Pointwise convergence of the iterates of a harris-recurrent Markov operator

LetP be a Markov operator recurrent in the sense of Harris, withσ-finite invariant measureμ. (1) Ifμ is finite andP aperiodic, then forf ∈L ₁(μ),P ⁿf →f fdμ a.e. (2) Ifμ is infinite,P ⁿf → 0 a.e. for everyf ∈L _p (μ), 1≦p <∞.     

The change of the vibrational frequencies of a chemisorbed diatomic caused by the electrostatic interactions with the metal surface

Results of density functional calculations are used to discuss the change of the vibrational frequency of an adsorbed molecule caused by the electrostatic interaction between a chemisorbed molecule — simulated by two effective charges — and a metallic surface.     

A one-dimensional microscopic model for the rate of thermal desorption of an atom. The role of multiphonon processes

A one-dimensional microscopic model is used to calculate the desorption rate and to investigate the role of multiphonon processes in desorption. If the vibrational frequency of the chemisorptive bond is larger than the Debye frequency, multiphonon processes of all orders must be included as in our one-dimensional microscopic multiphonon model.     

Characterization and chemistry of polyaldehyde microspheres

The chemical composition of polyacrolein (PA) microspheres of various types as well as polyglutaraldehyde (PGL) microspheres was elucidated. Nephelometric measurements were used for studying the stability properties of the polyaldehyde microspheres in different pH and salt concentrations. The stability of the aldehyde groups themselves at various pH and temperature was also determined. The polyaldehyde microspheres covalently bind amino ligands, e.g., proteins, antibodies, enzymes, and drugs in a single step. The effect of temperature and the influence of thiol compounds on the reaction between the polyaldehyde microspheres and amino ligands was examined. The reaction of the polyaldehyde microspheres with sodium hydrogen sulfite is also described.     

From azides to nitriles. A novel fast transformation made possible by BrF3

[reaction: see text]. Various alkyl and aryl azides, readily obtained from halides or alcohols, were transformed into the corresponding nitriles using bromine trifluoride in moderate to good yields. The reaction is general and gives positive results with aliphatic, aromatic, cyclic, and functionalized azides. It can also be applied to the synthesis of optically active nitriles.     

Synthesis and characterization of micrometer‐sized particles of narrow size distribution with chloromethyl functionality on the basis of single‐step swelling of uniform polystyrene template microspheres

Polystyrene template microspheres of 1.4 ± 0.1 μm were prepared by dispersion polymerization of styrene in a mixture of ethanol and 2‐methoxy ethanol. These template particles were then swelled at room temperature in a single step with emulsion that was prepared in sodium dodecyl sulfate aqueous solution from a swelling solvent (dibutyl phthalate) containing the initiator (benzoyl peroxide) and monomer(s) (chlormethylstyrene, divinylbenzene, or ethylene dimethacrylate). Composite uniform particles composed of the template polystyrene and noncrosslinked or crosslinked polychloromethylstyrene were prepared by polymerizing the monomer(s) within the swelled particles at 73 °C. Crosslinked uniform polychloromethylstyrene particles of higher surface area were formed by dissolving the template polystyrene polymer of the composite particles. The influence of various reaction parameters, such as dibuthyl phthalate concentration, chloromethylstyrene concentration, crosslinker type and concentration, and so forth on the molecular weight, size, size distribution, shape, morphology, surface area, and decomposition temperature of the particles was investigated. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1342–1352, 2002     

Some properties of a fractal-time continuous-time random walk in the presence of traps

The CTRW has often been applied to problems related to transport in a statistically homogeneous disordered medium, which means that there are no traps or reflecting boundaries to be found in the medium. Two physical applications, one to the migration of photons in a turbid medium and the second to the theory of diffusion-controlled reactions in a random medium, suggest that it might be useful to study properties of the CTRW, particularly as they refer to survival probability in the presence of a trap or a trapping surface. We calculate a number of these properties when the pausing-time density is asymptotically proportional to a stable law, i.e.,(t)T ⁺¹ as (t/T), where 0<<1. A forthcoming paper will establish the correspondence between properties of the CTRW and proprties of random walkers on a fractal with trapping boundaries.This paper is dedicated to Jerry Percus on the occasion of his 65th birthday. May he enjoy many more happy and productive years.     

Surface modification. II. Functionalization of solid surfaces with vinylic monomers

A new method to functionalize surfaces of solid substrates such as glass, silicon crystals, and silica microspheres with appropriate vinylic monomers, i.e., methyl vinyl ketone, methyl acrylate, methacrolein, and acrolein, is described. The surface modification process was performed through the following sequence of reactions: (a) derivatization of the surfaces with to-nitrile groups by interacting the substrates with SiCl₃(CH₂)₃CN; (b) subsequent reduction of the a)-nitrile groups with diborane to w-amine groups; (c) binding of the vinylic monomers to the surfaces via the to-amine groups. pK_1/2 of the surface primary amine groups, as determined by contact angle titration, was found to be 2–4 units lower than the pK_1/2 values of primary amine analogous in solution. Methyl vinyl ketone and methyl acrylate were covalently bound to the amine surfaces only under basic conditions via the Michael addition reaction. Methacrolein and acrolein were covalently bound to the amine surfaces under both acidic and basic conditions via two major reactions: the Michael addition reaction and Schiff base bond formation. The concentration of the aldehyde groups of the surfaces obtained by the reaction with methacrolein and acrolein was significantly higher than that obtained using the common, published method in which glutaraldehyde interacts with the amine surfaces.     

Autodetection of a Target by Eye Movement

Locating an unknown object position in a map by information stored in the unconscious mind is important from practical point of view. Locating captives, bomb, or terrorist secret bases by interrogation is problem that the intelligent agencies face daily. The person interrogated may have the desired information stored in unconscious or may not know it at all. In this article, we will present a novel way of retrieving the object location based on eye movement. The technique is based on a Bayesian mathematical approach to localization, in which measured count rates of eye fixation and duration, the probability of the location of the target is correlated with the count rate and drops as the distance increases from the fixation location. We focused on the discrete model and then generalized it to continuous model. © 2015 Wiley Periodicals, Inc. Complexity 21: 452–459, 2016     

Silicon/molecule interfacial electronic modifications

Electronic structures at the silicon/molecule interface were studied by X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy, inverse photoemission spectroscopy, and Kelvin probe techniques. The heterojunctions were fabricated by direct covalent grafting of a series of molecules (-C6H4-X, with X = NMe2, NH2, NO2, and Mo6 oxide cluster) onto the surface of four types of silicon substrates (both n- and p-type with different dopant densities). The electronic structures at the interfaces were thus systematically tuned in accordance with the electron-donating ability, redox capability, and/or dipole moment of the grafted molecules. The work function of each grafted surface is determined by a combination of the surface band bending and electron affinity. The surface band bending is dependent on the charge transfer between the silicon substrate and the grafted molecules, whereas electron affinity is dependent on the dipole moment of the grafted molecules. The contribution of each to the work function can be separated by a combination of the aforementioned analytical techniques. In addition, because of the relatively low molecular coverage on the surface, the contribution from the unreacted H-terminated surface to the work function was considered. The charge-transfer barrier of silicon substrates attached to different molecules exhibits a trend analogous to surface band bending effects, whereas the surface potential step exhibits properties analogous to electron affinity effects. These results provide a foundation for the utilization of organic molecule surface grafting as a means to tune the electronic properties of semiconductors and, consequently, to achieve controllable modulation of electronic characteristics in small semiconductor devices at future technology nodes.