Spacetime correlation functions of dynamic speckles produced by a series of moving phase screens

Spacetime correlation functions of the time-varying speckle intensity have been evaluated for the case where speckle patterns are produced in the Fresnel diffraction region by light propagating through a series of moving random-phase screens. The correlation functions are given by a set of recursion formulae which are useful for numerical computations. Three statistical quantities relating to the motion of speckle patterns are derived to examine the relationship between the velocity distribution of the phase screens and the temporal behaviour of resultant speckle patterns. It is found that the velocity differences between the phase screens have a strong effect on both the decorrelation of speckle patterns and the fluctuating speed of the speckle intensity.     

Applications of inversion formulas to the joint t-universality of Lerch zeta functions

In this paper, we define λ-joint, a^′-joint, (λ,λ)-joint, (λ,a^′)-joint and (a^′,a^′)-joint t-universality of Lerch zeta functions and consider the relations among those. Next we show the existence of (λ,λ)-joint t-universality. Finally, we also show the existence of λ-joint, a^′-joint, (λ,a^′)-joint and (a^′,a^′)-joint t-universality by using inversion formulas.     

Stability of the steady state for the Falk model system of shape memory alloys

In this article a stability result for the Falk model system is proven. The Falk model system describes the martensitic phase transitions in shape memory alloys. In our setting, the steady state is a nonlocal elliptic problem. We show the dynamical stability for the linearized stable critical point of the corresponding functional. Copyright © 2007 John Wiley & Sons, Ltd.     

A convergent approach to the formal total synthesis of hemibrevetoxin B

A convergent synthesis of the key synthetic intermediate of hemibrevetoxin B was achieved via the intramolecular allylation of an α-chloroacetoxy ether and subsequent ring-closing metathesis.     

Preparation and evaluation of oral dosage form using acylglycerols. II. Effect of food ingestion on dissolution and absorption of aspirin from the granules prepared by acylglycerols in human subjects.

The dissolution behavior of the aspirin enteric granule prepared using acylglycerols, glyceryl monostearate (GMS) and glyceryl trilaurate (GTL), was investigated in vitro and in human subjects in a fasting or non-fasting state. Aspirin was slowly released from the granule in vitro at pH 1.2. No acceleration of the aspirin dissolution rate in the medium without lipase and cholic acid was observed when the pH level of the medium increased to a neutral region (pH 6.4). However, the dissolution of aspirin was significantly increased by increasing the concentrations of lipase and cholic acid in the medium. Lipase appears to play an essential role in the dissolution process of aspirin granules. In human subjects, the average levels of the cumulative amount of total salicylate excreted in a urine-time curve, and the mean residence time (MRT) obtained after oral administration of a granule in the fasting state were markedly delayed in comparison with the results observed using an aqueous solution and a crystalline form of aspirin. In comparing the fasting condition with the non-fasting condition (after food ingestion), no significant difference was recognized in the total amount of salicylate excreted in urine to an infinite time (Ae(infinity)), whether the MRT was obtained by granule, crystalline form or aqueous solution. It can be concluded that aspirin granule prepared by GMS and GTL has a property of pancreatic lipase-sensitive dissolution, and its bioavailability is unaffected by food intake.     

A Genus-3 Topological Recursion Relation

In this paper, we give a new genus-3 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds. This formula also applies to intersection numbers on moduli spaces of spin curves. A by-product of the proof of this formula is a new relation in the tautological ring of the moduli space of 1-pointed genus-3 stable curves. Research of the first author was partially supported by NSF grant DMS-0204824 Research of the second author was partially supported by NSF grant DMS-0505835     

Palladium-catalyzed novel addition-elimination reaction of alkenyltin reagents to norbornene

Palladium-catalyzed reaction between 1-alkenyltin trichlorides and norbornene resulted in stereoselective formation of 3-alkylidenepentacyclo[9.2.1.^5,81.^1,110.^2,100^4,9]pentadecane instead of an expected simple alkenylstannylation product. Generation of trichlorostannane and its decomposition product, tin(II) chloride, was confirmed by trapping it with methyl propiolate and norbornene and analysis of the reaction by ¹¹⁹Sn NMR, respectively.