Representing a Functional Curve by Curves with Fewer Peaks

In this paper, we study the problems of (approximately) representing a functional curve in 2-D by a set of curves with fewer peaks. Representing a function (or its curve) by certain classes of structurally simpler functions (or their curves) is a basic mathematical problem. Problems of this kind also find applications in applied areas such as intensity-modulated radiation therapy (IMRT). Let f\bf f be an input piecewise linear functional curve of size n. We consider several variations of the problems. (1) Uphill–downhill pair representation (UDPR): Find two nonnegative piecewise linear curves, one nondecreasing (uphill) and one nonincreasing (downhill), such that their sum exactly or approximately represents f\bf f. (2) Unimodal representation (UR): Find a set of unimodal (single-peak) curves such that their sum exactly or approximately represents f\bf f. (3) Fewer-peak representation (FPR): Find a piecewise linear curve with at most k peaks that exactly or approximately represents f\bf f. Furthermore, for each problem, we consider two versions. For the UDPR problem, we study its feasibility version: Given ε>0, determine whether there is a feasible UDPR solution for f\bf f with an approximation error ε; its min-ε version: Compute the minimum approximation error ε ^∗ such that there is a feasible UDPR solution for f\bf f with error ε ^∗. For the UR problem, we study its min-k version: Given ε>0, find a feasible solution with the minimum number k ^∗ of unimodal curves for f\bf f with an error ε; its min-ε version: given k>0, compute the minimum error ε ^∗ such that there is a feasible solution with at most k unimodal curves for f\bf f with error ε ^∗. For the FPR problem, we study its min-k version: Given ε>0, find one feasible curve with the minimum number k ^∗ of peaks for f\bf f with an error ε; its min-ε version: given k≥0, compute the minimum error ε ^∗ such that there is a feasible curve with at most k peaks for f\bf f with error ε ^∗. Little work has been done previously on solving these functional curve representation problems. We solve all the problems (except the UR min-ε version) in optimal O(n) time, and the UR min-ε version in O(n+mlog m) time, where m<n is the number of peaks of f\bf f. Our algorithms are based on new geometric observations and interesting techniques.     

Empirically supporting school STEM culture—The creation and validation of the STEM Culture Assessment Tool (STEM‐CAT)

School STEM Culture—an aspect of culture within a school community—is defined as the beliefs, values, practices, and resources in STEM fields as perceived by students, parents, teachers, and administrators and counselors within a school. This study validates the STEM Culture Assessment Tool (STEM‐CAT), an instrument intended to advance the use of the School STEM Culture construct within the research community. Internal consistency was determined through the use of Cronbach's alpha and factor analyses, and the instrument was found to be a reliable measure of School STEM Culture. The instrument can be used in future research to quantify School STEM Culture to determine if interventions change the culture of a school to further STEM education.     

Epoxidation of Olefins Catalyzed by Sulfate-based Supramolecular Ion Pairs

The development of inexpensive and effective catalysts for the epoxidation of olefins to epoxides, which are key commodities for the chemical industry, is a continuing challenge. In this context, we present a supramolecular solution with the development of new host-guest assemblies of sulfate ions and amidoammonium receptor cations that, for the first time, are shown to act as catalysts for olefin epoxidation by hydrogen peroxide under biphasic conditions. Analysis of the reaction mechanism shows that the reactive and oxidizing peroxymonosulfate is formed in the organic phase. Furthermore, a variety of readily available precursors may be used to form the supramolecular ion pairs (SIPs), which is enabling a large-scale synthesis of the catalysts while maintaining catalytic control and effectiveness.     

Design and application of dielectric distributed Bragg back reflector in thin-film silicon solar cells

A dielectric distributed Bragg reflector (DBR) formed by four pairs of hydrogenated amorphous silicon/silicon nitride layers is used as the back reflector in thin-film silicon solar cells. The DBR was designed to perform in a broad wavelength range with the peak reflectance at 600 nm. The DBR was fabricated at low substrate temperature (172 °C) and applied at the rear side of flat and textured amorphous silicon single-junction solar cells in both superstrate (pin) and substrate (nip) configurations. The spectral response and electrical I–V characteristics were measured. Solar cells with optimized DBR exhibit an enhanced external quantum efficiency in the long wavelength range and the electrical performance is comparable to solar cells having conventional Ag back reflector.     

Slow flow of a non-Newtonian fluid past a micro-capsule

The streaming motion past a spherical microcapsule is studied. The particle consists of a thin elastic membrane enclosing an incompressible fluid. Since the problem is highly nonlinear, a perturbation solution is sought in the limiting case where the deviation from sphericity is small. Obviously, the capsule remains nearly spherical when λ, the ratio of viscous forces to elastic (shape-restoring) membrane forces is small. In this limit, the rheology of the inside fluid is immaterial and the problem is essentially characterized by three parameters: λ, the Reynolds number Re (interia effect), and the Weissenberg number We (non-newtonian effect). The deformation is obtained explicitly under the restriction We<1, Re<1. It is shown that to leading order, the capsule deforms exactly into a spheroid which can be either oblate or prolate, depending mainly upon the elasticity number We/Re: for We/Re<0.57 the spheroid is oblate, while for We/Re>0.81 a prolate spheroid results. For 0.57<We/Re<0.81 additional details of the rheology of the membrane and of the suspending fluid are needed. The degree of the deformation is governed by the parameters λ Re. All parameters of the problem enter into the expression of the drag force. On a qualitative basis, these results are similar to those for droplets although major differences exist quantitatively.     

Optimally Computing the Shortest Weakly Visible Subedge of a Simple Polygon

Given ann-vertex simple polygonP, the problem of computing the shortest weakly visible subedge ofPis that of finding a shortest line segmentson the boundary ofPsuch thatPis weakly visible froms(ifsexists). In this paper, we present new geometric observations that are useful for solving this problem. Based on these geometric observations, we obtain optimal sequential and parallel algorithms for solving this problem. Our sequential algorithm runs inO(n) time, and our parallel algorithm runs inO(log n) time usingO(n/log n) processors in the CREW PRAM computational model. Using the previously best known sequential algorithms to solve this problem would takeO(n²) time. We also give geometric observations that lead to extremely simple and optimal algorithms for solving, both sequentially and in parallel, the case of this problem where the polygons are rectilinear.     

Micro-scale and millimeter-scale rotating disk couette flows, experiments and analysis

Experimental results are presented for rotating Couette flows with and without circumferential pressure gradients between a rotating disk and a stationary fluid chamber. The spinning disk and the top of the C-shaped fluid chamber are separated by a μ-scale gap that forms the fluid chamber passage with inner and outer radii of 1.19 and 2.38 mm, respectively. Ranges of experimental conditions are presented to demonstrate the fluid dynamics of the test arrangement, and for determination of fluid viscosity, and gas slip flow accommodation coefficients. As such, the test arrangement provides means to determine such fluid and flow properties using microliter sample sizes, with relatively low magnitudes of experimental uncertainty.     

Spectroscopic and structural evidence for the hydrogen bond nature of CC---H…C=C contacts in ethynyl steroids

Structural and IR-spectroscopic evidence is given that directed contacts from terminal alkynes to C=C double bonds possess the essential characteristics of weak hydrogen bonds. The contacts are directed at the center of the π-bond rather than at one of the individual C-atoms. The contact distances from H to the center of the C=C bond are typically 2.8 Å, with the shortest distances being 2.5 Å. The interaction is of pronounced long-range nature and can be detected in the infrared spectrum even with a long H…π distance of almost 3.0 Å. The sample used is mainly composed of ethynyl steroids belonging to the progestine family.     

On a generalised Connes-Hochschild-Kostant-Rosenberg theorem

The central result of this paper is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby generalising some fundamental results of Connes and Hochschild-Kostant-Rosenberg. The Connes-Chern character is also identified here with the twisted Chern character.     

State sum models and simplicial cohomology

We study a class of subdivision invariant lattice models based on the gauge groupZ _p , with particular emphasis on the four dimensional example. This model is based upon the assignment of field variables to both the 1- and 2-dimensional simplices of the simplicial complex. The property of subdivision invariance is achieved when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-p flatness condition. By explicit computation of the partition function for the manifoldRP ³×S ¹, we establish that the theory has a quantum Hilbert space which differs from the classical one.Supported by Stichting voor Fundamenteel Onderzoek der Materie (FOM)