Pyramids in the complex projective plane

We study the critical points of the diameter functional on the n-fold Cartesian product of the complex projective plane C P ² with the Fubini-Study metric. Such critical points arise in the calculation of a metric invariant called the filling radius, and are akin to the critical points of the distance function. We study a special family of such critical points, P _kC P ¹C P ², k=1,2... We show that P _k is a local minimum of by verifying the positivity of the Hessian of (a smooth approximation to) at P _k. For this purpose, we use Shirokov's law of cosines and the holonomy of the normal bundle of C P ¹C P ². We also exhibit a critical point of , given by a subset which is not contained in any totally geodesic submanifold of C P ².     

Inclusivef 2 (1270) meson production in νp and\bar vp charged current interactions

Using data obtained with the bubble chamber BEBC at CERN, the inclusivef ₂ (1270) meson production invp and \(\bar vp\) charged current reactions is studied. It is found thatf ₂ production occurs mainly in events with a hadronic invariant massW?7 GeV. In these events, the averagef ₂ multiplicity is about half the average ρ^O multiplicity, and thex _F andp _T ² distributions of thef ₂ agree in shape with those of the ρ^O. The predictions of a semi-empirical model (Wells model) are in accord with the measured multiplicities atW>7 GeV, whereas at lowerW the model predicts too largef ₂ multiplicities.     

Production of hybrid 16-membered macrolides by expressing combinations of polyketide synthase genes in engineered Streptomyces fradiae hosts

Combinations of the five polyketide synthase (PKS) genes for biosynthesis of tylosin in Streptomyces fradiae (tylG), spiramycin in Streptomyces ambofaciens (srmG), or chalcomycin in Streptomyces bikiniensis (chmG) were expressed in engineered hosts derived from a tylosin-producing strain of S. fradiae. Surprisingly efficient synthesis of compounds predicted from the expressed hybrid PKS was obtained. The post-PKS tailoring enzymes of tylosin biosynthesis acted efficiently on the hybrid intermediates with the exception of TylH-catalyzed hydroxylation of the methyl group at C14, which was efficient if C4 bore a methyl group, but inefficient if a methoxyl was present. Moreover, for some compounds, oxidation of the C6 ethyl side chain to an unprecedented carboxylic acid was observed. By also expressing chmH, a homolog of tylH from the chalcomycin gene cluster, efficient hydroxylation of the 14-methyl group was restored.     

Milde alkalische Hydrolyse von Aconitin

Mild Alkaline Hydrolysis of Aconitine Hydrolysis of aconitine ( 1 ) with 0.04N K₂CO₃ in 90% MeOH at room temperature yields, besides the alkamine aconine 3 considerable amounts of 8-O-methylaconine ( 6 ) and smaller quantities of desbenzoyl-pyroaconitine ( 4 ) and 16-epi-desbenzoyl-pyroaconitine ( 5 ). Better yields of 4 and 5 are obtained when heating a solution of aconitine in 0.04N K₂CO₃ in 90% EtOH.     

Facility location in the presence of forbidden regions,I: Formulation and the case of Euclidean distance with one forbidden circle

A constrained form of the Weber problem is formulated in which no path is permitted to enter a prespecified forbidden region $\text{R}$ of the plane. Using the calculus of variations the shortest path between two points $\text{x}\text{,}\text{y}\text{?}\text{R}$ which does not intersect $\text{R}$ is determined. If $\text{d(}\text{x}\text{,}\text{y}\text{)}$ is unconstrained distance, we denote the shortes distance along a feasible path by $\text{d}\text{(}\text{x}\text{y}\text{)}$. The constrained Weber problem is, then: given points $\text{x}{}_{\mathrm{j}}\text{?}\text{R}$ and positive weights w_j, j = 1,2,…,n, find a point $\text{x}\text{?}\text{R}$ such that

$\text{f(}\text{x}\text{)=}\text{Σ}\text{n}\text{j=1}\text{d(}\text{x}\text{,}\text{x}{}_{\mathrm{j}}\text{)}$

is a minimum.An algorithm is formulated for the solution of this problem when $\text{d(}\text{x}\text{,}\text{y}\text{)}$ is Euclidean distance and $\text{R}$ is a single circular region. Numerical results are presented.     

Infrared spectra of two sexithiophenes in neutral and doped states: a theoretical and spectroscopic study

The FT-infrared spectra of two sexithiophenes having their end ,′-positions substituted by n-hexyl or -thiohexyl groups, in neutral and doped states, are studied with the main aim of deriving information about the π-electrons delocalization and about the electronic structure of the charged defects created upon doping with iodine. The analysis of the experimental data is aided by Density Functional Theory calculations. The modifications in the electronic structure of the sexithiophene backbone induced by the n-thiohexyl encapsulation are discussed from the point of view of single molecule interactions in thiol-terminated π-conjugated oligomers bound to metallic or cluster electrodes.     

Synthesis of Conjugated Optically Active Polymetallocenes

The development of methodology for synthesizing new materials in which metal atoms are linked by hydrocarbons whose electronic conjugation is unbroken is described. The fundamental idea is to twist the hydrocarbons into helices. By attaching bulky groups to their precursors, the helices can be made to twist mainly in one direction. The molecules synthesized are helicenes capped by five-membered rings to which metals are attached. If the size of the helix is chosen appropriately, a polymeric structure forms in which hydrocarbon rings and metal atoms alternate. An oligomer with Structure 22 is the first such material prepared. It and related structures might be precursors of molecular solenoids, examples of which are not yet known.     

An Improved Method for the Mono-Hydroxymethylation of Pyridines. A Modification of the Minisci Procedure

The reaction of N-methoxy-derivatives of pyridines in methanol with ammonium persulphate gives improved yields of mono-hydroxymethylated products. In contrast to the original Minisci procedure the reaction requires only catalytic amounts of ammonium persulphate. Evidence is presented which establishes that the reaction does not proceed via an intramolecular pathway.     

Arginine-hydrolyzing enzymes for electrochemical biosensors

Since l-Arginine (Arg) is a semi-essential amino acid for humans, its adequate amount must be consumed in the diet to prevent certain negative consequences related to insufficient synthesis of this amino acid under specific physiological conditions. Arg metabolism results in the production of a biochemically diverse range of such products as urea, some amino acids, creatine, polyamines, nitric oxide, etc. Arg, an important biomarker in clinical diagnostics, is also used for prevention/treatment of different diseases, including cancer and COVID-19. Furthermore, it serves as an indicator of food and beverages quality.A variety of optic and electrochemical methods for Arg determination have already been suggested. The biosensor systems based on the enzymes of Arg metabolism were shown to be the most promising tools for Arg assay. This review focuses on the peculiarities of electrochemical biosensors for Arg assay based on the use of Arg-degrading enzymes and on the analysis of their advantages as compared to other approaches.     

Analysis of conditions for determining the thermophysical characteristics of energetic materials by the laser pulse method

An analysis of conditions for determining the thermophysical characteristics of energetic materials by the laser pulse method is performed. Based on the results of numerical solution of the heat conduction problems for a sample of a material irradiated with a short heating laser pulse corresponding to actual experimental conditions, the time dependences on the sample surface temperature are determined. The heat pulse duration required to determine the thermophysical properties of materials and the ignition delay time are compared. It is shown that the determination of the thermophysical characteristics of a typical energetic material by the laser pulse method is possible at pulse durations of no longer than 0.24 s.