Acoustic Analyses of Developmental Changes and Emotional Expression in the Preverbal Vocalizations of Infants

The nonverbal vocal utterances of seven normally hearing infants were studied within their first year of life with respect to age- and emotion-related changes. Supported by a multiparametric acoustic analysis it was possible to distinguish one inspiratory and eleven expiratory call types. Most of the call types appeared within the first two months; some emerged in the majority of infants not until the 5th (“laugh”) or 7th month (“babble”). Age-related changes in acoustic structure were found in only 4 call types (“discomfort cry,” “short discomfort cry,” “wail,” “moan”). The acoustic changes were characterized mainly by an increase in harmonic-to-noise ratio and homogeneity of the call, a decrease in frequency range and a downward shift of acoustic energy from higher to lower frequencies. Emotion-related differences were found in the acoustic structure of single call types as well as in the frequency of occurrence of different call types. A change from positive to negative emotional state was accompanied by an increase in call duration, frequency range, and peak frequency (frequency with the highest amplitude within the power spectrum). Negative emotions, in addition, were characterized by a significantly higher rate of “crying,” “hic” and “ingressive vocalizations” than positive emotions, while positive emotions showed a significantly higher rate of “babble,” “laugh,” and “raspberry.”     

Clifford structures on Riemannian manifolds

We introduce the notion of even Clifford structures on Riemannian manifolds, which for rank r=2 and r=3 reduce to almost Hermitian and quaternion-Hermitian structures respectively. We give the complete classification of manifolds carrying parallel rank r even Clifford structures: Kähler, quaternion-Kähler and Riemannian products of quaternion-Kähler manifolds for r=2,3 and 4 respectively, several classes of 8-dimensional manifolds (for 5?r?8), families of real, complex and quaternionic Grassmannians (for r=8,6 and 5 respectively), and Rosenfeld?s elliptic projective planes OP², (C⊗O)P², (H⊗O)P² and (O⊗O)P², which are symmetric spaces associated to the exceptional simple Lie groups F₄, E₆, E₇ and E₈ (for r=9,10,12 and 16 respectively). As an application, we classify all Riemannian manifolds whose metric is bundle-like along the curvature constancy distribution, generalizing well-known results in Sasakian and 3-Sasakian geometry.     

Closed Formula for Options with Discrete Dividends and Its Derivatives

Abstract

We present a closed pricing formula for European options under the Black–Scholes model as well as formulas for its partial derivatives. The formulas are developed making use of Taylor series expansions and a proposition that relates expectations of partial derivatives with partial derivatives themselves. The closed formulas are attained assuming the dividends are paid in any state of the world. The results are readily extensible to time-dependent volatility models. For completeness, we reproduce the numerical results in Vellekoop and Nieuwenhuis, covering calls and puts, together with results on their partial derivatives. The closed formulas presented here allow a fast calculation of prices or implied volatilities when compared with other valuation procedures that rely on numerical methods.     

CsC2H: Synthese,Kristallstruktur und spektroskopische Eigenschaften

CsC₂H: Synthesis, Crystal Structure, and Spectroscopic Properties CsC₂H was synthesised by the reaction of caesium solved in liquid ammonia with acetylene. The crystal structure could be solved and refined from X‐ray and neutron powder diffraction data (space group: R3c, Z = 18). The structure is characterised by C₂H^– trimers which are surrounded by caesium ions. Spectroscopic investigations (IR and Raman) of the stable monoalkalimetal acetylides mainly confirm the data given in the literature and show that the alkalimetal cation has a marked influence on the vibrational properties of the C₂H^– anion.     

Investigation of the Catalytic Activity of a 2‐Phenylidenepyridine Palladium(II) Complex Bearing 4,5‐Dicyano‐1,3‐bis(mesityl)imidazol‐2‐ylidene in the Mizoroki‐Heck Reaction

The phenylidenepyridine (ppy) palladacycles [PdCl(ppy)(IMes)] ( 4 ) [IMes = 1,3‐bis(mesityl)imidazol‐2‐ylidene] and [PdCl(ppy){(CN)₂IMes}] ( 6 ) [(CN)₂IMes = 4,5‐dicyano‐1,3‐bis(mesityl)imidazol‐2‐ylidene] were prepared by facile two step syntheses, starting with the reaction of palladium(II) chloride with 2‐phenylpyridine followed by subsequent addition of the NHC ligand to the precatalyst precursor [PdCl(ppy)]₂. Suitable crystals for the X‐ray analysis of the complexes 4 and 6 were obtained. It was shown that 6 has a shorter NHC‐palladium bond than the IMes complex 4 . The difference of the palladium carbene bond lengths based on the higher π‐acceptor strength of (CN)₂IMes in comparison to IMes. Thus, (CN)₂IMes should stabilize the catalytically active central palladium atom better than IMes. As a measure for the π‐acceptor strength of (CN)₂IMes compared to IMes, the selone (CN)₂IMes · Se ( 7 ) was prepared and characterized by ⁷⁷Se‐NMR spectroscopy. The π‐acceptor strength of 7 was illuminated by the shift of its ⁷⁷Se‐NMR signal. The ⁷⁷Se‐NMR signal of 7 was shifted to much higher frequencies than the ⁷⁷Se‐NMR signal of IMes · Se. Catalytic experiments using the Mizoroki‐Heck reaction of aryl chlorides with n‐butyl acrylate showed that 6 is the superior performer in comparison to 4 . Using complex 6 , an extensive substrate screening of 26 different aryl bromides with n‐butyl acrylate was performed. Complex 6 is a suitable precatalyst for para‐substituted aryl bromides. The catalytically active species was identified by mercury poisoning experiments to be palladium nanoparticles.     

Bromo­di­methyl(N‐methyl­pyrrolidin‐2‐one‐O)­tin(IV)‐di‐μ‐bromo‐bromo­di­methyl­tin(IV)

The preparation and X‐ray analysis of the title compound, [Sn₂Br₄(CH₃)₄(C₅H₉NO)], are described. The compound contains two Sn atoms in the asymmetric unit, that complexed by N‐methyl­pyrrolidin‐2‐one being hexacoordinated (a), the other exhibiting pentacoordination (b). The most important features are three different Sn—Br bond lengths at both Sn atoms with the following values: (a) 2.5060 (9), 2.7152 (10) and 3.7118 (10) Å; (b) 2.5084 (10), 2.5279 (9) and 3.5841 (10) Å.