Equivalence of regularity for the Bergman projection and the\bar \partial-neumann operator

A necessary and sufficient condition for regularity of the -Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cⁿ is that the orthogonal projections onto -closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular. The first author partially supported by NSF Grant DMS-8701038     

Intra-operative acoustic hemostasis of liver: production of a homogenate for effective treatment

Objective: We have shown that High-Intensity Focused Ultrasound (HIFU) can effectively control bleeding from injuries to solid organs such as liver, spleen, and lung. Achievement of hemostasis was augmented when a homogenate of tissue and blood was formed. The objective of this study was to investigate quantitatively the effect of homogenate production on HIFU application time for hemostasis. Possible mechanisms involved in homogenate production were also studied.Methods: Ten anesthetized rabbits had laparotomy and liver exposure. Liver incisions, 15-25 mm long and 3-4 mm deep, were made followed immediately by HIFU application. Two electrical powers of 80 and 100 W corresponding to focal acoustic intensities of 2264 and 2829 W/cm², respectively were used. Tissue and homogenate temperatures were measured. Smear and histological tissue sample analysis using light microscopy were performed.Results: In treatments with homogenate formation, hemostasis was achieved in 76 ± 1.3 s (Mean ± Standard Error Mean: SEM) at 80 W. In treatments without homogenate formation (at 80 W), hemostasis was achieved in 106 ± 0.87 s. At 100 W, hemostasis was achieved in 46 ± 0.3 s. The time required for homogenate formation, at 80 and 100 W were 60 ± 2.5 and 23 ± 0.3 s, respectively. The homogenate temperature was 83 °C (SEM 0.6 °C), and the non-homogenate tissue temperature at the treatment site was 60 °C (SEM 0.4 °C). The smear and histological analysis showed significant blood components and cellular debris in the homogenate, with some intact cells.Conclusion: The HIFU-induced homogenate of blood and tissue resulted in a statistically significant shorter HIFU application time for hemostasis. The incisions with homogenate had higher temperatures as compared to incisions without homogenate. Further studies of the correlation between homogenate formation and temperature must be done, as well as studies on the long-term effects of homogenate in achieving hemostasis.     

Stokes beams formed by superposition of a completely unpolarized and a completely polarized Gaussian Schell-model beam

Analytic expressions and computed examples are given to elucidate the coherence and polarization properties of Stokes beams, i.e. beams formed by superposition of a completely unpolarized and a completely polarized electromagnetic Gaussian Schell-model beam. We found that superposition of such two beams cannot form a Stokes beam with a constant state of polarization on propagation. An additional constraint on the source plane parameters of the two Gaussian Schell-model beams is proposed. The resultant Stokes beam with a constant state of polarization on propagation is found to be a Gaussian Schell-model beam with the same variances as the two constituent Gaussian Schell-model beams. However, the modulus of the Gaussian intensity distributions across the source planes of these beams may be different.     

Single-site beta-diiminate zinc catalysts for the ring-opening polymerization of beta-butyrolactone and beta-valerolactone to poly(3-hydroxyalkanoates)

Polymerization of beta-butyrolactone (BBL) and beta-valerolactone (BVL) using the zinc alkoxide initiator (BDI-1)ZnO(i)()Pr [(BDI-1) = 2-((2,6-diisopropylphenyl)amido)-4-((2,6-diisopropylphenyl)imino)-2-pentene] proceeds very rapidly under mild conditions to produce poly(3-hydroxybutyrate) (PHB) and poly(3-hydroxyvalerate) (PHV), respectively. For the monomer-to-initiator ratio 200:1, PHB number-average molecular weights (M(n)) are proportional to conversion throughout the reaction and polydispersity indices (PDIs) are narrow, consistent with a living polymerization. Higher monomer-to-initiator ratios can be used to achieve high molecular weight PHB (M(n) > 100 000). End-group analysis verifies that the polymerization of BBL follows a coordination-insertion mechanism, where complexes of the form (BDI-1)ZnOCH(Me)CH(2)CO(2)R are the active species. Variable temperature NMR experiments show that (BDI-1)ZnO(i)()Pr is monomeric in benzene-d(6) solution. In contrast, (BDI-2)ZnO(i)()Pr [(BDI-2) = 2-((2,6-diethylphenyl)amido)-4-((2,6-diethylphenyl)imino)-2-pentene] is a poor initiator at room temperature because it prefers to form a bis-mu-isopropoxide dimer in solution. According to kinetic studies, propagation by (BDI-1)ZnO(i)()Pr is first order in both monomer as well as (BDI-1)ZnO(i)()Pr concentration. These results lead us to propose a monometallic active species. Several results suggest that elimination side reactions are slowly catalyzed by zinc alkoxides, leading to degradation of the polymer.     

Focal shift in focused truncated gaussian beams

It is known that under certain circumstances the point of maximum intensity in a focused aberration-free wave is not at the geometrical focus, but is closer to the focusing lens. In the present note such a focal shift is analyzed for the case of a gaussian beam, focused by a thin lens, which fills a circular aperture of any prescribed radius, the waist of the beam being assumed to be located in the aperture plane. Many previously known results follow as limiting cases of our analysis.     

Generalized stokes parameters of random electromagnetic beams

A generalization of the Stokes parameters of a random electromagnetic beam is introduced. Unlike the usual Stokes parameters, which depend on one spatial variable, the generalized Stokes parameters, depend on two spatial variables. They obey precise laws of propagation, both in free space and in any linear medium, whether deterministic or random. With the help of the generalized Stokes parameters, the changes in the ordinary Stokes parameters upon propagation can be determined. Numerical examples of such changes are presented. The generalized Stokes parameters contain information not only about the polarization properties of the beam but also about its coherence properties. We illustrate this fact by expressing the degree of coherence of the electromagnetic beam in terms of one of the generalized Stokes parameters.