On the Cartan Model of the Canonical Vector Bundles over Grassmannians

We give a representation of canonical vector bundles over Grassmannian manifolds as non-compact affine symmetric spaces as well as their Cartan model in the group of the Euclidean motions.Comment: 6 page

Giant magnetoresistance in semiconductor / granular film heterostructures with cobalt nanoparticles

We have studied the electron transport in SiO${}_2$(Co)/GaAs and SiO${}_2$(Co)/Si heterostructures, where the SiO${}_2$(Co) structure is the granular SiO${}_2$ film with Co nanoparticles. In SiO${}_2$(Co)/GaAs heterostructures giant magnetoresistance effect is observed. The effect has positive values, is expressed, when electrons are injected from the granular film into the GaAs semiconductor, and has the temperature-peak type character. The temperature location of the effect depends on the Co concentration and can be shifted by the applied electrical field. For the SiO${}_2$(Co)/GaAs heterostructure with 71 at.% Co the magnetoresistance reaches 1000 ($10^5$ %) at room temperature. On the contrary, for SiO${}_2$(Co)/Si heterostructures magnetoresistance values are very small (4%) and for SiO${}_2$(Co) films the magnetoresistance has an opposite value. High values of the magnetoresistance effect in SiO${}_2$(Co)/GaAs heterostructures have been explained by magnetic-field-controlled process of impact ionization in the vicinity of the spin-dependent potential barrier formed in the semiconductor near the interface. Kinetic energy of electrons, which pass through the barrier and trigger the avalanche process, is reduced by the applied magnetic field. This electron energy suppression postpones the onset of the impact ionization to higher electric fields and results in the giant magnetoresistance. The spin-dependent potential barrier is due to the exchange interaction between electrons in the accumulation electron layer in the semiconductor and $d$-electrons of Co.Comment: 25 pages, 16 figure

Semi-analytical hybrid approach for modelling wave motion excited by a piezoelectric transducer in a laminate with multiple cracks

A semi-analytical hybrid approach is presented here to simulate the dynamic behaviour of a multi-layered elastic waveguide with a system of delaminations and a piezoelectric transducer mounted on the surface of the waveguide. The proposed hybrid approach combines the advantages of the frequency domain spectral element method, which is applied to discretize a complex-shaped piezoelectric structure, and the boundary integral equation method employed to simulate wave propagation in multi-layered waveguide with multiple delaminations. The proposed method is applicable to the multi-parameter analysis of the phenomena related to elastic wave scattering and excitation. The advantages of the presented extended semi-analytical hybrid approach method along with the results of the parametric analysis of wave propagation in the considered structures are discussed

Synthesis and Characterization of Electro-Explosive Magnetic Nanoparticles for Biomedical Applications

Nowadays there are new magnetic nanostructures based on bioactive metals with low toxicity and high efficiency for a wide range of biomedical applications including drugs delivery, antimicrobial drugs design, cells' separation and contrasting. For such applications it is necessary to develop highly magnetic particles with less than100 nm in size. In the present study magnetic nanoparticles Fe, Fe[3]O[4] and bimetallic Cu/Fe with the average size of 60- 90 nm have been synthesized by electrical explosion of wire in an oxygen or argon atmosphere. The produced nanoparticles have been characterized with transmission electron microscopy, X-ray phase analysis, and nitrogen thermal desorption. The synthesized particles have shown antibacterial activity to gram-positive (S. aureus, MRSA) and gramnegative (E. coli, P. aeruginosa) bacteria. According to the cytological data Fe, Fe[3]O[4]and Cu/Fe nanoparticles have effectively inhibited viability of cancer cell lines Neuro-2a and J774. The obtained nanoparticles are promising for new antimicrobial drugs and antitumor agents' developmen

Cellulose-containing waste recycling using fungi

Accumulation of plant waste is a serious environmental problem. Mushrooms with high cellulolytic activity can process it into valuable products that will be useful in solving various industries and agriculture problems. The enzymes of the cellulolytic complex include 1,4-β-D-glucan-4-glucanohydrolase, exo-1,4-β-glucosidase, cellobiohydrolase, β-glucosidase. 1,4-β-D-glucan-4-glucanohydrolases destroy β-1,4-glycosidic bonds within the chain of cellulose and lichenin polysaccharides. Exoglucanases destroy β-1,3- and β-1,4-glycosidic bonds at the end of the molecule. Cellobiohydrolases cleave β-1,4-glycosidic bonds to form cellobiose and glucose. β-glucosidase complete the process of destruction. Fungi with high cellulolytic activity include both representatives of the Ascomycota and Basidiomycota divisions. Ascomycete Chaetomium globosum produces endoglucanases of two families and 8 cellobiohydrolases. Myceliophthora thermophila also produces endoglucanases and cellobiohydrolases, the most abundant of which is Mt Cel7A. The fungus is a promising producer of thermostable enzymes. Trichoderma reesei has a long history of safe use as a source of highly active cellulolytic enzymes and other valuable metabolites. LPMOs of the cellulolytic fungus Thielavia terrestris are considered auxiliary enzymes, but can negatively affect the main enzymes of the complex. Irpex lacteus also produces LPMO and a complete cellulolytic enzyme complex. The cellulolytic activity of fungi and their ability to grow on cheap substrates can be used to bioconvert plant waste into valuable products. One of the ways to utilize them is to convert into compound feed with a high protein content through the use of starter cultures. The use of mushrooms will increase the content of protein and simple carbohydrates, enrich the feed with fats. Another method is to obtain cellulases, which are widely used in many industries. Thanks to the production of biodiesel and bioethanol from cellulose-containing raw materials it is possible to solve the problem of lack of fuel by replacing energy carriers from non-renewable energy sources with their environmentally friendly counterparts. They are less toxic than diesel and gasoline and are also made from renewable resources

Synthesis and Characterization of Electro-Explosive Magnetic Nanoparticles for Biomedical Applications

Nowadays there are new magnetic nanostructures based on bioactive metals with low toxicity and high efficiency for a wide range of biomedical applications including drugs delivery, antimicrobial drugs design, cells' separation and contrasting. For such applications it is necessary to develop highly magnetic particles with less than100 nm in size. In the present study magnetic nanoparticles Fe, Fe[3]O[4] and bimetallic Cu/Fe with the average size of 60- 90 nm have been synthesized by electrical explosion of wire in an oxygen or argon atmosphere. The produced nanoparticles have been characterized with transmission electron microscopy, X-ray phase analysis, and nitrogen thermal desorption. The synthesized particles have shown antibacterial activity to gram-positive (S. aureus, MRSA) and gramnegative (E. coli, P. aeruginosa) bacteria. According to the cytological data Fe, Fe[3]O[4]and Cu/Fe nanoparticles have effectively inhibited viability of cancer cell lines Neuro-2a and J774. The obtained nanoparticles are promising for new antimicrobial drugs and antitumor agents' developmen

The Maslov index and nondegenerate singularities of integrable systems

We consider integrable Hamiltonian systems in R^{2n} with integrals of motion F = (F_1,...,F_n) in involution. Nondegenerate singularities are critical points of F where rank dF = n-1 and which have definite linear stability. The set of nondegenerate singularities is a codimension-two symplectic submanifold invariant under the flow. We show that the Maslov index of a closed curve is a sum of contributions +/- 2 from the nondegenerate singularities it is encloses, the sign depending on the local orientation and stability at the singularities. For one-freedom systems this corresponds to the well-known formula for the Poincar\'e index of a closed curve as the oriented difference between the number of elliptic and hyperbolic fixed points enclosed. We also obtain a formula for the Liapunov exponent of invariant (n-1)-dimensional tori in the nondegenerate singular set. Examples include rotationally symmetric n-freedom Hamiltonians, while an application to the periodic Toda chain is described in a companion paper.Comment: 27 pages, 1 figure; published versio

Three natural mechanical systems on Stiefel varieties

We consider integrable generalizations of the spherical pendulum system to the Stiefel variety $V(n,r)=SO(n)/SO(n-r)$ for a certain metric. For the case of V(n,2) an alternative integrable model of the pendulum is presented. We also describe a system on the Stiefel variety with a four-degree potential. The latter has invariant relations on $T^*V(n,r)$ which provide the complete integrability of the flow reduced on the oriented Grassmannian variety $G^+(n,r)=SO(n)/SO(r)\times SO(n-r)$.Comment: 14 page

Chemical behaviour of Al/Cu nanoparticles in water

Bimetallic Al/Cu nanoparticles with Al/Cu composition 10:90, 20:80, 40:60 were produced by method of simultaneous electrical explosion of metal pairs in the argon atmosphere. Nanopowders containing 20% and 40% (mass) of aluminum interacted with water at 40–70 °C and formed composite particles that were porous structures of nanopetal pseudoboehmite with nanosized copper-containing inclusions inside. Aluminum in nanopowder with Al/Cu composition 10:90 did not react with water, as far as it is in the phase of intermetallic compounds СuAl2 and Сu4Al9. Nanocomposite produced can be used as an active component of antibacterial agents