Conjugate points in

An example of a geodesic in with conjugate points is given, thus providing an affirmative answer to a question of V.I. Arnold.

     

Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

Realization of fixed point sets

Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University.     

Freezing points,osmotic coefficients,and activity coefficients of some salts in ethylene carbonate: A high dielectric constant solvent without hydrogen bonding

The freezing points, conductivities, and densities of NaI, KI, CsI, Bu₄NCl, Bu₄NBr, Bu₄NI, Et₄NBr, and Pr₄NBr (where Et = ethyl, Pr = propyl, and Bu =n-butyl) in ethylene carbonate have been measured. Osmotic and activity coefficients were calculated from the results. All of the salts studied are strong electrolytes. The trends in the osmotic coefficients of the alkali metal iodides are NaI>KI>CsI, showing that Na⁺ is more solvated by ethylene carbonate than Cs⁺. For the tetraalkylammonium halides, the order of osmotic coefficients are Et₄NBrPr₄NBrBu₄NCl>Bu₄NBr>Bu₄NI. This is the same order as observed in two other high-dielectric-constant solvents, water andN-methylacetamide. The results indicate that the smaller anions are more solvated than the larger anions in ethylene carbonate in contrast to the usual behavior of dipolar aprotic (basic) solvents, such as dimethyl sulfoxide.     

Location of saddle points and minimum energy paths by a constrained simplex optimization procedure

Two methods are proposed, one for the location of saddle points and one for the calculation of steepest-descent paths on multidimensional surfaces. Both methods are based on a constrained simplex optimization technique that avoids the evaluation of gradients or second derivative matrices. Three chemical reactions of increasing structural complexity are studied within the PRDDO SCF approximation. Predicted properties of reaction hypersurfaces are in good overall agreement with those determined by gradient minimization and gradient following algorithms in connection with various ab initio SCF methods. Computational efforts required by the new procedures are discussed.     

Intrinsic Surface Reaction Constant in 1-pK Model of Mg-Fe Hydrotalcite-like Compounds

The relationship among intrinsic surface reaction constant (K) in 1-pK model, point of zero net charge (PZNC) and structural charge density (σst) for amphoteric solid with structural charges was established in order to investigate the effect of σst on pK. The theoretical analysis based on 1-pK model indicates that the independent PZNC of electrolyte concentration (c) exists for amphoteric solid with structural charges. A common intersection point (CIP) should appear on the acid-base titration curves at different c, and the pH at the CIP is pHPZNC. The pK can be expressed as pK=-pHPZNC log[(1 2αPZNC)/(1-2αPZNC)], where αPZNC≡σst/eNANs, in which e is the elementary charge, NA the Avogadro‘s constant and Ns the total density of surface sites. For solids without structural charges, pK=-pHPZNC. The pK values of hydrotalcite-like compounds (HTlc) with general formula of [Mg1-xFex(OH)2](Cl,OH)x were evaluated. With increasing x, the pK increases, which can be explained based on the affinity of metal cations for H^- or OH^- and the electrostatic interaction between charging surface and H^- or OH^-.     

Two-stage Off-Gel isoelectric focusing: protein followed by peptide fractionation and application to proteome analysis of human plasma

This paper presents the recently introduced Off-Gel electrophoresis (OGE) technology as a versatile tool to reproducibly fractionate intact proteins and peptides into discrete liquid fractions. The coupling of two stages of OGE, i.e., the separation of intact proteins in a first-stage followed by fractionation of peptides derived from each protein fraction after proteolysis in a second stage, results in an array of 15 x 15 fractions that are directly amenable to additional peptide fractionation like reverse-phase liquid chromatography (RPC). The analysis of all second-stage peptide fractions from only the first-stage protein fraction representing pH 5.0 -5.15 by on-line reverse-phase LC-tandem mass spectrometry resulted in the identification of 53 proteins (337 peptides), of which 10 were on different immunoglobulin (Ig) chains, with an input of only 1.5 mg human blood plasma proteins. Increasing the protein load to approximately 12 mg increased the number of identified proteins in the same protein fraction to 73 proteins (449 peptides), of which 15 were Ig-related. Immunodepletion of six of the most abundant proteins (albumin, transferrin, haptoglobin, IgG, IgA, and alpha-1-antitrypsin) prior to first-stage OGE with an input of 1.5 mg of protein (equivalent to approximately 10 mg nondepleted plasma) resulted in the identification of 81 proteins (660 peptides), of which three were still Ig fragments. The pI-based separation of peptides appears to be nonuniform based on the theoretically determined pI values of identified peptides. This observation specifically accounts for the neutral zone (pI 5-8) and can be accounted for by the physicochemical properties of the peptides given by their amino acid composition. The power of OGE separation of proteins and peptides is discussed with a focus on the use of the knowledge about the pI of proteins and peptides that assist the validation of correct identifications together with the retention time of peptides on RPC.     

Mixed strategy solutions forN-person quadratic games

Mixed strategy -equilibrium points are given forN-person games with cost functions consisting of quadratic, bilinear, and linear terms and strategy spaces consisting of closed balls in Hilbert spaces. The results are applied to linear-quadratic differential games with no information and quadratic integral constraints on the control functions.This work was supported by a Commonwealth of Australia, Postgraduate Research Award.     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

Hydrolytically stable, diaminocarboxylic acid-based membranes buffering in the pH range from 6 to 8.5 for isoelectric trapping separations

Diaminocarboxylic acid carrier ampholytes, such as L-histidine, 2,3-diaminopropionic acid, L-ornithine, and L-lysine, were reacted with glycerol-1,3-diglycidyl ether (GDGE) and poly(vinyl alcohol) (PVA) in the presence of sodium hydroxide to produce hydrolytically and mechanically stable hydrogels, supported on a PVA substrate, for use as buffering membranes in isoelectric trapping (IET) separations. The pH values of the DACAPVA membranes were determined with the help of small-molecule pI markers and proteins and were found to be in the 6 < pH < 8.5 range. The membranes were successfully used to isoelectrically trap small ampholytes, desalt ampholyte solutions in IET mode, and effect the binary separation of chicken egg white proteins.