Cycles in dense digraphs

Let G be a digraph (without parallel edges) such that every directed cycle has length at least four; let β(G) denote the size of the smallest subset X ? E(G) such that G?X has no directed cycles, and let γ(G) be the number of unordered pairs {u, v} of vertices such that u, v are nonadjacent in G. It is easy to see that if γ(G) = 0 then β(G) = 0; what can we say about β(G) if γ(G) is bounded?

We prove that in general β(G) ≤ γ(G). We conjecture that in fact β(G) ≤ ½γ(G) (this would be best possible if true), and prove this conjecture in two special cases:

• when V(G) is the union of two cliques
• when the vertices of G can be arranged in a circle such that if distinct u, v, w are in clockwise order and uw is a (directed) edge, then so are both uv, vw.

     

One-dimensional iron-cyclopentadienyl sandwich molecular wire with half metallic, negative differential resistance and high-spin filter efficiency properties

We present a theoretical study on a series of novel organometallic sandwich molecular wires (SMWs), which are constructed with alternating iron atoms and cyclopentadienyl (Cp) rings, using DFT and nonequilibrium Green's function techniques. It is found that that the SMWs are stable, flexible structures having half-metallic (HM) properties with 100% negative spin polarization near the Fermi level in the ground state. Some SMWs of finite size show a nearly perfect spin filter effect (SFE) when coupled between ferromagnetic electrodes. Moreover, their I-V curves exhibit negative differential resistance (NDR), which is essential for certain electronic applications. The SMWs are the first linear molecules with HM, high SFE, and NDR and can be easily synthesized. In addition, we also analyze the underlying mechanisms via the transmission spectra and spin-dependent calculations. These findings strongly suggest that the SMWs are promising materials for application in molecular electronics.     

Concentrating colloids with electric field gradients. I. Particle transport and growth mechanism of hard-sphere-like crystals in an electric bottle

This work concerns the use of electric field gradients to manipulate the local particle concentration in a hard-sphere-like suspension. Inside a specially designed "electric bottle," we observed our colloids to collect in the regions of lowest field strength ("negative dielectrophoresis"). This allows for the use of larger field gradients and stronger dielectrophoretic forces than in the original electric bottle design, which was based on positive dielectrophoresis [M. T. Sullivan et al., Phys. Rev. Lett. 96, 015703 (2006)]. We used confocal scanning laser microscopy to quantitatively follow the time-dependent change in the particle density and the suspension structure. Within a few days, the dielectrophoretic compression was seen to initiate a heterogeneouslike growth of large single crystals, which took place far out-of-equilibrium. The crystals had a random hexagonal close-packed structure and displayed an intriguing growth mechanism, during which the entire crystal was continuously transported, while growing both on the "high-field" and the "low-field" sides, although at different rates. After switching off the electric field, the compressed crystals were found to relax to a lower packing fraction and melt, at a much slower rate than the crystal growth. Besides revealing the particular (far out-of-equilibrium) crystal growth mechanism in these electric bottles, our observations also shed light on the role of the different particle transport processes in the cell and some of the relevant tuning parameters. This is useful for different types of experiments, for instance, focusing more on melting, homogeneous crystallization, or the glass transition.     

The influence of coordinated defects on inhomogeneous broadening in cubic lattices

The joint probability distribution function (JPDF) of electric field gradient (EFG) tensor components in cubic materials is dominated by coordinated pairings of defects in shells near probe nuclei. The contributions from these inner shell combinations and their surrounding structures contain the essential physics that determine the PAC-relevant quantities derived from them. The JPDF can be used to predict the nature of inhomogeneous broadening (IHB) in perturbed angular correlation (PAC) experiments by modeling the G ₂ spectrum and finding expectation values for V _zz and η. The ease with which this can be done depends upon the representation of the JPDF. Expanding on an earlier work by Czjzek et al. (Hyperfine Interact. 14, 189–194, 1983), Evenson et al. (Hyperfine Interact. 237, 119, 2016) provide a set of coordinates constructed from the EFG tensor invariants they named W ₁ and W ₂. Using this parameterization, the JPDF in cubic structures was constructed using a point charge model in which a single trapped defect (TD) is the nearest neighbor to a probe nucleus. Individual defects on nearby lattice sites pair with the TD to provide a locus of points in the W ₁?W ₂ plane around which an amorphous-like distribution of probability density grows. Interestingly, however, marginal, separable PDFs appear adequate to model IHB relevant cases. We present cases from simulations in cubic materials illustrating the importance of these near-shell coordinations.     

Triplet energy dissipation in methylenecyclopropane rearrangement

Certain 1,1-dimethyl-2-aryl-3-methylenecyclopropanes containing carbonyl substituents undergo rearrangement when irradiated with 350 nm light. These rearrangements occur via the (n,pi*) triplet state, which fragments the strained cyclopropane bond. Intersystem crossing followed by ring closure gives the observed products. No photoreduction is seen in i-PrOH. Potential Norrish type II processes are also bypassed. It is suggested that the cyclopropane bond fragmentation dissipates the triplet energy and that the new intermediates are not energetic enough to abstract hydrogen atoms in an intramolecular fashion or from solvent. Nitro substituted systems undergo analogous photoinitiated rearrangements. Benzophenone sensitization of naphthyl, biphenyl, styrene, and phenylacetylene analogues also leads to rearrangement, presumably via the sensitized generation of triplet states. When triplet states cannot be accessed by direct irradiation or by sensitized processes, methylenecyclopropane rearrangements do not occur. An exception is the ferrocenyl analogue, which does not photorearrange, presumably due to the very short lifetime of the triplet intermediate.     

Sulfur based self-assembled monolayers (SAM’s) on piezoelectric crystals for immunosensor development

Self-assembled monolayers (SAM’s) of different thiols and sulfides with various structures were tested. They were investigated as a method to covalently bind antibodies to the surface of piezoelectric crystals. A capture assay using a Mouse IgG test system was performed. All tests were performed in solution. The reduction in frequency observed as binding occurred was monitored in real time. The SAM’s were activated with 1-ethyl-3-[3-(dimethylamino)propyl]carbodiimide hydrochloride (EDC) and N-hydroxysulfosuccinimide (NHS) prior to antibody immobilisation. Ethanolamine was used to block any available activated sizes after antibody immobilisation. The potential of this technique for immunosensor development is demonstrated. Received: 19 January 1999 / Revised: 1 March 1999 / Accepted: 4 March 1999     

Structurally different divalent metallasiloxanes [Mg{O(Ph2SiO)2}2]-μ-(LiPy)-μ-{(LiPy)3(OH)(Cl)}], [Cr{O(Ph2SiO)2}-μ-(LiPy2)2], and [{O(Ph2SiO)2}Co{O(Ph2SiO)3)}-μ-(LiPy2)2] from Ph2Si(OH)2/2BuLi and the metal dichlorides

Three structurally different metallasiloxanes were formed from reactions between in situ generated suspensions of Ph₂Si(OH)₂/BuLi (1∶2) in tetrahydrofuran (THF) with, metal dichlorides MgCl₂·2THF, CrCl₂, or CoCl₂ followed by toluene/Py (Py=pyridine) work-up. The X-ray structures are reported for: [Mg{O(Ph₂SiO)₂}₂]-μ-(LiPy)-μ-{(LiPy)₃(OH)(Cl)] (1) incorporating two six-membered magnesiasiloxane rings and an MgLi₃O₃Cl cubane fragment, [{O(Ph₂SiO)₂}Co{O(Ph₂SiO)₃}-μ-(LiPy₂)₂] (2) with both six-and eight-membered cobaltasiloxane rings and [Cr{O(Ph₂SiO)₂}₂-μ-(LiPy₂)₂] (3) with two six-membered chromiasiloxane rings. Structure assembly in these cases is apparently dictated by the metal dichloride. The compound [{O(Ph₂SiO)₂}Mg{O(Ph₂SiO)₃}-μ-(CoClPy)₂]·Py (4) is formed from [{O(Ph₂SiO)₂}Mg{O(Ph₂SiO)₃}-μ-(LiPy₂)₂] and CoCl₂ (1∶2).     

The synthesis, structural characterization and in vitro anti-cancer activity of novel N-(3-ferrocenyl-2-naphthoyl) dipeptide ethyl esters and novel N-(6-ferrocenyl-2-naphthoyl) dipeptide ethyl esters

N-(3-ferrocenyl-2-naphthoyl) dipeptide esters (5-7) and N-(6-ferrocenyl-2-naphthoyl) dipeptide esters (8-10) were prepared by coupling either 3-ferrocenylnaphthalene-2-carboxylic acid 2 or 6-ferrocenylnaphthalene-2-carboxylic acid 4 to the dipeptide ethyl esters GlyAla(OEt) (5, 8), AlaGly(OEt) (6, 9), and AlaAla(OEt) (7, 10) using the standard N-(3-dimethylaminopropyl)-N′-ethylcarbodiimide hydrochloride (EDC), 1-hydroxybenzotriazole (HOBt) protocol. All the compounds were fully characterized using a combination of ¹H NMR, ¹³C NMR, DEPT-135 and ¹H-¹³C COSY (HMQC) spectroscopy, electrospray ionization mass spectrometry (ESI-MS) and cyclic voltammetry (CV). In vitro, the cytotoxic effects of compounds 5-10 show improvements over the corresponding N-(ferrocenyl)benzoyl derivatives, with IC₅₀ values against the H1299 lung cancer cells ranging from 1.2 μM to 8.0 μM. N-(6-ferrocenyl-2-naphthoyl)-glycine-l-alanine ethyl ester 8 was found to be the most active derivative of the naphthoyl series so far, displaying an IC₅₀ value of 1.3 ± 0.1 μM. This value is slightly lower than that found for the clinically employed anti-cancer drug cisplatin (IC₅₀ = 1.5 ± 0.1 μM against H1299).     

Preparative routes to luminescent mixed-ligand rhenium(I) dicarbonyl complexes

A series of mixed-ligand 2,2'-bipyridine (bpy) and 1,10-phenanthroline (phen) rhenium(I) dicarbonyl complexes that are emissive in fluid solution has been prepared, which includes a new class of the type cis-[Re(CO)2(P-P)(N-N)]+ (where P-P is a chelating diphosphine and N-N is a chelating polypyridine ligand). The four synthetic routes that have been developed rely on either reactive triflate displacement or abstraction of labile chloro ligands, followed by the use of the strong trans-labilizing effect of P donors or direct use of the trans effect of P donors. The spectroscopic, photophysical, and electrochemical properties of these new complexes systematically vary with the net donor ability of the ligands in the coordination sphere, as shown by correlations with Lever's E(L) parameters. Lifetimes and quantum yields of the bipyridine complexes encompass a broad range, 25-1147 ns and ca. 0.002-0.11, respectively.