On a decomposition of conditionally positive-semidefinite matrices

A symmetric matrix C is said to be copositive if its associated quadratic form is nonnegative on the positive orthant. Recently it has been shown that a quadratic form x'Qx is positive for all x that satisfy more general linear constraints of the form Ax?0, x≠0 iff Q can be decomposed as a sum Q=A'CA+S, with Cstrictly copositive and S positive definite. However, if x'Qx is merely nonnegative subject to the constraints Ax?0, it does not follow that Q admits such a decomposition with C copositive and S positive semidefinite. In this paper we give a characterization of those matrices A for which such a decomposition is always possible.     

Minimal Degree and (k, m)-Pancyclic Ordered Graphs

Given positive integers k m n, a graph G of order n is (k, m)-pancyclic ordered if for any set of k vertices of G and any integer r with m r n, there is a cycle of length r encountering the k vertices in a specified order. Minimum degree conditions that imply a graph of sufficiently large order n is (k, m)-pancylic ordered are proved. Examples showing that these constraints are best possible are also provided.     

Untersuchungen von Relaxationserscheinungen an Quecksilberatomen im metastabilen 63 P 2-Zustand mit einem Impulsverfahren

Zeitschrift für Physik A Hadrons and nuclei - Excitation functions at 90° and 155° to the proton beam have been measured for the reaction41K(p, α)38Ar from 2.1 to 2.5 MeV proton...     

Nonequilibrium thermodynamics of spacetime

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=deltaQ/T hold for all local acceleration horizons through each spacetime point, where is one-quarter the horizon area change in Planck units and deltaQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS=deltaQ/T+diS, where diS is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.     

Examining the design features of a communication-rich,problem-centred mathematics professional development

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of professional development by examining and operationalizing the relationships among research-based features of effective professional development and the enacted features of a particular design.     

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.     

Porphyrin Nanocage‐Embedded Single‐Molecular Nanoparticles for Cancer Nanotheranostics

Single molecular nanoparticles (SMNPs) integrating imaging and therapeutic capabilities exhibit unparalleled advantages in cancer theranostics, ranging from excellent biocompatibility, high stability, prolonged blood lifetime to abundant tumor accumulation. Herein, we synthesize a sophisticated porphyrin nanocage that is further functionalized with twelve polyethylene glycol arms to prepare SMNPs ( porSMNPs ). The porphyrin nanocage embedded in porSMNPs can be utilized as a theranostic platform. PET imaging allows dynamic observation of the bio‐distribution of porSMNPs , confirming their excellent circulation time and preferential accumulation at the tumor site, which is attributed to the enhanced permeability and retention effect. Moreover, the cage structure significantly promotes the photosensitizing effect of porSMNs by inhibiting the π–π stacking interactions of the photosensitizers, ablating of the tumors without relapse by taking advantage of photodynamic therapy.     

Application of discrete-event simulation in health care clinics: A survey

In recent decades, health care costs have dramatically increased, while health care organisations have been under severe pressure to provide improved quality health care for their patients. Several health care administrators have used discrete-event simulation as an effective tool for allocating scarce resources to improve patient flow, while minimising health care delivery costs and increasing patient satisfaction. The rapid growth in simulation software technology has created numerous new application opportunities, including more sophisticated implementations, as well as combining optimisation and simulation for complex integrated facilities. This paper surveys the application of discrete-event simulation modeling to health care clinics and systems of clinics (for example, hospitals, outpatient clinics, emergency departments, and pharmacies). Future directions of research and applications are also discussed.     

Sensitive method for the determination of baclofen in plasma by means of solid-phase extraction and liquid chromatography-tandem mass spectrometry.

A simple and sensitive method for the determination of baclofen in plasma is described. Baclofen and the internal standard, KM 08205, were isolated from plasma by solid-phase extraction using C18 material. After separation by reversed-phase liquid chromatography, the analytes were detected with tandem mass spectrometry. The extraction procedure was optimised regarding the solid-phase extraction material, the pH in the conditioning solution and the washing volume. The method was proven to be selective and sensitive with an absolute recovery of about 95%, a relative standard deviation below 5% and a limit of quantification of 10 nmol/1.