Existence of quadrature surfaces for positive measures with finite support

Let be a positive measure with finite support in ⁿ (n2). Then we show that there is a bounded open set , containing the support of , whose single-layer potential coincides with the potential of outside .     

Calculation of the O-H stretching vibrational overtone spectrum of the water dimer

The O-H stretching vibrational overtone spectrum of the water dimer has been calculated with the dimer modeled as two individually vibrating monomer units. Vibrational term values and absorption intensities have been obtained variationally with a computed dipole moment surface and an internal coordinate Hamiltonian, which consists of exact kinetic energy operators within the Born-Oppenheimer approximation of the monomer units. Three-dimensional ab initio potential energy and dipole moment surfaces have been calculated using the internal coordinates of the monomer units using the coupled cluster method including single, double, and perturbative triple excitations [CCSD(T)] with the augmented correlation consistent valence triple zeta basis set (aug-cc-pVTZ). The augmented correlation consistent valence quadruple zeta basis set (aug-cc-pVQZ), counterpoise correction, basis set extrapolation to the complete basis set limit, relativistic corrections, and core and valence electron correlations effects have been included in one-dimensional potential energy surface cuts. The aim is both to investigate the level of ab initio and vibrational calculations necessary to produce accurate results when compared with experiment and to aid the detection of the water dimer under atmospheric conditions.     

The monohydrates of the four polar dipeptides l‐seryl‐l‐asparagine,l‐seryl‐l‐tyrosine,l‐tryptophanyl‐l‐serine and l‐tyrosyl‐l‐tryptophan

The crystal structures of the four dipeptides l ‐seryl‐l ‐asparagine monohydrate, C₇H₁₃N₃O₅·H₂O, l ‐seryl‐l ‐tyrosine monohydrate, C₁₂H₁₆N₂O₅·H₂O, l ‐tryptophanyl‐l ‐serine monohydrate, C₁₄H₁₇N₃O₄·H₂O, and l ‐tyrosyl‐l ‐tryptophan monohydrate, C₂₀H₂₁N₃O₄·H₂O, are dominated by extensive hydrogen‐bonding networks that include cocrystallized solvent water molecules. Side‐chain conformations are discussed on the basis of previous observations in dipeptides. These four dipeptide structures greatly expand our knowledge on dipeptides incorporating polar residues such as serine, asparagine, threonine, tyrosine and tryptophan.     

Free boundary regularity close to initial state for parabolic obstacle problem

In this paper we study the behavior of the free boundary , arising in the following complementary problem:

Here denotes the parabolic boundary, is a parabolic operator with certain properties, is the upper half of the unit cylinder in , and the equation is satisfied in the viscosity sense. The obstacle is assumed to be continuous (with a certain smoothness at , ), and coincides with the boundary data at time zero. We also discuss applications in financial markets.

     

Quantification of buserelin in a pharmaceutical product by multiple-injection CZE

An efficient and rapid separation method based on reversed-polarity multiple-injection CZE (MICZE), has been developed for the quantification of buserelin in a pharmaceutical product. The determinations were performed by serially injecting five standard solutions of buserelin (50-300 microg/mL) and one reference analyte into a Polybrene-coated capillary. All the samples contained goserelin, an analog peptide to buserelin, as internal standard (IS). Immediately after pressure injection, the applied sample plugs were subjected to electrophoresis for 2 min at -25 kV. Consequently, each sample plug became isolated from its neighboring plugs by the BGE, composed of 100 mM phosphate-triethanolamine buffer at pH 3.0 containing 10% v/v ACN. During separation the individual sample components migrated at similar velocities and as distinct zones through the capillary giving 24 peaks, 12 from the analyte and the IS and 12 from the sample matrix. The buserelin content of the pharmaceutical product was determined to be 0.94 +/- 0.05 mg/mL, which is only a slight deviation from the declared concentration (1 mg/mL).     

Complexation of tauro- and glyco-conjugated bile salts with three neutral beta-CDs studied by ACE

Complexation of the bile salts (BS) taurocholate, tauro-beta-muricholate, taurodeoxycholate, taurochenodeoxycholate, glycocholate, glycodeoxycholate, and glycochenodeoxycholate common in rat, dog, and man with natural beta-CD and the chemically modified beta-CDs 2-hydroxypropyl-beta-CD and 2-O-methyl-beta-CD was studied using mobility shift ACE. The CDs were selected due to their frequent use in preformulation and drug formulation as oral excipients for the solubilization of drug substances with low aqueous solubility. ACE was demonstrated to be a feasible and efficient technique for investigation of the interactions between BS and beta-CDs. All the investigated BS possessed affinity for the three CDs with stability constants ranging from 2x10(3) to 4x10(5) M(-) (1). The requirements and assumptions related to the use of ACE for estimating high affinity stability constants were discussed. The extent and pattern of hydroxylation significantly influenced the affinity of the glyco- and tauro-conjugated BS toward the beta-CDs (chenodeoxycholates > deoxycholates > cholates) whereas the nature of the beta-CD derivatization and BS conjugation played a minor role only. The results indicate that displacement of drug substances from beta-CD inclusion complexes is likely to occur in the small intestine where BS are present potentially influencing drug bioavailability.     

Comparison of diafiltration and size-exclusion chromatography to recover hemicelluloses from process water from thermomechanical pulping of spruce

Hemicelluloses constitute one of the most abundant renewable resources on earth. To increase their utilization, the isolation of hemicelluloses from industrial biomass side-streams would be beneficial. A method was investigated to isolate hemicelluloses from process water from a thermomechanical pulp mill. The method consists of three steps: removal of solids by microfiltration, preconcentration of the hemicelluloses by ultrafiltration, and purification by either size-exclusion chromatography (SEC) or diafiltration. The purpose of the final purification step is to separate hemicelluloses from small oligosaccharides, monosaccharides, and salts. The ratio between galactose, glucose, and mannose in oligo- and polysaccharides after preconcentration was 0.8:1:2.8, which is similar to that found in galactoglucomannan. Continuous diafiltration was performed using a composite fluoro polymer membrane with cutoff of 1000 Da. After diafiltration with four diavolumes the purity of the hemicelluloses was 77% (gram oligo- and polysaccharides/gram total dissolved solids) and the recovery was 87%. Purification by SEC was performed with 5, 20, and 40% sample loadings, respectively and a flow rate of 12 or 25 mL/min (9 or 19 cm/h). The purity of hemicelluloses after SEC was approx 82%, and the recovery was above 99%. The optimal sample load and flow rate were 20% and 25 mL/min, respectively. The process water from thermomechanical pulping of spruce is inexpensive. Thus, the recovery of hemicelluloses is not of main importance. If the purity of 77%, obtained with diafiltration, is sufficient for the utilization of the hemicelluloses, diafiltration probably offers a less expensive alternative in this application.     

A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games

We suggest the first strongly subexponential and purely combinatorial algorithm for solving the mean payoff games problem. It is based on iteratively improving the longest shortest distances to a sink in a possibly cyclic directed graph.We identify a new “controlled” version of the shortest paths problem. By selecting exactly one outgoing edge in each of the controlled vertices we want to make the shortest distances from all vertices to the unique sink as long as possible. The decision version of the problem (whether the shortest distance from a given vertex can be made bigger than a given bound?) belongs to the complexity class NP∩CONP. Mean payoff games are easily reducible to this problem. We suggest an algorithm for computing longest shortest paths. Player MAX selects a strategy (one edge from each controlled vertex) and player MIN responds by evaluating shortest paths to the sink in the remaining graph. Then MAX locally changes choices in controlled vertices looking at attractive switches that seem to increase shortest paths lengths (under the current evaluation). We show that this is a monotonic strategy improvement, and every locally optimal strategy is globally optimal. This allows us to construct a randomized algorithm of complexity , which is simultaneously pseudopolynomial (W is the maximal absolute edge weight) and subexponential in the number of vertices n. All previous algorithms for mean payoff games were either exponential or pseudopolynomial (which is purely exponential for exponentially large edge weights).     

A hypercyclicity criterion with applications

A continuous linear operator on a topological vector space X is called hypercyclic if there is x∈X such that the orbit {Tnx}_n?0 is dense in X. We establish a criterion for hypercyclicity, and study some applications. In particular, we establish hypercyclic left-multipliers on the space L(X,Y) of continuous linear operators between X and Y, provided with the topology of uniform convergence on bounded sets, for some spaces X,Y of holomorphic functions.     

Semistable points with respect to real forms

We consider actions of real Lie subgroups G of complex reductive Lie groups on Kählerian spaces. Our main result is the openness of the set of semistable points with respect to a momentum map and the action of G.