Crystal,electronic structure and hydrogenation properties of the Mg5.57Ni16Ge7.43 cluster phase with a new type of polyhedron

The ternary germanide Mg_5.57Ni₁₆Ge_7.43 (cubic, space group Fmm, cF116) belongs to the structural family based on the Th₆Mn₂₃-type. The Ge1 and Ge2 atoms fully occupy the 4a (mm symmetry) and 24d (m.mm) sites, respectively. The Ni1 and Ni2 atoms both fully occupy two 32f sites (.3m symmetry). The Mg/Ge statistical mixture occupies the 24e site with 4m.m symmetry. The structure of the title compound contains a three-core-shell cluster. At (0,0,0), there is a Ge1 atom which is surrounded by eight Ni atoms at the vertices of a cube and consequently six Mg atoms at the vertices of an octahedron. These surrounded eight Ni and six Mg atoms form a [Ge1Ni₈(Mg/Ge)₆] rhombic dodecahedron with a coordination number of 14. The [GeNi₈(Mg/Ge)₆] rhombic dodecahedron is encapsulated within the [Ni₂₄] rhombicuboctahedron, which is again encapsulated within an [Ni₃₂(Mg/Ge)₂₄] pentacontatetrahedron; thus, the three-core-shell cluster [GeNi₈(Mg/Ge)₆@Ni₂₄@Ni₃₂(Mg/Ge)₂₄] results. The pentacontatetrahedron is a new representative of Pavlyuk's polyhedra group based on pentagonal, tetragonal and trigonal faces. The dominance of the metallic type of bonding between atoms in the Mg_5.57Ni₁₆Ge_7.43 structure is confirmed by the results of the electronic structure calculations. The hydrogen sorption capacity of this intermetallic at 570 K reaches 0.70 wt% H₂.     

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.     

Generalized implicit Euler method for hyperbolic functional differential equations

Nonlinear hyperbolic functional differential equations with initial boundary conditions are considered. Theorems on the convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability of the difference functional problem is based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given functions are used. Numerical examples are given (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The constrained degree and fixed-point index theory for set-valued maps

In the first part of the paper we give a construction of a topological degree theory for set-valued tangent vector fields with convex and nonconvex values defined on nonsmooth closed subsets of a Banach space. The obtained homotopy invariant is an extension of the classical degree for vector fields on manifolds. In the second part we propose a fixed-point index for inward maps on arbitrary closed convex sets.     

The Conley index, cup-length and bifurcation

A module structure of the cohomology Conley index is used to define a relative cup-length. This invariant is applied then to prove a multiplicity theorem for periodic solutions to Hamiltonian systems.     

Dynamics of a Mobile Crane and Optimisation of the Slewing Motion of Its Upper Structure

In the paper the 3-D model of a telescopic mobile crane is presented. In the model flexibilities and damping have been taken into account and also the number of degrees of freedom can be chosen according to the complexity of an approach. The algorithm of optimisation of drive functions for the slewing upper structure is given. The main goal of optimisation was to ensure load positioning at the end point of a work cycle in the case when oscillations are minimal. In order to achieve appropriate numerical effectiveness, the optimisation problem was solved for the simple, fully rigid model of a mobile crane. The method of compensating neglected flexibilities of the base structure of the crane and inner disturbances connected with the feedback control system via digital PID controller is presented.     

Influence of velocity distribution in the multiphase flow on the building of aerobic granules in a Sequencing Batch Reactor (SBR)

In present contribution a study is presented, where fluid dynamic measurements are used to observe multiphase flow pattern in a bioreactor. It can be shown that hydrodynamic effects have a major influence on the formation, shape and size of Granular Activated Sludge (GAS) in a Sequencing Batch Reactor (SBR) under aerobic condition. In order to analyse multiphase flow pattern (water, air, granules) in the bioreactor in-situ techniques with optical measurements are applied. LASER IIIB and video lamp are used as a light source. Due to a transient spatial velocity distribution in the bioreactor our experiments are carried out in different levels of SBR. Tracer particles are employed to visualise the fluid flow pattern. Velocity field of the liquid phase in the bioreactor is determined by use of PIV method (Particle Image Velocimetry). PTV (Particle Tracking Velocimetry) is implemented to observe velocity field of individual granules (solid phase). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Infinite-dimensional homology and multibump solutions

We start by introducing a Čech homology with compact supports which we then use in order to construct an infinite-dimensional homology theory. Next we show that under appropriate conditions on the nonlinearity there exists a ground state solution for a semilinear Schr?dinger equation with strongly indefinite linear part. To this solution there corresponds a nontrivial critical group, defined in terms of the infinite-dimensional homology mentioned above. Finally, we employ this fact in order to construct solutions of multibump type. Although our main purpose is to survey certain homological methods in critical point theory, we also include some new results. Dedicated to Felix Browder on the occasion of his 80th birthday     

Graph algorithms for DNA sequencing – origins,current models and the future

With the ubiquitous presence of next-generation sequencing in modern biological, genetic, pharmaceutical and medical research, not everyone pays attention to the underlying computational methods. Even fewer researchers know what were the origins of the current models for DNA assembly. We present original graph models used in DNA sequencing by hybridization, discuss their properties and connections between them. We also explain how these graph models evolved to adapt to the characteristics of next-generation sequencing. Moreover, we present a practical comparison of state-of-the-art DNA de novo assembly tools representing these transformed models, i.e. overlap and decomposition-based graphs. Even though the competition is tough, some assemblers perform better and certainly large differences may be observed in hardware resources utilization. Finally, we outline the most important trends in the sequencing field, and try to predict their impact on the computational models in the future.     

Limit theorems for random walks

We consider a random walk $S_{\tau }$ which is obtained from the simple random walk $S$ by a discrete time version of Bochner’s subordination. We prove that under certain conditions on the subordinator $\tau$ appropriately scaled random walk $S_{\tau }$ converges in the Skorohod space to the symmetric $\alpha$-stable process $B^{\alpha }$. We also prove asymptotic formula for the transition function of $S_{\tau }$ similar to the Pólya’s asymptotic formula for $B^{\alpha }$.