Domination number in graphs with minimum degree two

A set D of vertices of a graph G = （V, E） is called a dominating set if every vertex of V not in D is adjacent to a vertex of D. In 1996, Reed proved that every graph of order n with minimum degree at least 3 has a dominating set of cardinality at most 3n/8. In this paper we generalize Reed＇s result. We show that every graph G of order n with minimum degree at least 2 has a dominating set of cardinality at most （3n ＋IV21）/8, where V2 denotes the set of vertices of degree 2 in G. As an application of the above result, we show that for k ≥ 1, the k-restricted domination number rk （G, γ） ≤ （3n＋5k）/8 for all graphs of order n with minimum degree at least 3.     

Bounds relating the weakly connected domination number to the total domination number and the matching number

Let G=(V,E) be a connected graph. A dominating set S of G is a weakly connected dominating set of G if the subgraph (V,E∩(S×V)) of G with vertex set V that consists of all edges of G incident with at least one vertex of S is connected. The minimum cardinality of a weakly connected dominating set of G is the weakly connected domination number, denoted . A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γ_t(G) of G. In this paper, we show that . Properties of connected graphs that achieve equality in these bounds are presented. We characterize bipartite graphs as well as the family of graphs of large girth that achieve equality in the lower bound, and we characterize the trees achieving equality in the upper bound. The number of edges in a maximum matching of G is called the matching number of G, denoted α^′(G). We also establish that , and show that for every tree T.     

Lower Bounds on the Size of Maximum Independent Sets and Matchings in Hypergraphs of Rank Three

In this paper, we study lower bounds on the size of a maximum independent set and a maximum matching in a hypergraph of rank three. The rank in a hypergraph is the size of a maximum edge in the hypergraph. A hypergraph is simple if no two edges contain exactly the same vertices. Let H be a hypergraph and let and be the size of a maximum independent set and a maximum matching, respectively, in H, where a set of vertices in H is independent (also called strongly independent in the literature) if no two vertices in the set belong to a common edge. Let H be a hypergraph of rank at most three and maximum degree at most three. We show that with equality if and only if H is the Fano plane. In fact, we show that if H is connected and different from the Fano plane, then and we characterize the hypergraphs achieving equality in this bound. Using this result, we show that that if H is a simple connected 3‐uniform hypergraph of order at least 8 and with maximum degree at most three, then and there is a connected 3‐uniform hypergraph H of order 19 achieving this lower bound. Finally, we show that if H is a connected hypergraph of rank at most three that is not a complete hypergraph on vertices, where denotes the maximum degree in H, then and this bound is asymptotically best possible. © 2012 Wiley Periodicals, Inc. J. Graph Theory     

The early exercise region for Bermudan options on two underlyings

This paper investigates the early exercise region for Bermudan options on two underlying assets. We present a set of analytical validation results for the early exercise region which can be used as a means of validating pricing techniques. When all strike prices are identical we show the existence of an intersection point such that for any asset price pair below this point early exercise is always optimal. We develop an approximation to this point in the two asset put case. When the strike prices are not all equal, we show that three separate cases exist for the early exercise region. For a Bermudan put on two assets we present these cases and show that there exists a critical point in which the boundaries of the two asset early exercise region bifurcate. Comparisons are drawn between the Bermudan results presented and the corresponding American option results.     

Programmable and Self-Healable Liquid Crystal Elastomer Actuators Based on Halogen Bonding

Shape-changing polymeric materials have gained significant attention in the field of bioinspired soft robotics. However, challenges remain in versatilizing the shape-morphing process to suit different tasks and environments, and in designing systems that combine reversible actuation and self-healing ability. Here, we report halogen-bonded liquid crystal elastomers (LCEs) that can be arbitrarily shape-programmed and that self-heal under mild thermal or photothermal stimulation. We incorporate halogen-bond-donating diiodotetrafluorobenzene molecules as dynamic supramolecular crosslinks into the LCEs and show that these relatively weak crosslinks are pertinent for their mechanical programming and self-healing. Utilizing the halogen-bonded LCEs, we demonstrate proof-of-concept soft robotic motions such as crawling and rolling with programmed velocities. Our results showcase halogen bonding as a promising, yet unexplored tool for the preparation of smart supramolecular constructs for the development of advanced soft actuators.     

Surface tension and fluid flow driven self-assembly of ordered ZnO nanorod films for high-performance field effect transistors

Colloidal nanorods of inorganic semiconductors are of interest for a range of optoelectronic devices. The ability to self-assemble these materials into ordered arrays by solution-processing techniques is crucial for achieving adequate device performance. Here we show that uniform ZnO nanorod films with defined nanorod alignment can be solution-deposited over large areas by controlling the surface energy of the nanorods through the choice of suitable ligands and by the fluid flow direction during growth. ZnO nanorods with long carbon chain ligands exhibit a smaller surface free energy than those with short carbon chain ligands resulting in better in-plane alignment and large domain sizes up to dozens of micrometers in spin-coated films. A model is presented to rationalize the observed self-assembly behavior. It is based on the formation of a lyotropic liquid crystalline phase on the surface of the liquid film which is facilitated by enhanced segregation of nanorods with low surface tension to the surface. Alignment of the nanorods is controlled by radial and vertical liquid flows in the drying solution. The ability to control the orientation of the nanorods and to achieve large domain size results in significant device performance improvement. Field-effect transistors with mobilities of up to 1.2-1.4 cm2/V.s are demonstrated in spin-coated, in-plane aligned ZnO nanorod films subject to postdeposition hydrothermal growth.     

Detection of protein-RNA crosslinks by nanoLC-ESI-MS/MS using precursor ion scanning and multiple reaction monitoring (MRM) experiments

Protein-RNA interactions within ribonucleoprotein particles (RNPs) can be investigated by UV-induced crosslinking of proteins to their cognate RNAs and subsequent isolation and mass-spectrometric analysis of crosslinked peptide-RNA oligonucleotides. Because of the low crosslinking yield, a major challenge in protein-RNA UV crosslinking is the detection of the crosslinked species over the excess of non-crosslinked material, especially when complex systems (native RNPs) are investigated. Here, we applied a novel approach that uses on-line nanoLC-ESI-MS/MS to detect and subsequently sequence peptide-RNA oligonucleotide crosslinks from crude mixtures. To detect the crosslinks we made use of features shared by crosslinks and phosphopeptides, that is, the phosphate groups that both carry. A precursor ion scan for m/z 79 (negative-ion mode, -ve) is applied to selectively detect analytes bearing the phosphate-containing species (i.e., residual non-crosslinked RNA and peptide-RNA crosslinks) from crude mixtures and to determine their exact m/z values. On this basis, a multiple reaction monitoring (MRM) experiment monitors the expected decomposition from the different precursor charge states of the putative crosslinks to one of the four possible RNA nucleobases [m/z 112, 113, 136, 152 (positive-ion mode, +ve)]. On detection, a high-quality MS/MS is triggered to establish the structure of the crosslink. In a feasibility study, we detected and subsequently sequenced peptide-RNA crosslinks obtained by UV-irradiation of (1) native U1 snRNPs and (2) [15.5K-61K-U4atac] snRNPs prepared by reconstitution in vitro. MRM-triggered collision-induced dissociation (CID) MS/MS enabled us to obtain sequence information about the crosslinked peptide and RNA moiety.     

Nonlinear current-voltage relationship of the plasma membrane of single CHO cells

The application of electric field pulses to Chinese Hamster Ovary (CHO) cells causes membrane electroporation (MEP). If a voltage or current ramp is applied to the cellular membrane of a single CHO cell, the membrane conductance increases nonlinearly with field strength reaching saturation. In particular, the kinetics of the induced conductance changes represents the data basis for the interpretation in terms of underlying structural changes. The current/voltage characteristic is found to be continuous, but displays occasionally a sharp increase in the conductance. The step-like increases are interpreted to reflect the formation of one (or more) larger pore(s). The analysis of current clamp data yields pores of radius (r(p)) in the range of 2.5< or =r(p)/nm< or =20; the pores of the voltage clamp data are in the range of 2.5< or =r(p)/nm< or =55. The larger pores occur predominantly during hyperpolarising and less frequently during depolarising conditions, respectively. The different kinetics of pore formation in the hyperpolarising condition, where the inward field increases, and the depolarising condition, where the inward field first decreases and then increases in the opposite direction, suggests structural asymmetry with respect to the direction of the electric membrane field. At the required higher voltage, the effect of the resting potential is negligibly small.     

1. Produkte aus Industrie und Landwirtschaft

Ohne Zusammenfassung     

Übergangsmetall-thioketen-komplexe: VII. Erzeugung eines vinyliden-liganden aus einem thioketen durch schwefelabspaltung

The thioketene iron cluster (CH₃)₄C₆H₆CS(PPh₃)₂(CO)₄Fe₂S (I) reacts with thioketene in excess quantitatively to a vinylidene complex, as confirmed by X-ray analysis.