Depth profile analysis of polyimide film treated by potassium hydroxide

The structural change in the depth direction of a polyimide (UPILEX‐S) film treated in alkaline solution, which was a representative surface treatment used to form a seed layer for plating and to improve the adhesive strength, was analyzed by means of micro Fourier transform infrared attenuated total reflection (FTIR‐ATR) line analysis with gradient shaving preparation. The polyimide film was treated with KOH. The imide ring opened through the alkaline treatment, and the amide structure and carboxylic acid salt were formed. The attainment depth of this structural change was almost proportional to the treatment time, and it reached about 8 μm after a 30‐min treatment. The degree of structural change through the alkaline treatment was almost constant after it reached a considerably degraded stage, and the chemically changed region penetrated into the inner part of the film from the surface. An intermediate layer before the final degraded stage appeared in the treated layer, and its thickness increased with the treatment time. The region that was changed chemically by the alkaline treatment progressed to the inner part simultaneously and continuously as the treatment time increased. The combined use of gradient shaving preparation and micro FTIR‐ATR line analysis was found to be extremely effective for the depth profiling of organic materials. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2071–2078, 2003     

Solving of second order nonlinear PDE problems by using artificial controls with controlled error

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region inR ². We transfer this problem to a new problem of second order nonlinear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error inL ₁ is controlled.     

On p-Extensions of Fields of Characteristic p

It is proved that a Galois extension of a field of characteristic p is completely determined by its Galois group and the endomorphism of the additive group of the group algebra that corresponds to the raising to the power p.     

Generalized Artin–Hasse and Iwasawa Formulas for the Hilbert Symbol in a High-Dimensional Local Field

The generalized Hilbert symbol in a cyclotomic extension of an absolutely unramified higher local field of characteristic 0 with a perfect last residue field of characteristic p > 2 is considered. Generalized Artin–Hasse and Iwasawa formulas are derived from an explicit Kummer Type Vostokov formula. Bibliography: 13 titles.     

A Kinematic Formula for Affine Diameters and Affine Medians of a Convex Set

For a planar convex set K with C ²-smooth boundary, the area of the set of the points lying on a given number of affine diameters of K is estimated. As a corollary, it is proved that the area of K is at most pM² /4\pi M^2 /4 , where M is the largest length of a chord of K halving the area of K. Bibliography: 2 titles.     

Multipulse regimes of excitation of optical superradiance due to a two-photon transition

Multimode triggered optical superradiance due to a two-photon transition is theoretically studied. Kinetic equations are derived for the dynamics of cooperative development of coherence and population inversion of optical centers interacting with each other through a common field of emitted photons. Various regimes of triggering of optical superradiance due to a two-photon transition are considered. The possibility of creating a quantum photomultiplier on the basis of the triggered optical superradiance is discussed.     

Focusing of singular beams

The process of focusing of an inhomogeneously polarized beam passed through a system consisting of a uniaxial crystal and a polarization filter is considered. It is shown that the action of this system is equivalent to the action of a phase transparency with a complex relief of the refractive index. In particular, if the angle between the axes of the quarter-wave plate and the polarizer is equal to 45°, this transparency has a helicoidal relief. Simultaneously, two singular beams with different curvatures of their wavefronts arise in the transparency. The action of the lens consists in formation of a combined singular beam having three focal waists. The boundary wave arising upon focusing is able not only to form a new spectrum of toroidal vortices, but also to straighten the focusing region, forming a fairly extended range with a weak divergence.     

Decrease in the group velocity of a light pulse in the Bose-Einstein condensate of a dilute gas

A semiclassical theory of electromagnetically induced transparency in a Bose-Einstein condensate is considered. A nonlinear Schrödinger equation that describes the interaction of the Bose-Einstein condensate with an electromagnetic field is derived. An analysis of the obtained solutions to this equation demonstrates a decrease in the group velocity of the light pulse.