Zeros of functions with finite Dirichlet integral

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

     

Restructuring ordered binary trees

We consider the problem of restructuring an ordered binary tree T, preserving the in-order sequence of its nodes, so as to reduce its height to some target value h. Such a restructuring necessarily involves the downward displacement of some of the nodes of T. Our results, focusing both on the maximum displacement over all nodes and on the maximum displacement over leaves only, provide (i) an explicit tradeoff between the worst-case displacement and the height restriction (including a family of trees that exhibit the worst-case displacements) and (ii) efficient algorithms to achieve height-restricted restructuring while minimizing the maximum node displacement.     

Writing Waveguide in LN With fs Laser

We investigated the waveguide formation in Lithium Niobate with Femtosecond laser pulse writing directly. The output optical field through waveguide has been observed and refractive-index change was characterized by using grating method.     

Polarity control of GaN epilayers grown on ZnO templates

We report the successful growth of Ga-polar GaN epilayers on O-polar ZnO templates pre-deposited on c-sapphire. Prior to GaN growth, NH₃ is exposed onto the ZnO template. The polarity of the GaN layers is confirmed by etching of the surface and by conversion beam electron diffraction (CBED), while the O-polar ZnO is confirmed by CBED. It is suggested that the NH₃ pre-exposure helps form a Zn₃N₂ layer, which possesses inversion symmetry and inverts the crystal from anion polar to cation polar.     

A second-order accurate numerical method for a fractional wave equation

We study a generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the error is of order k ² + h ², where k and h are the parameters for the time and space meshes, respectively.     

Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields

An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given.     

Characterization of charge trapping in submicrometer NMOSFET's bygate capacitance measurements

Trapping of net positive charge at low gate stress voltage, and of net negative charge at high gate stress voltage, is observed through changes in the gate-to-drain capacitance of the stressed junction. These observations can be explained in terms of electron trapping, hole trapping, and generation of acceptor-like interface states located in the upper half of the bandgap. Channel shortening is also observed and found to exhibit a logarithmic time dependence     

The harmonic consistency index for the analytic hierarchy process

A new consistency measure, the harmonic consistency index, is obtained for any positive reciprocal matrix in the analytic hierarchy process. We show how this index varies with changes in any matrix element. A tight upper bound is provided for this new consistency measure when the entries of matrix are at most 9, as is often recommended. Using simulation, the harmonic consistency index is shown to give numerical values similar to the standard consistency index but it is easier to compute and interpret. In addition, new properties of the column sums of reciprocal matrices are obtained.