Beyond Cartesian limits: Leibniz's passage from algebraic to “transcendental” mathematics

This article deals with Leibniz's reception of Descartes' “geometry.” Leibnizian mathematics was based on five fundamental notions: calculus, characteristic, art of invention, method, and freedom. On the basis of methodological considerations Leibniz criticized Descartes' restriction of geometry to objects that could be given in terms of algebraic (i.e., finite) equations: “Descartes's mind was the limit of science.” The failure of algebra to solve equations of higher degree led Leibniz to develop linear algebra, and the failure of algebra to deal with transcendental problems led him to conceive of a science of the infinite. Hence Leibniz reconstructed the mathematical corpus, created new (transcendental) notions, and redefined known notions (equality, exactness, construction), thus establishing “a veritable complement of algebra for the transcendentals”: infinite equations, i.e., infinite series, became inestimable tools of mathematical research.     

Heterograft copolymers of poly(ε‐caprolactone) prepared by combination of ATRA “grafting onto” and ATRP “grafting from” processes

This paper aims at reporting on the synthesis of a heterograft copolymer by combining the “grafting onto” process based on atom transfer radical addition (ATRA) and the “grafting from” process by atom transfer radical polymerization (ATRP). The statistical copolymerization of ε‐caprolactone (εCL) and α‐chloro‐ε‐caprolactone (αClεCL) was initiated by 2,2‐dibutyl‐2‐stanna‐1,3‐dioxepane (DSDOP), followed by ATRA of parts of the chlorinated units of poly(αClεCL‐co‐εCL) on the terminal double bond of α‐MeO,ω‐CH₂?CH? CH₂? CO₂‐poly(ethylene oxide) (PEO). The amphiphilic poly(εCL‐g‐EO) graft copolymer collected at this stage forms micelles as supported by dynamic light scattering (DLS) and transmission electron microscopy (TEM). The unreacted pendant chloro groups of poly(εCL‐g‐EO) were used to initiate the ATRP of styrene with formation of copolymer with two populations of randomly distributed grafts, that is PEO and polystyrene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6015–6024, 2006     

Bell's theorem based on a generalized EPR criterion of reality

First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedankenexperiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almostwith certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future.     

Bioprocessing of commodity chemicals research directions for government,industry, and academia

Applied Biochemistry and Biotechnology - The US chemical industry is facing maturing markets, variability in raw materials supply, and stiff competition from emerging chemical industries in other...     

HPLC-NMR of fatty alcohol ethoxylates

The application of HPLC-NMR for the analysis of a mixture of fatty alcohol ethoxylates (FAEs) is described. The use of the new generation, cryogenically cooled probes is investigated in respect of the sensitivity advantage that they provide. The FAE mixture is separated using liquid chromatography at the critical point of adsorption. The ability of the method to differentiate between the different end groups and the degree of polymerization of the mixture constituents is investigated. Both on-flow and stop-flow HPLC-NMR techniques were used together with two-dimensional NMR spectroscopy. The results are compared with those obtained by using an evaporative light scattering detector for the HPLC.     

Borchelate und Bormetallchelate, 4. Mitt.

The i.r., u. v.,¹H n.m.r.,¹³C n.m.r., and¹¹B n.m.r. spectra of several substituted diphenylboron chelates derived from salicylaldehyde azomethines were compared with respect to the influence of the amine substituentR. O–B–N-6-ring constitution of the chelates29–32 [R=OH, NH₂, NHC₆H₅, N(CH₃)₂] can be deduced from the spectra.

Als 3. Mitt. gilt:F. Umland undE. Hohaus mit Beiträgen vonW. Riepe, K. Brodte, C. Schleyerbach undD. Szonn. Untersuchungen über borhaltige Ringsysteme vom Chelattyp. Forschungsbericht des Landes Nordrhein-Westfalen Nr. 2538. Opladen: Westdeutscher Verlag. 1976.     

Substituenteneffekte auf azido-tetrazolo-gleichgewichte elektronische und sterische effekte bei s-triazolo[4,3-c]tetrazolo[1,5-a]pyrimidinen1

The azido tetrazolo valence isomerism of twenty 9-methyl-s-triazolo[4,3-c]tetrazolo[1,5-a]pyrimidines with different substituents at position 5 has been studied by means of ¹H NMR spectroscopy. All the compounds have been found to be tetrazoles in the solid state and in (CD₃)₂SO solution; in CF₃COOH azido and tetrazolo isomers are in equilibrium. From equilibrium constants K and thermodynamic data determined it is concluded that in this series K depends on both electronic effects and steric requirements of the 5-substituents. A linear relation between K and σ was found for 5-arylderivatives because ΔS° keeps approximately constant and the substituent mainly operates on ΔH°.