Nonlinear transformations of the canonical gauss measure on Hilbert space and absolute continuity

The papers of R. Ramer and S. Kusuoka investigate conditions under which the probability measure induced by a nonlinear transformation on abstract Wiener space(,H,B) is absolutely continuous with respect to the abstract Wiener measure. These conditions reveal the importance of the underlying Hilbert spaceH but involve the spaceB in an essential way. The present paper gives conditions solely based onH and takes as its starting point, a nonlinear transformationT=I+F onH. New sufficient conditions for absolute continuity are given which do not seem easily comparable with those of Kusuoka or Ramer but are more general than those of Buckdahn and Enchev. The Ramer-Itô integral occurring in the expression for the Radon-Nikodym derivative is studied in some detail and, in the general context of white noise theory it is shown to be an anticipative stochastic integral which, under a stronger condition on the weak Gateaux derivative of F is directly related to the Ogawa integral.Research supported by the National Science Foundation and the Air Force Office of Scientific Research Grant No. F49620 92 J 0154 and the Army Research Office Grant No. DAAL 03 92 G 0008.     

13C-Leucin-Atemtest zur Beurteilung der anabolen Verwertung von diätetischen Aminosäurengemischen bei Phenylketonurie

It is essential to establish whether and how environmental factors affect the reliability of [¹³C]methacetin breath test (¹³C-MBT). In 12 healthy volunteers (smokers), a standard ¹³C-MBT with 75 mg [¹³C]methacetin was performed twice in random order: on a control day without smoking and on another day with smoking two cigarettes antecedently. A considerable flattening of the curve of the momentary ¹³C recovery within the expiratory air was observed when the ¹³C-MBT was performed after smoking. The maximum of the momentary ¹³C recovery, D _max, decreased from 37.20±2.58 to 25.39±2.29% dose/h (p=0.00052). Moreover, the time to reach D _max was prolonged after cigarette smoking (26.5±3.1 vs. 16.5±1.9 min, p=0.0199). The curve of the cumulative ¹³C recovery on the cigarette smoking day appeared to be shifted downwards, and statistically significant differences relative to the control situation were found between the 24th and 75th minute following [¹³C]methacetin administration. Smoking cigarettes immediately prior to the ¹³C-MBT diminishes the ability of the liver to handle methacetin, and hence a possibility of such an interaction should be excluded in order to interpret the results of the test correctly.     

Effect of Solute‐Polymer Interactions on Sorption and Diffusion in Polyacrylamide Gels

Solute‐polymer interactions can exert a large effect on selective sorption and permeation in polyacrylamide (PAAm) gels. In order to investigate this effect, three probe polyelectrolytes, sodium polystyrene sulphonate (PSS), polyvinylpyrrolidone (PVP), and sulfonated polyaniline (SPANI), were chosen as probe species in sorption, release, and permeation experiments in PAAm gels. For PAAm gels with trapped SPANI, FTIR spectroscopy has confirmed that there exists hydrogen‐bonding between SPANI and PAAm. In addition, rigid‐chain SPANI has an intense tendency to aggregate; it is likely that the effective chains of the PAAm matrices are enwrapped in these aggregates. Hydrogen‐bonding and aggregation resulted in that the release kinetics of SPANI from PAAm gels exhibited a remarkable “lag time”, as long as 100 h (lag period means that in the initial period there is no detectable SPANI released from PAAm gels.), the releasing rate of SPANI was very slow, and the selective sorption of SPANI in PAAm gels was extremely high. On the other hand, the release and permeation of PVP and PSS through PAAm gels were much faster than SPANI, and the selective sorption were close to unity. From these facts it could be deduced that there is no or only weak interaction between PAAm and PSS (or PVP). Adding of concentrated support electrolyte resulted in decrease of the release rate and a two‐magnitude decrease of the calculated diffusion coefficients of PSS; the effect of support electrolyte on release and permeation of PSS was partly attributed to the electrostatic interaction.     

Prediction and characterisation of a chalcogen···π interaction with acetylene as a potential electron donor in XHS···HCCH and XHSe···HCCH (X = F,Cl, Br,CN, OH,OCH3, NH2, CH3) σ-hole complexes

It is well-known that many covalently bonded atoms of group VI have specific positive regions of electrostatic potential (σ-holes) through which they can interact with Lewis bases. This interaction is called ‘chalcogen bond’ by analogy with halogen bond and hydrogen bond. In this study, ab initio calculations are performed to predict and characterise chalcogen···π interactions in XHS···HCCH and XHSe···HCCH complexes, where X = F, Cl, Br, CN, OH, OCH₃, NH₂, CH₃. For the complexes studied here, XHS(Se) and HCCH are treated as a Lewis acid and a Lewis base, respectively. The CCSD(T)/aug-cc-pVTZ interaction energies of this type of σ-hole bonding range from ?1.18 to ?4.83 kcal/mol. The calculated interaction energies tend to increase in magnitude with increasing positive electrostatic potential on the extension of X–S(Se) bond. The stability of chalcogen···π complexes is attributed mainly to electrostatic and correlation effects. The nature of chalcogen···π interactions is unveiled by means of the atoms in molecules, natural bond orbital, and electron localisation function analyses.     

On the complexity of the disjoint paths problem

In this paper we consider the disjoint paths problem. Given a graphG and a subsetS of the edge-set ofG the problem is to decide whether there exists a family of disjoint circuits inG each containing exactly one edge ofS such that every edge inS belongs to a circuit inC. By a well-known theorem of P. Seymour the edge-disjoint paths problem is polynomially solvable for Eulerian planar graphsG. We show that (assumingPNP) one can drop neither planarity nor the Eulerian condition onG without losing polynomial time solvability. We prove theNP-completeness of the planar edge-disjoint paths problem by showing theNP-completeness of the vertex disjoint paths problem for planar graphs with maximum vertex-degree three. This disproves (assumingPNP) a conjecture of A. Schrijver concerning the existence of a polynomial time algorithm for the planar vertex-disjoint paths problem. Furthermore we present a counterexample to a conjecture of A. Frank. This conjecture would have implied a polynomial algorithm for the planar edge-disjoint paths problem. Moreover we derive a complete characterization of all minorclosed classes of graphs for which the disjoint paths problem is polynomially solvable. Finally we show theNP-completeness of the half-integral relaxation of the edge-disjoint paths problem. This implies an answer to the long-standing question whether the edge-disjoint paths problem is polynomially solvable for Eulerian graphs.Supported by Sonderforschungsbereich 303 (DFG)     

Air stability of PTCDI‐C13‐based n‐OFETs on polymer interfacial layers

This Letter reports the novel use of poly(9‐vinylcarbazole) (PVK) as a dielectric interfacial layer for n‐type organic field‐effect transistors (n‐OFETs). With PVK, both the air stability and electron mobility of N,N′‐ditridecylperylene‐3,4,9,10‐tetracarboxylic diimide (PTCDI‐C13)‐based OFETs were improved. Among the PVKs with different weight‐average molecular weight (M_w), PVK with high M_w showed good performance. The high glass transition temperature of PVK enabled thermal post annealing of the active layer, which resulted in a high electron mobility of 0.61 cm²/Vs. This mobility was maintained at 90% and 59% after 4 days and 105 days in air, respectively. The PVK interfacial layer reduced the trapped charges in the PTCDI‐C13‐based n‐OFET for air‐exposure and caused a decrease in the threshold voltage shift.

     

On sets of integers with prescribed gaps

For a fixed setI of positive integers we consider the set of paths (p _o,...,p _k ) of arbitrary length satisfyingp _l –p _l–1I forl=2,...,k andp ₀=1,p _k =n. Equipping it with the uniform distribution, the random path lengthT _n is studied. Asymptotic expansions of the moments ofT _n are derived and its asymptotic normality is proved. The step lengthsp _l –p _l–1 are seen to follow asymptotically a restricted geometrical distribution. Analogous results are given for the free boundary case in which the values ofp ₀ andp _k are not specified. In the special caseI={m+1,m+2,...} (for some fixed m) we derive the exact distribution of a random m-gap subset of {1,...,n} and exhibit some connections to the theory of representations of natural numbers. A simple mechanism for generating a randomm-gap subset is also presented.     

Some open categorical problems inTop

In this paper, a pendant to a recent survey paper, the authors discuss several open problems in categorical topology. The emphasis is on topology-oriented problems rather than on more general category-oriented ones. In fact, most problems deal with full subconstructs or superconstructs of the constructTop of topological spaces and continuous maps.     

Joint extension of two theorems of Kotzig on 3-polytopes

The weight of an edge in a graph is the sum of the degrees of its end-vertices. It is proved that in each 3-polytope there exists either an edge of weight at most 13 for which both incident faces are triangles, or an edge of weight at most 10 which is incident with a triangle, or else an edge of weight at most 8. All the bounds 13, 10, and 8 are sharp and attained independently of each other.