Spaces with Dual Order-Isomorphic to ℓ1

We establish that an ordered Banach space is order-isomorphic to c₀ if and only if it is a -Dedekind complete vector lattice and its norm dual is order-isomorphic to ₁.     

Effects of metal irises on the guided-mode properties in asymmetrical slab waveguides

The diffraction phenomenon caused by metal transverse irises placed into an asymmetrical slab waveguide is examined by using the integral equation method. We concentrate on the possibility of controlling the radiation characteristics of the structure by changing the irises positions and the slab waveguide asymmetry. The aperture electric-field distribution is expressed in terms of a finite series of Chebyshev polynomials. The dominant TE guided-mode reflection and transmission coefficients, the near-field distribution and the far-field radiation pattern are calculated, while numerical results are presented for several cases of asymmetrical slab waveguides and different irises’ positions.     

A Direct and Versatile Synthesis of 5-(2-Di-n-Propylaminoethyl)-7-methoxyindole

The Pummerer intermediate generated from 10 with TFAA was trapped intermolecularly in the presence of Lewis acid by the indoline 2 at position 5. Sequential treatment of the resulted compound 3 with Ra-Ni, LiAlH₄ and active MnO₂ gave compound 6 in high overall yield.     

Novel disposable microfabricated antimony-film electrodes for adsorptive stripping analysis of trace Ni(II)

This work describes a novel type of antimony electrode for adsorptive stripping voltammetry (AdSV). The electrode was microfabricated by coating a silicon chip with a thin antimony-film by means of sputtering and the active area of the electrode was defined by photolithography. The resulting antimony-film electrodes (SbFEs) were characterized by optical and electrochemical techniques. The sensors were tested for the detection of low concentrations of Ni(II) by AdSV in the presence of dimethylglyoxime. Well-formed stripping peaks and a linear dependence of the stripping peak current on the Ni(II) concentration were observed on the microfabricated SbFEs while comparative measurements attempted with electroplated SbFEs were unsuccessful. Utilizing thin-film technology for the formation of the antimony-film extends the scope of these devices as mercury-free sensors in AdSV.     

Towards a world‐sheet description of doubled geometry in string theory

Starting from a sigma‐model for a doubled target‐space geometry, we show that the number of target‐space dimensions can be reduced by half through a gauging procedure. We apply this formalism to a class of backgrounds relevant for double field theory, and illustrate how choosing different gaugings leads to string‐theory configurations T‐dual to each other. We furthermore discuss that given a conformal doubled theory, the reduced theories are conformal as well. As an example we consider the three‐dimensional WZW model and show that the only possible reduced backgrounds are the cigar and trumpet CFTs in two dimensions, which are indeed T‐dual to each other.     

Separation of cis/trans geometrical fatty acid isomers by silver-exchanged zeolite Y

The separation of cis and trans isomers is relevant for biological and nutritional applications, silver-exchanged zeolite Y was prepared and applied for the treatment of mixtures of cis and trans geometrical isomers of mono- and polyunsaturated fatty acid methyl esters (FAMEs). cis FAMEs were adsorbed into zeolite with a high degree of selectivity (cis/trans ratio in the range of 1.9-3.2). The effectiveness was due to the synergism of the π-complexation between the silver ion and the double bonds and the different FAME structures trapped into the zeolite cages. Some indication of the complex stabilities came from theoretical studies using unsaturated lipids. A prototype cartridge was also designed for application in the fractionation of cis/trans FAME mixtures.     

Resolving Lambertian surface orientation from fluctuating radiance

A maximum likelihood method for estimating remote surface orientation from multi-static acoustic, optical, radar, or laser images is presented. It is assumed that the images are corrupted by signal-dependent noise, known as speckle, arising from complex Gaussian field fluctuations, and that the surface properties are effectively Lambertian. Surface orientation estimates for a single sample are shown to have biases and errors that vary dramatically depending on illumination direction. This is due to the signal-dependent nature of speckle noise and the nonlinear relationship between surface orientation, illumination direction, and fluctuating radiance. The minimum number of independent samples necessary for maximum likelihood estimates to become asymptotically unbiased and to attain the lower bound on resolution of classical estimation theory are derived, as are practical design thresholds.     

Composition-dependent photosensitivity in As-S glasses induced by bandgap light: structural origin by Raman scattering

Massive photoinduced short- and medium-range structural changes (photopolymerization) in As-S glasses are induced by near-bandgap light and studied by Raman scattering. Structural changes involve bond restructuring in sulfur-rich nanodomains of these nanoscale-phase-separated glasses. The spectral dependence of the photopolymerization effect demonstrates that various wavelengths can be used to optically change the structure of As-S glasses. The immense structural changes are relevant to recent findings about the role of bandgap light illumination for fabricating channel waveguides in noncrystalline arsenic sulfides.     

Linear orderings and powers of characterizable cardinals

We say that a countable model M completely characterizes an infinite cardinal κ, if the Scott sentence of M has a model in cardinality κ, but no models in cardinality κ⁺. If a structure M completely characterizes κ, κ is called characterizable. In this paper, we concern ourselves with cardinals that are characterizable by linearly ordered structures (cf. Definition 2.1).Under the assumption of GCH, Malitz completely resolved the problem by showing that κ is characterizable if and only if κ=ℵ_α, for some α<ω₁ (cf. Malitz (1968) [7] and Baumgartner (1974) [1]). Our results concern the case where GCH fails.From Hjorth (2002) [3], we can deduce that if κ is characterizable, then κ⁺ is characterizable by a densely ordered structure (see Theorem 2.4 and Corollary 2.5).We show that if κ is homogeneously characterizable (cf. Definition 2.2), then κ is characterizable by a densely ordered structure, while the converse fails (Theorem 2.3).The main theorems are (1) If κ>2^λ is a characterizable cardinal, λ is characterizable by a densely ordered structure and λ is the least cardinal such that κ^λ>κ, then κ^λ is also characterizable (Theorem 5.4) and (2) if ℵ_α and κ^ℵ_α are characterizable cardinals, then the same is true for κ^ℵ_α+β, for all countable β (Theorem 5.5).Combining these two theorems we get that if κ>2^ℵ_α is a characterizable cardinal, ℵ_α is characterizable by a densely ordered structure and ℵ_α is the least cardinal such that κ^ℵ_α>κ, then for all β<α+ω₁, κ^ℵ_β is characterizable (Theorem 5.7). Also if κ is a characterizable cardinal, then κ^ℵ_α is characterizable, for all countable α (Corollary 5.6). This answers a question of the author in Souldatos (submitted for publication) [8].