Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.     

Guard sequence optimization for block transmission over linearfrequency-selective channels

We show that the optimum length-ν guard sequence for block transmission over a linear Gaussian-noise dispersive channel with memory ν is a linear combination of the N information symbols of the block. A closed-form expression for the optimum guard sequence is derived subject to a total average energy constraint on the information and guard symbols. The achievable channel block throughput with the optimum guard sequence is compared with that achievable with two common guard sequence types, namely zero stuffing and cyclic prefix     

Differential–algebraic equations in multibody system modeling

Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Advances in the chemical synthesis of brassinosteroids

This review generalizes the latest advances in the chemical synthesis of the plant growth regulators brassinosteroids in 1990–1994.Institute of Bioorganic Chemistry, Belarus Academy of Sciences, 220141, Minsk, ul. Zhodinskaya, 5/2. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 507–544, July–August, 1997.     

Weierstrass Points and Regular Maps

It was shown by G. A. Jones and the first author in [8] that underlying any map on a compact orientable surface S there is a natural complex structure making S into a Riemann surface. In this paper we consider regular maps and enquire about the Weierstrass points on the underlying Riemann surface. We are particularly interested to know when these are geometric, i.e. whether they lie at vertices, face-centres or edge-centres of the map.     

Distribution of melamine in polyester–melamine surface coatings cured under nonisothermal conditions

The influence of experimental cure parameters on the diffusion of reactive species in polyester–melamine thermoset coatings during curing has been investigated with X‐ray photoelectron spectroscopy and attenuated total reflectance Fourier transform infrared. The diffusion of melamine plays a vital role in the curing process and, therefore, in the ultimate properties of coatings. At a low (<20%) hexamethoxymethylmelamine (HMMM) crosslinker concentration, the matrix composition is uniform, but at high HMMM concentrations, excess HMMM rapidly segregates to the air–coating interface. The rate of migration is governed by the difference in the surface free energies of polyester and HMMM and the concentration gradient of HMMM between the bulk and the surface. An increased rate of energy absorption also increases the rate of migration of HMMM to the surface. A physical model has been proposed to explain this surface segregation phenomenon in terms of cocondensation and self‐condensation reactions. It suggests that an appropriate amount of melamine can be segregated on the surface and allowed to self‐condense to form a desired thickness of a melamine topcoat through the control of the binder composition and cure conditions. This technique can be implemented to apply a melamine topcoat during cure. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 83–91, 2004     

Surface leakage currents in SiN/sub x/ passivated AlGaN/GaN HFETs

A novel guarded surface leakage test structure is used to isolate the surface and bulk leakage contributions to gate current in AlGaN/GaN HFETs. Passivation with various recipes of SiN/sub x/ always resulted in the commonly observed increase in gate leakage, which was found to be dominated by bulk leakage through the AlGaN. However, high temperature deposited SiN/sub x/ recipes gave a 1-2 orders reduction in surface leakage, whereas low temperature deposition gave an increase. Gate lag measurements were found to correlate closely with the surface leakage component, giving direct evidence that the key device problem of current slump is associated with current flow at the AlGaN surface.     

Characterization and comparison of PECVD silicon nitride and silicon oxynitride dielectric for MIM capacitors

In this letter, we report on the electrical characteristic and the comparison of the metal-insulator-metal (MIM) capacitors with PECVD silicon nitride (SiN) and silicon oxynitride (SiON). Both capacitors are found to exhibit low leakage and high breakdown field strength, as well as absence of dispersive behavior, good linearity, and comparable quality factor behaviors.     

Mechanical stress control in a VLSI-fabrication process: a method for obtaining the relation between stress levels and stress-induced failures

An ideal fabrication process is designed to minimize mechanical stress in semiconductor devices and to improve device reliability. Mechanical stress levels were predicted by in-house simulations supported by a thin-film database. These stress levels were correlated with stress-induced defects by TEM analysis supported by fail bit addressing on matured megabit SRAMs. Amorphous-doped silicon film with various annealing temperatures were used for the gate electrode to change the mechanical stress in devices and to get the direct relationship between predicted stress levels and stress related defects. The authors describe brief guidelines for suppressing dislocations in the small geometry shallow-trench isolation process utilizing this system. Polysilicon thickness in the W-polycide gate electrode is designed to minimize mechanical stress in the gate oxide and to suppress the gate oxide failure in probe and class tests. Moreover, critical stress generates dislocations during post source/drain ion implantation anneal obtained by a ball indentation method. This indicated that lower temperature anneal is effective in suppressing the dislocations. A two-step anneal was introduced to suppress dislocations and to enable higher ion activation.