Stable branching rules for classical symmetric pairs

We approach the problem of obtaining branching rules from the point of view of dual reductive pairs. Specifically, we obtain a stable branching rule for each of 10 classical families of symmetric pairs. In each case, the branching multiplicities are expressed in terms of Littlewood-Richardson coefficients. Some of the formulas are classical and include, for example, Littlewood's restriction rule as a special case.Comment: 26 page

Introduction to Theatre Arts: More to the Stage Picture than Meets the Eye (& Ear)

As per our course theme, there’s “more to the stage picture than meets the eye (& ear).” Before an actor even enters a rehearsal studio or first steps onto the stage, months and often years of creative work and research will have gone into that play and production. In this course we will explore and try our hand at some of that pre-production creativity, as well as improvising, adapting, performing and writing short scenes and monologues that will be created and presented in small groups as part of your Final Project

Seller versus Broker: Timing of Promotion

Sellers and brokers may differ in preferred timing of costly promotion. Sellers with holding costs are anxious to sell. Sellers with showing costs want a slower approach. We find a standard listing contract where the broker chooses promotion timing can be efficient if sellers have no significant holding or showing costs. We then delineate the efficient listing contract provisions for duration and fee structure for sellers who have holding and/or showing costs.

Sequence of Tissue Responses in the Early Stages of Experimental Allergic Encephalomyelitis (EAE): Immunohistochemical, Light Microscopic, and Ultrastructural Observations in the Spinal Cord

Experimental allergic encephalomyelitis (EAE) was induced in adult Lewis rats with purified guinea pig CNS myelin and Freund's adjuvant. As soon as the very earliest clinical signs appeared the animals were perfused with fixatives and the spinal cord analyzed by electron microscopy, silver methods, and immunocytochemistry. Our findings suggest that in the early stages of EAE a sequence of events can be traced, although these events frequently overlap. The earliest morphological change appears to be astrocytic edema in both the cell body and processes. Increased amounts of glycogen particles and dispersion of glial filaments are prominent. These changes seem to occur just prior to the time when inflammatory cells begin to penetrate the capillary walls. Invasion of the neuropil mainly by macrophages and lymphocytes closely follows. Both macrophages and microglia seem to participate in phagocytosis of oligodendrocytes and myelin. Demyelination, however, is not a prominent feature at this early stage

Towards 3D Magnetic Force Microscopy

Magnetic force microscopy (MFM) is long established as a powerful tool for probing the local manifestation of magnetic nanostructures across a range of temperatures and applied stimuli. A major drawback of the technique, however, is that the detection of stray fields emanating from a samples surface rely on a uniaxial vertical cantilever oscillation, and thus are only sensitive to vertically oriented stray field components. The last two decades have shown an ever-increasing literature fascination for exotic topological windings where particular attention to in-plane magnetic moment rotation is highly valuable when identifying and understanding such systems. Here we present a new method of detecting in-plane magnetic stray field components, by utilizing a home made split-electrode excitation piezo that allows the simultaneous excitation of a cantilever at its fundamental flexural and torsional modes. This allows for the joint acquisition of traditional vertical mode (V-MFM) images and a lateral MFM (L-MFM) where the tip-cantilever system is only sensitive to stray fields acting perpendicular to the torsional axis of the cantilever

Production and characterization of biopowders made from gel-forming polymers

To date, many bioactive compounds have been encapsulated within microparticles to achieve specific purpose such as stabilization, protection, isolation, controlled-release, taste-masking, improving aesthetic and handling qualities. However, much work is still needed particularly to determine the way to control the size and shape of microparticles produced using the air-atomization method. In addition, the effect of drying on the properties of dried biopowders has yet to be evaluated. These problems form the missing gap that will be addressed by this project. In this work, alginate was chosen as a model polymeric material to form the biopowders. The first part of this work was to determine the key physical properties of the polymer solution since they have significant influence on the characteristics (i.e. size) of the particles formed. The density of Na-alginate solution increased slightly as the alginate concentration increased whereas the solution apparent viscosity at zero shear rates exhibited a typical exponential increment. A new method, LCP coefficient method, to measure surface tension of viscous biopolymer solutions has been developed. The surface tension at low alginate concentration (5 -20 g/L) was about 68 -72mN/m and it showed a decreasing trend as the concentration increased. Air-assist external mixing atomization with low mair/rituqwas developed to produce wet particles of wide range of mean diameters, from 50 to 2300 µm. A semi-empirical size prediction model was developed to assist and enhanced the productivity of desired size by changing the physical properties of the operating conditions. Increased in Weber number produced smaller particles size, wider particles size distribution and more spherical particles. Finally, biopowders were formed by drying the wet particles. The results showed that drying temperature, intermittent mixing, sample thickness and wet particle size were among factors affecting the drying kinetics. Effective diffusivity value of wet alginate particles was ranged from 5.4 x 10·10 to 8.0 x 10·9 m2/s while the activation energy was ranged from 15 to 20 KJ/mol. The drying kinetic was modelled according to a logarithmic model. In addition, smaller wet particles (75 µm) were found to agglomerate during the oven-drying process whereas larger particles (1300 µm) did not agglomerate. Freeze­drying process did not cause agglomeration for both particle sizes. The type of drying method (oven-drying or freeze-drying) was found to have significant influence on the size, size distribution and physical appearance of the biopowders formed