Remarks on unit indices of imaginary abelian number fields II

Satz 41 in Hasse's monograph [4] is modified because of the incorrectness of Satz 29. We investigate unit indices of imaginary abelian number fields of type (2,2) and (2,2, 2), some of which give counterexamples to Satz 41. We moreover give a relation between unit indices of certain imaginary fields of type (2,2²) and those of their real cyclic subfields.     

Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.     

Buchsbaum homogeneous algebras with minimal multiplicity

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras.     

Linear optical switching in a FLC/waveguide composite device

A fast electrooptic modulation in a polymer waveguide using a ferroelectric liquid crystal has been proposed. In this device, the surface stabilized ferroelectric liquid crystal and the soft mode ferroelectric liquid crystal are used as an active material on the passive polymer waveguide, and electrooptic switching is realized by controlling the total reflection at the polymer waveguide-liquid crystal interface. The response time is of the order of several microseconds. The analogue electrooptic modulation in the waveguide is realized using the field induced linear molecular tilt of the electroclinic effect in the soft mode ferroelectric liquid crystal.     

Some Recent Progress and Applications in Graph Minor Theory

In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with some other recent advances on graph minors are surveyed. Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number 16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists Supported in part by the Research Grant P1–0297 and by the CRC program On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia     

Studies on the formation of aliphatic aldehydes in the plasma and liver of vitamin E-deficient rats

The effects of vitamin E (E) deficiency on the formation of aliphatic aldehydes in rat plasma and liver were studied. Three-week-old Wistar male rats were fed either an E supplemented diet (2-ambo-alpha-tocopheryl acetate 20 mg/kg diet, designated as E supplemented diet group) or an E deficient diet (E deficient diet group). After 8 weeks, n-hexanal and (E)-4-hydroxy-2-nonenal (4-HN) in the plasma of the E deficient diet group were found to be 2.0 and 2.5-fold greater than those of the E supplemented diet group, respectively. The contents of aldehydes such as n-pentanal, n-hexanal, 4-HN in the liver were also significantly higher in the E deficient diet group than in the E supplemented diet group. These results indicate that some aldehydes, arising possibly from lipid peroxides, are produced and detected in the plasma and liver of rats under the condition like E deficiency. In this study we further found that the activity of the liver aldehyde dehydrogenase (ALDH, EC 1.2.1.3) was significantly changed; 5 and 8 weeks after the start it was lower in the E deficient diet group when compared to that in the E supplemented diet group. The decrease of enzyme activity was related to the increase of aldehydes such as n-hexanal in the liver. the aldehyde increase in the plasma of the E deficient diet group was thought to raise the injury of cells, namely, a strong hemolysis on erythrocytes prepared from the blood of rats fed the E deficient diet.     

Organic phosphorus compounds. IV. Asymmetric 4-(benzothiazol-2-yl)benzylphosphonates as potent calcium antagonistic vasodilators

Various asymmetric or cyclic ester derivatives of the phosphonic acid moiety in the calcium antagonist fostedil (KB-944) were synthesized. The coronary vasodilator activity of these compounds was assessed by Langendorff's method. Among them, the ethyl isopropyl ester 12 showed the most potent activity, which was comparable to that of fostedil.     

Absorption of diltiazem in beagle dog from pulsatile release tablet.

An orally applicable pulsatile drug delivery system in dry-coated tablet form was prepared using diltiazem hydrochloride as the model drug, and a polyvinyl chloride-hydrogenated castor oil-polyethyleneglycol mixture as the outer shell of the tablet. In vitro drug release from the prepared tablet exhibited a typical pulsatile pattern with a 7 h lag phase (non-drug release period). This dosage form was orally administered to three beagle dogs under non-fasting and fasting conditions, and the plasma concentration level of diltiazem was determined according to time after administration. The result of the in vivo study in non-fasting dogs suggested that the drug could be released in the gastrointestinal tract as in the in vitro test. However, under the fasting condition, a large difference in the plasma concentration profile was found, suggesting that the disintegration time of the tablet tended to be influenced by the feeding condition of subject.     

Electrical conducting and magnetic properties of (ethylenedithiotetrathiafulvalenothioquinone-1,3-diselenolemethide)2.FeBr4 (GaBr4) crystals with two different interlayer arrangements of donor molecules

Two donor molecules newly synthesized, dimethylthio- and ethylenedithio-tetrathiafulvalenothioquinone-1,3-diselenolemethides (1 and 2), were used to prepare their charge-transfer (CT) salts with a magnetic FeBr(4)(-) counteranion. For 1, a low electrical conducting 1:1 salt (1.FeBr(4)) was obtained, in which molecules of 1 are tightly dimerized in a one-dimensional (1D) stacking column. On the other hand, 2 gave a 2:1 salt (2(2).FeBr(4)) as two different kinds of plate crystals (I and II). Both I and II possess similar stacking structures of molecules of 2 in each 1D column with a half-cut pipelike structure along the c axis. However, for I, the stacking columns are aligned in the same direction along the a and b axes, while for II they are in the same direction along the a axis, but in the reverse direction along the b axis, resulting in the difference in the relative arrangement of molecules of 2 and FeBr(4)(-) ions between the two crystals. The room-temperature electrical conductivities of the single crystals of I and II were 13.6 and 12.7 S cm(-)(1), respectively. The electrical conducting behavior in I was metallic above 170 K but changed to be semiconducting with a very small activation energy of 7.0 meV in the temperature range 4-170 K. In contrast, II showed the semiconducting behavior in the whole temperature range 77-285 K. The corresponding nonmagnetic GaBr(4)(-) salts with almost the same crystal structure as I and II showed definitively different electrical conducting properties in the metal to semiconductor transition temperature in I as well as in the magnitude of activation energy in the semiconducting region of I and II. The interaction between the d spins of FeBr(4)(-) ions was weak and antiferromagnetic in both I and II, but the magnitude of the spin interaction was unexpectedly larger compared with that in the FeBr(4)(-) salt of the corresponding sulfur derivative of 2 with closer contact between the neighboring FeBr(4)(-) ions. These electrical conducting and magnetic results suggest a significant interaction between the conducting pi electrons and the d spins of FeBr(4)(-) ions located near the columns or layers.