Product of two positive contractions

Several characterizations are given for a square matrix that can be written as the product of two positive (semidefinite) contractions. Based on one of these characterizations, and the theory of alternating projections, a Matlab program is written to check the condition and construct the two positive contractions whose product equal to the given matrix, if they exist. (C) 2016 Elsevier Inc. All rights reserved

Processing Case Study with AVO and Pore Pressure Analyses: Eugene Island, Gulf of Mexico

Seismic exploration uses numerous tools and techniques for detecting hydrocarbon reservoirs in conventional plays as found on the shelf of the northern Gulf of Mexico (GOM). The tools include seismic data-processing attributes, well-log calibration, and AVO (Amplitude Versus Offset) and pore pressure analyses. While the supporting theory for each method has been well established, an integration of the methods to a real exploration project can be confusing for the uninitiated. Given a seismic dataset and well-log curves, how exactly would someone process and analyze the data using the techniques listed? This research proposes a practical workflow for creating an end product for exploration applications. Using a seismic dataset in the GOM and several well log datasets, an integration of the processed seismic image with pore pressure analysis, petrophysical analysis and calibrated seismic attributes derived from the petrophysical analysis indicates the area would be classified as a Class III AVO environment which is supported by the geologic background. The dataset is further processed to completion and then used to generate AVO and pore pressure fields. Available well logs in the area are then compared and tied to the seismic, in order to validate the presence of any potential hydrocarbon attributes. An abnormal overpressure zone is determined by seismic velocity analysis and confirmed by the structural continuity of reflections, which was bound within a fault block. The seismic attributes indicated a potential gas reservoir on the downthrown side of the fault block, which would correlate with the proximity of the abnormal pressure. The exploration tools of seismic data analysis, well log analysis, AVO analysis, and pore pressure analysis are found to be strongly correlated by this study.Earth and Atmospheric Sciences, Department o

MINKOWSKI PRODUCT OF CONVEX SETS AND PRODUCT NUMERICAL RANGE

Let K-1, K-2 be two compact convex sets in C. Their Minkowski product is the set K1K2 = {ab : a is an element of K-1, b is an element of K-2}. We show that the set K1K2 is star-haped if K-1 is a line segment or a circular disk. Examples for K-1 and K-2 are given so that K-1 and K-2 are triangles (including interior) and K1K2 is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product numerical range in the study of quantum information science. Additional results and open problems are presented

Cell polarization during monopolar cytokinesis

During cytokinesis, a specialized set of proteins is recruited to the equatorial region between spindle poles by microtubules and actin filaments, enabling furrow assembly and ingression before cell division. We investigate the mechanisms underlying regional specialization of the cytoskeleton in HeLa cells undergoing drug-synchronized monopolar cytokinesis. After forced mitotic exit, the cytoskeleton of monopolar mitotic cells is initially radially symmetric but undergoes a symmetry-breaking reaction that simultaneously polarizes microtubules and the cell cortex, with a concentration of cortical furrow markers into a cap at one side of the cell. Polarization requires microtubules, F-actin, RhoA, Myosin II activity, and Aurora B kinase activity. Aurora B localizes to actin cables in a gap between the monopolar midzone and the furrow-like cortex, suggesting a communication between them. We propose that feedback loops between cortical furrow components and microtubules promote symmetry breaking during monopolar cytokinesis and regional specialization of the cytoskeleton during normal bipolar cytokinesis

Preliminary Jitter Stability Results for the Large UV/Optical/Infrared (LUVOIR) Surveyor Concept Using a Non-Contact Vibration Isolation and Precision Pointing System

The need for high payload dynamic stability and ultra-stable mechanical systems is an overarching technology need for large space telescopes such as the Large Ultraviolet / Optical / Infrared (LUVOIR) Surveyor concept. The LUVOIR concept includes a 15-meter-diameter segmented-aperture telescope with a suite of serviceable instruments operating over a range of wavelengths between 100nm to 2.5 um. Wavefront error (WFE) stability of less than 10 picometers RMS of uncorrected system WFE per wavefront control step represents a drastic performance improvement over current space-based telescopes being fielded. Through the utilization of an isolation architecture that involves no mechanical contact between the telescope and the host spacecraft structure, a system design is realized that maximizes the telescope dynamic stability performance without driving stringent technology requirements on spacecraft structure, sensors or actuators. Through analysis of the LUVOIR finite element model and linear optical model, the wavefront error and Line-Of-Sight (LOS) jitter performance is discussed in this paper when using the Vibration Isolation and Precision Pointing System (VIPPS) being developed cooperatively with Lockheed Martin in addition to a multi-loop control architecture. The multi-loop control architecture consists of the spacecraft Attitude Control System (ACS), VIPPS, and a Fast Steering Mirror on the instrument. While the baseline attitude control device for LUVOIR is a set of Control Moment Gyroscopes (CMGs), Reaction Wheel Assembly (RWA) disturbance contribution to wavefront error stability and LOS stability are presented to give preliminary results in this paper. CMG disturbance will be explored in further work to be completed