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A hyperspectral “group shoot” was conducted during September 1999 by Analytical Imaging and Geophysics (AIG) in cooperation with HyVista Corporation, Sydney, Australia, utilizing HyMap, an advanced 126-band hyperspectral sensor covering the 0.4 - 2.5 micrometer region with 3-10 m spatial resolution. The purpose of this effort was to make high-quality hyperspectral data commercially available to customers for their sites of interest across the United States. Over 200 flightlines of HyMap data were collected throughout the United States for government, academic, and commercial customers. The standard product delivered by AIG/Hy Vista was fully-calibrated radiance data along with precision-geocoded, apparent reflectance spectral image data. This marks the first time that commercial hyperspectral data has been delivered in a standard map-referenced, reflectance-corrected, ready-to-use form. Preliminary work with these datasets has demonstrated unprecedented spectral mapping capabilities for a variety of disciplines, including geology, vegetation studies, environmental assessment, near-shore marine mapping, and military applications. Data were also acquired in support of data simulation efforts the proposed Warfighter and the Australian ARIES hyperspectral satellites. Examples of the 1999 data, a description of the production processing flow, and scientific analysis results are discussed here.

In this chapter we first establish a lemma reducing many questions of interest about matrix semigroups to the case of finite groups. We use the lemma to obtain reducibility and triangularizability results from assumptions of various “partial” spectral mapping properties, including sublinearity of spectra and the nilpotence of certain polynomials in semigroup elements.

We show that the Weyl spectrum of a dominant operator satisfies the spectral mapping theorem for analytic functions and then answer a question of Oberai.

We show that a classical counterexample to the spectral mapping theorem for the exponential function is not very surprising if we consider the example in a suitable nonstandard setting.

Let A = (A 1,... A n ) be an n-tuple of bounded linear operators in a Hubert space H. A point z = (z 1,..., z n ) ∈ C n is said to be a point of the left joint spectrum σ l (A) of the n-tuple A, if an n-tuple B = (B 1,..., B n ) of linear bounded operators in H, such that $$\sum\limits_{k = l}^n {{B_k}\left( {{A_k} - {z_k}I} \right)} = I$$ does not exist.

In the contribution we generalize the notion of spectrum to any (nonassociative) algebra. The spectra of elements of a given algebra are such sets of elements from some other algebra that the Spectrum mapping theorem is valid for polynomials. If the two algebras are topological, we extend the validity of Spectral mapping th. to functions which are limits of sequences of polynomials. In this case the spectral radius keeps its meaning almost unchanged.

We demonstrate the ability of a combined scanning electron microscope and cathodoluminescence (CL) spectral mapping system to provide important spatially resolved information. The degree of inhomogeneity in spectral output across a multi-quantum well sample is measured using the SEM-CL system as well as measuring the efficiency roll-off with increasing carrier concentration. The effects of low energy electron beam modification on the InGaN/GaN multi quantum wells have also been characterized.

The atrial cycle length during atrial fibrillation (AFIB) and flutter (AFL) waves has been shown to be correlated with atrial refractoriness and organization. In this study, a novel body surface 2-dimensional (2D) spectral mapping of AFIB and AFL was developed using vector-projected 187-channel ECG (187ch DREAM-ECG). The study consisted of 28 patients (24 AFIB and 4 AFL with valvular heart disease). Spectral analysis of a 4 seconds of non-averaged 187ch wave during AFIB and AFL was performed by maximum entropy modeling. The 2D body surface spectral feature was displayed according to the frequency and power magnitude components of the dominant frequency. The accuracy of this spectral feature was verified by 64ch magnetocardiography (MCG). The average dominant frequency in AFL by 187ch VP-ECG was lower than that in AFIB (4.6±0.9 Hz in AFL vs. 7.2±0.9 Hz in AFIB). The average dominant frequency by 187ch SACEG was agreed well with those by 64ch MCG (y=0.86x+0.84, r2=0.89). The body surface 2D spectral feature of the dominant frequency demonstrated a homogenous spectrum pattern in AFL and a non-homogenous pattern in AFIB. In conclusion, 2D novel body surface spectral mapping of the dominant frequency using 187ch DREAM-ECG may evaluate non-invasively the atrial cycle length during AFIB and AFL.

Let $\sigma(F)$ denote the point spectrum of a multivalued operator $F \colon H \rightrightarrows H $ defined over a real Hilbert space. The aim of this note is to explore the continuity properties of the spectral mapping $F \rightrightarrows \sigma(F)$.

LetT be a continuous scalar-type spectral operator defined on a quasi-complete locally convex spaceX, that is,T=∫fdP whereP is an equicontinuous spectral measure inX andf is aP-integrable function. It is shown that σ(T) is precisely the closedP-essential range of the functionf or equivalently, that σ(T) is equal to the support of the (unique) equicontinuous spectral measureQ* defined on the Borel sets of the extended complex plane ℂ* such thatQ*({∞})=0 andT=∫zdQ*(z). This result is then used to prove a spectral mapping theorem; namely, thatg(σ(T))=σ(g(T)) for anyQ*-integrable functiong: ℂ* → ℂ* which is continuous on σ(T). This is an improvement on previous results of this type since it covers the case wheng(σ(T))/{∞} is an unbounded set inℂ a phenomenon which occurs often for continuous operatorsT defined in non-normable spacesX.

SynopsisLetG: ε(G)⊂ℋ → ℋ be a maximal dissipative operator with compact resolvent on a complex separable Hilbert space ℋ andT(t) be theCosemigroup generated byG. A spectral mapping theorem σ(T(t))\{0} = exp (tσ(G))/{0} together with a condition for 0 ε σ(T(t)) are proved if the set {xε ⅅ(G) | Re (Gx, x) = 0} has finite codimension in ε(G) and if some eigenvalue conditions forGare satisfied. Proofs are given in terms of the Cayley transformationT= (G+I)(G−I)−1ofG. The results are applied to the damped wave equationutt+ γutx+uxxxx+ ßuxx= 0, 0 ≦t< ∞ 0

LetX be anL1- orL2-Banach lattice. Let (W(t))t≥0 be aC0-semigroup of positive operators onX with generator−T. Two examples ofC0-semigroups are presented for which the identity\(e^{\sigma ( - T)t} = \sigma (W(t)) - \left\{ 0 \right\}\) fails for almost allt>0.

The theory of A-scalar and generalized scalar operators of Colojoara and Foias [7] is generalized to unbounded closed operators. A spectral mapping theorem is proved for the (local) spectrum. Generalized scalar operators admit a calculus for , the C⋡-functions on the C⋡-manifold . B⋡(C), the C⋡-functions onC, which are bounded with all derivatives, is an other admissible algebra. If σ(T) is contained in a generalized circle , characterisations as in [7] and explicit expressions for the Cm(K)- and the Bm(R)-calculus are obtained.

Derivative spectroscopy was used in the interpretation and exploitation of data obtained from rapid-scan UV—VIS absorbance detectors for ascertaining the purity of chromatographic peaks. Two types of derivatives were examined. The derivative of the elution curve with respect to the specific wavelength at which the major compound has a zero derivative (referred to as the spectral derivative null technique) proved to be rapid and useful for the determination of co-eluting impurity peaks which might form in solution or during chromatography from compounds otherwise known to be pure. The derivatives of the spectral curves obtained during chromatography (referred to as the derivative spectral mapping technique) were also examined both by computer simulation and experimentally and found to have the potential for universal applications in screening compounds for possible overlapping impurities in high-performance liquid chromatographic scans. A novel approach using the derivative spectral mapping technique is described to relate impurity detection limits to chromatographic and spectral resolutions of closely absorbing species which are incompletely resolved chromatographically (Rc < 0.5). Using the above techniques, it was possible to detect, under suitable conditions, as little as 0.1% impurity which co-eluted chromatographically with the major compound.

LetZ be a generator of an exponentially boundedC-semigroup {St}t≥0 in a Banach space and letTt=C−1St. We show that the spectral mapping theorems such as exp(tσ(Z)) ⊂ σ(Tt) and exp(tσp(Z)) ⊂ tσp(Tt) ⊂ exp(tσp(Z)) ⋃ {0} for everyt≥0 hold.

On etablit un calcul fonctionnel f→f(S) pour des operateurs sous normaux S. On etudie l'espace associe a ce calcul. On considere la caracterisation du spectre clos de f(S) en fonction de f

In this note we continue the study of -functional calculi in several variables (introduced in [1] and [2]). In the situation of an inverse closed (see Def. 1.2) basic algebra of type I or II we characterize the algebra generated by an arbitrary -functional calculus φ and prove several variants of the spectral mapping theorem, thus generalizing corresponding results of F.-H. Vasilescu [10] (see also the more general version in [4], Th. 3.2.1) to the case of several commuting operators. By means of the spectral mapping theorem we prove the decomposability (in the sense of St. Frunza [6]) of m-tuples of the type (φ(f1),..., φ(fm)) with f1,...,fme .

Definition 1. An open semioroup ~ of ~3 will be called an F-semigroup/f (i) a, b ~ ~3 and ab = ba E ~ imply a ~ ~ and b ~ ~, and (ii) there exists a closed ideal R such that ~ = q-1 (S), where S is an open semigroup in ~B/R containin 9 G and havin 9 the property that S\G is also open. It is clear that ~ contains the invertible elements of ~B, and that ~+-qc~. (1-1) If a ~ ~ and if~a is the (maximal connected open) component of~ containing a, then a + R C ~a.

This paper is concerned with linear equations x′ = A(t)x (t∈ R , x∈ C n) having bounded growth and decay. Introducing a semigroup of linear operators Th, h≥0, by the formula (Thv)(t) = X(t, t − h)v(t − h), where v ∈ C0( C n) consisting of C n-valued bounded and continuous functions v on R satisfying lim v(t) = 0 as |t|→∞, X(t, s) is the evolutionary operator, one proves the spectral mapping theorem and the rotational invariance of σ(Th), and then discusses their applications.

Let a bounded domain G in C n be either strictly pseudoconvex with C2-boundary b(G) or a polydomain. For each u = (u1,…, uk) ⊂ H∞(G), u ⊂ A(G), resp. let \ gs(u) be a compact subset of C n. If so defined \ gs is a subspectrum [i.e., satisfies the projection property and \ gs(u) is a non-void subset of the “usual” joint spectrum of u], then it is shown that u( \ gs(z)∩ G) ⊂ \ gs(u) . Moreover, if u is continuously extendable to each point of \ gs(z) ∩ b(G), then u( \ gs(z)) = \ gs(u) . This provides spectral mapping theorems for H∞(G) [resp.A(G)]-functional calculi. The extended spectrum of a representation, introduced by C. Foias. and W. Mlak [Stud. Math. 64 (1979), 263–271], is also discussed.

The well-known Dunford-Taylor operational calculus for closed linear operators in Banach spaces has been generalized in two different ways: First, by H. A. Gindler ( Nagoya Math. J. 26 (1966), 31–38) and B. Nagy ( Acta Math. Acad. Sci. Hungar. 33 (1979), 379–390), to include meromorphic functions with poles in the extended spectrum which are not eigenvalues. Second, by M. Schechter and J. Shapiro ( Trans. Amer. Math. Soc. 175 (1973), 439–467), to include functions analytic on a neighborhood of the Fredholm spectrum. In this paper we give several results about the meromorphic calculus, in particular, spectral mapping theorems for essential spectra; and we apply our results to the study of the solutions of some integro-differential equations. Moreover, for functions admissible in both calculi, we verify that with suitable choice of quasi-resolvent and contour of integration, the Schechter-Shapiro calculus yields an extension of the operator provided by the meromorphic calculus.

It is shown that if T is a dominant operator or an analytic quasi-hyponormal operator on a complex Hilbert space and if f is a function analytic on a neighborhood of σ( T ), then σ w ( f ( T )) = f (σ w ( T )), where σ( T ) and σ w ( T ) stand respectively for the spectrum and the Weyl spectrum of T ; moreover, Weyl's theorem holds for f ( T ) + F if “dominant” is replaced by “ M -hyponormal,” where F is any finite rank operator commuting with T . These generalize earlier results for hyponormal operators. It is also shown that there exist an operator T and a finite rank operator F commuting with T such that Weyl's theorem holds for T but not for T + F . This answers negatively a problem raised by K. K. Oberai ( Illinois J. Math. 21, 1977, 84–90). However, if T is required to be isoloid, then the statement that Weyl's theorem holds for T will imply it holds for T + F .

Let A be a linear operator on a complex normed linear space (into itself). We denote by $N(A)$ and $R(A)$ the null-space and the range of A, respectively. The purpose of this paper is to show that \[ N\left( {\prod_{i = 1}^s {\left( {A - \alpha _i I} \right)^{n_i } } } \right) = \sum _{i = 1}^s { \oplus N\left( {\left( {A - \alpha _i I} \right)^{n_i } } \right)\quad ({\text{direct sum}})} \] and \[R\left( {\prod_{i = 1}^s {\left( {A - \alpha _i I} \right)^{n_i } } } \right) = \bigcap\limits_{i = 1}^s {R\left( {\left( {A - \alpha _i I} \right)^{n_i } } \right),} \] where the $\alpha _i $ are different complex numbers and I is the identity operator, and to note that some theorems in spectral theory follow directly from these formulas.

Spectral mapping is a classification technique that has been applied to the Liege physiognomies of the neuroleptics. The method makes use of a special projection that separate potency from spectral information. Principal component analysis revealed a dominant component resembling a bipolar incisive/sedative scale. A second antimanic/antiautistic scale is apparent in the revised. Liege physiognomie. Spectral mapping allows to compare observations on neuroleptics in different frames of reference and from different methodologies (e.g. clinical and pharmacological).

We give an elementary proof of the fact that given two polynomials P, Q without common zeros and a linear operator A, the operators P(A) and Q(A) verify some properties equivalent to the pair (P(A), Q(A)) being non-singular in the sense of J. L. Taylor. From these properties we derive expressions for the range and null space of P(A) and spectral mapping theorems for polynomials of continuous (or closed) operators in Banach spaces.

In this work we investigate the use of a speaker adaptation technique, for speech recognition, based on neural network spectral mapping. Different multilayer perceptron neural network architectures are analyzed in order to optimize the spectral difference reduction in acoustic data of two speakers. Experiments are carried out in a telecontrol environment, used to provide voice commands to a mobile robot, based on DTW pattern matching.

This paper is the first reported description of Raman Spectroscopy in the assessment of axillary lymph nodes in breast cancer patients. Raman Spectroscopy is an inelastic scattering spectroscopic technique appropriate for the assessment of unprocessed complex biological tissues. Spectra represent biochemical signatures of the tissue under scrutiny. The described method of Raman spectral mapping produces false-color spectral images of lymph node sections. These can be compared with standard histopathology slides and white light images of nodal tissue. This method has the potential to allow the detailed biochemical assessment of heterogeneous lymph node features, and to contribute towards the development of an optical diagnostic tool for use in a clinical setting.

This research investigates the spectral reflectance characteristics of soil and vegetation using multi-angular and single view hyperspectral data. The question of the thesis is “How much information can be obtained from multi-angular hyperspectral remote sensing in comparison with single view angle hyperspectral remote sensing of soil and vegetation?” This question is addressed by analysing multi-angular and single view angle hyperspectral remote sensing using data from the field, airborne and space borne hyperspectral sensors. Spectral mapping, spectral indices and Functional Data Analysis (FDA) are used to analyse the data. Spectral mapping has been successfully used to distinguish features of soil and cotton with hyperspectral data. Traditionally, spectral mapping is based on collecting endmembers of pure pixels and using these as training areas for supervised classification. There are, however, limitations in the use of these algorithms when applied to multi-angular images, as the reflectance of a single ground unit will differ at each angle. Classifications using six-class endmembers identified using single angle imagery were assessed using multi-angular Compact High Resolution Imaging Spectrometer (CHRIS) imagery, as well as a set of vegetation indices. The results showed no significant difference between the angles. Low nutrient content in the soil produced lower vegetation index values, and more nutrients increased the index values. This research introduces FDA as an image processing tool for multi-angular hyperspectral imagery of soil and cotton, using basis functions for functional principal component analysis (fPCA) and functional linear modelling. FDA has advantages over conventional statistical analysis because it does not assume the errors in the data are independent and uncorrelated. Investigations showed that B-splines with 20-basis functions was the best fit for multi-angular soil spectra collected using the spectroradiometer and the satellite mounted CHRIS. Cotton spectra collected from greenhouse plants using a spectrodiometer needed 30-basis functions to fit the model, while 20-basis functions were sufficient for cotton spectra extracted from CHRIS. Functional principal component analysis (fPCA) of multi-angular soil spectra show the first fPCA explained a minimum of 92.5% of the variance of field soil spectra for different azimuth and zenith angles and 93.2% from CHRIS for the same target. For cotton, more than 93.6% of greenhouse trial and 70.6% from the CHRIS data were explained by the first fPCA. Conventional analysis of multi-angular hyperspectral data showed significant differences exist between soil spectra acquired at different azimuth and zenith angles. Forward scan direction of zenith angle provides higher spectral reflectance than backward direction. However, most multi-angular hyperspectral data analysed as functional data show no significant difference from nadir, except for small parts of the wavelength of cotton spectra using CHRIS. There is also no significant difference for soil spectra analysed as functional data collected from the field, although there was some difference for soil spectra extracted from CHRIS. Overall, the results indicate that multi-angular hyperspectral data provides only a very small amount of additional information when used for conventional analyses.

A variant of electroencephalogram (EEG) power spectral mapping called power ratio index (PRI) mapping was used to monitor 15 patients with malignant brain tumors. This index is generated by dividing the low frequency (delta, theta) power by the high frequency (alpha, beta) power. Because the nonparoxysmal effect of a brain tumor on the EEG is reflected as a relative loss of high frequency power and a gain in low frequency power, utilization of the PRI has the effect of placing the epicenter of the “power dysfunction” coincident with the epicenter of the tumor.