Regulation of births for viability of populations governed by age-structured problems

We assume that the evolution of the population is governed by a controlled McKendrick age-structured partial differential equation where the mortality rate and immigrated population levels are no longer known coefficients, but contingent regulation parameters chosen for a given purpose, for instance, for requiring that the population satisfies prescribed viability constraints depending on time and age. The Lotka renewal equation relating the boundary condition (number of births) to the integral with respect to age of the population is replaced by the introduction of another regulation parameter in the boundary condition, regarded as a natality policy. We may control it by its derivative, regarded as a natality decision. We then construct a regulation map, associating with the population level, the time and the age the subset of natality policies, a mortality rates and an immigration levels needed for governing viable evolutions of the population.     

Une hypothèse topologique pour le problème de la courbure scalaire prescrite

By topological arguments, we set forth sufficient hypotheses for a given function K, on a compact Riemannian manifold (M, g), to be the scalar curvature of a metric conformal to g.     

Method validation for assay determination of cannabidiol isolates

The speed at which regulations have changed in the cannabis marketplace has increased the pressure for accurate, easy, and efficient analytical methodology. Purified isolates are used to formulate a variety of consumer products such as topicals, edibles, and beverages. Accuracy of the quantitative cannabinoid content of the isolates used in preparation of these products is directly dependent upon the reliability of the analytical methodology used for characterization. An inaccurate quantitative assay value does not only pose health, safety, and ethical concerns for consumers, it can generate a potential financial loss for manufacturers marketing isolates based upon purity. The aim of this work is to describe the validation of a rapid and reliable reversed-phase liquid chromatographic method coupled with UV detection for quantitative determination of Cannabidiol (CBD) purified isolate. Accuracy, precision, specificity, linearity, robustness and range of the analytical method were determined according to assay method requirements specified in the International Conference for Harmonization (ICH) Q2(R1), “Validation of Analytical Procedures: Test and Methodology” for quantitative evaluation of the active moiety in samples of drug substance by liquid chromatography. Additionally, the feasibility of manufacturer prepared DEA-exempt CBD reference standard solutions formulated at 1.0?mg/mL was explored for the quantification of CBD isolate.     

Chemoenzymatic synthesis of novel adenosine carbanucleoside analogues containing a locked 3′-methyl-2′,3′-β-oxirane-fused system

Starting from a readily available enantiopure building block, a straightforward enantioselective approach to 3′-methyl-2′,3′-β-oxirane-fused carbanucleosides bearing adenosine analogues is detailed. The key steps in the syntheses involved a lipase-catalyzed regioselective monoacylation of a diol to obtain the key intermediate and direct coupling of this key intermediate with diversely substituted purine nucleobases under Mitsunobu reaction conditions providing only the N⁹ target molecules.     

Ueber die Kjeldahl'sche Stickstoffbestimmungsmethode

Ohne Zusammenfassung     

Dinuclear Copper(II) Complexes Incorporating a New Septadentate Polyimidazole Ligand

The dinuclear copper(II) complexes [Cu(2)(tmihpn)(prz)](ClO(4))(2).2CH(3)CN (6) and [Cu(2)(tmihpn)(O(2)CCH(3))](ClO(4))(2).CH(3)CN (7) were prepared, where tmihpn is the deprotonated form of N,N,N',N'-tetrakis[(1-methylimidazol-2-yl)methyl]-1,3-diaminopropan-2-ol and prz is the pyrazolate anion. The crystal structures of 6 and 7 were determined and revealed that both complexes contain bridging alkoxide ligands as well as bridging pyrazolate and acetate ions, respectively. Crystal data: compound 6, triclinic, P&onemacr;, a = 18.089(2) ?, b = 22.948(3) ?, c = 9.597(2) ?, alpha = 93.37(2) degrees, beta = 94.49(2) degrees, gamma = 81.69(2) degrees, V = 3925.1 ?(3), Z = 4; compound 7, triclinic, P&onemacr;, a = 12.417(2) ?, b = 15.012(3) ?, c = 10.699(2) ?, alpha = 104.76(2) degrees, beta = 102.63(2) degrees, gamma = 99.44(2) degrees, V = 1830.1 ?(3), Z = 2. In compound 6, the coordination geometry around both copper centers resembles a distorted square pyramid, while the stereochemistry around the copper centers in 7 is best described as trigonal bipyramidal. Both complexes display well-resolved isotropically shifted (1)H NMR spectra. Selective substitution studies and integration data have been used to definitively assign several signals to specific ligand protons. Results from the solution (1)H NMR studies suggest that the basal and apical imidazole groups do not exchange rapidly on the NMR time scale and the solid state structures of the complexes are retained in solution. In addition, the magnetochemical characteristics of 6 and 7 were determined and provide evidence for "magnetic orbital switching". Antiferromagnetic coupling in 6 (J = -130 cm(-)(1)) is strong, while the copper centers in compound 7 are ferromagnetically coupled (J = +16.4 cm(-1)). Differences in the magnetic behavior of the two copper centers have been rationalized using the "ligand orbital complementary" concept. The ground state magnetic orbitals involved in spin coupling in 6 (d(x)()()2(-)(y)()()2) are different from those in 7 (d(z)()()2).