Analysis of amino acids in cell culture supernatant using capillary electrophoresis with contactless conductivity detection

CE-C⁴D methods for the analysis of amino acids (AAs) are presented. Combining the results from two methods with acetic acid and cyclodextrin-based BGEs, 20 proteinogenic AAs could be analyzed using CE. CE-C⁴D was also, for the first time, applied to analyze free AAs in samples of mammalian cell culture supernatant. After dilution as only sample preparation, combining the results of the two CE methods allowed monitoring the concentration changes of 17 AAs in samples taken during the cultivation of CHO cells.     

Parametrization of Contractive Block Operator Matrices and Passive Discrete-Time Systems

Passive linear systems τ = have their transfer function in the Schur class S . Using a parametrization of contractive block operators the transfer function is connected to the Sz.-Nagy–Foiaş characteristic function of the contraction A. This gives a new aspect and some explicit formulas for studying the interplay between the system τ and the functions and . The method leads to some new results for linear passive discrete-time systems. Also new proofs for some known facts in the theory of these systems are obtained. Dedicated to Eduard Tsekanovskiĭ on the occasion of his seventieth birthday This work was supported by the Research Institute for Technology at the University of Vaasa. The first author was also supported by the Academy of Finland (projects 212146, 117617) and the Dutch Organization for Scientific Research N.W.O. (B 61-553). Received: December 22, 2006. Revised: February 6, 2007.     

Failure of the Denjoy theorem for quasiregular maps in dimension

In 1929 L. V. Ahlfors proved the Denjoy conjecture which states that the order of an entire holomorphic function of the plane must be at least if the map has at least finite asymptotic values. In this paper, we prove that the Denjoy theorem has no counterpart in the classical form for quasiregular maps in dimensions . We construct a quasiregular map of with a bounded order but with infinitely many asymptotic limits. Our method also gives a new construction for a counterexample of Lindelöf's theorem for quasiregular maps of .

     

A study of 1,5-hydrogen shift and cyclization reactions of an alkali isomerized methyl linolenoate

Heating a mixture formed by alkali isomerization of methyl linolenoate (1) produces a complex mixture with the bicyclic hexahydroindenoic esters 4β-(7-methoxycarbonylheptyl)-5α-methyl-2,3,3aα,4,5,7aαhexahydroindene (CL5) and 4β-ethyl-5α-(6-methoxycarbonylhexyl)-2,3,3aα,4,5,7aα-hexahydroindene (CL6) as main components. Similar isomerization reactions of three synthetic model compounds, methyl 9Z,13E,15Z-octadecatrienoate (2), 9Z,14E,16E-octadecatrienoate (4) and 9Z,11E,15Z-octadecatrienoate (5) corroborated the results obtained with alkali isomerized methyl linolenoate.     

Computations on the growth of the first factor for prime cyclotomic fields

Denote byh(p) the first factor of the class number of the prime cyclotomic fieldk(exp (2i/p)). The theorem:h(p ₂)>h(p ₁) if 641 p ₂>p ₁ 19 is proved by straightforward computation.