k-alternating knots

A projection of a knot is k-alternating if its overcrossings and undercrossings alternate in groups of k as one reads around the projection (an obvious generalization of the notion of an alternating projection). We prove that every knot admits a 2-alternating projection, which partitions nontrivial knots into two classes: alternating and 2-alternating.     

Substitution derivatives of the heteronuclear cluster RuOs3(μ-H)2(CO)13: Monosubstituted group 15 derivatives

Tertiary group 15 ligand monosubstituted derivatives of the heteronuclear cluster RuOs₃(μ-H)₂(CO)₁₃ have been prepared and their solid state and solution structures examined. A number of isomeric structural types have been identified in solution, and these appear to be correlated to disorder in the solid state. Hydride fluxionality and restricted rotation about the metal-phosphorus bond have also been observed.     

Some arithmetical questions in the theory of the base

Sunto. Vengon studiate, dal punto di vista aritmetico, alcune varietà algebriche possedenti trasformazioni birazionali in sè      

On the Cutoff Wavelength of Rectangular-Shaped Microshield Line by Edge Element Method

In this paper, the cutoff characteristic of rectangular-shaped microshield transmission line has been analysed by edge element method. Dependence of cutoff wavelengths on the thickness of metallic signal strip, dielectric constant of dielectric substrate and the width of the rectangular-shaped ground conductor are presented in tabular form. Numerical results in this paper have important values in design of rectangular-shaped microshield lines in microwave and millimeter wave integrated circuits.     

Effectiveness of a Mathematics Methods Course in Reducing Math Anxiety of Preservice Elementary Teachers

In an attempt to find ways of reducing the mathematical anxiety of preservice elementary teachers, three cases were investigated. The first was a section of mathematics for elementary teachers taught in a very traditional manner, and the second was the same course taught in a manner consistent with the recent recommendations of the National Council of Teachers of Mathematics. The third case included two sections of a methods course which covered the same mathematical content, as well as addressing how it should be taught to children. The Mathematics Anxiety Rating Scale for Adults was administered before and after the courses. No significant reduction of anxiety was measured in either mathematics section, but both sections of the methods course showed a significant reduction.     

Experimental and calculated H, C and P NMR spectra of pyridine-2-phosphono-4-carboxylic acid

Pyridine-2-phosphono-4-carboxylic acid (MC1) is a compound that possesses potential neuroactivity. In this work the ¹H, ¹³C and ³¹P NMR spectra of MC1 dissolved in D₂O in solution, in the 1.5-9.0 pD range, are presented. Theoretical calculations of the NMR spectra, as well as structural parameters of expected compounds, were performed at the B3PW91/6-311G** and B3PW91/6-31G** level, respectively, for all five possible forms of MC1 (cation, zwitteranion and three anions). Consecutive deprotonation of MC1 and its influence on the structure of the ligand are discussed in detail.     

A hardware-software system for analysis of video images

The purpose of this paper is to describe a software/hardware systemfor the analysis of digitized video images and a number of applications for which it may be used. The system described includes a Macintosh computer, a frame-grabber board, and Image, a public domain software program available at no cost from the U.S. National Institutes of Health. In our clinic and laboratory, this system is routinely used to make quantitative measurements from videofluoroscopic x-ray images of dynamic swallow studies and studies performed to assess velopharyngeal dysfunction in speech. It can also be used to examine various laryngeal parameters obtained from videotaped endoscopic and stroboscopic examinations. With a videocamera attached to a microscope, the system permits quantitative analysis of tissue characteristics, e.g., thickness of epithelial or connective tissue layers of the vocal folds. The relatively low cost and ease of use of the image analysis system make it a particularly attractive option when quantitative assessment of clinical or research materials in video format is desirable.     

Synthesis of comb‐type polycarbosilanes via nucleophilic substitution reactions on the main‐chain silicon atoms

A series of comb‐type polycarbosilanes of the type [Si(CH₃)(OR)CH₂]_n {where R = (CH₂)_mR′, R′ = ? O‐p‐biphenyl? X [X = H (m = 3, 6, 8, or 11) or CN (m = 11)], and R′ = (CF₂)₇CF₃ (m = 4)} were prepared from poly(chloromethylsilylenemethylene) by reactions with the respective hydroxy‐terminated side chains in the presence of triethylamine. The product side‐chain polymers were typically greater than 90% substituted and, for R′ = ? O‐p‐biphenyl? X derivatives, they exhibited phase transitions between 27 and 150 °C involving both crystalline and liquid‐crystalline phases. The introduction of the polar p‐CN substituent to the biphenyl mesogen resulted in a substantial increase in both the isotropization temperature and the liquid‐crystalline phase range with respect to the corresponding unsubstituted biphenyl derivative. For R = (CH₂)₁₁? O‐biphenyl side chains, an analogous side‐chain liquid‐crystalline (SCLC) polysiloxane derivative of the type [Si(CH₃)(O(CH₂)₁₁? O‐biphenyl)O]_n was prepared by means of a catalytic dehydrogenation reaction. In contrast to the polycarbosilane bearing the same side chain, this polymer did not exhibit any liquid‐crystalline phases but melted directly from a crystalline phase to an isotropic liquid at 94 °C. Similar behavior was observed for the polycarbosilane with a fluorocarbon chain, for which a single transition from a crystalline phase to an isotropic liquid was observed at ?0.7 °C. The molecular structures of these polymers were characterized by means of gel permeation chromatography and high‐resolution NMR studies, and the crystalline and liquid‐crystalline phases of the SCLC polymers were identified by differential scanning calorimetry, polarized optical microscopy, and X‐ray diffraction. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 984–997, 2003     

Rotational invariance in the M(atrix) formulation of type IIB theory

The matrix model formulation of M-theory can be generalized by compactification to ten-dimensional type II string theory, formulated in the infinite momentum frame. Both the type IIA and IIB string theories can be formulated in this way. In the M-theory and type IIA cases, the transverse rotational invariance is manifest, but in the IIB case, one of the transverse dimensions materializes in a completely different way from the other seven. The full O(8) rotational symmetry then follows in a surprising way from the electric-magnetic duality of supersymmetric Yang-Mills field theory.