Normalization of complex-valued planar vector fields which degenerate along a real curve

Taking as a start point the recent article of Meziani [7], we present several results concerning the normalization of a class of complex vector fields in the plane which degenerate along a real curve. We mainly deal with operators with finite regularity and analyze both the local situation as well as the case of normalization near a circle. Some related questions (e.g., on semi-global solvability and on the normalization of a class of generalized Mizohata operators) are also discussed.     

Rank one perturbations at infinite coupling in Pontryagin spaces

In this paper we relate the operators in the operator representations of a generalized Nevanlinna function N(z) and of the function −N(z)⁻¹ under the assumption that z=∞ is the only (generalized) pole of nonpositive type. The results are applied to the Q-function for S and H and the Q-function for S and H^∞, where H is a self-adjoint operator in a Pontryagin space with a cyclic element w, H^∞ is the self-adjoint relation obtained from H and w via a rank one perturbation at infinite coupling, and S is the symmetric operator given by S=H∩H^∞.     

Investigations of low- and high-spin states of <Superscript>132</Superscript>La

The fusion evaporation reaction ¹²²Sn(¹⁴N, 4n)¹³²La was used to populate the high-spin states of ¹³²La at the beam energy of 60 MeV. A new band consisting of mostly E2 transitions has been discovered. This band has the interesting links to the ground state 2^- and the isomeric state 6^-. A new transition of energy 351 keV connecting the low-spin states of the positive-parity band based on the πh _11/2 ⊗ νh _11/2 particle configuration, has been found. This has played a very important role in resolving the existing ambiguities and inconsistencies in the spin assignment of the band head. Received: 12 August 2002 / Accepted: 18 March 2003 / Published online: 7 May 2003     

Attractors for 2D-Navier-Stokes models with delays

The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays, etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation.     

Controlling rough paths

We formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints. This allows us to define a good notion of integral with respect to irregular paths with Hölder exponent greater than 1/3 (e.g. samples of Brownian motion) and study the problem of the existence, uniqueness and continuity of solution of differential equations driven by such paths. We recover Young's theory of integration and the main results of Lyons’ theory of rough paths in Hölder topology.     

A priori estimates and existence of positive solutions for strongly nonlinear problems

In this paper we study the existence of positive solutions for a nonlinear Dirichlet problem involving the m-Laplacian. The nonlinearity considered depends on the first derivatives; in such case, variational methods cannot be applied. So, we make use of topological methods to prove the existence of solutions. We combine a blow-up argument and a Liouville-type theorem to obtain a priori estimates. Some Harnack-type inequalities which are needed in our reasonings are also proved.     

Estimation of growth rate in unidirectionally solidified multicrystalline silicon by the growth-induced striation method

Multicrystalline silicon was grown by unidirectional solidification method using the accelerated crucible rotation technique. The application of the accelerated crucible rotation technique in unidirectional solidification method induced growth striations across the axial direction of the grown crystal. This striation pattern was observed from carbon concentration distribution, obtained by using Fourier transform infrared spectroscopy. The generated striation pattern was found to be weak and discontinuous. Some striations were absent, probably due to back melting, caused during each crucible rotation. From the growth striations and applied time period in crucible rotation, the growth rate was estimated by using Fourier transformation analysis.     

Minimal Bar Tableaux

Motivated by recent results of Stanley, we generalize the rank of a partition λ to the rank of a shifted partition S(λ). We show that the number of bars required in a minimal bar tableau of S(λ) is max(o, e + (ℓ(λ) mod 2)), where o and e are the number of odd and even rows of λ. As a consequence we show that the irreducible projective characters of S_n vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur’s Q_λ symmetric functions in terms of the power sum symmetric functions. Received November 20, 2003     

The role of As2O3 on the stability and some physical properties of PbO-Sb2O3 glasses

PbO-Sb₂O₃ glasses added with different concentrations of As₂O₃ (10-55 mol%) were prepared to understand their IR spectra, elastic properties (Young's modulus E, Shear modulus G, microhardness H), optical absorption and dielectric properties (constant ε, loss tan δ, ac conductivity σ_ac over a moderately wide range of frequency and temperature and breakdown strength in air medium at room temperature). Results have indicated that the structure of the PbO-Sb₂O₃-As₂O₃ glass is more rigid when the concentration of As₂O₃ is around 40 mol%.     

旋光性与电光效应交互作用及其对旋光晶体电光Q开关的影响

研究了晶体的旋光性与电光效应的交互作用、以及此交互作用对 旋光晶体电光Q开关的影响. 关键词： 旋光性 电光效应 电光Q开关 3Ga₅SiO₁₄晶体')" href="#">La₃Ga₅SiO₁₄晶体