Multifractal analysis of Brownian zero set

We present a method for the derivation of the generating function and computation of critical exponents for several cluster models (staircase, bar-graph, and directed column-convex polygons, as well as partially directed self-avoiding walks), starting with nonlinear functional equations for the generating function. By linearizing these equations, we first give a derivation of the generating functions. The nonlinear equations are further used to compute the thermodynamic critical exponents via a formal perturbation ansatz. Alternatively, taking the continuum limit leads to nonlinear differential equations, from which one can extract the scaling function. We find that all the above models are in the same universality class with exponents _u =-1/2, _i =-1/3, and =2/3. All models have as their scaling function the logarithmic derivative of the Airy function.     

Disordered ground states for classical discrete-state problems in one dimension

It is known that one-dimensional lattice problems with a discrete, finite set of states per site generically have periodic ground states (GSs). We consider slightly less generic cases, in which the Hamiltonian is constrained by either spin (S) or spatial (I) inversion symmetry (or both). We show that such constraints give rise to the possibility ofdisordered GSs over a finite fraction of the coupling-parameter space—that is, without invoking any nongeneric fine tuning of coupling constants, beyond that arising from symmetry. We find that such disordered GSs can arise for many values of the number of statesk at each site and the ranger of the interaction. The Ising (k=2) case is the least prone to disorder:I symmetry allows for disordered GSs (without fine tuning) only forr5, whileS symmetry never gives rise to disordered GSs.     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

Solvent effects on 17O nuclear magnetic shielding: N-methylformamide in polar and apolar solutions

The solvent effect on ¹⁷O isotropic shielding was computed by different methods: the polarizable continuum model and a mixed approach, including a few real solvent molecules treated as the solute. The experimental data show that the behavior of protic and aprotic solvents is markedly different: we found that the continuum approach describes well the observed shielding at various dielectric constants for aprotic solvents, while the mixed procedure is needed when hydrogen bonds to the magnetic centre are present.Contribution to the Jacopo Tomasi Honorary Issue     

Surface tension and universality in the three-dimensional Ising model

The amplitude ₀ of the interfacial free energy per unit area (or surface tension) of the body-centered-cubic Ising model is found using a direct monte carlo simulation technique. The combination ²/k_BT_c, where is the correlation length, is shown to agree within the precision of the simulations with a previously reported estimate for the simple cubic lattice. Evidence is also presented for the universality of the finite-size scaling amplitude for the surface tension.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Zur Chemie der Pyrrolpigmente, 56. Mitt.

From an investigation of the ICD of bilatrienes-abc and 2,3-dihydrobilatrienes-abc induced by mixtures of CCl₄ with (+)-cis-Pinane, (–)-lactic and (+)-tartaric acid esters it is concluded that specific interactions between chromophore and the chiral reagents afford a partial resolution of the labile racemate of helices. Attaching chiral residues covalently to the chromophore induces very low resolution of the same kind in case of apolar ligands like a cholesteryl-residue. However, with polar ligands as in the case ofBoc-lysyl derivatives enantiomeric excesses up to 90% are achieved depending on the solvent used.

Herrn Prof. Dr.Karl Schlögl zu seinem 60. Geburtstag gewidmet.     

Comparison of micro- and mesoporous inorganic materials in the uptake and release of the drug model fluorescein and its analogues

The uptake of the three species of the drug model fluorescein (fluorescein sodium salt (FNa), fluorescein free acid (F), and fluorescein diacetate (FDA)) by zeolite NaX and the mesoporous zeotype MCM-41 was investigated as well as their release rates into solutions at pH 7 and pH 4.5. UV/Vis analysis was carried out at a wavelength of 490 nm. Uptakes of the sodium salt of 9 % for zeolite X and 14 % for MCM suggest little penetration of the pores. The use of ethanol as the loading solvent for F resulted in little uptake for both zeolitic materials due to the successful competition of the ethanol for binding sites. Use of acetone (weaker proton acceptor) as loading solvent significantly improved the uptake of F to 17 % and 12 % for zeolite X and MCM, respectively, whilst the uptake of FDA in acetone increased still further to 22 % and 17 % for zeolite X and MCM, respectively. Generally there was a large initial release of the fluorescein analogues from the surface of the zeolites with very little further increase over time. The prescence of an esterase enzyme in the release medium of FDA tripled the release from MCM to 15 % but left the release from zeolite X unaffected at 6 %. The results obtained show that uptake of fluorescein and its analogues is dependent on the loading solvent used, the amount released is influenced by not only the solvent but the pH and the presence of enzymes in the release medium.     

Lattice models of peptide aggregation: evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.