Convex Multivariable Trace Functions

For any densely defined, lower semi-continuous trace \tau on a C*-algebra A with mutually commuting C*-subalgebras A_1, A_2, ... A_n, and a convex function f of n variables, we give a short proof of the fact that the function (x_1, x_2, ..., x_n) --> \tau (f(x_1, x_2, ..., x_n)) is convex on the space \bigoplus_{i=1}^n (A_i)_{self-adjoint}. If furthermore the function f is log-convex or root-convex, so is the corresponding trace function. We also introduce a generalization of log-convexity and root-convexity called \ell-convexity, show how it applies to traces, and give a few examples. In particular we show that the trace of an operator mean is always dominated by the corresponding mean of the trace values.Comment: 13 pages, AMS TeX, Some remarks and results adde

Analysis and computations for a model of quasi-static deformation of a thinning sheet arising in superplastic forming

We consider a mathematical model for the quasi-static deformation of a thinning sheet. The model couples a first-order equation for the thickness of the sheet to a prescribed curvature equation for the displacement of the sheet. We prove a local in time existence and uniqueness theorem for this system when the sheet can be written as a graph. A contact problem is formulated for a sheet constrained to be above a mould. Finally we present some computational results

Dynamic characteristics of far-field radiation of current modulated phase-locked diode laser arrays

A versatile and powerful streak camera/frame grabber system for studying the evolution of the near and far field radiation patterns of diode lasers was assembled and tested. Software needed to analyze and display the data acquired with the steak camera/frame grabber system was written and the total package used to record and perform preliminary analyses on the behavior of two types of laser, a ten emitter gain guided array and a flared waveguide Y-coupled array. Examples of the information which can be gathered with this system are presented

Research on experiential psychotherapies

Reviews research on experiential or humanistic psychotherapies, including meta-analysis of outcome research and studies of particular change processes. Outcome meta-analysis shows large client pre-post change, as well as large controlled effects relative to untreated controls and statistical equivalence to nonexperiential psychotherapies, including CBT

Phase Separation of Saturated and Mono-unsaturated Lipids as determined from a Microscopic Model

A molecular model is proposed of a bilayer consisting of fully saturated DPPC and mono unsaturated DOPC. The model not only encompasses the constant density within the hydrophobic core of the bilayer, but also the tendency of chain segments to align. It is solved within self-consistent field theory. A model bilayer of DPPC undergoes a main chain transition to a gel phase, while a bilayer of DOPC does not do so above zero degrees centigrade because of the double bond which disrupts order. We examine structural and thermodynamic properties of these membranes and find our results in reasonable accord with experiment. In particular, order-parameter profiles are in good agreement with NMR experiments. A phase diagram is obtained for mixtures of these lipids in a membrane at zero tension. The system undergoes phase separation below the main-chain transition temperature of the saturated lipid. Extensions to the ternary DPPC, DOPC, and cholesterol system are outlined.Comment: 29 pages, 4 figures, 1 table. revised versio

Bearing detection in the presence of two sources of varying coherence using the complex cepstrum

The effect of the presence of two acoustic sources (one, the primary, whose location is to be detected) of varying coherence on a cepstral bearing finding procedure is experimentally studied. The coherence between the acoustic sources was altered by adding random noise of various SNR (signal-to-noise ratio) to the input signal of the primary source; the same base signal being fed to both sources. The results demonstrate that, when block liftering is used, the primary source bearing is reliably estimated for coherences as low as gamma sup 2 greater than or approx equal to 0.5. The results also imply that background noise (unreflected) of SNR greater than or approx equal to 10 dB will not markedly affect the accuracy of the bearing estimation algorithm

Development and Validation of NDE Standards for NASAs Advanced Composites Project

The adoption of composite materials in aircraft manufacturing for use in structural applications continues to increase but is still relatively new to the industry. Composite components have large development and certification costs in comparison to metallic structures. Traditional methods of nondestructive evaluation (NDE) used for isotropic materials such as metals may not be adequate for composite applications and therefore is a contributing factor to the cost and complexity of developing new structural composites. Additionally, the defects of interest in composite materials are significantly different from metals. Thus, good quality composite reference standards are essential to obtaining reliable and quantifiable NDE results. Ideally, reference standards contain flaws or damage whose NDE indications most closely represent those created by actual flaws/damage. They should also be easy to duplicate and inexpensive to manufacture. NASAs Advanced Composites Project, working with industry partners, developed a set of composite standards that contain a range of validated defects representing those typically found in aerospace composite materials. This paper will provide an overview of the standards fabricated, the manufacturing plans used to fabricate them, the types of defects included, and validation testing that has performed. Also discussed is an inter-laboratory round-robin test that is being performed on these standards. The paper will describe a guidance document being compiled to outline relevant inspection procedures for challenging and critical defects unique to composites where conventional techniques may not be appropriate