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.     

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.     

VNCl2(Pyridin)2 Synthese,IR-Spektrum und Kristallstruktur

VNCl₂(Pyridine)₂; Synthesis, I. R. Spectrum, and Crystal Structure VNCl₂(Pyridine)₂ is formed from the cyclothiazeno-vanadium(IV) complex [VCl(N₃S₂)(Pyridine)₂]₂ · 2 CH₂Cl₂ in boiling toluene in form of brown-red, hydrolysis sensitive crystal. It was characterized by its I.R. spectrum and an X-ray crystal structure determination. VNCl₂(Pyridine)₂crystallizes in the orthorhombic space group Pccn with four formula units per unit cell (668 observed independent reflexions, R = 0.055). Lattice constants: a = 1550, b = 924, c = 832 pm. Monomer molecules are situated on twofold rotation axes. They are stacked along the V?N axis to form columns V?N…V. The short VN bond of 160 pm corresponds to a triple bond, whereas the V…N distance of 256 pm indicates a weak interaction. The V? N(Pyridine) and V? Cl bond lengths are 213.0 and 233.5 pm, respectively.     

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.     

SINGLE- and DOUBLE-STRAND BREAK FORMATION IN DOUBLE-STRANDED DNA UPON NANOSECOND LASER-INDUCED PHOTOIONIZATION

Double-stranded (ds) calf thymus DNA (0.4 mM), excited by 20 ns laser pulses at 248 nm, was studied in deoxygenated aqueous solution at room temperature and pH 6.7 in the presence of a sodium salt (10 mM). The quantum yields for the formation of hydrated electrons (phi c-), single-strand breaks (phi ssb) and double-strand breaks (phi dsb) were determined for various laser pulse intensities (IL). phi c- and phi ssb increase linearly with increasing IL; however, phi ssb has a tendency to reach saturation at high IL (greater than 5 X 10(6) Wcm-2). The ratio phi ssb/phi c-, representing the number of ssb per radical cation, is about 0.08 at IL less than or equal to 5 X 10(6) Wcm-2. For comparison, the number of ssb per OH radical reacting with dsDNA is 0.22. On going from argon to N2O saturation, phi ssb and phi dsb become larger by factors of approximately 5 and 10-15, respectively. This enhancement is produced by attack on DNA bases by OH radicals generated by N2O-scavenging of the photoelectrons. While phi ssb is essentially independent of the dose (Etot), phi dsb depends linearly on Etot in both argon- and N2O-saturated solutions. The linear dependence of phi dsb implies a square dependence of the number of dsb on Etot. This portion of dsb formation is explained by the occurrence of two random ssb, generated within a critical distance (h) in opposite strands. For both argon- and N2O-saturated solutions h was found to be of the order of 40-70 phosphoric acid diester bonds. On addition of electron scavengers such as 2-chloroethanol (or N2O plus t-butanol), phi dsb is similar to that in neat, argon-saturated solutions. Thus, hydrated electrons are not involved in the chemical pathway leading to laser-pulse-induced dsb of DNA.