 2018 Society for Industrial and Applied Mathematics. We consider a vector-Laplace problem posed on a two-dimensional surface embedded in a three-dimensional domain, which results from the modeling of surface fluids based on exterior Cartesian differential operators. The main topic of this paper is the development and analysis of a finite element method for the discretization of this surface partial differential equation. We apply the trace finite element technique, in which finite element spaces on a background shape-regular tetrahedral mesh that is surface independent are used for discretization. In order to satisfy the constraint that the solution vector field is tangential to the surface we introduce a Lagrange multiplier. We show well-posedness of the resulting saddle point formulation. A discrete variant of this formulation is introduced which contains suitable stabilization terms and is based on trace finite element spaces. For this method we derive optimal discretization error bounds. Furthermore algebraic properties of the resulting discrete saddle point problem are studied. In particular an optimal Schur complement preconditioner is proposed. Results of a numerical experiment are included.