Hamiltonian cycles in cubic Cayley graphs: the 〈2,4k,3〉 case

It was proved by Glover and Maru?i? (J. Eur. Math. Soc. 9:775–787, 2007), that cubic Cayley graphs arising from groups G=〈a,x∣a ²=x ^s =(ax)³=1,…〉 having a (2,s,3)-presentation, that is, from groups generated by an involution a and an element x of order s such that their product ax has order 3, have a Hamiltonian cycle when |G| (and thus also s) is congruent to 2 modulo 4, and have a Hamiltonian path when |G| is congruent to 0 modulo 4. In this article the existence of a Hamiltonian cycle is proved when apart from |G| also s is congruent to 0 modulo 4, thus leaving |G| congruent to 0 modulo 4 with s either odd or congruent to 2 modulo 4 as the only remaining cases to be dealt with in order to establish existence of Hamiltonian cycles for this particular class of cubic Cayley graphs.     

Extremal 1-codes in distance-regular graphs of diameter 3

We study 1-codes in distance-regular graphs of diameter 3 that achieve three different bounds. We show that the intersection array of a distance-regular graph containing such a code has the form $${\{a(p+1), cp, a+1; 1, c, a p\}\quad{\rm or}\quad\{a(p+1), (a+1)p,c; 1, c, a p\}}$$ for c =? c ₂,?a =? a ₃ and ${p = p_{33}^3}$ . These two families contain 10?+?15 known feasible intersection arrays out of which four are uniquely realized by the Sylvester graph, the Hamming graph H(3, 3), the Doro graph and the Johnson graph J(9, 3), but not all members of these two families are feasible. We construct four new one-parameter infinite subfamilies of feasible intersection arrays, two of which have a nontrivial vanishing Krein parameter: $${\{(2r^2-1)(2r+1), 4r(r^2-1), 2r^2; 1, 2(r^2-1), r(4r^2-2)\}}$$ and $${\{2r^2(2r+1), (2r-1)(2r^2+r+1), 2r^2; 1, 2r^2, r(4r^2-1)\}}$$ for r > 1 (the second family actually generalizes to a two-parameter family with the same property). Using this information we calculate some triple intersection numbers for these two families to show that they must contain the desired code. Finally, we use some additional combinatorial arguments to prove nonexistence of distance-regular graphs with such intersection arrays.     

On the Impact of Elastic Bodies with Adhesive Forces

We analyze the problem of an elastic sphere impacting against another elastic body for the case when adhesive forces act between the bodies. Depending on the parameter describing the (relative) influence of the adhesive forces, the bodies will either separate or continue to be in contact and perform an oscillatory motion after the rebound. The value of the adhesive forces parameter defining separation and capture is calculated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Three-Dimensional Collagen Gel Networks for Neural Stem Cell-Based Neural Tissue Engineering

Stem and progenitor cells isolated from the embryonic rat cerebral cortex were immobilized by matrix entrapment in three-dimensional (3D) Type I collagen gels, and cultured in serum-free medium containing basic fibroblast growth factor. The cells trapped within the collagen networks actively proliferated and formed clone-like aggregates. Neurons were the first differentiated cells to appear within the aggregates, followed by generation of astrocytes and oligodendrocytes. In addition, necrotic cores were developed as the aggregate diameter increased and cell viability declined significantly after 3 weeks in culture. To overcome these problems, the cell-collagen constructs were transferred to Rotary Wall Vessel bioreactors for up to 10 weeks. In the rotary culture, the collagen gels compacted 3-4 folds and a long-term growth and differentiation of neural stem and progenitor cells was dynamically maintained. Remarkably, the cell-collagen constructs formed a complex two-layered structure that superficially emulated to a certain extent the cerebral cortex of the embryonic brain in architecture and functionality. The engineered 3D tissue-like constructs displaying characteristic properties of neuronal circuits may have potential use in tissue replacement therapy for injured brain and spinal cord.     

Mechanistic Insights into Cu-Catalyzed Asymmetric Aldol Reactions: Chemical and Spectroscopic Evidence for a Metalloenolate Intermediate

In situ IR spectroscopy and transmetalation experiments confirm a postulated catalytic cycle. The metalloenolate 1 describes the active intermediate in the aldol reaction catalyzed by [CuF₂{(S)-tol-binap}] (see reaction scheme). (S)-tol-binap=(S)-(−)-2,2′-bis(di-p-tolylphosphanyl)-1,1′-binaphthyl.     

Interpolyelectrolyte complexes formation in dependence on the nature of polyelectrolytes

Interpolyelectrolyte complexes (PECs) were obtained starting from polycations with (N,N-dimethyl-2-hydroxypropylenammonium chloride) units in the main chain and sodium salts of the poly(acrylic acid), on one hand, and poly (2-acrylamido-2-methylpropane sulfonic acid), on the other hand, as polyanions. The polycations were different as concerns both the content of the quaternary ammonium salt groups and the degree of branching. The polyanions were different both by their structure and molecular weight. The complex formation was followed through the variation of the reduced viscosity and of the conductivity of the reaction medium vs. the unit molar ratio polyanion/polycation in two ranges of concentration.     

A detailed experimental and computational study of Cd complexes with pyridyl-based thiazolyl hydrazones

Interest in Cd complexes has been growing in recent years. Cd complexes are considered a potential solution in the search for novel antibiotics that can fight antimicrobial resistance. In addition, Cd complexes draw attention to material chemistry. The main objective of this work was to prepare the first Cd(II) complexes with anionic forms of pyridine-based thiazolyl hydrazone (THs) ligands HLS² [(E)-4-(4-methoxyphenyl)-2-(2-[pyridine-2-ylmethylene]hydrazinyl)thiazole] and HLS³ [(E)-2-(2-[pyridine-2-ylmethylene]hydrazinyl)-4-(p-tolyl)thiazole] and perform their structural and spectroscopic characterization, as well as stability in solution and upon heating. Studies related to their biological activities and possible electrochromic applications are also being conducted. Complexes [Cd(HLS²)₂] ( 1 ) and [Cd(HLS³)₂] ( 2 ) have been characterized by a single-crystal X-ray diffraction and computational analysis of intermolecular interactions responsible for their solid-state structures was performed. Thermal stability of 1 and 2 in the solid-state was analyzed by TGA/MS, where as their solution stability was determined by the spectrophotometric titration method. Electrochemical and in situ UV–Vis spectroelectrochemical analyses of 1 and 2 were carried out to determine redox mechanisms and the influence of the substituents and electrolytes on their redox responses. The antioxidant capacity of both complexes was tested in antioxidant assays, while their antimicrobial activity was tested against five Gram-positive and four Gram-negative bacteria, as well as against three fungi. The obtained results indicate their potent antioxidant capacity. The antimicrobial activity of investigated compounds on almost all tested bacterial strains was stronger than that of the standard antibiotic erythromycin. The results of docking studies indicate that the minor groove DNA is the possible biological target of 1 and 2 .     

Galvanic displacement of Co with Rh boosts hydrogen and oxygen evolution reactions in alkaline media

Journal of Solid State Electrochemistry - The growing energy crisis put an emphasis on the development of novel efficient energy conversion and storage systems. Here we show that surface...     

Nonstoichiometric interpolyelectrolyte complexes as colloidal dispersions based on NaPAMPS and their interaction with colloidal silica particles

Preparation and characterization of some nonstoichiometric interpolyelectrolyte complexes (NIPECs) as stable colloidal dispersions by the interaction between poly(sodium 2-acrylamido-2-methylpropanesulfonate) (NaPAMPS) and three strong polycations bearing quaternary ammonium salt centres in the backbone, poly(diallyldimethylammonium chloride) (PDADMAC) and two polycations containing N,N-dimethyl-2-hydroxypropyleneammonium chloride units (PCA₅ and PCA₅D₁), have been followed in this study as a function of the polycation structure and polyelectrolyte concentration. Complex characteristics were followed by polyelectrolyte titration, turbidity and quasi-ellastic light scattering. Almost monodisperse NIPECs nanoparticles with a good storage stability were prepared when total concentration of polyelectrolyte was varied in the range 0.85-6.35 mmol/L, at a ratio between charges (n⁻/n⁺) of 0.7. NIPECs as a new kind of flocculants were used to flocculate a stable monodisperse silica suspension. The main advantage of NIPECs as flocculants is the broad flocculation window, which is a very important aspect for industrial applications.