Extension is a three-sectional, one-movement composition for orchestra exploring various permutations of a single motivic unit. The central priority has been to present this motive in a variety of textural situations with a harmonic accompaniment evolving from a macrotonal to a microtonal setting. Some of the devices utilized to realize this priority are mixed-instrument timbral combinations, tone clusters, multiphonics for brass and woodwinds, multiple stops for strings, and superimpositions of multiphonics. Extension is unique in two areas. First, the evolutionary progression from a macrotonal to microtonal harmonic texture is made possible by expanding the priorities of instrumental performing. Second, the use of multiphonics for full orchestra is unique to this work.

We survey standard topics in elementary differential geometry and complex analysis to build up the necessary theory for studying applications of univalent harmonic function theory to minimal surfaces. We then proceed to consider convex combination harmonic mappings of the form f=sf_1+(1-s) f_2 and give conditions on when f lifts to a one-parameter family of minimal surfaces via the Weierstrauss-Enneper representation formula. Finally, we demand two minimal surfaces M and M' be locally isometric, formulate a system of partial differential equations modeling this constraint, and calculate their symmetry group. The group elements generate transformations that when applied to a prescribed harmonic mapping, lift to locally isometric minimal surfaces with varying graphs embedded in mathbb{R}^3.

A planar harmonic mapping is a complex-valued function ƒ : D → C of the form ƒ(x+iy) = u(x,y) + iv(x,y), where u and v are both real harmonic. Such a function can be written as ƒ = h+g where h and g are both analytic; the function w = g'/h' is called the dilatation of ƒ. This thesis considers the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping p;(z) = z/(1-z) with respective dilatations e^iθz and e^ipz, θ, p ∈ R. We prove that any such convolution is univalent. We also derive a convolution identity that extends this result to shears of p(z) = z/(1-z) in other directions.

Thesis: M.S., Massachusetts Institute of Technology, Sloan School of Management, 1980 / Bibliography: leaf 53. / by Jai Yong Oum. / M.S. / M.S. Massachusetts Institute of Technology, Sloan School of Management

Results of research on surface emission from a waveguide due to second-harmonic generation are presented. This concept has been applied and demonstrated here in the InP-InGaAsP material system for the first time, using a fundamental wavelength of 1.32 |im and a harmonic surface emission at 660 nm. The surface emission is the result of the nonlinear mixing of two counterpropagating modes in a waveguide. The theory of nonlinear optics that produces this effect is explained, leading up to a model that describes the behaviour of the surface emitting waveguide (SEWG). This model is then used to design a pseudo-optimized structure that was subsequently grown, characterized and tested. Device performance and behaviour are compared with theoretical predictions. / Thesis / Master of Engineering (ME)

No / A coplanar edge-fed triangular patch antenna with an integrated stubline is proposed for harmonic rejection application. The design is aimed to achieve a good impedance matching to 50 ω at the fundamental frequency while suppressing radiation of the first and second harmonics. The antenna is attended to operate around 1GHz, with acceptable power gain above 1dBi and less than -15dBi at the harmonics. Simulated and measured results show a reasonable agreement.

Most digital control architectures for power system applications require synchronization with the distribution system voltage. Therefore, a phase-locked loop (PLL), implemented in a DSP, is generally among the digital control blocks of the control system. The PLL analyzes the bus voltage and provides power system information for some of the other blocks to do further calculation. Thus, the performance of the PLL has a broad impact on the system performance. Small-scale power systems, such as naval systems, pose a challenging environment for PLL design due to voltage distortion and variation in the fundamental frequency that is large as compared to large terrestrial systems. Our objective is to improve the accuracy of the PLL digital block and hence enhance the digital control system. This research compares two PLL algorithms, as well as the use of a PI controller or lag controller with respect to their steady state and transient performance.

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