Noise Path Synthesis with Nonlinear Joints

An efficient synthesis approach is developed which permits thecalculation of the steady-state frequency response of an assembly whichis comprised of linear components and nonlinear joints. Receptancematrices are used to characterize the linear components, which permitscondensation of the system to just the joint degrees-of-freedom.Furthermore, the calculated nonlinear joint forces are then used tostudy the power flow in the assembly, as well as detailed dynamicbehavior within the components. Integrated into the technique is acontinuation scheme which permits efficient parametric studies.     

The many facets of linear programming

We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex, ellipsoid, interior-point, and other methods. Received: June 22, 2000 / Accepted: April 4, 2001?Published online October 2, 2001     

Local algorithms in exterior tomography

Exterior tomographic data are taken over lines outside a central region, and such data occur in the industrial nondestructive evaluation of large objects such as rockets. We explain, using microlocal analysis, which singularities are well reconstructed from exterior data, and we explain how this phenomenon is reflected in the singular value decomposition for the exterior transform [E.T. Quinto, Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform, J. Math. Anal. Appl. 95 (1983) 437–448]. We extend Lambda Tomography to exterior data and to limited angle exterior data. The algorithm is tested on industrial data from Perceptics, Inc.     

Xor on one‐defect systems

We present a network experiment that investigates the computational power of cellular automata on the simplest irregular lattice. One cellular automaton whose apparent complexity increased is Rule 60, the left neighbor Xor operator. It went from being nested to complex. That makes Xor a candidate for universal computational power. We present the evidence in terms of the size of cycle lengths, transients, and size of boolean expressions. © 2006 Wiley Periodicals, Inc. Complexity 12: 13–29, 2006     

Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

The Weierstrass mean

Theorem.Let the sequences {e _i ⁽ⁿ⁾ },i=1, 2, 3,n=0, 1, 2, ...be defined by where the e ⁽⁰⁾ s satisfy and where all square roots are taken positive. Then where the convergence is quadratic and monotone and where The discussions of convergence are entirely elementary. However, although the determination of the limits can be made in an elementary way, an acquaintance with elliptic objects is desirable for real understanding.     

Competitive decay at two- and three-state conical intersections in excited-state intramolecular proton transfer

We demonstrate the existence of a simultaneous degeneracy (not required by symmetry) of three electronic states in malonaldehyde. This is one of the first reports of such a triple degeneracy involving S0, S1, and S2 in a molecule with a closed-shell ground state. We further report on a two-state S2/S1 conical intersection which is higher in energy than the three-state intersection, but closer to the Franck-Condon point. First-principles quantum dynamics calculations of the photochemistry after excitation to S2 show that there is a competition between these intersections, with more than half of the population decaying to S1 through the higher energy S2/S1 intersection. Surprisingly, much of the population which makes it to the triple degeneracy point is not funneled directly to S0, but rather remains trapped on S1. We attribute this to the large dimensionality of the branching plane at a three-state intersection (the degeneracy is lifted along at least five distinct molecular displacements).     

Coligand role in the NHC nickel catalyzed C–F bond activation: investigations on the insertion of bis(NHC) nickel into the C–F bond of hexafluorobenzene

The reaction of [Ni(Mes₂Im)₂] (1) (Mes₂Im = 1,3-dimesityl-imidazolin-2-ylidene) with polyfluorinated arenes as well as mechanistic investigations concerning the insertion of 1 and [Ni(ⁱPr₂Im)₂] (1ipr) (ⁱPr₂Im = 1,3-diisopropyl-imidazolin-2-ylidene) into the C–F bond of C₆F₆ is reported. The reaction of 1 with different fluoroaromatics leads to formation of the nickel fluoroaryl fluoride complexes trans-[Ni(Mes₂Im)₂(F)(Ar^F)] (Ar^F = 4-CF₃-C₆F₄2, C₆F₅3, 2,3,5,6-C₆F₄N 4, 2,3,5,6-C₆F₄H 5, 2,3,5-C₆F₃H₂6, 3,5-C₆F₂H₃7) in fair to good yields with the exception of the formation of the pentafluorophenyl complex 3 (less than 20%). Radical species and other diamagnetic side products were detected for the reaction of 1 with C₆F₆, in line with a radical pathway for the C–F bond activation step using 1. The difluoride complex trans-[Ni(Mes₂Im)₂(F)₂] (9), the bis(aryl) complex trans-[Ni(Mes₂Im)₂(C₆F₅)₂] (15), the structurally characterized nickel(i) complex trans-[Ni^I(Mes₂Im)₂(C₆F₅)] (11) and the metal radical trans-[Ni^I(Mes₂Im)₂(F)] (12) were identified. Complex 11, and related [Ni^I(Mes₂Im)₂(2,3,5,6-C₆F₄H)] (13) and [Ni^I(Mes₂Im)₂(2,3,5-C₆F₃H₂)] (14), were synthesized independently by reaction of trans-[Ni(Mes₂Im)₂(F)(Ar^F)] with PhSiH₃. Simple electron transfer from 1 to C₆F₆ was excluded, as the redox potentials of the reaction partners do not match and [Ni(Mes₂Im)₂]⁺, which was prepared independently, was not detected. DFT calculations were performed on the insertion of [Ni(ⁱPr₂Im)₂] (1ipr) and [Ni(Mes₂Im)₂] (1) into the C–F bond of C₆F₆. For 1ipr, concerted and NHC-assisted pathways were identified as having the lowest kinetic barriers, whereas for 1, a radical mechanism with fluoride abstraction and an NHC-assisted pathway are both associated with almost the same kinetic barrier.

A combined experimental and theoretical study on the mechanism of the C–F bond activation of C₆F₆ with [Ni(NHC)₂] is provided.     

Analysis of partially resolved liquid chromatographic peaks using dynamic modeling with the kalman filter

Establishing a calibration model is an important part of any mathematical method for multi-component determination. Use of a calibration model based on single spectra is subject to error, because the model spectrum chosen may not be representative of the response over the full range of the calibration. Alternative calibration models require more time to establish calibration, an these may not be convenient for real-time determinations. A novel calibration method is reported for use with Kalman filters. The method, dynamic modeling, is based on the use of libraries of calibration spectra. The set of used to describe the model at any time is based on component concentrations, estimated for the multi-component mixture, as determined from the Kalman filter, so that several spectra can be used to best describe a varying response. Through application of the dynamic modelingt to simulated and real chromatograms, it is demonstrated that use of the method decreases estimation errors cause by model data mismatches, and that full benefit can be obtained from relatively small libraries.