Total absolute curvature and tightness of noncompact manifolds

In the first part we prove an extension of the Chern-Lashof inequality for noncompact immersed manifolds with finitely many ends. For this we give a lower bound of the total absolute curvature in terms of topological invariants of the manifold. In the second part we discuss tightness properties for such immersions. Finally, we give an upper bound for the substantial codimension.

     

Orientational ordering of liquid crystals containing a difluoro-substituted phenyl ring

The orientational ordering of several liquid crystals containing a difluorosubstituted phenyl ring has been studied through the use of C-13 NMR. The fluorinated phenyl ring of these liquid crystals have C_s symmetry, so three order parameters are required to completely describe the ordering of this ring. All three of these order parameters have been calculated from carbon-fluorine dipolar coupling constants obtained from the carbon-fluorine splittings in the C-13 NMR spectra. Because of the complexity of the fluorine-coupled spectra, variable angle spinning (VAS) was used to resolve the carbon-fluorine splittings. In order to study the orientational ordering over wide ranges of temperature, we have developed an empirical correlation between the order parameter and the value of a carbon-fluorine dipolar coupling constant. This enabled us to study the change in the order parameter with temperature. The results of applying this method to several structurally similar liquid crystals containing the same type of difluorinated phenyl ring are presented. A comparison is made to a similar mono-fluorinated liquid crystal.     

A review of otoacoustic emissions

Otoacoustic emissions measured in the external ear canal describe responses that the cochlea generates in the form of acoustic energy. For the convenience of discussing their principal features, emitted responses can be classified into several categories according to the type of stimulation used to evoke them. On this basis, four distinct but interrelated classes can be distinguished including spontaneous, transiently evoked, stimulus-frequency, and distortion-product otoacoustic emissions. The present review details the findings that have been described for each emission type according to this classification schema. Additionally, the known features of emitted responses are discussed for both normally hearing and hearing-impaired humans and experimental animals, and with respect to their potential clinical applications. The findings reviewed here clearly indicate that future studies of otoacoustic emissions will significantly increase our understanding of the basic mechanisms of cochlear function while, at the same time, provide a new and important clinical tool.     

Photon-exchange processes at hadron colliders as a probe of the dynamics of diffraction

The rich structure of photon-exchange processes at hadron colliders is studied. We discuss central vector meson production , W production and production. Each process has distinct, and large, soft pp rescattering effects, which can be directly observed by detecting the outgoing protons. This allows a probe of the optical density of the proton, which plays a crucial role in the evaluation of the rapidity gap survival probabilities in diffractive-like processes at hadron colliders. We note that an alternative mechanism for production is odderon, instead of photon, exchange; and that the ratio of odderon to photon contributions is enhanced (suppressed) for vector meson production. Received: 1 February 2002 / Revised version: 4 April 2002 / Published online: 22 May 2002     

Performance analysis of 1300 nm SLEDs – impact of temperature and length scaling

The impact of self-heating and cavity length on the spectral emission properties of SLEDs is investigated using a state-of-the-art simulation tool. Simulated data are compared to measurements for two InP-based benchmark devices operating around 1300 nm, and excellent agreement is achieved in either case.     

Harmonic Algebraic Curves and Noncrossing Partitions

Motivated by Gauss's first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bounded components; its topology is determined by the combinatorial data of a noncrossing matching. Similarly, every complex polynomial gives rise to a related combinatorial object that we call a basketball, consisting of a pair of noncrossing matchings satisfying one additional constraint. We prove that every noncrossing matching arises from some harmonic curve, and deduce from this that every basketball arises from some polynomial.     

Establishing vicinal proton-proton connectivities using two-dimensional proton zero quantum coherence NMR

Phenanthro[3,4:3′,4′]phenanthro[2,1-b]thiophene ( 1 ) served as the model system to evaluate two-dimensional proton zero quantum coherence nmr in order to establish the vicinal proton-proton connectivities. The utility of the two-dimensional proton zero quantum nmr experiment has been compared with the utility of the traditional autocorrelated proton-proton (COSY) experiment. In the case of a molecule such as 1 , where the proton chemical shifts are so highly congested, the zero quantum coherence experiment provides data not obtainable from the COSY experiment.     

New reals: Can live with them,can live without them

We give a self‐contained proof of the preservation theorem for proper countable support iterations known as “tools‐preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)