Spectral properties of unbounded symmetric Jacobi matrices are studied. Under mild assumptions on the coefficients absolute continuity of spectral measure is proved. Only operator theoretic proofs are provided. Some open problems of Ifantis are solved.

Physicochemical properties of the plasma membrane have been shown to play an important role in cellular functionality. Among those properties, the molecular order of the lipids, or the lipid packing, is of high importance. Changes in lipid packing are believed to compartmentalize cellular signaling by initiating coalescence and conformational changes of proteins. A common way to infer membrane ...

Light-adapted spectral sensitivity of the goldfish was measured using the dorsal light reaction-the reflexive tendency of fish to tilt their dorsal surface toward bright light. Subjects were placed between two 150” extended monochromatic fields. one of which was always 532nm. The angle of tilt toward or away from the 532nm light was measured. and the relative intensities of the fields were adju...

Compound identification in gas chromatography-mass spectrometry (GC-MS) is usually achieved by matching query spectra to spectra present in a reference library. Although several spectral similarity measures have been developed and compared using a small reference library, it still remains unknown how the relationship between the spectral similarity measure and the size of reference library affe...

We discuss regularization by noise of the spectrum of large random non-normal matrices. Under suitable conditions, we show that the regularization of a sequence of matrices that converges in ∗-moments to a regular element a by the addition of a polynomially vanishing Gaussian Ginibre matrix forces the empirical measure of eigenvalues to converge to the Brown measure of a.

The EEG is a valuable tool because it reflects cerebral physiology, it is a continuous and non-invasive measure, and it changes markedly on the administration of anesthetic drugs. The objective of this project is to find the excellent features to discriminate between different anesthesia states. Spectral Edge Frequency (SEF), spectral entropy and bicoherence can be used to differentiate differe...

In a variety of applications of audio signal processing, for example blind source separation (BSS), harmonic signals need to be treated differently from percussive signals. Thus, recognizing if a signal is harmonic or percussive is a very helpful and frequently used preprocessing step. Different measures have been proposed to capture either the harmonicity or the percussivity of a signal, using...

We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure μ̂ of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N ×N symmetric matrix YσN whose (i, j) entry is σ( i N , j N )xij where (xij , 1 ≤ i ≤ j < ∞) is an infinite array of i.i.d real variables with common distribution in the domain of attraction of an α-...

We introduce a novel approach for defining a δ′-interaction on a subset of the real line of Lebesgue measure zero which is based on Sturm– Liouville differential expression with measure coefficients. This enables us to establish basic spectral properties (e.g., self-adjointness, lower semiboundedness and spectral asymptotics) of Hamiltonians with δ′-interactions concentrated on sets of complica...

A Borel measure μ in R is called a spectral measure if there exists a set Λ ⊂ R such that the set of exponentials {exp(2πiλ · x) : λ ∈ Λ} forms an orthogonal basis for L(μ). In this paper we prove some properties of spectral measures. In particular, we prove results that highlight the 3/2-rule.