Toeplitz Operators with Special Symbols on Segal-Bargmann Spaces

We study the boundedness of Toeplitz operators on Segal-Bargmann spaces in various contexts. Using Gutzmer's formula as the main tool we identify symbols for which the Toeplitz operators correspond to Fourier multipliers on the underlying groups. The spaces considered include Fock spaces, Hermite and twisted Bergman spaces and Segal-Bargmann spaces associated to Riemannian symmetric spaces of compact type.

Irreversibility line and the hierarchy of weak links in Bi2Sr2CaCu2O8+?

The irreversibility line for H?c in a single crystal specimen of Bi2Sr2CaCu2O8+? (Bi2212) has been determined via vanishing of hysteresis in isothermal dc magnetization measurements. The hysteresis loops (H?c) in Bi2212 appear to show signatures of two-component magnetic response in several temperature regions where the temperature dependence of irreversibility field charges sharply. It is proposed that the observed behavior may be a consequence of existence of weak links of varying strength in Bi2212

A template-free, combustion-chemical route to macroporous nickel monoliths displaying a hierarchy of pore sizes

Recently, we demonstrated a very general route to monolithic macroporous materials prepared without the use of templates (Rajamathi et al. J. Mater. Chem. 2001, 11, 2489). The route involves finding a precursor containing two metals, A and B, whose oxides are largely immiscible. Firing of the precursor followed by suitable sintering results in a monolith from which one of the oxide phases can be chemically leached out to yield a macroporous mass of the other oxide phase. The metals A and B that we employed in the demonstration were Ni and Zn. From the NiO-ZnO monolith that was obtained by decomposing the precursor, ZnO could be leached out at high pH to yield macroporous NiO. In the present work, we show that combustion-chemical (also called self-propagating) decomposition of a mixture of Ni and Zn nitrates with urea as a fuel yields an intimate mixture of the oxides that can be sintered and leached with alkali to form a macroporous NiO monolith. The new process that we present here thereby avoids the need for a crystalline single-source precursor. A novel and unanticipated aspect of the present work is that the combination of high temperatures and rapid quenching associated with combustion synthesis results in an intimate mixture of wurtzite ZnO and the metastable rock-salt Ni1-xZnxO where x is about 0.3. Leaching this monolith with alkali gives a macroporous mass of rock-salt Ni1-xZnxO, which upon reduction in H-2/Ar forms macroporous Ni and ZnO. There are thus two stages in the process that lead to two modes of pore formation. The first is associated with leaching of ZnO by alkali. The second is associated with the reduction of porous Ni1-xZnxO to give porous Ni and ZnO.

Special Issue: Engineering applications of representations of function, Part 1

In engineering design, the end goal is the creation of an artifact, product, system, or process that fulfills some functional requirements at some desired level of performance. As such, knowledge of functionality is essential in a wide variety of tasks in engineering activities, including modeling, generation, modification, visualization, explanation, evaluation, diagnosis, and repair of these artifacts and processes. A formal representation of functionality is essential for supporting any of these activities on computers. The goal of Parts 1 and 2 of this Special Issue is to bring together the state of knowledge of representing functionality in engineering applications from both the engineering and the artificial intelligence (AI) research communities.