[Ni(bpy)(mal)(H2O)3]·H2O and [Ni(4,4′-dmbpy)(mal)(H2O)3]·1.5H2O: syntheses,crystal structures,magnetic properties,and computational study of stacking interactions

[Ni(bpy)(mal)(H₂O)₃]·H₂O and [Ni(4,4′-dmbpy)(mal)(H₂O)₃]·1.5H₂O (mal = maleato; bpy = 2,2′-bipyridine; 4,4′-dmbpy = 4,4′-dimethyl-2,2′-bipyridine) exhibit molecular crystal structures. The Ni(II) central ions in both complexes are six-coordinate by one chelate bonded L–L ligand, three aqua ligands, and one position is occupied by a maleato oxygen donor atom. Hydrogen bonded ribbon-like supramolecular structural motifs are present in both studied complexes; these are linked by weaker C–H?O hydrogen bonds in [Ni(bpy)(mal)(H₂O)₃]·H₂O, whereas in [Ni(4,4′-dmbpy)(mal)(H₂O)₃]·1,5H₂O the hydrogen bonded ribbons are linked by O?H-O-H?O hydrogen bonds with the participation of the additional water solvate molecule positioned on the twofold axis. In both structures, π–π stacking interactions with different patterns in respective structures were found. The role of dispersion energy and many-body effects in the stabilization of bpy and 4,4′-dmbpy stacking interactions were investigated using methods of computational chemistry. Those confirm the dispersion-dominated stabilization of the 4,4′-dmbpy supramolecular chain-like structure, with only marginal impact of cooperativity effects. Thermal decompositions of both complexes start with dehydration. Magnetic susceptibility studies performed from 2 to 300 K revealed a dominant effect of the zero-field splitting of the Ni(II) ion, governing the low-temperature magnetic properties of both compounds.     

Synthesis,crystal structures and antimicrobial activity of azido and isocyanato Zn(II) complexes with the condensation product of 2-quinolinecarboxaldehyde and Girard’s T reagent

Two Zn(II) complexes with the condensation product of 2-quinolinecarboxaldehyde and trimethylammonium acetohydrazide chloride (Girard’s T reagent) (HLCl) and monodentate pseudohalides (azide and cyanate) have been synthesized and characterized by elemental analysis, IR and NMR spectroscopy, and single-crystal X-ray diffraction. In both complexes, the coordination surroundings of the Zn(II) ions consist of a deprotonated hydrazone ligand coordinated through an NNO set of donor atoms and two monodentate pseudohalides (N₃^– or NCO^–) at the remaining coordination sites. The Zn(II) complexes showed low to moderate activity against laboratory control strains of pathogenic bacteria and fungi.     

Strain in strain-free benzenoid hydrocarbons: the case of fibonacenes

In a recent paper (Radenkovic et al. Chem Phys Lett 625:69–72, 2015), a new method for quantifying the strain energy in benzenoid molecules, resulting from the repulsion between the bay H-atoms was elaborated. In this work, we present a modified procedure, capable of estimating the strain energy in a single-step calculation. Strain energies were obtained at the B3LYP/def2-TZVP level of density functional theory. It was found that in benzenoid molecules with a single bay region, the strain energy is essentially constant, equal to around 7.3 kJ/mol. On the other hand, in the case of the first four members of the fibonacene series, the strain energy is found to be linearly proportional to the number of bay regions.     

Competing processes in the photochemistry of picolines and their <Emphasis Type="Italic">N</Emphasis>-methyl salts: photoinduced charge transfer,phototransposition and photohydration

Photochemical reactivity of a series of picolines and their N-methylated salts has been investigated by preparative irradiations and UV–vis spectroscopy. Understanding competing photochemical processes and knowledge of their relative efficiencies is important in the application of pyridines as photocages or in the synthesis of complex polycycles. Contrary to previous reports for the gas phase, picolines are not reactive in the phototransposition, presumably due to protonation of the pyridine nitrogen in the excited state. Deuterium exchange was observed upon irradiation in CD₃CN–D₂O, but it was rationalized by photoionization and radical formation. On the other hand, N-methylated picoline salts are not protonated upon excitation. They undergo photohydration and phototransposition (Φ _R = 0.01–0.06). Upon irradiation of iodides, azabicyclic [3.1.0] hydration products were obtained. A difference in product distribution was observed between iodides and perchlorates, due to photoelimination of perchloric acid leading to the thermal aziridine ring opening. Moreover, excitation of iodide derivatives gives rise to change transfer transition forming iodide radicals that eventually give I₃ ^? with the quantum efficiency Φ _R = 0.015–0.02.     

Parenchyma cell wall structure in twining stem of <Emphasis Type="Italic">Dioscorea balcanica</Emphasis>

Anatomical adaptation of liana plants includes structural changes in cell walls of different tissues: fibers, vessel elements and tracheids. However, the contribution of parenchyma cells to stem twining in liana plants is mostly unknown. The aim of this investigation is to determine changes in stem parenchyma cell walls that are correlated with the twinning process in liana plants. Parenchyma cell wall structure was studied on the stem cross sections of straight and twisted internodes of monocotyledonous liana Dioscorea balcanica, by different microscopy techniques: light microscopy, scanning electron microscopy, fluorescence detected linear dichroism microscopy and Fourier transform infrared microspectrometry. In addition, chemical analysis of the entire stem internodes was performed using photometric and chromatographic methods. Parenchyma cell walls of twisted D. balcanica internodes are characterized by: lower amounts of cellulose (obtained by FTIR microspectrometry) with different cellulose microfibril orientation (shown by Scanning electron microscopy), but no changes in “cellulose fibril order” (obtained by Differential polarization laser scanning microscopy); lower amounts of xyloglucan, higher amounts of xylan, higher amounts of lignin with modified organization—less condensed lignin (obtained by FTIR microspectrometry). At the same time, chemical analysis of the entire internodes did not show significant differences in lignin content and cell wall bound phenols related to stem twining, except for the presence of diferulate cross-links exclusively in twisted internodes. Our results indicate that adaptations to mechanical strain in D. balcanica stems involve modifications in parenchyma cell wall structure and chemistry, which provide decreased stiffness, higher strength and increased elasticity of twisted internodes.     

Oscillation theorems for fourth‐order delay differential equations with a negative middle term

This paper deals with the oscillation of the fourth‐order linear delay differential equation with a negative middle term under the assumption that all solutions of the auxiliary third‐order differential equation are nonoscillatory. Examples are included to illustrate the importance of results obtained.     

On Synge-type angle condition for <Emphasis Type="Italic">d</Emphasis>-simplices

The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in ? ^d that degenerate in some way.     

On the radius and the attachment number of tetravalent half-arc-transitive graphs

In this paper, we study the relationship between the radius $r$ and the attachment number $a$ of a tetravalent graph admitting a half-arc-transitive group of automorphisms. These two parameters were first introduced in Maru?i? (1998), where among other things it was proved that $a$ always divides $2r$. Intrigued by the empirical data from the census (Poto?nik et al., 2015) of all such graphs of order up to 1000 we pose the question of whether all examples for which $a$ does not divide $r$ are arc-transitive. We prove that the answer to this question is positive in the case when $a$ is twice an odd number. In addition, we completely characterise the tetravalent graphs admitting a half-arc-transitive group with $r=3$ and $a=2$, and prove that they arise as non-sectional split $2$-fold covers of line graphs of $2$-arc-transitive cubic graphs.     

Adaptive stochastic approximation algorithm

In this paper, stochastic approximation (SA) algorithm with a new adaptive step size scheme is proposed. New adaptive step size scheme uses a fixed number of previous noisy function values to adjust steps at every iteration. The algorithm is formulated for a general descent direction and almost sure convergence is established. The case when negative gradient is chosen as a search direction is also considered. The algorithm is tested on a set of standard test problems. Numerical results show good performance and verify efficiency of the algorithm compared to some of existing algorithms with adaptive step sizes.     

Cliques in dense inhomogeneous random graphs

The theory of dense graph limits comes with a natural sampling process which yields an inhomogeneous variant of the Erd?s–Rényi random graph. Here we study the clique number of these random graphs. We establish the concentration of the clique number of for each fixed n , and give examples of graphons for which exhibits wild long‐term behavior. Our main result is an asymptotic formula which gives the almost sure clique number of these random graphs. We obtain a similar result for the bipartite version of the problem. We also make an observation that might be of independent interest: Every graphon avoiding a fixed graph is countably‐partite. © The Authors Random Structures & Algorithms Published byWiley Periodicals, Inc. Random Struct. Alg., 2016 © 2017 The Authors Random Structures & Algorithms Published by Wiley Periodicals, Inc. Random Struct. Alg., 51, 275–314, 2017