Simultaneous approximation and interpolation of increasing functions by increasing entire functions

We prove that, under suitable assumptions, an isomorphism g of dense subsets A,B of the real line can be taken to approximate a given increasing Cⁿ surjection f with the derivatives of g agreeing with those of f on a closed discrete set. For example, we have the following theorem. Let be a nondecreasing Cⁿ surjection. Let be a positive continuous function. Let be a closed discrete set on which f is strictly increasing. Let each of {A_i}, {B_i} be a sequence of pairwise disjoint countable dense subsets of such that for each and xE we have xA_i if and only if f(x)B_i. Then there is an entire function such that and the following properties hold.

(a) For all , Dg(x)>0.

(b) For k=0,…,n and all , |D^kf(x)−D^kg(x)|<ε(x).

(c) For k=0,…,n and all xE, D^kf(x)=D^kg(x).

(d) For each , g[A_i]=B_i.

This provides a version for increasing functions of a theorem of Hoischen. In earlier work, we proved that it is consistent that a similar theorem, omitting clause (c), holds when the sets A_i,B_i are of cardinality ₁ and have second category intersection with every interval. (See the introduction for the exact statement.) In this paper, we show how to incorporate clause (c) into the statement of the earlier theorem.

Multilayered polymer microspheres by thermal imprinting during microsphere growth

Modulation of the polymerization temperature in precipitation polymerizations was used to form onion-type polymer microspheres consisting of multiple nested layers. Specifically, the copolymerization of chloromethylstyrene and divinylbenzene-55 in acetonitrile, at temperatures ramping between 65 and 75 degrees C, led to monodisperse, cross-linked microspheres of about 10 mum diameter that have radial density profiles closely reflecting the thermal profiles used. This thermal imprinting is attributed to the copolymer formed being close to its theta point during the polymerization. As the microspheres grow by continuously capturing oligomers from solution, the resulting transient surface gel layer expands and contracts with temperature, and thus records the reaction temperature profile in the form of a corresponding density profile, even as it cross-links.     

Theoretical studies of borazynes and azaborines

Four isomers of didehydroborazine, B3N3H4, borazyne, and three isomers of azaborine, C4H4BN, are studied by DFT, CCSD, and CCSD(T) computational methods. The singlets of 1,2-borazyne (I) and 1,4-borazyne (IV) have angles about the boron of ca. 150 degrees . In 1,2-azaborine (V), the angles are ca. 140 degrees , while the N angles are ca. 112 degrees except in IV (127 degrees ) and 1,4- azaborine (VII, 120 degrees ). These geometries are almost reversed in the triplets. The 1,3-borazyne (III) shows more bicyclic character than the corresponding m-benzyne, with an N-N distance of 1.7 A. In all cases I was found to be lower in energy than the 2,4-borazyne (II), III, and IV. The order of stability of the azaborines is V > VII > 1,3- azaborine (VI). The nucleus-independent chemical shift (NICS) indicates that all isomers of borazyne are less aromatic than benzene and all isomers of azaborine are about as aromatic as benzene. Time-dependent DFT (TD-DFT) is used to study the excited states of the singlets. The significant structural differences between the singlet and triplet states suggest long phosphoresence lifetimes.     

Counter-ion perturbation of the fragmentation pathways of multiply charged anions: evidence for exit channel complexes on the fragmentation potential energy surfaces

We report the first low-energy collisional excitation measurements and density functional theory calculations to characterize the ground state potential energy surfaces of contact ion-pair complexes that contain multiply charged anions (MCAs). Excitation of K+.Pt(CN)(4) (2-) and K+.Pt(CN)(6) (2-) result in fragmentation products associated with decay of the isolated constituent dianions, revealing that the ground state ion-pair surfaces are dominated by the intrinsic characteristics of the MCA. This observation is important since it indicates that counter-ion complexation only weakly perturbs the electronic structure of an MCA. For K+.Pt(CN)(4) (2-), where the Pt(CN)(4) (2-) dianion decays with production of two ionic fragments, we observe evidence for the existence of a novel exit-channel complex corresponding to a polar KCN salt unit bound to the Pt(CN)(3) (-) anion. The results described provide a basis for understanding the potential energy surfaces and fragmentation characteristics of other ion-pair complexes that involve MCAs.     

Hydrazone- and hydrazide-containing N-substituted glycines as peptoid surrogates for expedited library synthesis: application to the preparation of Tsg101-directed HIV-1 budding antagonists

Replacing the Pro6 in the p6(Gag)-derived 9-mer "P-E-P-T-A-P-P-E-E" with N-substituted glycine (NSG) residues is problematic. However, incorporation of hydrazone amides ("peptoid hydrazones") can be readily achieved in library fashion. Furthermore, reduction of these hydrazones to N-substituted "peptoid hydrazides" affords a facile route to library diversification. This approach is demonstrated by application to Tsg101-binding compounds designed as potential HIV budding antagonists. [reaction: see text]     

Design of near-field irregular diffractive optical elements by use of a multiresolution direct binary search method

A multiresolution direct binary search iterative procedure is used to design small dielectric irregular diffractive optical elements that have subwavelength features and achieve near-field focusing below the diffraction limit. Designs with a single focus or with two foci, depending on wavelength or polarization, illustrate the possible functionalities available from the large number of degrees of freedom. These examples suggest that the concept of such elements may find applications in near-field lithography, wavelength-division multiplexing, spectral analysis, and polarization beam splitters.     

Measurements of branching fractions, polarizations, and direct CP-violation asymmetries in B-->rhoK* and B-->f0(980)K* decays

We report searches for B-meson decays to the charmless final states rhoK* and f0(980)K* with a sample of 232x10(6) BB pairs collected with the BABAR detector at the PEP-II e+e- collider. We measure in units of 10(-6) the following branching fractions, where the first error quoted is statistical and the second systematic, or upper limits are given at the 90% confidence level: B(B+-->rho0K*+)<6.1, B(B+-->rho+K*0)=9.6+/-1.7+/-1.5, B(B0-->rho-K*+)<12.0, B(B0-->rho0K*0)=5.6+/-0.9+/-1.3, B(B+-->f0(980)K*+)=5.2+/-1.2+/-0.5, and B(B0-->f0(980)K*0)<4.3. For the significant modes, we also measure the fraction of longitudinal polarization and the charge asymmetry: fL(B+-->rho+K*0)=0.52+/-0.10+/-0.04, fL(B0-->rho0K*0)=0.57+/-0.09+/-0.08, ACP(B+-->rho+K*0)=-0.01+/-0.16+/-0.02, ACP(B0-->rho0K*0)=0.09+/-0.19+/-0.02, and ACP(B+-->f0(980)K*+)=-0.34+/-0.21+/-0.03.     

Hybrid variable neighbourhood approaches to university exam timetabling

In this paper, we investigate variable neighbourhood search (VNS) approaches for the university examination timetabling problem. In addition to a basic VNS method, we introduce variants of the technique with different initialisation methods including a biased VNS and its hybridisation with a Genetic Algorithm. A number of different neighbourhood structures are analysed. It is demonstrated that the proposed technique is able to produce high quality solutions across a wide range of benchmark problem instances. In particular, we demonstrate that the Genetic Algorithm, which intelligently selects appropriate neighbourhoods to use within the biased VNS, produces the best known results in the literature, in terms of solution quality, on some of the benchmark instances. However, it requires relatively large amount of computational time. Possible extensions to this overall approach are also discussed.     

Observation of Upsilon(4S) decays to pi(+)pi(-)Upsilon(1S) and pi(+)pi(-)Upsilon(2S)

Observation of Upsilon(4S) decays to pi(+)pi(-)C and pi(+)pi(-)Upsilon(2S)We present the first measurement of Upsilon(4S) decays to pi(+)pi(-)Upsilon(1S) based on a sample of 230 x 106(4S) mesons collected with the BABAR detector. We measure the product branching fractions Beta(Upsilon(4S) --> pi(+)pi(-)Upsilon(1S)) x BetaUpsilon(1S) --> mu(+)mu(-) = (2.23 +/- 0.25(stat) +/- 0.27(syst))x 10(-6) and Beta(Upsilon(4S) --> pi(+)pi(-)Upsilon(2S) x Beta(Upsilon(2S) --> mu(+)mu(-))=(1.69 +/-0.26(stat) +/- 0.20(syst)) x 10(-)6, from which we derive the partial widths Gamma(Upsilon(4S) --> pi(+)pi(-)Upsilon(1S))=(1.8 +/-0.4) keV and Gamma(Upsilon(4S) --> pi(+)pi(-)Upsilon(2S))=(2.7 +/- 0.8) keV.     

Descent methods for composite nondifferentiable optimization problems

We present a framework for the development of globally defined descent algorithms for the minimization of non-differentiable objective functionsF := h º f withh convex. Within our structure the global convergence properties of the Cauchy, Modified Newton, Gauss—Newton, and Variable-Metric methods are easily established along with that of several new approaches. Examples illustrating the calculational techniques are provided.