Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary

We consider a fully discrete qualocation method for Symm’s integral equation. The method is that of Sloan and Burn (1992), for which a complete analysis is available in the case of smooth curves. The convergence for smooth curves can be improved by a subtraction of singularity (Jeon and Kimn, 1996). In this paper we extend these results for smooth boundaries to polygonal boundaries. The analysis uses a mesh grading transformation method for Symm’s integral equation, as in Elschner and Graham (1995) and Elschner and Stephan (1996), to overcome the singular behavior of solutions at corners. This revised version was published online in August 2006 with corrections to the Cover Date.     

All orders transport theory from the multiple scattering expansion of the self-energy: The central cuts

We use the full multiple scattering expansion of the retarded self-energy to obtain the gain and loss rates present in the Kadanoff-Baym relativistic transport equation. The rates we obtain include processes with any number of particles. As a first approximation, we only consider central cuts in the self-energies, but otherwise our results are general. We specialize to the case of scalar field theory to compare with lowest order results. The main application of this work is relativistic transport theory of very dense systems, such as the quark-gluon plasma or the early universe, where multi-particle interactions are important.     

Optical encryption of gray-level image using on-axis and 2-f digital holography with two-step phase-shifting method

In this paper we propose an encryption/decryption technique of gray-level image information using an on-axis 2-f digital holographic optical encrypting system with two-step phase-shifting method. This technique reduces the number of holograms in phase-shifting digital holography and minimizes the setup of the encryption system more than multistep phase-shifting technique. We are able to get the complete decrypted image by controlling the K-ratio which is defined as the reference beam intensity versus the object beam intensity. We remove the DC-term of the phase-shifting digital hologram to reconstruct and decrypt the original image information. Simulation results show that the proposed method can be used for encryption and decryption of a 256 gray-level image. Also, the result shows some errors of the decrypted image according to K-ratio.     

Dental biothermophotonics: How photothermal methods are winning the race with X-rays for dental caries diagnostic needs of clinical dentistry

Recent trends in biothermophotonics of teeth are presented. The presentation is centered on the development of clinical-level frequency-domain photothermal radiometry and modulated luminescence to address issues associated with the early diagnosis of demineralization caries in human teeth. Biothermophotonic principles and applications to the detection of the carious state in human teeth as embodied by laser photothermal radiometry are presented and further supported by modulated luminescence. The emphasis is on recent developments with regard to abilities of these techniques to diagnose interproximal lesions between teeth, etching with phosphoric acid and with an artificial demineralization gel in order to simulate early demineralization, as well as demineralization and remineralization of dental crown enamel and root dentin. These are lesions which normally go undetected by X-ray radiographs. Comparisons with X rays, Micro-Computed Tomography (μ-CT) and Transverse Micro-Radiography (TMR) are discussed. A theoretical model involving coupled diffuse photon density and thermal-wave fields is developed and applied to frequency scans from demineralized artificial lesions to produce quantitative values for optical and thermophysical parameters of teeth as well as the thickness of the induced lesion.     

Electro-Optic Coefficient Measurements for Zn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Cd<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript> Te Single Crystals at 1550 nm Wavelength

Nonlinear optical materials of the type Zn _x Cd_1-x Te single crystals, where x = 0.0, 0.2, 0.4, 0.6, 0.7, 0.8, and 1.0, have been grown by the Bridgman method, using a vertical furnace. We have investigated the electro-optic (E-O) coefficient and refractive index of Zn _x Cd_1-x Te single crystals at optical communication wavelength (1550 nm). In the case of CdTe crystal, the E-O coefficient was 15.5 × 10^-12 m/V, which is the biggest among the E-O coefficients of Zn _x Cd_1-x Te crystals. The E-O modulation signal was very big in low frequency range (DC-100kHz), but the signal amplitude became smaller as we increased frequency above 100 kHz. We also found the acousto-optic modulation at CdTe single crystals.     

Enhancement of red spectral emission intensity of Y3Al5O12:Ce phosphor via Pr co-doping and Tb substitution for the application to white LEDs

We have enhanced color-rendering property of a blue light emitting diode (LED) pumped white LED with yellow emitting Y₃Al₅O₁₂:Ce³⁺ (YAG:Ce) phosphor using addition of Pr and Tb as a co-activator and host lattice element, respectively. Pr³⁺ addition to YAG:Ce phosphor resulted in sharp emission peak at about 610 nm through ¹D₂→³H₄ transition. And when Tb³⁺ substituted Y³⁺ sites, Ce³⁺ emission band shifted to a longer wavelength due to larger crystal field splitting. Y₃Al₅O₁₂:Ce³⁺, Pr³⁺ and (Y_1−xTb_x)₃Al₅O₁₂:Ce³⁺ phosphors were coated on blue LEDs to fabricate white LEDs, respectively, and their color-rendering indices (CRIs, R_a) were measured. As a consequence of the addition of Pr³⁺ or Tb³⁺, CRI of the white LEDs improved to be R_a=83 and 80, respectively. Especially, blue LED pumped (Y_0.2Tb_0.8)₃Al₅O₁₂:Ce³⁺ white LED showed both strong luminescence and high color-rendering property.     

New locally conservative finite element methods on a rectangular mesh

A new family of locally conservative, finite element methods for a rectangular mesh is introduced to solve second-order elliptic equations. Our approach is composed of generating PDE-adapted local basis and solving a global matrix system arising from a flux continuity equation. Quadratic and cubic elements are analyzed and optimal order error estimates measured in the energy norm are provided for elliptic equations. Next, this approach is exploited to approximate Stokes equations. Numerical results are presented for various examples including the lid driven-cavity problem.     

The McCoy Condition on Noncommutative Rings

We introduce the multiplication algebra of a Bernstein algebra, establish its Peirce decomposition relative to an idempotent of A and state some basic properties of this algebra of endomorphtsms     

Enantiomerically pure synthesis of beta-substituted gamma-butyrolactones: a key intermediate to concise synthesis of pregabalin

Chiral beta-substituted gamma-butyrolactones are known to be important intermediates for many biologically active compounds such as gamma-aminobutyric acid (GABA) derivatives and lignans. We have developed a general, convenient, and scalable synthetic method for enantiomerically pure beta-substituted gamma-butyrolactones, with either configuration, via nucleophilic cyclopropane ring opening of (1S,5R)- or (1R,5S)-bicyclic lactone followed by decarbethoxylation. The utility of our method was demonstrated by streamlined synthesis of pregabalin ((S)-3-isobutyl-gamma-aminobutyric acid), an anticonvulsant drug for the treatment of peripheral neuropathic pain.     

Synthesis of tri-, hexa-, and nonasaccharide subunits of the atypical O-antigen polysaccharide of the lipopolysaccharide from Danish Helicobacter pylori strains

Synthesis of trisaccharide repeating unit, -->3)-alpha-D-Rhap-(1-->2)-alpha-D-Manp3CMe-(1-->3)-alpha-L-Rha p-(1-->, and its dimeric hexa- and trimeric nonasaccharide subunits of the atypical O-antigen polysaccharide of the lipopolysaccharide from Danish H. pylori strains D1, D3, and D6 has been accomplished. Successful synthesis of the hexasaccharide and the nonasaccharide was possible by dimerization and trimerization of the suitably protected trisaccharide repeating unit, in which three monosaccharide moieties were arranged in a proper order by placing the sterically demanding 3-C-methyl-D-mannose moiety in between D- and L-rhamnoses. Key steps include the coupling of three monosaccharide moieties and dimerization and trimerization of the trisaccharide unit by glycosylations employing the 2'-carboxybenzyl glycoside method. Also presented is a method for the synthesis of the novel branched sugar, 3-C-methyl-D-mannose moiety by elaboration of its equatorial hydroxyl and axial methyl groups at C-3' in the disaccharide stage.