On a fixed point theorem in 2-Banach spaces and some of its applications

The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability results concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.     

Fixed-point theorem in classes of function with values in a dq-metric space

We prove a fixed point result for nonlinear operators, acting on some classes of functions with values in a dq-metric space, and show some applications of it. The result has been motivated by some issues arising in Ulam stability. We use a restricted form of a contraction condition.     

Boron doped carbon nanotubes via ceramic catalysts

A facile metal catalyst free route to synthesize boron doped (0.6%–1.0%) carbon nanotubes via ceramic nanowires in which the formation of the nanowires (probably serving as templates), the carbon nanotubes and their doping all occur unanimously in the reaction, is presented.

     

Principal Lyapunov Exponents and Principal Floquet Spaces of Positive Random Dynamical Systems. III. Parabolic Equations and Delay Systems

This is the third part in a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. The current part focuses on applications of general theory, developed in the authors’ paper Mierczyński and Shen (Trans Am Math Soc 365(10):5329–5365, 2013), to positive continuous-time random dynamical systems on infinite dimensional ordered Banach spaces arising from random parabolic equations and random delay systems. It is shown under some quite general assumptions that measurable linear skew-product semidynamical systems generated by random parabolic equations and by cooperative systems of linear delay differential equations admit measurable families of generalized principal Floquet subspaces, and generalized principal Lyapunov exponents.     

Bis-(bis-(1,3-diaminopropane)-copper(II) Tetracyanonickellate(II)) Tetrahydrate: Preparation, Characterization, and Crystal Structure of a Novel Molecular Tetracyanonickellate

Summary.  [Cu(tn)₂Ni(CN)₄]₂ċ4H₂O and Cu(tn)₂Ni(CN)₄ (tn = 1,3-diaminopropane) were prepared and characterized. The hydrate is unstable on air and readily dehydrates to Cu(tn)₂Ni(CN)₄. Crystal structure analysis of the hydrate at 150 K revealed a novel tetranuclear molecular structure of the tetracyanonickellate. The building elements are two [Cu(tn)₂]²⁺ cations (coordination numbers of Cu: 5 and 6, respectively), two [Ni(CN)₄)²⁻ anions, and crystal water. The two cations are linked by one tetracyanonickellate anion via bridging cyano groups placed in cis positions. The second anion is bound weakly (Cu-N = 2.82 ?) via one μ₂-bridging cyano ligand. The tetranuclear molecules and pairs of solvate water molecules are linked by strong hydrogen bonds, thus forming infinite planes which are linked in the third dimension by considerably weaker hydrogen bonds. Received May 9, 2000. Accepted (revised) August 21, 2000     

Ultrasound measurements of skin thickness after UV exposure: a feasibility study

High-frequency ultrasound images were used to measure the thickness of the dermis and epidermis of four human subjects. These measurements were performed before and after a single exposure to ultraviolet radiation (UV). Doses ranging from 0.5 to 3 minimal erythema doses (MED) were delivered to the skin of the back of four human subjects, and thickness measurements were made over a period of 16 days. We found: (1) exposures > or = 2 MED caused a 10-30% increase in the thickness of the dermis-epidermis layer; (2) the thickening response was not always in direct proportion to the UV dose; (3) maximum thickening response time was 48 h for the 2.8-3.0 MED exposure levels; (4) "diffusion" or spreading of the thickening response to neighboring areas occurred in some cases, as far as 4 cm from the exposed region (center-to-center), with changes ranging from 12% to 17%; (5) decreased thickness of the dermis-epidermis layer of up to 12% was observed for 3 out of 4 of the subjects.     

Rearrangement of N-(3-pyridyl)nitramine

Contrary to other N-(pyridyl)nitramines, the title compound cannot be rearranged to 3-amino-2-nitropyridine or other isomers. Hypothetical products of its transformation under influence of concentrated sulphuric acid, viz. 3-hydroxypyridine, 3,3′-azoxypyridine and 3,3′-azopyridine, were obtained from 3-nitro- and 3-aminopyridine in oxidation and reduction reactions. N-(3-Pyridyl)nitramine was prepared and rearranged in concentrated sulphuric acid. 3-Hydroxypyridine and 3,3′-azoxypyridine were isolated from the reaction mixture, other products were identified by the HPLC and GCMS methods. The results indicate that N-(3-pyridyl)hydroxylamine is an intermediate formed from N-(3-pyridyl)nitramine under the influence of concentrated sulphuric acid. The reaction path, leading to the final products, is discussed in context of the mechanism of nitramine rearrangement.     

Development and evaluation of needle trap device geometry and packing methods for automated and manual analysis

For air/headspace analysis, needle trap devices (NTDs) are applicable for sampling a wide range of volatiles such as benzene, alkanes, and semi-volatile particulate bound compounds such as pyrene. This paper describes a new NTD that is simpler to produce and improves performance relative to previous NTD designs. A NTD utilizing a side-hole needle used a modified tip, which removed the need to use epoxy glue to hold sorbent particles inside the NTD. This design also improved the seal between the NTD and narrow neck liner of the GC injector; therefore, improving the desorption efficiency. A new packing method has been developed and evaluated using solvent to pack the device, and is compared to NTDs prepared using the previous vacuum aspiration method. The slurry packing method reduced preparation time and improved reproducibility between NTDs. To evaluate the NTDs, automated headspace extraction was completed using benzene, toluene, ethylbenzene, p-xylene (BTEX), anthracene, and pyrene (PAH). NTD geometries evaluated include: blunt tip with side-hole needle, tapered tip with side-hole needle, slider tip with side-hole, dome tapered tip with side-hole and blunt with no side-hole needle (expanded desorptive flow). Results demonstrate that the tapered and slider tip NTDs performed with improved desorption efficiency.     

Foreword

Abstract

The crystal structure of the dinucleating 2,2′:6′,2″-terpyridine ligand 6′,6″-bis(2-pyridyl)-2,2′:4′,4″:2″,2?-quaterpyridine (btpy) has been determined and the two metal-binding tpy domains shown to be essentially planar and co-planar (P 1, a = 6.304(2), b = 8.208(2), c = 11.535(3) Å, α = 97.42(2), β = 104.25(2), γ = 96.23(2)°, Z = 1, d _c = 1.36 g cm^?3, 2214 unique observed reflections with I > 1.5[sgrave] (I), R = 0.0583); a methodology involving sequential reaction with non-labile and labile metal centres allows the specific assembly of heterometallic supramolecular oligomers such as [(Xtpy)Ru(btpy)M(btpy)Ru(Ytpy)]ⁿ⁺ (M = cobalt(II), cobalt(III) or iron).     

Ring-opening of 2,3-epoxy-1-propanol with R3Al: Unprecedented regiochemical switching simply achieved by changing alkyl substituents of aluminium reagent

Several control experiments were designed to optimize the reaction of 2,3-epoxy-1-propanol with R₃Al (R = Me, Et or ⁱBu) and to probe for the nature of aluminium-bound alkyl groups that influence the reactivity and selectivity. The reported studies revealed that the Et₃Al mediated reaction leads to the C-2 product in contrast to the well-known C-3 substitution promoted by Me₃Al.