Multiple expansions of real numbers with digits set $$\left\{ 0,1,q\right\} $$ 0 , 1 , q

Mathematische Zeitschrift - For $$q>1$$ we consider expansions in base q with digits set $$\left\{ 0,1,q\right\} $$ . Let $${{\mathcal {U}}}_q$$ be the set of points which have a unique...     

Evaluation of Support in Singing

This study searched for perceptual, acoustic, and physiological correlates of support in singing. Seven trained professional singers (four women and three men) sang repetitions of the syllable [pa:] at varying pitch and sound levels (1) habitually (with support) and (2) simulating singing without support. Estimate of subglottic pressure was obtained from oral pressure during [p]. Vocal fold vibration was registered with dual-channel electroglottography. Acoustic analyses were made on the recorded samples. All samples were also evaluated by the singers and other listeners, who were trained singers, singing students, and voice specialists without singing education (a total of 63 listeners). We rated both the overall voice quality and the amount of support. According to the results, it seemed impossible to observe any auditory differences between supported singing and good singing voice quality. The acoustic and physiological correlates of good voice quality in absolute values seem to be gender and task dependent, whereas the relative optimum seems to be reached at intermediate parameter values.     

Dislocation-pairing transitions in hot grain boundaries

We report the finding of a novel grain-boundary structural phase transition in both molecular-dynamics and phase-field-crystal simulations of classical models of bcc Fe. This transition is characterized by pairing of individual dislocations with mixed screw and edge components. We demonstrate that this type of transition is driven by a combination of factors including elastic softening, core interaction, and core disordering. At high homologous temperatures the occurrence of this transition is shown to prevent premelting at misorientation angles where it would otherwise be expected.     

Discriminant Analysis of Volatile Organic Compounds data related to a new location method of entrapped people in collapsed buildings of an earthquake

Discriminant Analysis is used as a part of a research, which aims at using expired air analysis for the early location of entrapped people under the ruins of collapsed buildings in an earthquake. This work focuses on the possibility of distinguishing Volatile Organic Compounds (VOCs) in the entrapment area which originate from different sources. Five categories of samples were analyzed by Thermal Desorption-Gas Chromatography-Mass Spectrometry (TD-GC-MS). Expired air samples from healthy humans (Category 1) and fasting people (Category 2) were analyzed for studying the VOCs attributed to entrapped people. Headspace air of urban waste disposal bins (Category 3), headspace air of bags with decaying human bodies (Category 4) and urban air samples (Category 5) were analyzed for studying the VOCs attributed to background sources. Discriminant Rotation, a specific type of Discriminant Analysis was applied on the VOCs concentration matrix of the five categories. Combinations of VOCs that best discriminated each category were determined. Cluster Analysis was used to validate the results of Discriminant Analysis. The advantages and limitations of the method are presented and discussed.     

Approximation in eigenvalue problems for holomorphic fredholm operator functions I

The approximation of a holomorphic eigenvalue problem is considered. The main purpose is to present a construction by which the derivation of the asymptotic error estimations for the approximate eigenvalues of Fredholm operator functions can be reduced to the derivation of these estimations for the case of matrix functions. (Some estimations for the latter problem can be derived, in one's turn, from the error estimations for the zeros of the corresponding determinants.) The asymptotic error estimations are considered in part II of this paper, in [10]. By the presented construction also the stability of the algebraic multiplicity of eigenvalues by regular approximation is proved in Section 3

The presented construction, in essence, reproduces the constructions in [7] for the case of the compact approximation in subspaces and in [9] for the case of projection—like methods. It is simpler to use than similiar construction in [8], and allows unified consideration of the general case and the case of projection—like methods, what in [8, 9] was not achieved     

A natural extension for the greedy β-transformation with three arbitrary digits

We construct a planar version of the natural extension of the piecewise linear transformation T generating greedy β-expansions with digits in an arbitrary set of real numbers A = {a ₀, a ₁, a ₂}. As a result, we derive in an easy way a closed formula for the density of the unique T-invariant measure µ absolutely continuous with respect to Lebesgue measure. Furthermore, we show that T is exact and weak Bernoulli with respect to µ.     

Equipartition of interval partitions and an application to number theory

We give wider application and simpler proofs of results describing the rate at which the digits of one number-theoretic expansion determine those of another. The proofs are based on general measure-theoretic covering arguments and not on the dynamics of specific maps.