Spectral Analogue Research Articles

The spectral order of accuracy: A new unified tool in the design methodology of excitation-adaptive wave equation FDTD schemes

We define a new concept, termed the spectral order of accuracy (SOoA), which is the spectral domain analogue of the familiar order of accuracy (OoA). The SOoA is pivotal in a refined version of a recently-introduced methodology for formulating excitation-adaptive wave equation FDTD (WE-FDTD) schemes, described below. This concept is the basis for a unified classification for both existing and new schemes. Both one- and two-dimensional cases are presented for boundless, source free, homogeneous, isotropic and lossless media. The 1-D and 2-D cases are developed in detail for the (3, 2 M + 1) (temporal, spatial) and (3, 3) 2-D stencils, respectively. Stability analysis is built into the methodology in terms of either analytical conditions or “stability maps” defined herein. The methodology is seen as a generalization of many existing schemes that also provides a unified tool for a systematical design of WE-FDTD schemes subject to specific requirements in terms of the spectral content of the excitation. The computational efficiency for all schemes remains the same for a given stencil, since the core of the FDTD code is unchanged between schemes, the difference being only in the values of scheme coefficients.

Bahadur exact slopes of some tests for spectral densities

The large deviation result is proved for two functionals of the empirical spectral process in zero-mean Gaussian stationary processes. As a statistical application, we deal with the Bahadur asymptotic efficiencies of two statistics for testing H: f 1 = f (specified), which are spectral analogue to the Kolmogorov-Smirnov (KS) and Kuiper statistics for testing hypothesis about distribution function in the iid setting. It is shown that the Kuiper type statistic is superior to the KS type statistic in terms of the Bahadur exact slope. We also discuss the a( ≥ 2)-sample problem. Especially, for the two-sample problem, we investigate the Bahadur asymptotic efficiencies of several statistics for testing not only the goodness-of-fit hypothesis H 1: f 1 = f 2 = f (specified) but also the homogeneity hypothesis H 2: f 1 = f 2 (unspecified).

Fidelity Recovery in Chaotic Systems and the Debye-Waller Factor

Using supersymmetry calculations and random matrix simulations, we study the decay of the average of the fidelity amplitude ${f}_{ϵ}(\ensuremath{\tau})=⟨\ensuremath{\psi}(0)|\mathrm{exp}(2\ensuremath{\pi}i{H}_{ϵ}\ensuremath{\tau})\mathrm{exp}(\ensuremath{-}2\ensuremath{\pi}i{H}_{0}\ensuremath{\tau})|\ensuremath{\psi}(0)⟩$, where ${H}_{ϵ}$ differs from ${H}_{0}$ by a slight perturbation characterized by the parameter $ϵ$. For strong perturbations a recovery of ${f}_{ϵ}(\ensuremath{\tau})$ at the Heisenberg time $\ensuremath{\tau}=1$ is found. It is most pronounced for the Gaussian symplectic ensemble, and least for the Gaussian orthogonal one. Using Dyson's Brownian-motion model for an eigenvalue crystal, the recovery is interpreted in terms of a spectral analogue of the Debye-Waller factor known from solid state physics, describing the decrease of x-ray and neutron diffraction peaks with temperature due to lattice vibrations.

Real cobordism and greek letter elements in the geometric chromatic spectral sequence

In this paper, we give a basic application of our AdamsNovikov spectral sequence analogue based on Real cobordism. Concretely, using that technique, we prove restrictions on Greek letter elements which can be permanent cycles or targets of dierentials in the geometric chromatic spectral sequence.

Phyllosilicate‐poor palagonitic dust from Mauna Kea Volcano (Hawaii): A mineralogical analogue for magnetic Martian dust?

The mineralogical and elemental composition of dust size fractions (<2 and <5 μm) of eight samples of phyllosilicate‐poor palagonitic tephra from the upper slopes of Mauna Kea Volcano (Hawaii) were studied by X‐ray diffraction (XRD), X‐ray fluorescence (XRF), visible and near‐IR reflectance spectroscopy, Mössbauer spectroscopy, magnetic properties methods, and transmission electron microscopy (TEM). The palagonitic dust samples are spectral analogues of Martian bright regions at visible and near‐IR wavelengths. The crystalline phases in the palagonitic dust are, in variable proportions, plagioclase feldspar, Ti‐containing magnetite, minor pyroxene, and trace hematite. No basal reflections resulting from crystalline phyllosilicates were detected in XRD data. Weak, broad XRD peaks corresponding to X‐ray amorphous phases (allophane, nanophase ferric oxide (possibly ferrihydrite), and, for two samples, hisingerite) were detected as oxidative alteration products of the glass; residual unaltered glass was also present. Mössbauer spectroscopy showed that the iron‐bearing phases are nanophase ferric oxide, magnetite/titanomagnetite, hematite, and minor glass and ferrous silicates. Direct observation by TEM showed that the crystalline and X‐ray amorphous phases observed by XRD and Mössbauer are normally present together in composite particles and not normally present as discrete single‐phase particles. Ti‐bearing magnetite occurs predominantly as 5–150 nm particles embedded in noncrystalline matrix material and most likely formed by crystallization from silicate liquids under conditions of rapid cooling during eruption and deposition of glassy tephra and prior to palagonitization of glass. Rare spheroidal halloysite was observed in the two samples that also had XRD evidence for hisingerite. The saturation magnetization Js and low‐field magnetic susceptibility for bulk dust range from 0.19 to 0.68 Am2/kg and 3.4×10−6 to 15.5×10−6 m3/kg at 293 K, respectively. Simulation of the Mars Pathfinder Magnet Array (MA) experiment was performed on Mauna Kea Volcano in areas with phyllosilicate‐poor palagonitic dust and with copies of the Pathfinder MA. On the basis of the magnetic properties of dust collected by all five MA magnets and the observation that the Pathfinder MAs collected dust on the four strongest magnets, the value for the saturation magnetization of Martian dust collected in the MA experiments is revised downward from 4±2 Am2/kg to 2.5±1.5 Am2/kg. The revised value corresponds to 2.7±1.6 wt % magnetite if the magnetic mineral is magnetite (using Js = 92 Am2/kg for pure magnetite, Fe3O4) or to 5.0±3.0 to 3.4±2.0 wt % maghemite if the magnetic mineral is pure maghemite (using Js = 50 to 74 Am2/kg for pure maghemite, γ‐Fe2O3). Comparison of the magnetic properties of bulk Mauna Kea palagonitic dust to those for dust collected by MA magnets shows that the MA magnets extracted (culled) a subset (25–34 wt %) of composite magnetic particles from bulk dust. The extent of culling of Martian dust is not well constrained. Because the Mauna Kea palagonitic dust satisfies the essential constraints of the Pathfinder magnetic properties experiment (composite and magnetic particles capable of being collected by five MA magnets), a working hypothesis for the strongly magnetic mineral present in Martian dust and soil is magnetite (possibly Ti‐bearing) formed by rapid crystallization from silicate liquids having volcanic and/or impact origins. Subsequent palagonitization of the glass produces the nanophase ferric oxide phases that dominate the spectral properties of Martian bright regions at visible and near‐IR wavelengths. Magnetic and phyllosilicate‐poor palagonitic dust from Mauna Kea Volcano is thus a spectral and magnetic analogue for magnetic Martian dust.

A joint spectral characterization of primeness for C$^*$-algebras

We prove that a C*-algebra A is prime iff YT((La, Rb), A) = a-(a) x a(b) for every a, b E A, where UT denotes Taylor spectrum and La, Rb are the left and right multiplication operators acting on A. Let A be a unital C*-algebra, let La, Rb denote the left and right multiplication operators induced by a,b E A (i.e., La( := ax, Rb(X) := xb, x E A), and set Ma,b := LaRb. We obtain a characterization of primeness for C*-algebras in terms of the spectral theory of (La, Rb). Recall that an ideal I in A is said to be prime if, whenever I1, 12 are ideals in A such that 1112 C 1, it follows that I1 C I or 12 C I; A is said to be prime if (0) is a prime ideal. In [Mal], M. Mathieu obtained the following result. Theorem 1 ([Mal]). Let A be a unital C*-algebra. The following statements are equivalent. (i) A is prime. (ii) HlMa,bl = 1lall 1IbI1 for all a, b E A. (iii) J(Ma,b) = a(a)a(b) for all a, b E A. In this note we prove a joint spectral analogue of Theorem 1. First, we recall the definition of the (joint) Taylor spectrum of (La, Rb). The Koszul complex associated with (La) Rb) is Ca~b 0 -? AXL4A0A f4Aa -0a , where Dab (x) := ax @ xb (x E A) and Dab(x ($ y) :=-xb + ay (x, y E A). We say that (La, Rb) is Taylor invertible if Cab is exact, i.e., if the following three implications hold: KerDab= : xEA, ax=O=xb =>x=O; Received by the editors December 6, 1995 and, in revised form, June 12, 1996. 1991 Mathematics Subject Classification. Primary 46L05, 47A10, 47A13, 47C15, 47D25; Secondary 47A62, 18G35.

NMR study of the phosphate-binding elements of Escherichia coli elongation factor Tu catalytic domain

The phosphoryl-binding elements in the GDP-binding domain of elongation factor Tu were studied by heteronuclear proton observe methods. Five proton resonances were found below 10.5 ppm. Two of these were assigned to the amide groups of Lys 24 and Gly 83. These are conserved residues in each of the consensus sequences. Their uncharacteristic downfield proton shifts are attributed to strong hydrogen bonds to phosphate oxygens as for resonances in N-ras-p21 [Redfield, A. G., & Papastavros, M. Z. (1990) Biochemistry 29, 3509-3514]. The Lys 24 of the EF-Tu G-domain has nearly the same proton and nitrogen shifts as the corresponding Lys 16 in p21. These results suggest that this conserved lysine has a similar structural role in proteins in this class. The tentative Gly 83 resonance has no spectral analogue in p21. A mutant protein with His 84 changed to glycine was fully 15N-labeled and the proton resonance assigned to Gly 83 shifted downfield by 0.3 ppm, thereby supporting the assignment.

A spectral commutant lifting theorem

The commutant lifting theorem of [24] may be regarded as a very general interpolation theorem from which a number of classical interpolation results may be deduced. In this paper we prove a spectral version of the commutant lifting theorem in which one bounds the spectral radius of the interpolant and not the norm. We relate this to a spectral analogue of classical matricial Nevanlinna-Pick interpolation.

Reactive Ion Etching of Tungsten with Chlorinated Fluorocarbons

Tungsten reactive ion etch (RIE) rate and resist selectivity behavior of three unique Freon systems are investigated using optical emission spectroscopy and electron scanning for chemical analysis (ESCA). An oxygen‐rich formulation exhibits an etch rate and selectivity to photoresist on the order of two‐three times that possible with . An optical emission spectral analogue has led to the discovery that 5–15% added to or yields a similar etch rate and selectivity advantage.

848. Vacuum-deposited thin-films circuits: J C Karp,Electro-Technology, 75 (2), Feb 1965, 79–83

We define a new concept, termed the spectral order of accuracy (SOoA), which is the spectral domain analogue of the familiar order of accuracy (OoA). The SOoA is pivotal in a refined version of a recently-introduced methodology for formulating excitation-adaptive wave equation FDTD (WE-FDTD) schemes, described below. This concept is the basis for a unified classification for both existing and new schemes. Both one- and two-dimensional cases are presented for boundless, source free, homogeneous, isotropic and lossless media. The 1-D and 2-D cases are developed in detail for the (3, 2M + 1) (temporal, spatial) and (3, 3) 2-D stencils, respectively. Stability analysis is built into the methodology in terms of either analytical conditions or “stability maps” defined herein. The methodology is seen as a generalization of many existing schemes that also provides a unified tool for a systematical design of WE-FDTD schemes subject to specific requirements in terms of the spectral content of the excitation. The computational efficiency for all schemes remains the same for a given stencil, since the core of the FDTD code is unchanged between schemes, the difference being only in the values of scheme coefficients.