New algorithms for generalized network flows

This paper, of which a preliminary version appeared in ISTCS'92, is concerned with generalized network flow problems. In a generalized network, each edgee = (u, v) has a positive flow multipliera _e associated with it. The interpretation is that if a flow ofx _e enters the edge at nodeu, then a flow ofa _e x _e exits the edge atv. The uncapacitated generalized transshipment problem (UGT) is defined on a generalized network where demands and supplies (real numbers) are associated with the vertices and costs (real numbers) are associated with the edges. The goal is to find a flow such that the excess or deficit at each vertex equals the desired value of the supply or demand, and the sum over the edges of the product of the cost and the flow is minimized. Adler and Cosares [Operations Research 39 (1991) 955–960] reduced the restricted uncapacitated generalized transshipment problem, where only demand nodes are present, to a system of linear inequalities with two variables per inequality. The algorithms presented by the authors in [SIAM Journal on Computing, to appear result in a faster algorithm for restricted UGT.Generalized circulation is defined on a generalized network with demands at the nodes and capacity constraints on the edges (i.e., upper bounds on the amount of flow). The goal is to find a flow such that the excesses at the nodes are proportional to the demands and maximized. We present a new algorithm that solves the capacitated generalized flow problem by iteratively solving instances of UGT. The algorithm can be used to find an optimal flow or an approximation thereof. When used to find a constant factor approximation, the algorithm is not only more efficient than previous algorithms but also strongly polynomial. It is believed to be the first strongly polynomial approximation algorithm for generalized circulation. The existence of such an approximation algorithm is interesting since it is not known whether the exact problem has a strongly polynomial algorithm.Corresponding author. Research was done while the first author was attending Stanford University and IBM Almaden Research Center. Research partially supported by ONR-N00014-91-C-0026 and by NSF PYI Grant CCR-8858097, matching funds from AT&T and DEC.Research partially supported by ONR-N00014-91-C-0026.     

Anionenstrukturen in Alkalisilicatschmelzen

Silicate Anions in Alkali Silicate Melts Melts of alkali silicates with molar ratios of alkali (Li, Na, K, Cs) to silicon between R = 4.0 and ca. 2.0 were prepared, quenched and worked up to the trimethylsilyl silicic acid esters. These were identified by comparison to the GC and silicon-29 NMR data of trimethylsilyl silicic acid esters from other sources. It was found that with cations of Li and Na mostly linear silicates were formed. But with the cations of K and Cs a considerable amount of the cyclic species Si₆O₉^6? was present. Branched silicates were of minor importance only. Besides the alkali silicon ratio, the temperature of the melt before quenching influences the composition of the silicate mixture.     

Struktur der Valenciaxanthine und Valenciachrome

Structure of the Valenciaxanthins and Valenciachromes Valenciaxanthin, a carotenoid first isolated from Californian Valencia orange juice in 1952/1954 by American scientists, was re-isolated from fresh Spanish ‘Navelinas’ and shown, by spectroscopical and chiroptical examination, to have the unexpected (9Z)-10′-apo-11′,12′-dihydroviolaxantin-10′-ol structure 6 . A further, very minor component represents the (all-E)-structure 7 . Therefore, the Valenciachromes are the furanoid rearrangement products of 6 and 7 and, thus, stereoisomers of the 10′-apo-11′,12′-dihydroauroxanthiiv 10′-ols 8 . Valenciaxanthin represents a modification of the common cleavage of carotenoids in higher plants according to the scheme C₄₀ → C₂₇ + C₁₃, insofar as the reduction step not only includes the aldehyde function but also the subsequent conjugated double bond.     

Cis/trans copolyamides of 1,4-bisaminomethylcyclohexane

Copolyamides prepared from cis- and trans-1,4-bisaminomethylcyclohexane with adipic, sebacic, and dodecanoic acids showed a decrease in melting point with increasing cis diamine content and increasing chain length of the diacid. Most unusual was the fact that the glass transition temperature of these copolymers were essentially independent of diamine isomer content. The existence of an intermediate conformation for some of the cyclohexane rings such as the “twistmer” is suggested to account for this discrepancy. The T_g, T_c, and T_m all decreased with increasing chain length of the diacid. The thermal stability as exemplified by the polysebacamides, was independent of diamine isomer content.     

In situ electrode modification for direct differential pulse polarography of 2,6-diaminopurine and its metabolite, 2,6-diamino-8-purinol

Preferential adsorption of allopurinol (1H-pyrazolo-[3,4-d]-pyrimidin-4-ol) at graphite electrodes from pH 7.0 phosphate buffer solutions of 2,6-diaminopurine and 2,6-diamino-8-purinol allowed in situ electrode modification. Modified electrodes were applied to the simultaneous determination of 2,6-diaminopurine and 2,6-diamino-8-purinol in phosphate buffer at pH 7.0. Differential pulse polarography allowed both compounds to be quantified in the concentration range 1 × 10^?6–5 × 10^?4 M. The relative standard deviation of the peak current is about 10%. Calibration curve characteristics are C (μM) = 0.0094 ± 0.0002 I (μA) + 0.22 ± 0.07 μA, with r = 0.9985 and C (μM) = 0.0065 ± 0.0001 I (μA) + 0.03 ± 0.04 μA with r = 0.9990 for 2,6-diamino-8-purinol and 2,6-diaminopurine, respectively.