Mechanisms of Methylenecyclobutane Hydrogenation over Supported Metal Catalysts Studied by Parahydrogen-Induced Polarization Technique

In this work the mechanism of methylenecyclobutane hydrogenation over titania-supported Rh, Pt and Pd catalysts was investigated using parahydrogen-induced polarization (PHIP) technique. It was found that methylenecyclobutane hydrogenation leads to formation of a mixture of reaction products including cyclic (1-methylcyclobutene, methylcyclobutane), linear (1-pentene, cis-2-pentene, trans-2-pentene, pentane) and branched (isoprene, 2-methyl-1-butene, 2-methyl-2-butene, isopentane) compounds. Generally, at lower temperatures (150–350 °C) the major reaction product was methylcyclobutane while higher temperature of 450 °C favors the formation of branched products isoprene, 2-methyl-1-butene and 2-methyl-2-butene. PHIP effects were detected for all reaction products except methylenecyclobutane isomers 1-methylcyclobutene and isoprene implying that the corresponding compounds can incorporate two atoms from the same parahydrogen molecule in a pairwise manner in the course of the reaction in particular positions. The mechanisms were proposed for the formation of these products based on PHIP results.     

Roughness-induced effects on the thermomicropolar fluid flow through a thin domain

In this paper, we study the asymptotic behavior of the thermomicropolar fluid flow through a thin channel with rough boundary. The flow is governed by the prescribed pressure drop between the channel's ends and the heat exchange through the rough wall is allowed. Depending on the limit of the ratio between channel's thickness and the wavelength of the roughness, we rigorously derive different asymptotic models clearly showing the roughness-induced effects on the average velocity and microrotation. To accomplish that, we employ the adaptation of the unfolding method to a thin-domain setting.     

AF-algebras and topology of mapping tori

The paper studies applications of C*-algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2, 3 and 4. In conclusion, we consider two numerical examples illustrating our main results.     

Transition absorption as a mechanism of surface photoelectron emission from metals

Transition absorption of a photon by an electron passing through a boundary between two media with different permittivities is described both classically and quantum mechanically. Transition absorption is shown to make a substantial contribution to photoelectron emission at a metal/semicon‐ductor interface in nanoplasmonic systems, and is put forth as a possible microscopic mechanism of the surface photoelectric effect in photodetectors and solar cells containing plasmonic nanoparticles.

     

Tiling simply connected regions with rectangles

In 1995, Beauquier, Nivat, Rémila, and Robson showed that tiling of general regions with two bars is NP-complete, except for a few trivial special cases. In a different direction, in 2005, Rémila showed that for simply connected regions by two rectangles, the tileability can be solved in quadratic time (in the area). We prove that there is a finite set of at most 10⁶ rectangles for which the tileability problem of simply connected regions is NP-complete, closing the gap between positive and negative results in the field. We also prove that counting such rectangular tilings is #P-complete, a first result of this kind.     

Effective elastic shear stiffness of a periodic fibrous composite with non-uniform imperfect contact between the matrix and the fibers

In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method, for oblique two-phase fibrous periodic composites with non-uniform imperfect contact conditions at the interface. This work is an extension of previous reported results, where only the perfect contact for elastic or piezoelectric composites under imperfect spring model was considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the non uniform imperfection on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.     

Updated projections in continuation methods

This paper is concerned with the approximation of solutions of nonlinear operator equations depending on a parameter For solving the augmented systems arising in predictor-corrector continuation methods, the use of iterative schemes based on updating projection techniques is discussed.     

MR Study of Water Distribution in a Beech (Fagus sylvatica) Branch Using Relaxometry Methods

Wood is a widely used material because it is environmentally sustainable, renewable and relatively inexpensive. Due to the hygroscopic nature of wood, its physical and mechanical properties as well as the susceptibility to fungal decay are strongly influenced by its moisture content, constantly changing in the course of everyday use. Therefore, the understanding of the water state (free or bound) and its distribution at different moisture contents is of great importance. In this study, changes of the water state and its distribution in a beech sample while drying from the green (fresh cut) to the absolutely dry state were monitored by 1D and 2D ¹H NMR relaxometry as well as by spatial mapping of the relaxation times T₁ and T₂. The relaxometry results are consistent with the model of homogeneously emptying pores in the bioporous system with connected pores. This was also confirmed by the relaxation time mapping results which revealed the moisture transport in the course of drying from an axially oriented early- and latewood system to radial rays through which it evaporates from the branch. The results of this study confirmed that MRI is an efficient tool to study the pathways of water transport in wood in the course of drying and is capable of determining the state of water and its distribution in wood.     

The combinatorial derivation and its inverse mapping

Let G be a group and P _G be the Boolean algebra of all subsets of G. A mapping Δ: P _G → P _G defined by Δ(A) = {g ∈ G: gA ∩ A is infinite} is called the combinatorial derivation. The mapping Δ can be considered as an analogue of the topological derivation d: P _X → P _X , A ? A ^d , where X is a topological space and A ^d is the set of all limit points of A. We study the behaviour of subsets of G under action of Δ and its inverse mapping ?. For example, we show that if G is infinite and I is an ideal in P _G such that Δ(A) ∈ I and ?(A) ? I for each A ∈ I then I = P _G .