Functions of Pairs of Unbounded Noncommuting Self-Adjoint Operators under Perturbation

Doklady Mathematics - For a pair $$(A,B)$$ of not necessarily bounded and not necessarily commuting self-adjoint operators and for a function f on the Euclidean space $${{\mathbb{R}}^{2}}$$ that...     

Holovideo: Real-time 3D range video encoding and decoding on GPU

We present a 3D video-encoding technique called Holovideo that is capable of encoding high-resolution 3D videos into standard 2D videos, and then decoding the 2D videos back into 3D rapidly without significant loss of quality. Due to the nature of the algorithm, 2D video compression such as JPEG encoding with QuickTime Run Length Encoding (QTRLE) can be applied with little quality loss, resulting in an effective way to store 3D video at very small file sizes. We found that under a compression ratio of 134:1, Holovideo to OBJ file format, the 3D geometry quality drops at a negligible level. Several sets of 3D videos were captured using a structured light scanner, compressed using the Holovideo codec, and then uncompressed and displayed to demonstrate the effectiveness of the codec. With the use of OpenGL Shaders (GLSL), the 3D video codec can encode and decode in realtime. We demonstrated that for a video size of 512×512, the decoding speed is 28 frames per second (FPS) with a laptop computer using an embedded NVIDIA GeForce 9400 m graphics processing unit (GPU). Encoding can be done with this same setup at 18 FPS, making this technology suitable for applications such as interactive 3D video games and 3D video conferencing.     

Surface second-harmonic generation: A novel technique for ps-pulse duration measurements

Second-harmonic generation from dye adsorbates has been successfully used to measure the duration of ps pulses. In the red and in the blue-green spectral range pulse durations of 2.4 and 6.1 ps—in agreement with streak camera measurements — have been obtained from collinear, slow autocorrelation traces.     

Current-induced coupling between conductance channels in membranes

The driven system of conducting channels in a nerve membrane is investigated. A current flow generates a coupling between the channels: the current through a channel is influenced by the presence of other conducting channels via the deformation of the equipotential surfaces within the media adjacent to the membrane. We derive an integral equation for the membrane voltageV(s) (s in the membrane plane) and solve it for different membrane conductance distributions(s) including models for stochastic distributions of conducting channels.V(s) is a nonlinear functional of(s). The system of coupled channels is compared with an Ising model. The system exhibits a multi-channel interaction which can be characterized by two different rangesd _int andD ₁. For a mean channel distanced ₀d _int interaction effects are negligible, and ford ₀D ₁ all channel-voltages are equal and thus represent a mean-field for the channels. Increasing conductivity of the medium decreasesd _int and increasesD ₁. With experimental data on sodium channels in nerve membranes we find:d _intd ₀, i.e. a 50% decrease of the channel-voltages by the interaction, andD ₁10³10⁴ d ₀, which indicates mean-field behaviour of the channels. In a subsequent paper we shall treat the statistics of channels which open and close stochastically under the influence of the local membrane voltage.     

Carbon-13 Assignments and Revision of the Stereostructures of the Cadinanes 2-Hydroxy-8α-angeloyloxycalamenene and 2-Hydroxy-8α-hydroxycalamenene

The two known cadinanes 2-hydroxy-8α-hydroxycalamenene and 2-hydroxy-8α-angeloyloxycalamenene were isolated from a Louisiana population of Heterotheca subaxillaris.

Their ¹³C NMR spectra were fully assigned by the application of HETCOR, COLOC, COSY, NOESY and DEPT experiments. It was shown on the basis of NOESY experiments that both cadinanes require revision at the stereogenic centre C-7.     

Eine einfache apparative Anordnung zur emissionsspektroskopischen 15N-Bestimmung im Mikromaßstab

A simple device for emission-spectroscopic ¹⁵N determination with photoelectric recording is described. The nitrogen is stimulated for light emission in glass tubes between capacitor plates of an oscillator circuit. The frequency is regulated to 13.9 MHz by means of a high frequency generator (DX-60, Heathkit) with an effective power of 15–20 W. The dispersion and detection of the emitted light is performed by a Zeiss Spectrophotometer PMQ II, used with a wave-length scanner and a recorder.     

Massenspektrometrische Identifizierung von biogenen Aminen in Form ihrer 1-Dimethylamino-naphthalin-5-sulfonyl-Derivate

Zusammenfassung Von etwa 80 1-Dimethylamino-naphthalin-5-sulfonyl-(DANS-)Derivaten biogener Amine und verwandter Verbindungen mit unterschiedlichen strukturellen Elementen wurden die durch Elektronenstoß induzierten Fragmentierungen untersucht. Die Prinzipien dieser Fragmentierungen und die Brauchbarkeit der Massenspektrometrie bei niedrigem Auflösungsvermögen für die Identifizierung dünnschicht-chromatographisch getrennter DANS-Derivate biogener Amine aus Gewebsextrakten werden diskutiert.

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Mass spectrometric identification of biogenic amines as 1-dimethylamino-naphthalene-5-sulphonyl derivatives

The fragmentation by electron impact of approximately 80 1-dimethylamino-naphthalene-5-sulphonyl (DANS) derivatives of biogenic amines and related substances of different structural features has been studied. The principles of these fragmentations and the suitability of low resolution mass spectrometry for the identification of thin-layer chromatographically separated DANS-derivatives of biogenic amines from tissue extracts are discussed.

     

New guaianolides from Berlandiera Pumila and B. Texana,and the X-ray crystal structure of pumilin

The isolation and structure determination of two new guaianolides, pumilin and its 2,3-epoxide, from Berlandiera pumila and B. texana are reported. The structure of pumilin was determined from nmr and mass spectral data, and from an X-ray single crystal study; the structure of the epoxide was found by comparison of nmr spectra. Pumilin is shown to be a Δ¹⁽¹⁰⁾-cis-guaianolide with a cyclopentenone ring attached to C1 and C5, and an α-methylene-γ-lactone ring trans-fused to C6 and C7. The absolute configuration was inferred from spectral considerations and knowledge of previous structural determinations. The cd spectrum of pumilin exhibits a negative Cotton effect, and the lactone chromophore has left-handed chirality. The cyclo-heptene ring is in the chair configuration, with the lactone a half-chair and the cyclopentenone essentially planar. Crystals are orthorhombic, a = 7.065, b = 13.652, c = 19.586 Å, space group P2₁2₁2₁, Z = 4, and the final R value is 3.9%. The crystal structure is strengthened by an O···O hydrogen bond linking the molecules into infinite chains.