Number and length of attractors in a critical Kauffman model with connectivity one

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a frozen and a disordered phase, and is therefore used for studies of real network problems. We prove here that the mean number and mean length of attractors in critical random Boolean networks with connectivity one both increase faster than any power law with network size. We derive these results by generating the networks through a growth process and by calculating lower bounds.     

Experimental determination of human erythrocyte membrane permeability coefficients for a series of amides

Erythrocyte membrane permeability coefficients have been determined for a series of amides by a method based on the physical and mathematical modelling of hypotonic haemolysis process. The results show that penetration of the substances occurs by two alternative ways through aqueous pores formed by proteins and by the direct dissolving of the molecules in membrane lipids. This conclusion can be confirmed by the correlation analysis between permeability coefficients of native erythrocytes and those pre-incubated with the monosodium salt of p-chloromercuribenzenesulfonic acid (pCMBS), and the partition coefficients of the substances in hydrophilic-hydrophobic phases. Penetration of substances through hydrophilic channels is limited by the sterical factor and diameter in particular. Permeability coefficients for erythrocytes pre-incubated with pCMBS increase in an accordance with the rise of the partition coefficients with correlation coefficient of 0.94, thereby indicating a lipid route of permeation of molecules through erythrocyte membranes.     

Decay properties of isomeric states in radium isotopes close to N = 126

Isomeric states in ^210-215Ra have been populated by the decay of the compound nuclei ^216,220Ra produced in irradiations of ^204,208Pb with ¹²C at MeV. Published values for -ray energies and half-lives were confirmed for Ra. Our data for Ra agree with the -energies and the half-life measured at the RITU separator, University of Jyväskylä (Finland). Its decay pattern is complex. Two series of -rays of keV and keV were observed. A half-life of s was measured. The isomeric state is attributed to an 8 ⁺ state at E ^* = 2053.8keV. A previously unknown isomeric state was assigned to Ra. It has a half-life of ( ) and it decays by emission of -rays with energies of 396.1keV and 802.0keV. It is attributed to a 13/2 ⁺ state at E ^* = 1198.1 keV.PACS: 23.60. + e decay - 27.90. + b      

Design of two-dimensional random surfaces with specified scattering properties

A method is proposed for designing a two-dimensional randomly rough Dirichlet surface that, when illuminated at normal incidence, scatters a scalar plane wave with a specified angular distribution of its intensity. The method is validated by computer simulation calculations.     

\alpha-decay spectroscopy of light odd-odd Bi isotopes - II: 186Bi and the new nuclide 184Bi

Alpha-decay of the new nuclide ¹⁸⁴Bi has been studied in the complete-fusion reaction ⁹³Nb(⁹⁴Mo, 3n)¹⁸⁴Bi at the velocity filter SHIP. The evaporation residues were separated in-flight and subsequently identified on the basis of recoil- , recoil- - analysis and excitation functions measurements. Two -decaying isomeric states in ¹⁸⁴Bi with half-life values of 13(2) ms and 6.6(1.5) ms were identified. The -branching ratio of ¹⁸⁰Tl was deduced for the first time as . Improved data on the fine-structure -decay of ¹⁸⁶Bi were obtained in the ⁹³Nb(⁹⁵Mo, 2n)¹⁸⁶Bi reaction. A similarity of the decay energies and half-life values of ^184,186Bi is pointed out and a possible explanation for this effect is suggested.Received: 14 March 2003, Revised: 29 April 2003, Published online: 2 September 2003PACS: 23.60.+e decay - 27.70.+q - 27.80.+w K. Heyde: Present address: EP-ISOLDE, CERN, CH-1211, Geneva 23, Switzerland.     

Isomeric states in 214Th and 213Th

Isomeric states in ²¹⁴Th and ²¹³Th were identified by means of γ -rays measured in delayed coincidence with the implanted evaporation residues. These were produced in irradiations of ¹⁶⁴Dy with ⁵⁴Cr projectiles and separated in-flight by the velocity filter SHIP. An isomeric state of I ^π = 8⁺ with a half-life of (1.24±0.12) μs was identified in ²¹⁴Th . The configuration π[1h _9/2 ⊗ 2f _7/2] was assigned to this state. An isomeric state with a half-life of (1.4±0.4) μs was observed in ²¹³Th . Tentatively it was assigned to an I ^π = 13/2⁺ state.     

Ultrafast intramolecular charge transfer with strongly twisted aminobenzonitriles: 4-(di-tert-butylamino)benzonitrile and 3-(di-tert-butylamino)benzonitrile

The newly synthesized aminobenzonitriles with two bulky amino substituents 4-(di-tert-butylamino)benzonitrile (DTABN) and 3-(di-tert-butylamino)benzonitrile (mDTABN) have strongly twisted amino groups in the ground state. From X-ray crystal analysis it is found that the amino twist angle theta of mDTABN equals 86.5 degrees , whereas a twist angle of around 75 degrees is deduced for DTABN from the extinction coefficient of its lowest-energy absorption band in n-hexane. Because of the electronic decoupling between the amino and benzonitrile groups caused by these large twist angles, the absorption of DTABN and mDTABN is relatively weak below 40000 cm-1, with extinction coefficients around 25 times smaller than those of the planar 4-(dimethylamino)benzonitrile (DMABN). DTABN as well as mDTABN undergo efficient intramolecular charge transfer (ICT) in the singlet excited state, in nonpolar (n-hexane) as well as in polar (acetonitrile) solvents. Their fluorescence spectra consist of an ICT emission band, without evidence for locally excited (LE) fluorescence. The occurrence of efficient ICT with mDTABN is different from the findings with all other N,N-dialkylaminobenzonitriles in the literature, for which ICT only appears with the para-derivative. From solvatochromic measurements, an ICT dipole moment of 17 D is determined for DTABN as well as for mDTABN, similar to that of DMABN. The picosecond fluorescence decays of DTABN (time resolution 3 ps) are effectively single exponential. Their decay time is equal to the ICT lifetime tau'0(ICT), which increases with solvent polarity from 0.86 ns in n-hexane to 3.48 ns in MeCN at 25 degrees C. The femtosecond excited-state absorption (ESA) spectra of DTABN in n-hexane and MeCN at 22 degrees C show a decay of the LE and a corresponding rise of the ICT absorption. The ICT reaction time is 70 fs in n-hexane and 60 fs in MeCN. DTABN and mDTABN may have a strongly twisted ICT state, similar to that of 6-cyanobenzoquinuclidine but different from that of DMABN.     

Phosphaniminato‐Acetato‐Cluster von Kupfer und Zink. Kristallstrukturen von [Cu4(NPEt3)2(O2CCH3)6] und [Zn4(NPEt3)2(O2CCH3)6]

Phosphoraneiminato Acetate Cluster of Copper and Zinc. Crystal Structures of [Cu₄(NPEt₃)₂(O₂CCH₃)₆] and [Zn₄(NPEt₃)₂(O₂CCH₃)₆] The anhydrous acetates of copper(II) and zinc react with the silylated phosphaneimine Me₃SiNPEt₃ in dichloromethane at 20 °C forming the mixed phosphoraneiminato acetate clusters [Cu₄(NPEt₃)₂(O₂CCH₃)₆] ( 1 ), which forms emerald crystals, and colourless [Zn₄(NPEt₃)₂ · (O₂CCH₃)₆] ( 2 ). In spite of analogous composition the structures of 1 and 2 are completely different. In the asymmetric unit of 1 three copper atoms of an almost isosceles triangle are linked via two nitrogen atoms of the NPEt₃^– groups to form a trigonal bipyramidal aggregate. One of these three copper atoms is chelated by an acetate group, another one is connected with the fourth copper atom via three μ₂‐O₂C–CH₃ groups. The asymmetric units are associated via a μ₂‐O₂C–CH₃ group and a μ₃‐OC(O)CH₃ group at a time so that infinite chains result. In 2 two zinc atoms are linked via the nitrogen atoms of the two NPEt₃^– groups to form an almost centrosymmetric four‐membered ring. Both nitrogen atoms of the four‐membered ring are connected with another zinc atom each. These zinc atoms again are linked with the zinc atoms of the Zn₂N₂ four‐membered ring via two μ₂‐O₂C–CH₃ groups each and additionally coordinated with a terminal acetate ligand each.