The Polyakov path integral over bordered surfaces

Following the general scheme of the convariant path integral quantization of gauge systems, two alternative formulations of the first quantized closed bosonic string in a position representation are presented. In both approaches the covariant path integral representations of the propagator and of the higher order off-shell amplitudes are constructed. For a wide class of gauges the explicit formulae for off-shell amplitudes are obtained. This paper is the continuation of our previous work where the corresponding problems in the open string case were considered [20].     

Fibres of width 3 ordered sets

We show that in an ordered setP of width 3 there always exists a fibre (i.e., a subset intersecting each maximal nontrivial antichain) of size at most 11/18|P|. This improves previously known results.Research supported by Polish KBN Grant 2 2037 92 03.     

On mechano-chemical Calcium waves

The influence of mechano-chemical coupling on calcium concentration waves is considered. The propagation of calcium waves is described by a reaction–diffusion equation with the reaction term dependent on the mechanical stress responsible for the release of calcium. Similarly the balance of mechanical forces is influenced by the calcium concentration through the so-called traction force.     

Rulers and slaves in a random social group

LetD(n, d) be a digraph chosen at random from a family of alld-out-regular digraphs onn points. LetK(n, p) be a simple graph onn points in which each edge appears independently with probabilityp. A relationship between the properties of extreme in-degrees ofD(n,d) and extreme degrees ofK(n, p) in the case whend = (n – 1)p = o(n) is presented. A sociological interpretation is also provided.     

Bemerkungen zur colorimetrischen Bestimmung von Vanadium mit Phosphorwolframs?ure

Zusammenfassung Die colorimetrische Bestimmungsmethode von Vanadium mit Phosphorwolframsäure wurde in bezug auf den Einfluß der Reagenskonzentrationen untersucht. Außerdem wurde die Bestimmungsmöglichkeit in Gegenwart von Eisen geprüft. Es zeigte sich, daß die Konzentrationen an Phosphorsäure und Wolframat in weiten Grenzen geändert werden können, ohne die Bestimmungsgenauigkeit zu beeinflussen. Zu große Mengen Salpetersäure bewirken negative Fehler, indem die Extinktionen mit zunehmender HNO₃-Konzentration linear abnehmen. Nach der angegebenen Vorschrift kann Vanadium in Gegenwart von bis zu 150 mg Eisen(III)-ionen in einem Volumen von 25 ml bestimmt werden.     

Some analytical semigroups occurring in probability theory

One-parameter semigroups occurring in operator-limit distributions are investigated. The topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup.     

Structure of colloid silica determined by viscosity measurements

The viscosity of nanosized colloid silica suspensions, used as binders in the investment casting, was determined as a function of their weight fraction reaching 52%. A new capillary viscometer was used whose construction eliminated sedimentation effects. The experiments have been carried out at fixed pH 10.0 and controlled ionic strength. It was found that for a low silica concentration range (weight fraction below 5%) the suspension viscosity increased more rapidly than the Einstein theory predicts. This anomalous behavior could not be explained in terms of the primary electroviscous effect predicted to be a few orders of magnitude smaller as observed. This discrepancy was accounted for by postulating a fuzzy, gel-like structure of colloid silicas used in our experiments. Hence, the apparent hydrodynamic radius of silica particles in aqueous suspensions was found to be larger than the primary particle size in accordance with previous observations. Based on this postulate, an apparent density of the silica sols was found to be 1.32-1.37 g/cm(3) instead of 2.2-2.32 g/cm(3) as determined from the suspension dilution method. This behavior was interpreted in terms of the core/shell model with high shell porosity, reaching 85%. Similarly, for higher concentration ranges, silica viscosity increased more rapidly with increased sol concentration than predicted by the Batchelor model derived for hard particles. The deviation was attributed to the secondary electroviscous effect stemming from the electrostatic interactions among silica particles in sheared suspensions. This effect has quantitatively been interpreted in terms of Russel's theory. On the other hand, for the high concentration range the experimental results were well accounted for by the Dougherty-Krieger model. By exploiting our experimental findings a sensitive method of determining the structure and apparent density of silica sols in aqueous media was proposed.     

Quecksilber(II)-Titrationen mit Variaminblau als Redoxindicator

Zusammenfassung Es wird eine volumetrische Methode zur Bestimmung von Cyanid- und Quecksilber(II)-ionen mit titrierter Quecksilber(II)-nitratlösung gegen Variaminblau als Indicator beschrieben. Das Verfahren liefert genaue, wenig streuende Werte.Vorgetragen auf der III. Arbeitstagung für analytische Chemie in Prag am 1. September 1959.     

Structural changes in the monomeric despentapeptide (B30-B26) insulin crystal

Insulin modified by the removal of its 5 B chain C terminal residues is monomeric but remains substantially potent. The crystal structures of the beef and insulin (dpi) with two molecules in the asymmetric unit has been determined by x-ray analysis. The 3-dimensional structure ofdpi proves to be generally similar to that of native molecule in 2Zn insulin. More detailed comparison reveals that the slight differences in the two independent molecules of beefdpi are distributed uniformly throughout the structure in contrast to insulin in 2Zn insulin, where the structural changes are concentrated in specific regions. The loss of symmetry in thedpi crystal appears to be the inability of the A9 serine to pack effectively in the C2 cell. The efficient packing of the sheepdpi molecule whose crystal structure has also been determined and where A9 is glycine supports this conclusion.