Metric entropy of convex hulls in type spaces--The critical case

Given a precompact subset of a type Banach space , where , we prove that for every and all

holds, where is the absolutely convex hull of and denotes the dyadic entropy number. With this inequality we show in particular that for given and with for all the inequality holds true for all . We also prove that this estimate is asymptotically optimal whenever has no better type than . For this answers a question raised by Carl, Kyrezi, and Pajor which has been solved up to now only for the Hilbert space case by F. Gao.

     

Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario

We demonstrate the influence of vectorial coupling on the synchronization behavior of complex systems. We study two semiconductor lasers subject to delayed optical feedback which are unidirectionally coherently coupled via their optical fields. Our experimental and numerical results demonstrate a characteristic synchronization scenario in dependence on the relative feedback phase leading cyclically from chaos synchronization to almost uncorrelated states, and back to chaos synchronization. Finally, we reveal the influence of the feedback phase on the dynamics of the solitary delay system.     

The influence of hyperoxia on regional cerebral blood flow (rCBF), regional cerebral blood volume (rCBV) and cerebral blood flow velocity in the middle cerebral artery (CBFVMCA) in human volunteers

Conflicting results reported on the effects of hyperoxia on cerebral hemodynamics have been attributed mainly to methodical and species differences. In the present study contrast-enhanced magnetic resonance imaging (MRI) perfusion measurement was used to analyze the influence of hyperoxia (fraction of inspired oxygen (FiO2) = 1.0) on regional cerebral blood flow (rCBF) and regional cerebral blood volume (rCBV) in awake, normoventilating volunteers (n = 19). Furthermore, the experiment was repeated in 20 volunteers for transcranial Doppler sonography (TCD) measurement of cerebral blood flow velocity in the middle cerebral artery (CBFV(MCA)). When compared to normoxia (FiO2 = 0.21), hyperoxia heterogeneously influenced rCBV (4.95 +/- 0.02 to 12.87 +/- 0.08 mL/100g (FiO2 = 0.21) vs. 4.50 +/- 0.02 to 13.09 +/- 0.09 mL/100g (FiO2 = 1.0). In contrast, hyperoxia diminished rCBF in all regions (68.08 +/- 0.38 to 199.58 +/- 1.58 mL/100g/min (FiO2 = 0.21) vs. 58.63 +/- 0.32 to 175.16 +/- 1.51 mL/100g/min (FiO2 = 1.0)) except in parietal and left frontal gray matter. CBFV(MCA) remained unchanged regardless of the inspired oxygen fraction (62 +/- 9 cm/s (FiO2 = 0.21) vs. 64 +/- 8 cm/s (FiO2 = 1.0)). Finding CBFV(MCA) unchanged during hyperoxia is consistent with the present study's unchanged rCBF in parietal and left frontal gray matter. In these fronto-parietal regions predominantly fed by the middle cerebral artery, the vasoconstrictor effect of oxygen was probably counteracted by increased perfusion of foci of neuronal activity controlling general behavior and arousal.     

Conversion of a head-mounted microphone signal intocalibrated SPL units

A method is reviewed for conversion of a microphone signal into calibrated Sound Pressure Level (SPL) units. The method follows American National Standards Institute (ANSI) standard for S1.4 SPL meters and requires an accurate SPL meter and an accurate calibration sound source for conversion. Accuracy and validation data from test signals and human phonation are provided. The results indicate that under typical speech conditions, an absolute accuracy of plus or minus 1.6 dB (type I SPL meter) can be obtained with a miniature head-mounted microphone.     

Verification of X-ray line coincidences by high-resolution spectroscopy

Photo-resonant pumping of X-ray lasers requires close coincidence of a strong emission line with a suitable absorbing transition. We use a high-resolution crystal spectrometer to verify five coincidences, one of which has apparently not yet appeared in published work. All but one of the coincidences are found to lie within one linewidth. With respect to X-ray laser photo-pumping three of the five coincidences seem to be promising candidates.     

On the theory of impurities in a lattice of magnetic ions: Crystalline field effects

We present a formalism for treating the problem of impurities in a lattice of magnetic rare earth ions. Latter are subject to a crystalline field and special attention is paid to non-Kramers ions in a singlet ground state. Our calculations are restricted to the paramagnetic regime. We derive the conditions for magnetic localized modes to occur and discuss the appearance of local magnetic instabilities. It is shown that the impurity effects are especially large if the system is close to a magnetic phase transition. Furthermore we compute the influence of impurities on the magnetic transition temperature. For the case of vacancies or nonmagnetic impurities the dependence of the Curie temperature on impurity concentration is derived. It is demonstrated that small amounts of impurities can often completely suppress magnetic ordering.     

A theoretical study on the formation of EX4+ and E2X5+(E = P, As; X = Br, I) from Ag+ and EX3/X2

The mechanism and the thermodynamics of the formation of EX2+, EX4+ and E2X5+ (E = As, P; X = Br, I) was carefully analyzed with MP2/TZVPP calculations and inclusion of entropy and solvation effects (COSMO model approximating CH2Cl2). Thus, as likely intermediates the complexes of Ag+ and one or two EX3 as well as EX3/X2 were optimized. The global minimum isomers of the Ag(EX3)2+ intermediates were found to be P-coordinated Ag(PI3)2+ and (BrPBr2)Ag(PBr3)+ but exclusively halogen coordinated Ag(X2AsX)2+ complexes. Similarly complicated is the situation for the Ag(EX3)(X2)+ intermediates: (I3E)Ag(I2)+, (BrAsBr2)Ag(Br2)+ and (Br3P)(Br-Br)Ag+ complexes were found to be the global minima. Based on all available results likely mechanisms for the formation of the known PX4+, AsBr4+, P2X5+ salts (X = Br, I) from these intermediates were proposed. An explanation for the failure to prepare an AsI4+ salt is also given.     

Noncoordinating Anions—Fact or Fiction? A Survey of Likely Candidates

Is there anything resembling a truly noncoordinating anion? Would it not be great to be able to prepare any crazy, beautiful, or simply useful cationic species that one has in mind, or has detected by mass spectroscopy? In condensed phases the target cation has to be partnered with a suitable counteranion. This is the moment when difficulties arise and many wonderful ideas end in the sink owing to coordination or decomposition of the anion. However, maybe these counteranion problems can be overcome by one of the new weakly coordinating anions (WCAs). Herein is an overview on the available candidates in the quest for the least coordinating anion and a summary of new applications, available starting materials, and general strategies to introduce a WCA into a system. Some of the unusual properties of WCA salts such as high solubility in low dielectric media, pseudo gas‐phase conditions in condensed phases, and the stabilization of weakly bound and low‐charged complexes are rationalized on thermodynamic grounds. Limits of the WCAs, that is, anion coordination and decomposition, are shown and a quantum chemical analysis of all types of WCAs is presented which allows the choice of a particular WCA to be based on quantative data from a wide range of different anions.