Embeddings and hyperplanes of the Lie incidence geometry of type E7,1

This paper continues a program to show that for most of the standard Lie incidence geometries, all geometric hyperplanes arise from a necessarily absolutely universal embedding, by addingE _7,1 to the list. It follows from [5, 12] that any projective embedding of this point line geometry is a homomorphic image of the one afforded by the 56-dimensional module for the groupE ₇(K).This work was supported by a grant from the National Science Foundation.     

Continuous modified Newton’s-type method for nonlinear operator equations

A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point x ₀ and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated. Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003 This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks DAAD for support     

III-Nitride Quantum Devices—Microphotonics

Photonic devices based on III-nitrides offer benefits such as UV/blue emission, large band offsets of InN/GaN/AlN heterostructures allowing novel quantum well (QW) device design, and inherently high-emission efficiencies. Furthermore, due to their mechanical hardness and larger band gaps (when compared with conventional semiconductor devices), III-nitride-based devices may operate at much higher temperatures and voltages/power levels for any dimensional configuration and in harsher environments than other semiconductor devices and are expected to provide much lower temperature sensitivities. These are crucial advantages for many applications. Over the last decade, the physics of microsize photonic devices has been investigated. New physical phenomena and properties are expected to dominate as the device size scales down. The microsize light emitters offer benefits over edge emitters such as the ability to create arrays of individually controllable pixels on a single chip, enhanced quantum efficiency, and greatly reduced lasing threshold. Rapid progress in the area of III-nitride microphotonics has been made. The growth and fabrication of micron and submicron size photonic structures based on III-nitride wide bandgap semiconductors has been achieved, and the technology has made it possible to integrate arrays of optical elements to form active photonic-integrated devices. One example is an interconnected µ-LED with enhanced emission efficiency over the conventional LEDs for the same device area. Another example is a µ-LED array with independently addressed pixels or III-nitride microdisplay. III-nitride microdisplay may offer performance that is superior to microdisplays fabricated from liquid crystals and organic LEDs. The third example presented is III-nitride UV Focal Plane Arrays (UV-FPA) of detectors. So far, the operation of AlGaN UV-FPA with size up to 256×256 pixels with 30×30?μm² unit cells has been demonstrated. Together with the nature of their two-dimensional array, these active micro-photonic devices show promise in many important applications, such as optical communications, signal and image processing, optical interconnects, computing, enhanced energy conversion and storage, chemical, biohazard substances, and disease detection, missile and shellfire, atmospheric ozone-level, and flame sensing. III-nitride microlens arrays have been fabricated successfully for blue and UV wavelength applications on GaN and AlN. The successful fabrication of microlens arrays based on III-nitride materials opens the possibility for monolithically integrating nitride-based micro-size photonic devices, as well as coupling light into, out of, and between arrays of III-nitride emitters and detectors, especially for short wavelengths covering the green-blue to deep UV (200?nm) region. Nanofabrication and characterization of photonic crystals with diameter/periodicity as small as 100/180?nm on InGaN/GaN MQW has been achieved. An unprecedented maximum enhancement factor of 20 was obtained under optical pumping. Single-mode ridged optical waveguide devices using GaN/AlGaN heterostructures have been designed, fabricated, and characterized for operation in 1550?nm wavelength window. The feasibility of developing novel photonic integrated circuits based on III-nitride wide bandgap semiconductors for fiber-optical communications has been investigated.     

Analytical utility of valence band X-ray photoelectron spectroscopy of iron and its oxides,with spectral interpretation by cluster and band structure calculations

The valence band and core-level X-ray photoelectron spectroscopy (XPS) of iron and its oxides are reported, and the valence band spectra interpreted by various calculation models. The paper focuses upon the valence band region, which shows significant differences between the metal and the following oxidized iron species: FeO, Fe(3)O(4), alpha-Fe(2)O(3), gamma-Fe(2)O(3), alpha-FeOOH and gamma-FeOOH. The core region is of little analytical value as a means of distinguishing between these species, but the valence band region shows significant differences. These differences are consistent with spectra predicted by cluster and band structure calculations. Cluster calculations are valuable as a means for interpreting the spectra of iron oxides with multiple iron sites and defect characteristics.     

Commutator-finite orthomodular lattices

The class of orthomodular lattices which have only finitely many commutators is investigated. The following theorems are proved: contains the block-finite orthomodular lattices. Every irreducible element of is simple. Every element of is a direct product of a Boolean algebra and finitely many simple orthomodular lattices. The irreducible elements of which are modular, or are M-symmetric with at least one atom, have height two or less.     

Aggregation-fragmentation in a model of DNA-mediated colloidal assembly

We present results from an off-lattice Monte Carlo simulation of DNA-mediated colloidal assembly. In this simulation, the aggregation-fragmentation of a binary mixture of DNA-coated colloidal particles is studied through a simplified model of base-pair hybridization. Bonding between monomers is modeled as a simple temperature-sensitive A/B-type interaction, where type A and B monomers can bond to only the opposite type (no A/A or B/B attachments are allowed). The actual chemistry of base-pair hybridization is not included in the model. The morphological structures of the clusters formed as well as the kinetics of growth are analyzed in our 2D simulations. The fractal dimension and kinetic growth exponents for clusters formed near the DNA "melting" temperature agree with those seen previously for 2D diffusion-limited cluster aggregation (DLCA) models. The clusters appear more compact, exhibiting signs of local order at intermediate temperature values. At higher temperatures, the formation of large clusters is not favorable under the action of temperature-dependent fragmentation, and the system eventually reaches a steady state as a collection of small aggregates. The temperature profile for this dissolution of the colloidal assembly is sharp, indicating that the selective hybridization process provides a highly sensitive measurement tool. At high temperatures, we analyze the steady-state behavior of the average cluster size in terms of an aggregation-fragmentation model.     

Consistency of a rank test against general alternatives of change points (surfaces) and continuous trend

Considered are modifications of a rank test of randomness for the one- and multi-dimensional regular design cases as well as for the one- and multi-dimensional random design cases. The null hypothesis is that all observations are independent and identically distributed. The main result is the proof of consistency of the test in each of the above cases against two general alternatives.Alternative 1: there exists a pairwise disjoint partion U _i =1 ^m D _i =D, where D d1, is a bounded domain inside which one makes observations, such that (1) if an observation point falls insideD _i , then the corresponding observed value is the realization of a random variable _i i = l,...,m; (2) there exists an ordering % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbaiab-Tha7jabe67a4Hqbdiab% +LgaPnaaBaaaleaacaWGRbaabeaakiab-1ha9naaDaaaleaacaWGRb% Gaeyypa0JaaGymaaqaaiaad2gaaaaaaa!4C2D!\[\{ \xi i_k \} _{k = 1}^m \], where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabe67a4nXvP5wqonvsaeHbfv3ySLgzaGqbdiab-LgaPnaaBaaa% leaacaWGRbaabeaaaaa!454D!\[\xi i_k \] is stochastically smaller than % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabe67a4nXvP5wqonvsaeHbfv3ySLgzaGqbdiab-LgaPnaaBaaa% leaacaWGRbaabeaakmaaBaaaleaacqGHRaWkcaaIXaaabeaakiaacY% cacaWGRbGaeyypa0JaaGymaiaacYcacaGGUaGaaiOlaiaac6cacaGG% SaGaamyBaiabgkHiTiaaigdaaaa!509B!\[\xi i_k _{ + 1} ,k = 1,...,m - 1\], (3) the partition is independent of the number of observation points. Note thatm, this ordering, and the sets D _i are not known a priori: one tests only for the existence of such a partition. Note also that in the one-dimensional case the initial sequence need not be stochastically monotone under the alternative.Alternative 2: there exists an arbitrary asymptotically continuous trend in location. Asymptotically continuous means that the trend converges to some continuous, not identically constant function as the number of data points goes to infinity. This function need not be monotone.A numerical example illustrating the use of the obtained results for image analysis (edge detection) is presented.     

Computing the Fukui function from ab initio quantum chemistry: approaches based on the extended Koopmans’ theorem

The extended Koopmans’ theorem is related to Fukui function, which measures the change in electron density that accompanies electron attachment and removal. Two approaches are used, one based on the extended Koopmans’ theorem differential equation and the other based directly on the expression of the ionized wave function from the extended Koopmans’ theorem. It is observed that the Fukui function for electron removal can be modeled as the square of the first Dyson orbital, plus corrections. The possibility of useful generalizations to the extended Koopmans’ theorem is considered; some of these extensions give approximations, or even exact expressions, for the Fukui function for electron attachment.     

Controlling diffusion in sol-gel derived monoliths

Redox probes were trapped within a silica monolith prepared in part with organoalkoxysilanes containing a quaternary ammonium functional group. The diffusion coefficients of the entrapped molecules were measured as the gels were slowly dried using chronoamperometry and cyclic voltammetry with ultramicroelectrodes. Gel-entrapped cobalt(II) tris(bipyridine) (Co(bpy)(3)(2+)) diffuses at rates similar to that measured in the sols by incorporating a small amount of the positively charged functional group in the matrix. In comparison, the diffusion coefficient of gel-entrapped ferricyanide (Fe(CN)(6)(3-)) drops an order of magnitude relative to its value in the sol soon after gelation. These results demonstrate the ease at which diffusion in hydrated gels can be easily controlled by simply changing the charge on the walls of the silica host.     

Synthesis of spherical silver nanoparticles by digestive ripening, stabilization with various agents, and their 3-D and 2-D superlattice formation

Capped nanoparticles of silver were synthesized via the solvated metal atom dispersion (SMAD) technique followed by a digestive ripening procedure producing gram quantities of monodisperse spherical nanoparticles. This shows for the first time that a digestive ripening protocol is possible for an element other than gold. The particle size and optical spectra were found to be dependent on the capping agent used. Particles capped with dodecane thiol had a mean diameter of 6.6+/-1 nm, while trioctyl phosphine capped particles were 6.0+/-2 nm determined via TEM microscopy. These particles were found to organize into two- and three-dimensional superlattices with a well defined geometry through self-assembly in a liquid solution, that was dictated by the ligand used resulting in a triangular or circular lattice.