Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators A_j on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.     

Dynamics of the periodic type-K competitive Kolmogorov systems

For time-periodic dissipative and irreducible type-K competitive Kolmogorov systems, it is proved that there is a canonically defined countable family F of unordered, disjoint invariant sets with the property that, for every persistent trajectory whose ω-limit set is not a cycle, there exists a unique trajectory in some element of F such that these two trajectories are asymptotic and the corresponding points in these two trajectories are K-related.     

Optimal detection of crack echo families in elastic solids

Optimal detection of a striplike crack residing in an isotropic elastic solid with coarse microstructure by means of ultrasonic nondestructive evaluation (NDE) is considered. A physics-based approach to derive an optimal detector, which achieves the theoretical limitations constrained by the underlying physics, is presented. State-of-the-art physical models of crack echoes and of stochastic backscattering from the material structure in elastic solids are introduced and unified with the theory of optimal detection to yield a practically useful nonlinear filter bank implementation of the optimal detector. Monte Carlo simulations of the detection performance for the special case of a striplike crack with uncertain angular orientation are presented in the form of receiver operating characteristics (ROCs). These new results represent the physical limitations for detecting a crack under the stated conditions and serve as performance bounds to which other detectors should be compared. A physics-based generalized likelihood ratio (GLR) detector, which relies on the same nonlinear filter bank as the optimal detector, is also presented for the special case of a striplike crack. A comparison between the optimal and the GLR detectors shows that the GLR detector only slightly reduces the performance.     

Interference and interactions in mesoscopic rings

We consider a mesoscopic ring connected to external reservoirs by tunnel junctions. The ring is capacitively coupled to an external gate electrode and may be pierced by a magnetic field. Due to strong electron–electron interactions within the ring the conductance shows Coulomb blockade oscillations as a function of the gate voltage, while Aharonov–Bohm interference effects lead to a dependence on the magnetic flux. The Hamiltonian of the ring is given by a Luttinger model that allows for an exact treatment of both interaction and interference effects. We conclude that the positions of conductance maxima as a function the external parameters can be used to determine the interaction parameter , and the shapes of conductance peaks are strongly affected by electron correlations within the ring.     

Thiol–ene coupling reaction of fatty acid monomers

The reactivities and reaction rates of the thiol–ene coupling reaction of 2‐ethyl‐(hydroxymethyl)‐1,3‐propanediol trimercapto acetate and 2‐ethyl‐(hydroxymethyl)‐1,3‐propanediol trimercapto propionate with two common unsaturated fatty acid methyl esters (methyl oleate and methyl linoleate) were evaluated. The reactions were monitored with real‐time IR and ¹H NMR, which both showed that the mercapto acetate was more reactive than the mercapto propionate. Both thiols were more prone to add to the monounsaturated methyl oleate than to methyl linoleate, which contained two unconjugated double bonds. According to bond energy calculations, the thiol hydrogen of mercapto acetate was somewhat more difficult to abstract than the hydrogen of mercapto propionate. Consequently, the formed S? C bond in the acetate case was stronger than in the propionate case, and so the equilibrium was more shifted toward the addition products. The real‐time IR measurements also showed that the cis unsaturation in methyl oleate isomerized much more quickly than that in methyl linoleate, and this also had an impact on the overall addition rate of the thiols because a trans unsaturation was more reactive than a cis unsaturation. The higher isomerization rates in the oleate systems, compared with those of the linoleate systems, was suggested to be due to a more restricted rotation along the C? C bond of the reacted unsaturation in linoleate. This study showed the importance of trans unsaturations in obtaining reasonable reaction rates in thiol–ene reactions with fatty acid derivatives. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6346–6352, 2004     

Microwave-enhanced and metal-catalyzed functionalizations of the 4-aryl-dihydropyrimidone template

Progress in organometallic catalysis and recent advancements in the development of carbonylative reaction protocols without direct use of carbon monoxide have been utilized for efficient functionalizations of 4-aryl-dihydropyrimidone structures. The use of modern microwave technology enabled both high reaction rates and convenient handling. Examples of palladium-catalyzed cross-couplings, Heck reactions, amino- and alkoxycarbonylations, and direct N-amidations of 4-(bromophenyl)-dihydropyrimidones were performed. Further, the first N3-arylations of the dihydropyrimidone ring system were successfully completed using the copper-catalyzed Goldberg reaction. Altogether, these protocols provide new tools for rapid generation of novel and diverse dihydropyrimidone derivatives.     

Microstructural prototyping of ceramics by kinetic engineering: applications of spark plasma sintering

The significance of kinetics on the development of microstructures in connection with sintering of ceramics is well recognized. In practice, however, it still remains a challenge to prepare designed microstructures via engineering the sintering kinetics because of an insufficient understanding of the different operative mechanisms that are in many cases overlapping. In this article the kinetic issues involved in sintering are described and discussed with respect to their potential for prototyping microstructures that yield desired properties. By exploiting and mastering the differences present in the kinetics of grain sliding, densification, chemical reactions, and grain growth, respectively, we have established processing principles for producing bulk ceramics with microstructures consisting of nano-sized grains, aligned grains, and/or non-equilibrium-phase constitutions, and for achieving radically improved superplasticity in brittle ceramics. Although the studies quoted in this article were mainly carried out by spark plasma sintering, more general implications of them are expected, including efficient particle sliding, deformation-induced dynamic ripening, superplastic deformation-induced dynamic ripening, and non-equilibrium integration.     

Scanning tunneling spectroscopy of Cl vacancies in NaCl films: strong electron-phonon coupling in double-barrier tunneling junctions

Broad Gaussian line shapes are observed in scanning tunneling spectroscopy of single, localized electronic states induced by Cl vacancies in ultrathin NaCl films on Cu surfaces. Using a simple inelastic resonance tunneling model, we show that the observed broad line shapes are caused by a strong coupling between the localized state and the optical phonons in the film. The parameters for the model are obtained from density functional calculations, in which the occupation of the vacancy state temporarily taking place in the experiment has also been accounted for.