The ?2-cohomology of hyperplane complements

We compute the l^2-Betti numbers of the complement of any finite collection of affine hyperplanes in complex n-space. At most one of the l^2-Betti numbers is non-zero. <br/

A Unified Approach to High-Gain Adaptive Controllers

It has been known for some time that proportional output feedback will stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback gain is sufficiently large. High-gain adaptive controllers achieve stability by automatically driving up the feedback gain monotonically. More recently, it was demonstrated that sample-and-hold implementations of the high-gain adaptive controller also require adaptation of the sampling rate. In this paper, we use recent advances in the mathematical field of dynamic equations on time scales to unify and generalize the discrete and continuous versions of the high-gain adaptive controller. We prove the stability of high-gain adaptive controllers on a wide class of time scales

The Miscible-Immiscible Quantum Phase Transition in Coupled Two-Component Bose-Einstein Condensates in 1D Optical Lattices

Using numerical techniques, we study the miscible-immiscible quantum phase transition in a linearly coupled binary Bose-Hubbard model Hamiltonian that can describe low-energy properties of a two-component Bose-Einstein condensate in optical lattices. With the quantum many-body ground state obtained from density matrix renormalization group algorithm, we calculate the characteristic physical quantities of the phase transition controlled by the linear coupling between two components. Furthermore we calculate the Binder cumulant to determine the critical point and draw the phase diagram. The strong-coupling expansion shows that in the Mott insulator regime the model Hamiltonian can be mapped to a spin 1/2 XXZ model with a transverse magnetic field.Comment: 10 pages, 10 figures, submitted to Phys. Rev.

TITAN Wireless Camera Control System

The Titan Camera Control System is an eletromechanical device that allows the user to wirelessly control a camera’s digital operations as well as physical orientation through the use of a mobile device application. The Titan system accepts input in the form of virtual user commands on the mobile app and performs system output in the form of sending photos/video from the camera back to the app as well as changing the orientation of the camera in accordance with the user’s commands

Data Logging System for a Synthetic Aperture Radar Unit

A small, existing radar unit lacked the ability to automatically store the data it was receiving, which made its use clunky and cumbersome. A system was constructed to allow an on-board microprocessor to track distance traveled, and automatically store the data output from the radar unit to a portable memory unit for later data processing. Distance traveled is determined using a specially designed mobile cart, which electronically converts the rotation of a wheel into an electrical signal while also providing stability for taking accurate radar measurements. The output data from the radar unit is stored as a properly-formatted sound file to allow for immediate data analysis

Responses to supplementation by dairy cows given low pasture allowances in different seasons 2. Milk production

Two factorial experiments were designed to determine the effects of stage of lactation, and season of the year, on cow responses to supplementary feeding. These experiments were conducted over consecutive years with 128 high genetic merit multiparous Holstein-Friesian cows in early, mid and late lactation in spring, summer, autumn and winter. At each stage of lactation, and in each season of the year, cows were offered a restricted pasture allowance (25 to 35 kg dry matter (DM) per cow per day), either unsupplemented (control) or with supplement at 50 MJ metabolizable energy (ME) per cow per day in experiment 1 and 80 MJ ME per cow per day in experiment 2. The two supplements given in both years were rolled maize grain (MG) and a mixture of foods formulated to nutritionally balance the diet (BR). In experiment 2, another treatment, of a generous pasture allowance (60 to 75 kg DM per cow per day) (AP), was imposed on an additional group of early lactation cows during each season. Direct milk solids (MS) (milk fat plus milk protein) responses in experiment 1 to MG were 169, 279, 195 and 251 g MS per cow per day in spring, summer, autumn and winter, respectively, while those to BR were 107, 250, 192, 289 g MS per cow per day. In experiment 2, however, milk solids responses to both supplements during spring were slightly below the control treatment, with values similar to those in experiment 1 in summer and autumn for cows on the BR but not the MG supplement. Milk solids responses to supplementary foods were largest during seasons of the year when the quantity and quality of pasture on offer resulted in the lowest milk solids yield from unsupplemented cows. When carry-over effects of feeding MG and BR on milk solids production were detected, they were only about half the magnitude of the direct effects. Serum urea concentrations were higher in control cows than those offered MG with a similar effect for BR in all but summer in experiment 1, while serum glucose concentrations were highest in winter and lowest in summer. The most important factor influencing milk solids responses was the relative food deficit (RFD) represented by the decline in milk solids yield of the respective control groups after,changing from a generous pasture allowance to restricted allowance when the feeding treatments were imposed. Total milk solids responses (direct and carry-over) to supplements were greatest when severe food restrictions, relative to the cows' current food demand, resulted in large reductions in milk solids yield of the control groups. The RFD was the best predictor of milk solids response to supplementary foods. Therefore, it is likely that cows are most responsive to supplementary foods during or immediately after the imposition of a severe food restriction