Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

Expanding the Scope of Atropisomeric Monodentate P‐Donor Ligands in Asymmetric Catalysis: Hydrogen‐Transfer Reduction of α,β‐Unsaturated Acid Derivatives by Rhodium/Ph‐binepine Catalysts

A range of α,β‐unsaturated acids and esters have been selectively reduced to the corresponding saturated acid derivatives by hydrogen transfer. As the reducing agent, formic acid was used in the presence of Rh^I complexes formed with the powerful chiral ligand Ph‐binepine ( 1 ), an axially chiral binaphthalene‐type monodentate P‐donor ligand. Very high stereoselectivities (up to 97% ee) were obtained in the case of itaconic acid ( 2a ).     

Comparison estimates in anisotropic variational problems

A pointwise inequality between the radially decreasing symmetrals of minimizers of (possibly) anisotropic variational problems and the minimizers of suitably symmetrized problems is established. As a consequence, a priori sharp estimates for norms of the relevant minimizers are derived.     

Effect of 808 nm Diode Laser on Swimming Behavior,Food Vacuole Formation and Endogenous ATP Production of Paramecium primaurelia (Protozoa)

Photobiomodulation (PBM) has been used in clinical practice for more than 40 years. To clarify the mechanisms of action of PBM at cellular and organism levels, we investigated its effect on Paramecium primaurelia (Protozoa) irradiated by an 808 nm infrared diode laser with a flat‐top handpiece (1 W in CW). Our results led to the conclusion that: (1) the 808 nm laser stimulates the P. primaurelia without a thermal effect, (2) the laser effect is demonstrated by an increase in swimming speed and in food vacuole formation, (3) the laser treatment affects endogenous adenosine triphosphate (ATP) production in a positive way, (4) the effects of irradiation dose suggest an optimum exposure time of 50 s (64 J cm^?2 of fluence) to stimulate the Paramecium cells; irradiation of 25 s shows no effect or only mild effects and irradiation up to 100 s does not increase the effect observed with 50 s of treatment, (5) the increment of endogenous ATP concentration highlights the positive photobiomodulating effect of the 808 nm laser and the optimal irradiation conditions by the flat‐top handpiece.     

Hydrogenation of Esters to Alcohols with a Well‐Defined Iron Complex

We present the first base‐free Fe‐catalyzed ester reduction applying molecular hydrogen. Without any additives, a variety of carboxylic acid esters and lactones were hydrogenated with high efficiency. Computations reveal an outer‐sphere mechanism involving simultaneous hydrogen transfer from the iron center and the ligand. This assumption is supported by NMR experiments.     

Photobiomodulation by Infrared Diode Laser: Effects on Intracellular Calcium Concentration and Nitric Oxide Production of Paramecium

In Paramecium, cilia beating is correlated to intracellular calcium concentration ([Ca²⁺]i) and nitric oxide (NO) synthesis. Recent findings affirm that photobiomodulation (PBM) can transiently increase the [Ca²⁺]i in mammalian cells. In this study, we investigated the effect of both 808 and 980 nm diode laser irradiated with flat‐top hand‐piece on [Ca²⁺]i and NO production of Paramecium primaurelia, to provide basic information for the development of new therapeutic approaches. In the experiments, the laser power in CW varied (0.1; 0.5; 1; and 1.5 W) to generate the following respective fluences: 6.4; 32; 64; and 96 J cm^?2. The 6.4 J cm^?2 did not induce PBM if irradiated by both 808 and 980 nm diode laser. Conversely, the 32 J cm^?2 fluence had no effect on Paramecium cells if irradiated by the 808 nm laser, while if irradiated by the 980 nm laser induced increment in swimming speed (suggesting an effect on the [Ca²⁺]i, NO production, similar to the 64 J cm^?2 with the 808 nm wavelength). The more evident discordance occurred with the 96 J cm^?2 fluence, which had the more efficient effect on PBM among the parameters if irradiated with the 808 nm laser and killed the Paramecium cells if irradiated by the 980 nm laser. Lastly, the 980 nm and 64 or 96 J cm^?2 were the only parameters to induce a release of stored calcium.     

A palladium-catalyzed alkylation/direct arylation synthesis of nitrogen-containing heterocycles

A norbornene-mediated palladium-catalyzed sequence is described in which an alkyl-aryl bond and an aryl-heteroaryl bond are formed in one reaction vessel. The aryl-heteroaryl bond-forming step occurs via a direct arylation reaction. A number of six-, seven-, and eight-membered ring-annulated indoles, pyrroles, pyrazoles, and azaindoles were synthesized from the corresponding bromoalkyl azole and an aryl iodide.     

Stereospecific synthesis and catalytic activity of L-histidylidene metal complexes

We report on the synthesis, metal coordination, and catalytic impact of histidylidene, a histidine-derived N-heterocyclic carbene (NHC) ligand. The histidinium salt 3, comprising methyl substituents at both heterocyclic nitrogens and protected at the C- and N-terminus of the amino acid, was rhodated and iridated by a transmetallation protocol using Ag(2)O. Ambient temperature and short reaction times were pivotal for full retention of configuration at the α-carbon. The stereospecificity of the reaction was conveniently probed by (31)P NMR spectroscopy after transmetallation with rhodium(I) and coordination of enantiopure (S)-Ph-binepine. The histidylidene rhodium complexes are highly efficient catalysts for the mild hydrosilylation of ketones. For the cationic complexes [Rh(cod)(histidylidene)(phosphine)](+), lowering the temperature shifted the rate-limiting step of the catalytic reaction to an earlier stage that is not enantioselective. Hence the asymmetric induction-which is governed by the chiral phosphine-did not improve at low temperature.     

Boundedness of Solutions to Anisotropic Variational Problems

We investigate the global boundedness of minimizers of fully anisotropic minimum problems for integral functionals of the calculus of variations and of weak solutions to fully anisotropic quasilinear elliptic equations in divergence form.