Realizations for Schur upper triangular operators centered at an arbitrary point

Reproducing kernel spaces introduced by L. de Branges and J. Rovnyak provide isometric, coisometric and unitary realizations for Schur functions, i.e. for matrix-valued functions analytic and contractive in the open unit disk. In our previous paper [12] we showed that similar realizations exist in the nonstationary setting, i.e. when one considers upper triangular contractions (which appear in time-variant system theory as transfer functions of dissipative systems) rather than Schur functions and diagonal operators rather than complex numbers. We considered in [12] realizations centered at the origin. In the present paper we study realizations of a more general kind, centered at an arbitrary diagonal operator. Analogous realizations (centered at a point of the open unit disk) for Schur functions were introduced and studied in [3] and [4].     

The Jacobian conjecture,the <Emphasis Type="Italic">d</Emphasis>-inversion approximation and its natural boundary

Let F ? \mathbbC[ X, Y ]² F \in \mathbb{C}{\left[ {X,\,Y} \right]^2} be an étale map of degree deg F = d. An étale map G ? \mathbbC[ X,Y ]² G \in \mathbb{C}{\left[ {X,Y} \right]^2} is called a d-inverse approximation of F if deg G ≤ d and F ◦ G =(X + A(X, Y), Y + B(X, Y)) and G ◦ F =(X + C(X, Y), Y + D(X, Y)), where the orders of the four polynomials A, B, C, and D are greater than d. It is a well-known result that every \mathbbC² {\mathbb{C}^2} -automorphism F of degree d has a d-inverse approximation, namely, F ⁻¹. In this paper, we prove that if F is a counterexample of degree d to the two-dimensional Jacobian conjecture, then F has no d-inverse approximation. We also give few consequences of this result. Bibliography: 18 titles.     

A moderate deflection composite helicopter rotor blade model with an improved cross-sectional analysis

The compatibility between a composite beam cross-sectional analysis based on the variational asymptotic approach, and a helicopter rotor blade model which is part of a comprehensive rotorcraft analysis code is examined. It was found that the finite element cross-sectional analysis code VABS can be combined with a moderate deflection rotor blade model in spite of the differences between the formulations. The new YF/VABS rotor blade model accounts for arbitrary cross-sectional warping, in-plane stresses, and moderate deflections. The YF/VABS composite rotor blade model was validated against experimental data and various rotor blade analyses by examining displacements and stresses under static loads, as well as aeroelastic stability of a composite rotor blade in hover, and forward flight vibratory hubloads of a four bladed composite rotor.     

New parameter correlations for deep penetration welding with high energy focused beams

As a result of the unification of two models previously described by the author, a three-dimensional treatment of the workpiece temperature distribution, which takes into consideration the solid to liquid phase change of the processed material, is presented for deep penetration welding (d.p.w.) with high energy focused beans.The new model improves the accuracy of weld geometry prediction by better correlating the shape, width and depth of the cross-section of the resolidified weld with beam characteristics, material thermophysical properties, workpiece velocity and preheating temperature.     

How can self-regulated learning support the problem solving of third-grade students with mathematics anxiety?

The study compares 140 third-grade Israeli students (lower and higher achievers) who were either exposed to self-regulated learning (SRL) supported by metacognitive questioning (the MS group) or received no direct SRL support (the N_MS group). We investigated: (a) mathematical problem solving performance; (b) metacognitive strategy use in three phases of the problem-solving process; and (c) mathematics anxiety. Findings indicated that the MS students showed greater gains in mathematical problem solving performance than the N_MS students. They reported using metacognitive strategies more often, and showed a greater reduction in anxiety. In particular, the lower MS achievers showed these gains in the basic and complex tasks, in strategy use during the on-action phase of the problem solving process and a decrease in negative thoughts. The higher achievers showed greater improvement in transfer tasks and an increase in positive thoughts towards mathematics. Both the theoretical and practical implications of this study are discussed.     

Preparation,proton and carbon-13 structure determination,and fungicidal activity of chlorinated 1-arylamino-1H-pyrrole-2,5-diones

1-(2′,4′-dichloro)phenylamino-1H-pyrrole-2,5-dione and 1-(2′,4′,6′-trichloro)phenylamino-1H-pyrrole-2,5-dione were prepared via direct chlorination of 2-phenyl-3-oxo-6-hydroxy-2H-pyridazine. Both pmr and mass spectroscopy clearly showed that dichloro substitution occurred in the aromatic moiety and not in the vinylic region of the molecule. The former method showed that pyridiazine- to pyrrole-ring isomerization had occurred already at the level of dichlorination. The identical 2′,4′-dichlorophenyl and 2′,4′,6′-trichlorophenylpyr-rolediones were also prepared by reaction of maleic anhydride with the appropriate arylhydrazine. Similar 2′,4-dichlorophenyl and 2′,4′,6′-trichlorophenyl analogues were prepared using dichloromaleic anhydride. Cmr spectroscopic techniques were used for pyridazine-/pyrrole-ring stereochemical assignment of products derived from dichloromaleic anhydride. 1-(2′,4′-dichloro)phenylamino-1H-pyrrole-2,5-dione and the trichloro-phenyl analogue were shown to exhibit fungicidal activity in both in-vivo and in-vitro assays.