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 .     

Dinuclear copper(II) perchlorate complexes with 6-(benzylamino)purine derivatives: Synthesis,X-ray structure,magnetism and antiradical activity

The reactions of Cu(ClO₄)₂·6H₂O with 6-(benzylamino)purine derivatives in a stoichiometric 1:2 metal-to-ligand ratio led to the formation of penta-coordinated dinuclear complexes of the formula [Cu₂(μ-L^1–8)₄(ClO₄)₂](ClO₄)₂·nsolv, where L¹ = 6-(2-fluorobenzylamino)purine (complex 1), L² = 6-(3-fluorobenzylamino)purine (2), L³ = 6-(4-fluorobenzylamino)purine (3), L⁴ = 6-(2-chlorobenzylamino)purine (4), L⁵ = 6-(3-chlorobenzylamino)purine (5), L⁶ = 6-(4-chlorobenzylamino)purine (6), L⁷ = 6-(3-methoxybenzylamino)purine (7) and L⁸ = 6-(4-methoxybenzylamino)purine (8); n = 0–4 and solv = H₂O, EtOH or MeOH. All the complexes have been fully characterized by elemental analysis, FTIR, UV–Vis and EPR spectroscopy, and by magnetic and conductivity measurements. Variable temperature (80–300 K) magnetic susceptibility data of 1–8 showed the presence of a strong antiferromagnetic exchange interaction between two Cu(II) (S = 1/2) atoms with J ranging from −150.0(1) to −160.3(2) cm⁻¹. The compound 6·4EtOH·H₂O was structurally characterized by single crystal X-ray analysis. The Cu?Cu separation has been found to be 2.9092(8) Å. The antiradical activity of the prepared compounds was tested by in vitro SOD-mimic assay with IC₅₀ in the range 8.67–41.45 μM. The results of an in vivo antidiabetic activity assay were inconclusive and the glycaemia in pre-treated animals did not differ significantly from the positive control.     

Use of a Simple Additive Scheme to Predict the GC Retention Indices of Aromatic Compounds with Different Structures

A simple algorithm is proposed for prediction of linear retention indices, RI, of organic compounds with different structures. The algorithm is based on the hypothesis that any structural moiety of a molecule contributes to gas chromatographic retention to a different extent, depending on its molecular environment. For a given moiety the mean structural increment (MSI) is calculated from the difference between the retention indices of two molecules, one containing it and one not, in different compound families. The mean of these values is the MSI for the corresponding moiety. The correlation between predicted and experimental values affords r ² = 0.992 and the mean relative error is 1.65% for n = 92 compounds.     

Factorial Design in Optimization of Chromatographic Separation of Ramipril and Its Impurities

In this paper optimization of chromatographic retention of ramipril and its five impurities employing factorial design is presented. On the basis of preliminary experiments three factors were chosen as inputs (acetonitrile content, pH of the mobile phase and buffer concentration) and retention factor as output. As optimal full factorial design 2³ was chosen, factors were examined at two different levels “low” and “high”. Three replications at zero level were added in order to check linearity and complete statistical tests. Relationship between inputs and output is presented in form of second order interaction model. Adequacy of model was explained using analysis of variance. After analysis of results optimal chromatographic conditions were set. Separations were conducted on a C₁₈ column with a mixture of acetonitrile and water phase (TEA in potassium dihydrogen phosphate) in ratio 23:77 v/v. Finally, the LC method was validated and applied for quality control analysis of commercially available tablets. The proposed method is simpler and faster as compared to existing official methods and therefore more adequate for routine control of ramipril during shelf life. Also a general approach which includes factorial design in method optimization offers a possibility for predicting and following the chromatographic behavior of such complex mixtures.     

Magnetic resonance imaging methods for in situ studies in heterogeneous catalysis

Magnetic resonance imaging (MRI) is a very powerful instrument used extensively in modern medical diagnostics because of its ability to look inside a body in a non-invasive and non-destructive way. Furthermore, MRI is more than just a single tool for extracting structural information. It is more of a sophisticated and versatile toolkit able to provide all sorts of useful information about the internal properties of an object under study and various processes within it, including heat and mass transport, composition and chemical transformations, in a spatially resolved mode. While a living body is different from a catalyst body or a reactor, the in situ and Operando studies in catalysis can clearly benefit from the use of this non-destructive toolkit as a powerful complement to other available spectroscopic tools. This tutorial review gives an introduction to the field and describes the examples of the applications of MRI to the studies of the preparation, deactivation and regeneration of solid catalysts and to the spectroscopy, thermometry and imaging studies of heterogeneous catalysts and model catalytic reactors performed during actual catalytic processes.     

Silica hydrogel formation and aging monitored by pyrene-based fluorescence probes

Fluorescent probes pyrene (Py), di(1-pyrenylmethyl)ether (DiPyM) and newly synthesized 2,3-bis-[4-(1-pyrenemethoxy)methylphenyl]butane (DiPyS) were used to monitor the formation and aging of silica hydrogel prepared from poly(glyceryl silicate) (PGS) sol. The fluorescence emission spectra of these probes are sensitive to their environment and this feature is utilized for monitoring the evolution of silica hydrogels prepared in this work. The polarity of hydrogel matrix during sol–gel transition assessed by all three pyrene probes decreases in the first stage of hydrogel formation, for about 2 h, followed by a gradual increase in polarity and reaching the constant level after 24 h for at least 2 weeks. The process of crosslinking was assessed by DiPyM and DiPyS. These fluorescent probes possess two pyrene structures, which ability to form a dynamic intramolecular excimer can be used to monitor the degree of hydrogel crosslinking with time. These data support the polarity measurements that the hydrogel network is predominatly formed within the first 2 h, stabilized within the 24 h, and that there is a minor increase in the network density for about 10 days until reaching the constant level. In addition, utilizing the second-order diffraction of scattered excitation light may also be used to obtain an adequate information about the silica hydrogel evolution. In summary, this paper demonstrates that pyrene-type fluorescent probes represent simple and precise tool for characterization of formation and aging of the silica hydrogels.