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.     

A mass,energy, vorticity,and potential enstrophy conserving lateral fluid–land boundary scheme for the shallow water equations

A numerical scheme for treating fluid–land boundaries in inviscid shallow water flows is derived that conserves the domain-summed mass, energy, vorticity, and potential enstrophy in domains with arbitrarily shaped boundaries. The boundary scheme is derived from a previous scheme that conserves all four domain-summed quantities only in periodic domains without boundaries. It consists of a method for including land in the model along with evolution equations for the vorticity and extrapolation formulas for the depth at fluid–land boundaries. Proofs of mass, energy, vorticity, and potential enstrophy conservation are given. Numerical simulations are carried out demonstrating the conservation properties and accuracy of the boundary scheme for inviscid flows and comparing its performance with that of four alternative boundary schemes. The first of these alternatives extrapolates or finite-differences the velocity to obtain the vorticity at boundaries; the second enforces the free-slip boundary condition; the third enforces the super-slip condition; and the fourth enforces the no-slip condition. Comparisons of the conservation properties demonstrate that the new scheme is the only one of the five that conserves all four domain-summed quantities, and it is the only one that both prevents a spurious energy cascade to the smallest resolved scales and maintains the correct flow orientation with respect to an external forcing. Comparisons of the accuracy demonstrate that the new scheme generates vorticity fields that have smaller errors than those generated by any of the alternative schemes, and it generates depth and velocity fields that have errors about equal to those in the fields generated by the most accurate alternative scheme.     

Irregularity strength of digraphs

It is an elementary exercise to show that any non-trivial simple graph has two vertices with the same degree. This is not the case for digraphs and multigraphs. We consider generating irregular digraphs from arbitrary digraphs by adding multiple arcs. To this end, we define an irregular labeling of a digraph D to be an arc-labeling of the digraph such that the ordered pairs of the sums of the in-labels and out-labels at each vertex are all distinct. We define the strength of D to be the smallest of the maximum labels used across all irregular labelings. Similar definitions for graphs have been studied extensively and a different formulation of digraph irregularity was given in [H. Hackett, Irregularity strength of graphs and digraphs, Masters Thesis, University of Louisville, 1995]. Here we continue the study of irregular labelings of digraphs. We give a general lower bound on and determine exactly for tournaments, directed paths and cycles and the orientation of the path where all vertices have either in-degree 0 or out-degree 0. We also determine the irregularity strength of a union of directed cycles and a union of directed paths, the latter which requires a new result pertaining to finding circuits of given lengths containing prescribed vertices in the complete symmetric digraph with loops.     

Testing the conformational hypothesis of passive membrane permeability using synthetic cyclic peptide diastereomers

Little is known about the effect of conformation on passive membrane diffusion rates in small molecules. Evidence suggests that intramolecular hydrogen bonding may play a role by reducing the energetic cost of desolvating hydrogen bond donors, especially amide N-H groups. We set out to test this hypothesis by investigating the passive membrane diffusion characteristics of a series of cyclic peptide diastereomers based on the sequence cyclo[Leu-Leu-Leu-Leu-Pro-Tyr]. We identified two cyclic hexapeptide diastereomers based on this sequence, whose membrane diffusion rates differed by nearly two log units. Results of solution NMR studies and hydrogen/deuterium (H/D) exchange experiments showed that membrane diffusion rates correlated with the degree of intramolecular hydrogen bonding and H/D exchange rates. The most permeable diastereomer, cyclo[d-Leu-d-Leu-Leu-d-Leu-Pro-Tyr] (1), exhibited a passive membrane diffusion rate comparable to that of the orally available drug cyclosporine A.     

Solid-state bonding technique for template-stripped ultraflat gold substrates

A simple procedure using gold diffusion bonding for the preparation of template-stripped gold (TSG) surfaces is described. TSG surfaces are useful for surface studies because a very consistent flat gold surface with few defects can be easily prepared. We have developed a method of producing TSG surfaces that relies only on gold diffusion bonding rather than epoxies. The resulting substrates are free from concerns of solvent compatibility, heat stability, and impurities. Bonding of centimeter-sized substrates is performed at 300 degrees C for 2 h using a vise and aluminum foil.