Proper holomorphic mappings between hyperbolic product manifolds

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.Comment: 9 pages; small revisions in the abstract & on p. 1, which reflect better the major revision (in Thm. 1.5) made in v

Stability of water-in-oil-in-water emulsions formed by membrane emulsification : a thesis presented in partial fulfilment of the requirements for the degree of Master of Technology in Food Technology at Massey University, Palmerston North, New Zealand

The main objectives of this study were to determine i. The effectiveness of encapsulating whey protein concentrates (WPC) within water-in-oil-in-water multiple emulsions produced by membrane emulsification. ii. The effect of the primary and secondary emulsification conditions and membrane operating parameters on the multiple emulsion properties; of particular concern were the yield and physical stability of the emulsions. The multiple emulsions were prepared by a two-stage emulsification process. The emulsification conditions were varied widely to determine the optimum conditions for the production of multiple emulsions. Ultra-Turrax, ultrasound and valve homogenisation were tried for the preparation of the primary emulsion; an Ultra-Turrax and Shirazu porous glass (SPG) membrane emulsification were used for secondary emulsification. The standard primary emulsions (water-in-oil) were prepared with 10% of the WPC and 6.4% glucose (as a marker) in the water phase with a water-in-oil volume fraction of 0.25. The oil phase (soybean oil) consisted of 10% hydrophobic emulsifier (Polyglycerol polyricinoleate [PGPR] or Span 80). Typically pre-emulsification was carried out in an Ultra-Turrax at 20500 rpm and the primary emulsification was done in a homogeniser at a pressure of 500/100 bars in the two stages; secondary emulsions were prepared with an SPG membrane of pore size 2μm or 3.8µm with the dispersed phase (water-in-oil) being pushed through the pores of the membrane at a specific transmembrane pressure (125-150 kPa) and dispersed phase flux into a continuous phase (water with a hydrophilic emulsifier concentration, usually Tween 80, of 1%) flowing through the inside of the membrane at a particular velocity (standard of 1 m/s). The yield of the multiple emulsions formed was estimated by measuring glucose release using an Advantage Glucose meter. Unlike Span 80, PGPR was able to form stable o/w emulsions and hence the initial yield of the multiple emulsions varied from 80% at 2.5% to 100% at 10% PGPR. The higher the concentration of water in the inner phase the lower the yield of the multiple emulsions and the higher the droplet size of the primary emulsions. A valve homogeniser gave the best results for primary emulsification. Of the 3 homogenisation pressures (250 bar, 500 bar, 1000 bar) tried, the w/o emulsion produced with 500 bar and 10% PGPR was taken as the standard as this was found to be stable for 6 months without physical damage. A 30% maximum loading of the WPC in the inner water phase was also determined. A further increase may destabilise the process by causing blockage to the membrane pores. The yield as well as the droplet size of the multiple emulsions was found to increase as the membrane pore-size was increased from 1.4 µm to 3.8 µm. Transmembrane pressure and continuous phase velocity did not have much influence on the yield of the multiple emulsions. However an increase in continuous phase velocity increased the opacity of the serum layer formed indicating that an increased amount of smaller droplets were formed. The dispersed phase flux was increased by increases in any of the transmembrane pressure, PGPR concentration and membrane pore-size. Hydrophilic emulsifiers (whey protein isolate, soy protein isolate and sodium caseinate) did not influence the yield; however the Tween 80 stabilised multiple emulsions showed a smaller droplet size. An increase in temperature from 20 - 50°C resulted in a lower yield as well as a higher droplet size. The osmotic gradient set up by glucose and WPC in the inner phase of the emulsion resulting in an influx of water from the outer phase causing bulging of the droplets. Sorbitol added at 1.7% in the outer phase gave a high initial yield (100%) as well as a low droplet size (2-3 µm). The cream layer formed as a result of storage was found to decrease with increase in sorbitol concentration (to 5.9%) due to the lower size ot the droplets formed. The key issues identified were to find an alternative to PGPR with lower Accepted Daily Intake (ADI) value without compromising the emulsification properties and to standardise ways to analyse droplet size of w/o emulsions. Overall the study proved that functional ingredients can be encapsulated using stable w/o/w multiple emulsions prepared using SPG membranes under standardised conditions and hence appears to offer promise for manufacture of commercial products

Proper holomorphic mappings of balanced domains in Cn\mathbb{C}^n

We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in $\mathbb{C}^n, \ n > 1$. Specifically: we prove that any proper holomorphic self-map of a certain type of balanced, finite-type domain in $\mathbb{C}^n, \ n > 1$, is an automorphism. The main novelty of our proof is the use of a recent result of Opshtein on the behaviour of the iterates of holomorphic self-maps of a certain class of domains. We use Opshtein's theorem, together with the tools made available by finiteness of type, to deduce that the aforementioned map is unbranched. The monodromy theorem then delivers the result.Comment: 12 pages; article extensively rewritten; additional hypothesis added to the main result; to appear in Math. Zeitschrif

Proper holomorphic maps between bounded symmetric domains revisited

We prove that a proper holomorphic map between two bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the various special cases in which this result is known. We discuss an application of these methods to domains having noncompact automorphism groups that are not assumed to act transitively.Comment: 19 pages; typos corrected; missing hypothesis added to the statement of Lemma 4.2; to appear in Pacific J. Mat

Schwannoma of the nasal septum-a case report

Schwannomas of the nasal cavity and paranasal sinuses are very rare. We report the case of a50-year-old woman with a schwannoma arising from the nasal septum. We discuss the clinical presentation, differential diagnosis, imaging characteristics and treatment of thisrarely encountered lesion.Schwannoma (neurilemmoma) is a benign neoplasm arising from Schwann cells in the peripheral nerve sheath. It can arise throughout the body, but is most commonly observed in the head and neck. This region accounts for 25–45% of all schwannoma [1]. Tumors arisingfrom nasal septum are extremely rare with only less than 20 cases been reported in the English literature

The dynamin inhibitor dynasore inhibits bone resorption by rapidly disrupting actin rings of osteoclasts

松本歯科大学大学院歯学独立研究科博士（歯学）学位申請論