Assessing the Impact of Bridging Analogies in Mechanics

The effects of bridging analogies teaching strategy and gender on Turkish high school students' misconceptions in mechanics were investigated. After a pilot study with 67 students in a nearby high school, the researchers administered the revised Mechanics Misconception Test to 119 high school students as a pretest. Students in the experimental group were instructed by using bridging analogies teaching strategy. At the end of a 3‐week treatment period, the same test was administered to all students as a posttest. The data were analyzed by using analysis of covariance (ANCOVA). The statistical results showed that bridging analogies teaching strategy was an effective means of reducing the number of misconceptions students held about normal forces, frictional forces, tension, gravity, inertia, and Newton's third law.     

The stable set problem and the lift-and-project ranks of graphs

We study the lift-and-project procedures for solving combinatorial optimization problems, as described by Lovász and Schrijver, in the context of the stable set problem on graphs. We investigate how the procedures' performances change as we apply fundamental graph operations. We show that the odd subdivision of an edge and the subdivision of a star operations (as well as their common generalization, the stretching of a vertex operation) cannot decrease the N₀-, N-, or N₊-rank of the graph. We also provide graph classes (which contain the complete graphs) where these operations do not increase the N₀- or the N-rank. Hence we obtain the ranks for these graphs, and we also present some graph-minor like characterizations for them. Despite these properties we give examples showing that in general most of these operations can increase these ranks. Finally, we provide improved bounds for N₊-ranks of graphs in terms of the number of nodes in the graph and prove that the subdivision of an edge or cloning a vertex can increase the N₊-rank of a graph.Research of these authors was supported in part by a PREA from Ontario, Canada and research grants from NSERC.Mathematics Subject Classification (2000): 0C10, 90C22, 90C27, 47D20     

New polyphenylene‐g‐polystyrene and polyphenylene‐g‐polystyrene/poly(ε‐caprolactone) copolymers by combined controlled polymerization and cross‐coupling processes

1,4‐Dibromo‐2‐(bromomethyl)benzene and 1,3‐dibromo‐5‐(bromomethyl)benzene were used as initiators in the atom transfer radical polymerization of styrene in conjunction with CuBr/2,2′‐bipyridine as a catalyst. The resulting polystyrene (PSt)‐based macromonomers, possessing at one end a 2,5‐dibromophenylene or 3,5‐dibromophenylene moiety, were used in combination with 2,5‐dihexylbenzene‐1,4‐diboronic acid for Suzuki coupling in the presence of Pd(PPh₃)₄ as a catalyst or with the system NiCl₂/2,2′‐bipyridine/triphenylphosphine/Zn for Yamamoto polymerization. Polyphenylenes (PPs) with PSt chains as substitution groups were obtained. The same macromonomers were used in Yamamoto copolycondensation reactions, in combination with a poly(ε‐caprolactone) (PCL) macromonomer, and this resulted in PPs with PSt/PCL side chains. The obtained PPs had good solubility properties in common organic solvents at room temperature similar to those of the starting macromonomers. The new polymers were characterized with ¹H (¹³C) NMR, IR, and gel permeation chromatography. The optical properties of the polymers were monitored with UV and fluorescence spectroscopy. The thermal behaviors of the macromonomers and final PPs were investigated with differential scanning calorimetry and compared. The morphology of PPs containing PSt and PCL blocks was characterized with atomic force microscopy, and a microphase‐separated layered morphology was observed. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 879–896, 2005     

New approach to relativity and gravitation

A theory of gravitation, where the stress-energy tensor of the gravitational field is part of the source term of the geometric curvatures, is presented. The theory predicts correctly all the Newtonian and post-Newtonian effects of gravity currently considered as crucial. For extremely strong and nonstatic fields, such as are presumed to exist in quasars and exploding stars, new predictions differing from those of the conventional theory are implied. In the correspondence limit of special relativity the theory recovers the conservation of energy-momentum properly and seems to represent a more satisfactory extension of special theory of relativity.     

Tuning the surface hydrophobicity of polymer/nanoparticle composite films in the Wenzel regime by composition

Surface hydrophobicity of composite films containing polymer and nanoparticles has been studied as a function of composition. We show that the hydrophobicity can be tuned by adjusting the amount of particles in the two-component system. A sharp transition from a polymer-rich surface to a nanoparticles-rich surface was observed with increasing mass fraction of particles in spin-coated thin films. Water drops on the films did not slide down even at tilt angles of 90 degrees . Contact angle hysteresis increased with the mass fraction of particles indicating that the surface roughness increased as the surfaces remained in the Wenzel regime. Contact angle hysteresis data were quantitatively consistent with predictions of a recent theory.     

X-ray photoelectron spectroscopic investigation of conducting polymer blends

Electrochemically prepared films of conducting polymers of polypyrrole and polythiophene and their blends with polyamide have been investigated by X-ray photoelectron spectroscopy. In the N1s region of the spectra of films containing polypyrrole the peak corresponding to N⁺ at 402.0 eV is separated from that of neutral N. The intensity of the N⁺ peak can be correlated with the electrical conductivity of the films and the spectroscopically derived ratio of F/N⁺ is close to 4 indicating that one BF^-₄ dopant ion is incorporated for every oxidized nitrogen center. In the spectra of films of polythiophene and its blends peaks corresponding to S and S⁺ can not be resolved but again the F/C ratio correlates with the electrical conductivity.     

Principal Congruence Subgroups of Hecke Groups H（√q）

Using the notion of quadratic reciprocity, we discuss the principal congruence subgroups of the Hecke groups H（√q）,q 〉 5 prime number.     

Rhodium-catalyzed carbonylative arylation of alkynes with arylboronic acids: an efficient and straightforward method in the synthesis of 5-aryl-2(5H)-furanones

5-Aryl-2(5H)-furanones can be synthesized by the Rh-catalyzed reactions of arylboronic acids with internal alkynes under a CO atmosphere.     

Light harvesting and efficient energy transfer in a boron-dipyrrin (BODIPY) functionalized perylenediimide derivative

[reaction: see text] Click chemistry has been successfully applied in the synthesis of a bay region tetraboron-dipyrrin (BODIPY) appended perylenediimide (PDI). This light-harvesting molecule presents a large cross section for the absorption of light in the visible region. Excitation energy is efficiently channeled to the perylenediimide core. This novel antenna system is the first demonstration of the efficiency of energy transfer in a BODIPY-PDI bichromophoric system and appears to be highly promising for the design and synthesis of similar dendritic structures.     

A family of p-adic twisted interpolation functions associated with the modified Bernoulli numbers

The main purpose of this paper is to construct a family of modified p-adic twisted functions, which interpolate the modified twisted q-Bernoulli polynomials and the generalized twisted q-Bernoulli numbers at negative integers. We also give some applications and examples related to these functions and numbers.