Abstract functions with continuous differences and Namioka spaces

Let be a semigroup and a topological space. Let be an Abelian topological group. The right differences of a function are defined by for . Let be continuous at the identity of for all in a neighbourhood of . We give conditions on or range under which is continuous for any topological space . We also seek conditions on under which we conclude that is continuous at for arbitrary . This led us to introduce new classes of semigroups containing all complete metric and locally countably compact quasitopological groups. In this paper we study these classes and explore their relation with Namioka spaces.

     

Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP _c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP _c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.     

Conformational dependence of the intrinsic acidity of the aspartic acid residue sidechain in N-acetyl- -aspartic acid-N′-methylamide

The sidechain conformational potential energy hypersurfaces (PEHS) for the γ_L, β_L, α_L, and α_D backbone conformations of N-acetyl- -aspartate-N′-methylamide were generated. Of the 81 possible conformers initially expected for the aspartate residue, only seven were found after geometric optimizations at the B3LYP/6-31G(d) level of theory. No stable conformers could be located in the δ_L, _L, γ_D, δ_D, and _D backbone conformations. The ‘adiabatic’ deprotonation energies for the endo and exo forms of N-acetyl- -aspartic acid-N′-methylamide were calculated by comparing their optimized relative energies against those found for the seven stable conformers of N-acetyl- -aspartate-N′-methylamide. Sidechain conformational PEHSs were also generated for the estimation of ‘vertical’ deprotonation energies for both endo and exo forms of N-acetyl- -aspartic acid-N′-methylamide. All backbone–sidechain (N–H⁻O–C) and backbone–backbone (N–HO=C) hydrogen bond interactions were analyzed. A total of two backbone–backbone and four backbone–sidechain interactions were found for N-acetyl- -aspartate-N′-methylamide. The deprotonated sidechain of N-acetyl- -aspartate-N′-methylamide may allow the aspartyl residue to form strong hydrogen bond interactions (since it is negatively charged) which may be significant in such processes as protein–ligand recognition and ligand binding. As a primary example, the molecular geometry of the aspartyl residue may be important in peptide folding, such as that in the RGD tripeptide.     

N,N'-ethylenebis(pyridoxylideneiminato) and N,N'-ethylenebis(pyridoxylaminato): synthesis, characterization, potentiometric, spectroscopic, and DFT studies of their vanadium(IV) and vanadium(V) complexes

The Schiff base N,N'-ethylenebis(pyridoxylideneiminato) (H(2)pyr(2)en, 1) was synthesized by reaction of pyridoxal with ethylenediamine; reduction of H(2)pyr(2)en with NaBH(4) yielded the reduced Schiff base N,N'-ethylenebis(pyridoxylaminato) (H(2)Rpyr(2)en, 2); their crystal structures were determined by X-ray diffraction. The totally protonated forms of 1 and 2 correspond to H(6)L(4+), and all protonation constants were determined by pH-potentiometric and (1)H NMR titrations. Several vanadium(IV) and vanadium(V) complexes of these and other related ligands were prepared and characterized in solution and in the solid state. The X-ray crystal structure of [V(V)O(2)(HRpyr(2)en)] shows the metal in a distorted octahedral geometry, with the ligand coordinated through the N-amine and O-phenolato moieties, with one of the pyridine-N atoms protonated. Crystals of [(V(V)O(2))(2)(pyren)(2)].2 H(2)O were obtained from solutions containing H(2)pyr(2)en and oxovanadium(IV), where Hpyren is the "half" Schiff base of pyridoxal and ethylenediamine. The complexation of V(IV)O(2+) and V(V)O(2) (+) with H(2)pyr(2)en, H(2)Rpyr(2)en and pyridoxamine in aqueous solution were studied by pH-potentiometry, UV/Vis absorption spectrophotometry, as well as by EPR spectroscopy for the V(IV)O systems and (1)H and (51)V NMR spectroscopy for the V(V)O(2) systems. Very significant differences in the metal-binding abilities of the ligands were found. Both 1 and 2 act as tetradentate ligands. H(2)Rpyr(2)en is stable to hydrolysis and several isomers form in solution, namely cis-trans type complexes with V(IV)O, and alpha-cis- and beta-cis-type complexes with V(V)O(2). The pyridinium-N atoms of the pyridoxal rings do not take part in the coordination but are involved in acid-base reactions that affect the number, type, and relative amount of the isomers of the V(IV)O-H(2)Rpyr(2)en and V(V)O(2)-H(2)Rpyr(2)en complexes present in solution. DFT calculations were carried out and support the formation and identification of the isomers detected by EPR or NMR spectroscopy, and the strong equatorial and axial binding of the O-phenolato in V(IV)O and V(V)O(2) complexes. Moreover, the DFT calculations done for the [V(IV)O(H(2)Rpyr(2)en)] system indicate that for almost all complexes the presence of a sixth equatorial or axial H(2)O ligand leads to much more stable compounds.     

The existence of sensitive optimal policies in two multi-dimensional queueing models

Recently Dekker and Hordijk [3,4] introduced conditions for the existence of deterministic Blackwell optimal policies in denumerable Markov decision chains with unbounded rewards. These conditions include- uniform geometric recurrence.The-uniform geometric recurrence property also implies the existence of average optimal policies, a solution to the average optimality equation with explicit formula's and convergence of the value iteration algorithm for average rewards. For this reason, the verification of-uniform geometric convergence is also useful in cases where average and-discounted rewards are considered.On the other hand,-uniform geometric recurrence is a heavy condition on the Markov decision chain structure for negative dynamic programming problems. The verification of-uniform geometric recurrence for the Markov chain induced by some deterministic policy together with results by Sennott [14] yields the existence of a deterministic policy that minimizes the expected average cost for non-negative immediate cost functions.In this paper-uniform geometric recurrence will be proved for two queueing models: theK competing queues and the two centre open Jackson network with control of the service rates.The research of the author is supported by the Netherlands Organization for Scientific Research N.W.O.     

Stability theorems for infinitely constrained mathematical programs

The primary concern of this paper is to investigate stability conditions for the mathematical program: findx E ⁿ that maximizesf(x):g ^j(x)0 for somej J, wheref is a real scalarvalued function and eachg is a real vector-valued function of possibly infinite dimension. It should be noted that we allow, possibly infinitely many, disjunctive forms. In an earlier work, Evans and Gould established stability theorems wheng is a continuous finite-dimensional real-vector function andJ=1. It is pointed out that the results of this paper reduce to the Evans-Gould results under their assumptions. Furthermore, since we use a slightly more general definition of lower and upper semicontinuous point-to-set mappings, we can dispense with the continuity ofg (except in a few instances where it is implied by convexity assumptions).     

Necessary and sufficient conditions for Hölder continuity of Gaussian processes

The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition.     

Heinz‐type inequality and bi‐Lipschitz continuity for quasiconformal mappings satisfying inhomogeneous biharmonic equations

Let be the class of all sense‐preserving homeomorphic self‐mappings of . The aim of this paper is twofold. First, we obtain Heinz‐type inequality for (K,K′)‐quasiconformal mappings satisfying inhomogeneous biharmonic equation Δ(Δω) = g in unit disk with associated boundary value conditions and . Second, we establish biLipschitz continuity for (K,K′)‐quasiconformal mappings satisfying aforementioned inhomogeneous biharmonic equation when and are small enough.