A discrete four vertex theorem

A discrete four vertex theorem is proved for a general plane polygon using a method of proof that also yields a proof, that appears to be new, for the classical four vertex theorem.     

Quasi-state rigidity for finite-dimensional Lie algebras

We say that a Lie algebra g is quasi-state rigid if every Ad-invariant continuous Lie quasi-state on it is the directional derivative of a homogeneous quasimorphism. Extending work of Entov and Polterovich, we show that every reductive Lie algebra, as well as the algebras C ⁿ ? u(n), n ≥ 1, are rigid. On the other hand, a Lie algebra which surjects onto the three-dimensional Heisenberg algebra is not rigid. For Lie algebras of dimension ≤ 3 and for solvable Lie algebras which split over a codimension one abelian ideal, we show that this is the only obstruction to rigidity.     

Variable neighborhood search for extremal graphs. 21. Conjectures and results about the independence number

A set of vertices S in a graph G is independent if no neighbor of a vertex of S belongs to S. The independence number α is the maximum cardinality of an independent set of G. A series of best possible lower and upper bounds on α and some other common invariants of G are obtained by the system AGX 2, and proved either automatically or by hand. In the present paper, we report on such lower and upper bounds considering, as second invariant, minimum, average and maximum degree, diameter, radius, average distance, spread of eccentricities, chromatic number and matching number.     

Onf-vectors and Betti numbers of multicomplexes

A multicomplexM is a collection of monomials closed under divisibility. For suchM we construct a cell complex M whosei-dimensional cells are in bijection with thef _i monomials ofM of degreei+1. The bijection is such that the inclusion relation of cells corresponds to divisibility of monomials. We then study relations between the numbersf _i and the Betti numbers of M. For squarefree monomials the construction specializes to the standard geometric realization of a simplicial complex.This work was supported by the Mittag-Leffler Institute during the Combinatorial Year program 1991–92. The second author also acknowledges support from the Serbian Science Foundation, Grant No. 0401D.     

Combined effects of microcavity and dielectric capping layer on bidirectional organic light-emitting diodes

We report on highly enhanced and controlled light outcoupling of bidirectional organic light-emitting diodes by introduction of an enhanced microcavity structure as well as an organic capping layer (OC). Combining both OC and microcavity, we find that the overall external quantum, as well as current efficiency (CE), can be greatly enhanced. Especially, the CE with an appropriate thickness of OC is almost 1.75 times larger than that of the reference device without OC. Furthermore, we also analyze our devices with a numerical optical model calculating the flux of outcoupled photons, and compare theoretical predictions with our experimental results.     

Finite width in out-of-equilibrium propagators and kinetic theory

We derive solutions to the Schwinger–Dyson equations on the Closed-Time-Path for a scalar field in the limit where backreaction is neglected. In Wigner space, the two-point Wightman functions have the curious property that the equilibrium component has a finite width, while the out-of equilibrium component has zero width. This feature is confirmed in a numerical simulation for scalar field theory with quartic interactions. When substituting these solutions into the collision term, we observe that an expansion including terms of all orders in gradients leads to an effective finite-width. Besides, we observe no breakdown of perturbation theory, that is sometimes associated with pinch singularities. The effective width is identical with the width of the equilibrium component. Therefore, reconciliation between the zero-width behaviour and the usual notion in kinetic theory, that the out-of-equilibrium contributions have a finite width as well, is achieved. This result may also be viewed as a generalisation of the fluctuation–dissipation relation to out-of-equilibrium systems with negligible backreaction.     

Fractionation of cesium isotopes and90Sr in snowmelt run-off and lake waters from a contaminated Norwegian mountain catchment

Cesium isotopes and⁹⁰Sr have been determined in the inflow and outflow rivers of a Norwegian subalpine lake. The lake is situated in an area contaminated by Chernobyl fallout. Sampling was carried out during the spring peak discharge period associated with snowmelt. Transported coatse particulate plant material was collected by traps. Particles and colloids were removed from water samples by hollow fibre ultrafiltration. The results illustrate that run-off during the spring snowmelt is an important pathway for these radionuclides. The cesium isotopes are predominantly transported as colloids, while⁹⁰Sr is present in the form of low molecular weight mobile species. Based on lake budget calculations, more than 50% of the cesium input is retained in the lake, while more than 90% of the⁹⁰Sr is transported through the lake and into lower parts of the drainage system.     

The electronic structure and spectrum of the geometric isomers of 1,4-diphenyl-1,3-butadiene

Using the results of energy calculations to determine the stable conformations, LCAO-SCF-CI semi-empirical computations have been performed on the three geometric isomers of 1,4-diphenyl-1,3-butadiene. The predicted wavelength and intensity changes for the fundamental band, which has been assigned to a ¹ B¹ A transition, are in agreement with experiment. The second transition has been assigned to be primarily ¹ G¹ A and the third transition, observed only in the trans-trans isomer, ¹ H ¹ A.

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Zusammenfassung Zunächst warden die stabilsten Konformationen der drei Isomeren des 1,4-Diphenyl-1,3-butadiens bestimmt. Für diese Geometrien wurden dann PPP-Rechnungen durchgeführt. Wellenlängen und Intensitäten der Hauptbande stimmen mit den experimentellen Werten sehr gut überein. Die Hauptbande ist vom Typ ¹ B¹ A, die zweite Bande beruht hauptsächlich auf ¹ G¹ A-Übergängen, der bisher nur beim trans-trans-Isomeren beobachteten dritten Bande wird ein ¹ H¹ A-Übergang zugeordnet.

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Résumé Des calculs L.C.A.O. S.C.F. C.I. semi-empiriques ont été effectués sur les trois isomères géométriques du 1,4-diphényl-1,3-butadiène, en utilisant les résultats des calculs d'énergie pour déterminer la stabilité des conformations. Les variations de longueur d'onde et d'intensité de la bande fondamentale, attribuée à une transition ¹ B¹ A, sont en accord avec l'éxpérience. La seconde transition a été attribuée essentiellement à ¹ G¹ A et la troisième, observée seulement dans l'isomère trans.trans, à ¹ H¹ A.

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On leave from the Institute of Physical Chemistry, Uppsala University, Uppsala, Sweden. Financial support from the Swedish National Science Research Council.

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On Sabbatic leave 1966—1967 from the Physics Department and Materials Science Institute, University of Connecticut, Storrs, Connecticut, U.S.A. Financial Support from the University of Connecticut Research Foundation, Storrs, Connecticut, U.S.A.     

Die schwingungsspektren der tetra-cyclopropyl-verbindungen von silicium,germanium und zinn

The IR and Raman spectra of Si(C₃H₅)₄, Ge(C₃H₅)₄ and Sn(C₃H₅)₄ were recorded and assigned on the basis of D_2d symmetry, which, however, is strictly realised only for the tin compound. The assignments are in accordance with the dipole moments (1.8, 3.4, 2.0 Debye, respectively).     

Design and synthesis of effective antagonists of substance P

The agonist/antagonist activities of four background analogs of substance P (SP) facilitated design and synthesis of 12 new analogs to achieve effective antagonists. (D-Pro2, D-Phe7, D-Trp9)-SP, (D-Pro2, D-Trp7,9)-SP and (D-Arg1, D-Phe7, D-Trp9)-SP showed no agonist activity; 9 analogs showed weak agonist activity of SP. (D-Pro2, D-Trp7,9)-SP was the most potent antagonist which at a concentration of 10(-5) required a 3-fold increase in SP to allow a 50% response by SP. (D-Pro2, Lys6, D-Phe7)-SP and (D-Pro2, D-pClPhe7, D-Trp9)-SP were also potent, and the antagonism was competitive. For specific pairs of peptides, Lys6 is a promising substituent. D-Trp7,9 was as effective as Lys6, D-Phe7. D-pClPhe7 was three times as effective as D-Phe7. D-Dln6 was 1.33-fold better than D-Gln5. D-Pro2 and D-Pro4 were equally effective. D-Pro2 was 1.5 times as effective as D-Lys3. D-Pro2 may not be important. D-pClPhe9 and D-Trp9 were equally effective.