On the computation of sound in free and wall-bounded domains

A new Dispersion-Relation-Preserving (DRP) scheme has been developed using the Lax-Wendroff methodology. Two collocated grids are placed in a staggered formation and a staggered DRP scheme is used to calculate the spatial differentiation of the propagation and convection terms. A staggered filtering scheme of a six points stencil is developed to complete the transformation from one grid to another. Existing DRP Runge-Kutta schemes are used for the time marching. Stability limits and accuracy issues are investigated using a simple 1D advection equation. The new method is then tested for monopole and quadrupole radiation, diffraction effects of an aperture in a wall, and convection effects of shear flow. All demonstrate the good accuracy and numerical stability of the new method.     

Identification of a light-regulated protein kinase activity from seedlings of Arabidopsis thaliana

Protein kinase transduction pathways are thought to be involved in light signaling in plants, but other than the photoreceptors, no protein kinase activity has been shown to be light-regulated in vivo. Using an in-gel protein kinase assay technique with histone H III SS as an exogenous substrate, we identified a light-regulated protein kinase activity with an apparent molecular weight ca 50 kDa. The kinase activity increased transiently after irradiation of dark-grown seedlings with continuous far red light (FR) and blue light (B) and decreased after irradiation with red light (R). The maximal activation was achieved after 30 min to 1 h with FR or B. After irradiation times longer than 2 h, the kinase activity decreased to below the sensitivity level of the assay. In Arabidopsis mutants lacking either the photoreceptors phytochrome A, phytochrome B or the blue-light receptor cryptochrome 1, kinase activity was undetectable, whereas in the photomorphogenic mutants cop1 and det1 the kinase activity was also observed in the absence of light signals, though still stimulated by B and FR. Interestingly, the R inhibition of the kinase activity was lost in the mutant hy5. Pretreatment with cycloheximide blocked the kinase activity.     

Achiral Calcium‐Oxalate Crystals with Chiral Morphology from the Leaves of Some Solanacea Plants

The leaves of some plants, particularly among the Solanacea, contain crystals of calcium oxalate with a peculiar chiral pseudo‐tetrahedral morphology, even though the calcium oxalate crystal structure is centrosymmetric, hence achiral. We studied the morphology of these crystals extracted from the leaves of three Solanacea plants: the potato, the hot pepper, and a species of wild Solanum. The crystal morphology was the same in all three species. Based on the examination of more than 100 crystals from each plant, we showed that the crystal morphology is chiral with invariant chirality. We suggest that morphological chirality is induced by macromolecules during nucleation from a specific, genetically encoded crystal plane, and is further established during subsequent controlled crystal growth. This is one of few examples where it is possible to deduce a molecular mechanism for biologically induced breaking of morphological symmetry in organisms. A very high level of recognition is required by the macromolecules to allow them to distinguish between symmetry‐related crystal planes. It is also surprising that this finely controlled mechanism of crystal formation, including the chiral morphology, has been conserved during evolution.     

On groups with conjugacy classes of distinct sizes

A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct cardinality. We show that if G is an ah-group, then the non-abelian socle of G is isomorphic to one of the following:

1. , for 1a5, a≠2.

2. A₈.

3. PSL(3,4)^e, for 1e10.

4. A₅×PSL(3,4)^e, for 1e10.

Based on this result, we virtually show that if G is an ah-group with π(G) 2,3,5,7 , then F(G)≠1, or equivalently, that G has an abelian normal subgroup.In addition, we show that if G is an ah-group of minimal size which is not isomorphic to S₃, then the non-abelian socle of G is either trivial or isomorphic to one of the following:

1. , for 3a5.

2. PSL(3,4)^e, for 1e10.

Our research lead us to interesting results related to transitivity and homogeneousity in permutation groups, and to subgroups of wreath products of form Z₂S_n. These results are of independent interest and are located in appendices for greater autonomy.     

Quantitative optical imaging of the pharmacokinetics of fluorescent-specific antibodies to tumor markers through tissuelike turbid media

Fluorescent optical imaging of tumors deep within tissue depends on specific binding of antibodies to the tumors' surface markers. These fluorescent antibodies propagating in the vicinity of the tumor can be attached to and (or) diffused away from it. We illustrate application of a new tool, based on the random-walk theory in turbid media, for extracting the pharmacokinetics of these fluorescent antibodies by data deconvolution, excluding the effect of upper turbid tissue layers.     

Comparison of amine-induced cyclization of 6-chloro-1-hexynylphosphonate and isobutyl 7-chlorohept-2-ynoate

The reaction of 6-chloro-1-hexynylphosphonate with primary and secondary amines afforded exclusively 2-aminocyclohexenylphosphonates in 62-85% isolated yields. In contrast, reaction of various amines with isobutyl 7-chlorohept-2-ynoate in acetonitrile at 70 °C gave (E)-sec-butyl 2-(1-alkylpiperidin-2-ylidene)acetates in 65-78% isolated yields. Calculations offer an explanation for the difference in the behavior of the two compounds classes. It is shown that C-C cyclization in the alkyne-phosphonate group occurs via an initial formation of a zwitterionic intermediate, which is stabilized by both an inductive effect of the phosphonate group and a newly formed hydrogen bond. The alkyne-carboxylate group, on the other hand, proceeds via enamine formation as a result of the smaller inductive effect of the carboxylate combined with involvement of an allene-like resonance form. This resonance form both delocalizes the negative charge in the zwitterionic intermediate making it to be less available for attack, and affects the geometry thus preventing formation of the stabilizing hydrogen bond. Hence, the zwitterionic intermediate of the alkyne-carboxylates is less stable leading to formation of an enamine, which is followed by N-C cyclization to give the azaheterocycles.     

The conjugacy character ofS n tends to be regular

Consider the regular and the conjugacy characters ofS _n as vectors in Euclidean space, with the standard inner product. Asn grows, the angle between them tends to zero and the ratio of their lengths tends to one. The two characters have therefore asymptotically similar decompositions into irreducible components.     

Rank of inclusion matrices and modular representation theory

We use results from the modular representation theory of the groupsS _n and GL _n (F _q ) to determine the rank of inclusion matrices.     

Mach Wave Radiation by Mixing Layers. Part II: Analysis of the Source Field

In Part II a large-scale sound source in a time-developing planar free mixing layer is studied using an acoustic analogy approach. It is shown that only the non-compact character of the source resembles well the character of the corresponding source in a spatially developing flow. A model based on a continuous assembly of wave packets is derived and applied to direct numerical simulation results of two supersonic time-developing mixing layers undergoing transition to turbulence. The analysis predicts two distinctive dominant Mach wave sources in agreement with the direct analysis of Part~I. The first dominates during the stage of the Λ-vortex structure and the second just prior to the final breakdown to a fine-scale structure. The convective velocity of the second Mach wave source is higher than the first and thus its Mach angle of radiation is higher. The second source has a reduced strength at the higher free-stream Mach number. Directivity and frequency spectra compare well with the results of Part I, demonstrating that the assumptions inherent in the analogy are quite reasonable. Received 5 August 1997 and accepted 6 April 1998     

Solution- and solid-state conformations of C(α)-alkyl analogues of methylphenidate (Ritalin) salts: avoidance of gauche(+)gauche(-) interactions

Alkyl analogues of methylphenidate (Ritalin) salts are slow onset, long duration dopamine reuptake inhibitors with a potential use as a cocaine abuse pharmacotherapy. X-ray crystallographic studies and nuclear magnetic resonance (NMR) investigations strongly suggest that avoidance of sterically unfavorable gauche(-)gauche(+) orientations effectively influences both the C(α)-alkyl side chain conformation and the formation of a predominant rotamer about the CH-CH bond ligating piperidine and C(Ar)R moieties. The favored CH-CH rotamer in D(2)O and in CD(2)Cl(2) of the pharmacologically interesting i-Bu and CH(2)-cyc-Pnt (RS,RS)-salts has the same antiperiplanar arrangement that was found in the crystal structures, although there clearly is a fast equilibrium involving smaller amounts of synclinal partners. While the rotamer in the (RS,SR)-i-Bu HCl crystal structure exhibits a synclinal orientation for the vicinal pair of adjacent methine protons, the weighted time-averaged arrangement for these protons becomes almost completely antiperiplanar when the crystals are dissolved in D(2)O. Increased steric congestion around the CH-CH bond in the analogous N-methyl tertiary ammonium salts seems to augment the quantity of the preferred rotamer within the mixture. The stereochemistry of the species observed via NMR seems to arise from specific combinations of N-methyl orientation and avoidance of sterically unfavorable gauche(-)gauche(+) arrangements.