The impact of integrated STEM professional development on teacher quality

This study of a state‐funded, 3‐year implementation of an integrated STEM professional development (PD) program for teachers from two middle schools in the midwestern U.S. examined if participants in the PD were enabled to transform their practice and perceptions of STEM. An integrated STEM approach includes a focus on the STEM disciplines, along with leveraging social studies/history and English/language arts as important context and tools for solving society’s biggest challenges. Findings in this study indicated that teachers implemented more effective STEM teaching strategies and had more positive perceptions regarding STEM overall. Further, participants became more aware of their personal needs for resources and support to teach through integrated STEM. Implications for research and practice are discussed.     

A new three-component one pot reaction of trinitromethane, epoxides and alkenes via dinitronitronates: synthesis of highly functionalized 3,3-dinitroisoxazolidines

A novel approach to acyclic alkyldinitronitronates using nucleophilic opening of epoxides with the trinitromethyl anion is presented. The scope and limitations of this synthetic procedure are presented. A series of highly functionalized 3,3-dinitroisoxazolidines were synthesized as mixtures of diastereomers.     

Free states of the canonical anticommutation relations

Each gauge invariant generalized free state _A of the anticommutation relation algebra over a complex Hilbert spaceK is characterized by an operatorA onK. It is shown that the cyclic representations induced by two gauge invariant generalized free states _A and _B are quasi-equivalent if and only if the operatorsA ^1/2–B ^1/2 and (I–A)^1/2–(I–B)^1/2 are of Hilbert-Schmidt class. The combination of this result with results from the theory of isomorphisms of von Neumann algebras yield necessary and sufficient conditions for the unitary equivalence of the cyclic representations induced by gauge invariant generalized free states.Work supported in part by US Atomic Energy Commission, under Contract AT (30-1)-2171 and by the National Science Foundation.     

Fast-Fourier-Transform Spectral-Analysis Techniques as a Plasma Fluctuation Diagnostic Tool

A review is given of the key ideas involved in computing power spectral density functions from fast-Fourier-transformed plasma fluctuation data. Next a model is described which enables one to determine, from the computer-generated power spectra, the amplitude, frequency, and wavenumber of each of several waves present in the plasma. The potential of digitally implemented spectral analysis techniques as a plasma diagnostic tool is demonstrated in an experimental study of the evolution, and ultimate turbulent destruction, of a multi-mode drift wave spectrum.     

A remark on the domain of an unbounded derivation of a C1-algebra

It is shown that if A is an hermitian element of a C¹-algebra and A is in the domain of a closed unbounded derivation δ of the C¹-algebra and if ? is a continuously differentiable complex valued function defined on a closed interval containing the spectrum of A then $\text{?(A)}$ is in the domain of δ and the norm of $\text{δ(?(A))}$ is bounded by the norm of δ(A) times the least upper bound of the absolute value of the derivative of ?. This result is generalized to the case of continuously differentiable functions of several variables.     

Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.This research was supported by the National Science Foundation under Grant Nos. GK-30115 and ENG 74-21618 and by the National Aeronautics and Space Administration under Contract No. NAS 9-12872.     

Unsteady mass and energy transfer in binary gas mixtures

Thermodynamic analysis and a theory of unsteady-state process of thermal diffusion and diffusional thermal effect in gas mixtures are presented. A mathematical model for unsteady mass transfer process in gas mixtures is developed.     

Average boundary conditions in Cauchy problems

We consider the general Cauchy problem with initial data in a Hilbert space and with a formal dissipative linear generator. A complete parametrization is known of the (abstract) boundary conditions which make this problem well set. We exhibit a distinguished subset $\text{B}$_E of the set $\text{B}$ of boundary conditions and demonstrate explicitly that the evolution associated with each B in $\text{B}$ can be represented as a (time independent) average over the evolutions associated with B′ in $\text{B}$_E. Applications are discussed to Schrödinger equations in bounded regions or with singular potentials.     

Measurement of neutron energy spectra and neutron-gamma angular correlations for the muon capture process 16O(μ−, νμxn)14, 15N

Neutron-gamma coincidence spectra have been measured for muon capture in ¹⁶O. The γ-spectrum is dominated by the ground state transitions from the $\text{3}\text{2}{}^{\mathrm{?}}\text{(6.32}\text{MeV}\text{)}\text{and}\text{1}\text{2}{}^{\mathrm{+}}\text{+}\text{5}\text{2}{}^{\mathrm{+}}\text{(5.3}\text{MeV}\text{)}$ states of ¹⁵N that are populated after the emission of one neutron. The neutron energy spectra and the neutron energy dependence of the ny angular correlation coefficient A₂ for these final states are presented. The observed transitions in ¹⁴N and the associated neutron spectra give direct evidence for the emission of two correlated neutrons. The data are discussed in terms of direct neutron emission plus emission via giant resonance intermediate states of ¹⁶N. The large yield for the emission of one and two fast neutrons is explained by a capture mechanism involving short-range nucleon-nucleon correlations.