Minimum degree and disjoint cycles in generalized claw-free graphs

For s≥3$s\ge 3$ a graph is _K1,s$K_{1,s}$-free if it does not contain an induced subgraph isomorphic to _K1,s$K_{1,s}$. Cycles in _K1,3$K_{1,3}$-free graphs, called claw-free graphs, have been well studied. In this paper we extend results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions to _K1,s$K_{1,s}$-free graphs, normally called generalized claw-free graphs. In particular, we prove that if G$G$ is _K1,s$K_{1,s}$-free of sufficiently large order n=3k$n=3k$ with δ(G)≥n/2+c$\delta \left(G\right)\ge n/2+c$ for some constant c=c(s)$c=c\left(s\right)$, then G$G$ contains k$k$ disjoint triangles. Analogous results with the complete graph _K3$K_3$ replaced by a complete graph _Km$K_m$ for m≥3$m\ge 3$ will be proved. Also, the existence of 2$2$-factors for _K1,s$K_{1,s}$-free graphs with minimum degree conditions will be shown.     

Assessment of pulmonary air trapping and obstruction in expiration: an experimental MRI study

PURPOSE: The aim of this experimental study was to evaluate the potential of a simple expiration technique by means of magnetic resonance imaging (MRI) in an animal model to detect pulmonary air-trapping areas after artificial bronchial obstruction. MATERIAL AND METHODS: Sixteen pigs were evaluated by means of a modified T1-weighted FLASH with fat saturation in respiratory arrest (TR=4.6 ms, TE=1.8 ms, alpha=10 degrees, S.D.=3-5 mm). A measurement of the signal intensity (SI) in the peripheral lung tissue was made in both inspiration and expiration before and after inhalation of 2 ml of 0.5% acetylcholine to simulate a bronchial obstruction. A final measurement of the lung SI was also made after bronchospasmolytic induction through salbutamol (beta2-mimetic bronchodilator). RESULTS: In expiration, a mean SI increase in peripheral lung tissue of about 183% was seen in comparison to inspiration (mean SI increase of 11-32). After inhalation of 0.5% acetylcholine, the expirational signal increase in peripheral lung tissue was only 114% of the original SI. The expirational signal homogeneity decreased after inhalation of acetylcholine. After inhalation of salbutamol, the lung tissue signal elevation in expiration was 193%. CONCLUSION: We interpret the low expiratory signal elevation after acetylcholine inhalation as a result of an air-trapped bronchial constriction in certain areas. The simple expiratory technique in an animal model showed that it is suitable to demonstrate obstructive air trapping using MRI.     

Scalar-type spectral operators and holomorphic semigroups

We show that a linear operator (possibly unbounded), A, on a reflexive Banach space, X, is a scalar-type spectral operator, with non-negative spectrum, if and only if the following conditions hold.

1. A generates a uniformly bounded holomorphic semigroup {e?^zA}_Re(z)≥0.
2. If \(F_N (s) \equiv \int_{ - N}^N {\tfrac{{\sin (sr)}}{r}} e^{irA} dr\) , then {‖F_N‖} _N=1 ^∞ is uniformly bounded on [0,∞) and, for all x in X, the sequence {F_N(s)x} _N=1 ^∞ converges pointwise on [0, ∞) to a vector-valued function of bounded variation.

The projection-valued measure, E, for A, may be constructed from the holomorphic semigroup {e^?zA}_Re(z)≥0 generated by A, as follows. $$\frac{1}{2}(E\{ s\} )x + (E[0,s)) x = \mathop {\lim }\limits_{N \to \infty } \int_{ - N}^N {\frac{{\sin (sr)}}{r}} e^{irA} x\frac{{dr}}{\pi }$$ for any x in X.     

Boundary and Lens Rigidity of Lorentzian Surfaces

Let be a Lorentzian metric on the plane that agrees with the standard metric outside a compact set and so that there are no conjugate points along any time-like geodesic of . Then and are isometric. Further, if and are two dimensional compact time oriented Lorentzian manifolds with space--like boundaries and so that all time-like geodesics of maximize the distances between their points and and are ``boundary isometric', then there is a conformal diffeomorphism between and and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

     

The connectivity of a graph on uniform points on [0,1]

A random graph G_n(x) is constructed on independent random points U₁,…,U_n distributed uniformly on [0,1]^d, d1, in which two distinct such points are joined by an edge if the l_∞-distance between them is at most some prescribed value 0<x<1. The connectivity distance c_n, the smallest x for which G_n(x) is connected, is shown to satisfy

(1)

For d2, the random graph G_n(x) behaves like a d-dimensional version of the random graphs of Erdös and Rényi, despite the fact that its edges are not independent: c_n/d_n→1, a.s., as n→∞, where d_n is the largest nearest-neighbor link, the smallest x for which G_n(x) has no isolated vertices.     

The triplet spectrum of tetramethyl-1,3-cyclobutanedione

The low-temperature single-crystal spectrum of TMCBD has revealed a low-lying triplet state at 25 718 cm^-1 (72·5 kcal/mol). The observed band is ascribed to a ³ A_u (³ A ₂) ← ¹ A_g nπ* transition on the basis of its small singlet-triplet splitting, its polarization behaviour, and its vibrational structure. The ³ A_u state is first-order spin-orbit coupled to either or both of the ¹ B _2u or ¹ B _3u states. No evidence for two or more nπ* transitions was found. Several multi-membered progressions in the carbonyl wagging mode indicate the presence of a distorted excited state, in which the carbonyl carbons attain a pyramidal conformation. Analysis of the site symmetry shows that TMCBD is distorted to a boat-shaped C _2v structure in its triplet nπ* state.     

The materials science X‐ray beamline BL8 at the DELTA storage ring

The hard X‐ray beamline BL8 at the superconducting asymmetric wiggler at the 1.5 GeV Dortmund Electron Accelerator DELTA is described. This beamline is dedicated to X‐ray studies in the spectral range from ～1 keV to ～25 keV photon energy. The monochromator as well as the other optical components of the beamline are optimized accordingly. The endstation comprises a six‐axis diffractometer that is capable of carrying heavy loads related to non‐ambient sample environments such as, for example, ultrahigh‐vacuum systems, high‐pressure cells or liquid‐helium cryostats. X‐ray absorption spectra from several reference compounds illustrate the performance. Besides transmission measurements, fluorescence detection for dilute sample systems as well as surface‐sensitive reflection‐mode experiments have been performed. The results show that high‐quality EXAFS data can be obtained in the quick‐scanning EXAFS mode within a few seconds of acquisition time, enabling time‐resolved in situ experiments using standard beamline equipment that is permanently available. The performance of the new beamline, especially in terms of the photon flux and energy resolution, is competitive with other insertion‐device beamlines worldwide, and several sophisticated experiments including surface‐sensitive EXAFS experiments are feasible.     

Cucurbituril‐mediated immobilization of fluorescent proteins on supramolecular biomaterials

The reversible introduction of functionality at material surfaces is of interest for the development of functional biomaterials. In particular, the use of supramolecular immobilization strategies facilitates mild reaction and processing conditions, as compared to other covalent analogues. Here, the engineering of multicomponent supramolecular materials, beyond the use of a single supramolecular entity is proposed. Cucurbit[8]uril (Q8) mediated host–guest chemistry is combined with hydrogen bonding supramolecular 2‐ureido‐4‐pyrimidinone (UPy)‐based materials. The modular incorporation of a UPy‐additive that presents one guest to incorporate into the Q8 host allows for selective supramolecular functionalization at the water–polymer material interface. Supramolecular ternary complex formation at the material surface was studied by X‐ray photoelectron spectroscopy, which as a result of large overlap in atomic composition of the different components showed minor changes is surface composition upon complex formation. Surface MALDI‐ToF MS measurements revealed useful insights in the formation of complexes. Protein immobilization was monitored using both fluorescence spectroscopy and quartz crystal microbalance with dissipation monitoring, which successfully demonstrated ternary complex formation. Although proteins could selectively be immobilized onto the surfaces, control of the system's stability remains a challenge as a result of the dynamicity of the host–guest assembly. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3607–3616     

Stereospecific Palladium-Catalyzed Acylation of Enantioenriched Alkylcarbastannatranes: A General Alternative to Asymmetric Enolate Reactions

We report the development of a Pd-catalyzed process for the cross coupling of unactivated primary, secondary, and tertiary alkylcarbastannatrane nucleophiles with acyl electrophiles. Reactions involving optically active alkylcarbastannatranes occur with exceptional stereofidelity and with net retention of absolute configuration. Because the stereochemistry of the resulting products is entirely reagent-controlled, this process may be viewed as a general, alternative approach to the preparation of products typically accessed via asymmetric enolate methodologies. Additionally, we report a new method for the preparation of optically active alkylcarbastannatranes, which should facilitate their future use in stereospecific reactions.