Spectral theory and L∞-time decay estimates for Klein–Gordon equations on two half axes with transmission: The tunnel effect

Consider two copies N₁, N₂ of the interval [0, ∞]. Consider Klein-Gordon equations with (different) constant coefficients on ? × N_j ( = time × space). Assume the coincidence of the values of the solution at the boundary points of the N_j for all times and a transmission condition relating its first (one-sided) space derivatives at these points. Under a symmetry condition, we extend the spatial part of the equation and the transmission conditions to a self-adjoint operator (by Friedrichs extension) and reformulate our problem in terms of an abstract wave equation in a suitable Hilbert space. We derive an expansion of the solution in generalized eigenfunctions of this self-adjoint extension and show, that the L^∞-norms (in space) of the solution and its first k space derivatives at the time t decay for t → ∞ at least as const. t^¼, if the initial conditions satisfy a compatibility condition of order k derived in this paper. The loss of decay rate in comparison with the full line case (const. t^?½, cf. [28]) is caused by the tunnel effect. Further we show that an abstract wave equation in a Hilbert space with a Friedrichs extension as spatial part can always be derived from a stationarity principle for an associated action-type functional. This yields a physical legitimation of our model by the principle of stationary action and moreover a criterion for the physical interpretability of all models created by the linear interaction concept [4, 6, 8, 10], in particular for the coupling of media of different dimension (alternative to [13, 16] for similar models).     

Synthesis and photophysical properties of fluorescent 2-aryl-1,3-dialkylbenzimidazolium ions and a l-alkyl-2-arylbenzimidazole with excited state intramolecular proton-transfer

To improve the solubility, photostability and fluorescence quantum yield (Φ) of 2-arylbenzimidazolium ions the N-1 hydrogen was replaced by an alkyl group before N-3 was quatemized; this substitution did not reduce Φ, proving the absence of steric inhibition to attainment of coplanarity in the excited state. A related symmetrical 2,2′-arylenebis(1,3-dimethyldibenzimidazolium ion) had Φ = 0.86. The related 2,5-bis(1-methyl-2-benzimidazolyl)phenol had Φ = 0.38 at 22° as well as a very large Stokes' shift due to proton-transfer. These findings supported a new insight into the electron distribution of the first excited singlet state of oligophenylenes. The compounds are of interest as laser dyes and scintillation fluors.     

Compact WLAN disc antennas

A novel conical beam patch antenna design, suitable for local area network applications, uses a central cylindrical connection from the disc to ground to achieve a large reduction in resonant size. Results on efficiency, bandwidth, and pattern are reported for several prototypes.     

Dynamic bandwidth allocation for quality-of-service over Ethernet PONs

Ethernet-based passive optical network (EPON) technology is being considered as a promising solution for next-generation broadband access networks due to the convergence of low-cost Ethernet equipment and low-cost fiber infrastructures. A major feature for this new architecture is the use of a shared transmission media between all users; hence, medium access control arbitration mechanisms are essential for the successful implementation of EPON: i.e., to ensure a contention-free transmission and provide end users with equal access to the shared media. We propose to use the multipoint control protocol defined by the IEEE 802.3ah task force to arbitrate the transmission of different users, and we present different dynamic bandwidth allocation (DBA) algorithms to allocate bandwidths effectively and fairly between end users. These DBA algorithms are also augmented to support differentiated services, a crucial requirement for a converged broadband access network with heterogeneous traffic. We show that queueing delays under strict bandwidth allocation algorithms result in an unexpected behavior for certain traffic classes, and we suggest the use of DBA with appropriate local queue management to alleviate this inappropriate behavior. We conduct detailed simulation experiments to study the performance and validate the effectiveness of the proposed protocols.     

A novel silicon Schottky diode for NLTL applications

The design and simulation of a novel silicon Schottky diode for nonlinear transmission line (NLTL) applications is discussed in this paper. The Schottky diode was fabricated on a novel silicon-on-silicide-on-insulator (SSOI) substrate for minimized series resistance. Ion implantation technology was used as a low-cost alternative to molecular beam epitaxy to approximate the delta (/spl delta/) doping profile, which results in strong nonlinear CV characteristics. The equivalent circuit model of the Schottky diode under reverse bias conditions was extracted from the S-parameter measurement performed on the diode. The measured CV characteristics show strong nonlinearity, the junction capacitance varies from 182 to 47.5 fF as the reverse bias voltage is varied from 0 to -5 V. A parasitic inductance of 40 pH was measured for the silicon Schottky diode, which is much smaller than a comparable sized GaAs Schottky diode. This small inductance is an advantage for the silicon Schottky diode offering improvement in the silicon NLTL performance.     

Spectroscopic studies of biologically active organotin(IV) derivatives of 2-[N-(2,4,6-tribromophenylamido]propanoic acid

Herein we describe the synthesis and characterization of compounds having the formulae R₂SnL₂ and R₃SnL, where R = Me, n-Bu, Ph and n-Oct and L = 2-[N-(2,4,6-tribromophenylamido]propanoic acid. All the complexes have been characterized by various spectroscopic methods (IR and ¹H, ¹³C, ¹¹⁹Sn NMR), elemental analysis, mass spectrometry and physical data. These compounds were also screened for their biological activity and found some encouraging results.     

Trichloroisocyanuric acid as a novel oxidizing agent for the oxidation of 1,3,5-trisubstituted pyrazolines under both heterogeneous and solvent free conditions

Trichloroisocyanuric acid is used as an effective oxidizing agent for the oxidation of 1,3,5-trisubstituted pyrazolines to their corresponding pyrazoles under both heterogeneous and also solvent free conditions with good yields at room temperature.     

1,1‐Organoboration of bis(trimethylstannyl)ethyne with trimethylsilyl‐ and dimethylsilyl‐dialkylboryl‐substituted alkenes: organometallic‐substituted allenes

The reactions of bis(trimethylstannyl)ethyne, Me₃Sn–C?C–SnMe₃ ( 4 ), with trimethylsilyl‐ or dimethylsilyl‐dialkylboryl‐substituted alkenes 1 – 3 afford organometallic‐substituted allenes 5 , 6 and 8 , 9 in high yield. In the case of (E)‐2‐trimethylsilyl‐3‐diethylboryl‐2‐pentene ( 1) , a butadiene derivative 7 could be detected as an intermediate prior to rearrangement into the allene. All reactions were monitored by ²⁹Si and ¹¹⁹Sn NMR, and the products were characterized by an extensive NMR data set (¹H, ¹¹B, ¹³C, ²⁹Si, ¹¹⁹Sn NMR). Copyright © 2003 John Wiley & Sons, Ltd.