Opposed flow oxy-flame synthesis of carbon and oxide nanostructures on molybdenum probes

The formation of carbon and metal-oxide nanostructures on molybdenum probes inserted in a counter-flow oxy-fuel flame is studied experimentally. Flame position and probe diameter were varied to achieve a controlled growth of carbon and metal-oxide nanostructures at fuel and oxygen-rich flame zones. Mo probes of 1-mm diameter were introduced in the flame at various heights, starting from the upper hydrocarbon-rich zone on the fuel side of the flame to the oxygen-rich zone on the oxidizer side. High density layers of carbon nanocoils (CNCs) and filamentous structures containing ribbon shapes and straight nanofibers were formed in the upper hydrocarbon-rich flame zone. The formation of carbon micro-trees was observed on the fuel side closer to the flame front. The structures formed in the oxidizer part of the flame were composed of molybdenum-oxides. MoO₂ micron-sized channel structures were formed on the oxidizer side in the vicinity of the flame front. The micro-channels had rectangular and square-framed shapes; they were completely hollow, closed, and semi-open with a small circular cavity at their tips. The application of probes with diameters of 0.75 and 0.25 mm resulted in the formation of spectacular 3-D structures with unique and distinct morphologies.     

Complex Padé approximant operators for wide-angle beam propagation

The conventional rational Hadley(m, n) approximant of wide-angle beam propagator based on real Padé approximant operators incorrectly propagates the evanescent modes. In order to overcome this problem, two complex Padé approximants of wide-angle beam propagator are presented in this paper. The complex propagators of the first approach are obtained by using the same recurrence formula from the scalar Helmholtz equation of the conventional approximant method with a different initial value while those of the second method derived from Hadley(m, n) approximant of a square-root operator that has been rotated in the complex plane. These resulting approaches allow more accurate approximations to the Helmholtz equation than the well-known real Padé approximant. Furthermore, our proposed complex Padé approximant operators give the evanescent modes the desired damping.     

Spectrum of signals

Finite-energy high frequency signals, band-pass frequency signals, and band-stop frequency signals are characterized.     

Applications of vinylogous Mannich reactions. Total syntheses of the Ergot alkaloids rugulovasines A and B and setoclavine.

Concise syntheses of the Ergot alkaloids rugulovasine A (3a), rugulovasine B (3b), and setoclavine (2) have been completed by strategies that feature inter- and intramolecular vinylogous Mannich reactions as the key steps. Thus, the first synthesis of 3a,b commenced with the conversion of the known indole 17 into 24 via the addition of the furan 22 to the iminium ion 21, which was generated in situ from the aldehyde 19. Cyclization of 24 by a novel S(RN)1 reaction followed by removal of the N-benzyl group furnished a mixture (1:2) of 3a and 3b. In an alternative approach to these alkaloids, the biaryl 35 was reduced with DIBAL-H to give an intermediate imine that underwent spontaneous cyclization via an intramolecular vinylogous Mannich addition to provide 36a,b. N-Methylation of the derived benzyl carbamates 37a,b followed by global deprotection gave a mixture (2:1) of rugulovasines A and B (3a,b). Setoclavine (2) was then prepared from the biaryl 41 using a closely related intramolecular vinylogous Mannich reaction to furnish the spirocyclic lactones 42a,b. These lactones were subsequently transformed by hydride reduction and reductive methylation into the ergoline derivatives 43a,b, which were in turn converted into 2 by deprotection and solvolytic 1,3-rearrangement of the allylic hydroxyl group.     

Perfect matchings in balanced hypergraphs

We generalize Hall's condition for the existence of a perfect matching in a bipartite graph, to balanced hypergraphs.This work was partially supported in part by NSF grants DMI-9424348, DMS-9509581 and ONR grant N00014-89-J-1063. Ajai Kapoor was also supported by a grant from Gruppo Nazionale Delle Riccerche-CNR. Finally, we acknowledge the support of Laboratiore ARTEMIS, Université Joseph Fourier, Grenoble.     

Complete reduction of fermion-antifermion Bethe-Salpeter equation with static kernel. II

Recent work with the Bethe-Salpeter (BS) equation for a $\text{spin}\text{-}\text{1}\text{2}$ fermion-antifermion system is developed further and extended in a number of ways. Static kernels are considered, as previously, but in the present case, the structure of the kernels serves to suppress completely all pair terms. The reduction of the 16 coupled integro-differential equations involving the BS bispinor wavefunctions can be carried out much more simply than before. The effective Hamiltonians of the eigenvalue equations which result for single scalar and vector wavefunctions are not only in formally closed operator form, correct to all orders in the coupling constant and $\text{v}\text{c}$, but have an explicit and simple structure. They depend at most linearly on the static potential, and also on powers of momentum and simple functions of the relativistic free-particle energies.Previous work is further generalized by the consideration of static four-vector interactions (vector gluons or photons) in an arbitrary “gauge” for equal mass particles and antiparticles on the one hand, and the fourth (scalar) component of a vector potential for unequal mass particle and antiparticle on the other hand, the latter in order to study the mass dependence of the effective interactions and of the wavefunctions.Spin-orbit, spin-spin, and tensor interactions are expected to arise from the Breit-like four-vector interactions in conventional $\text{v}\text{c}$ expansions, but the present results are correct to all orders in $\text{v}\text{c}$. Furthermore, such types of interactions also arise, as previously, for the case of a Coulomb-like potential, for which they are not, at first guess, expected. In the unequal mass case, an interesting new type of effective tensor interaction is also generated which serves to mix triplet and singlet states.Various special “gauges” are considered in the equal mass case. The general structure of the BS amplitude is also discussed, and specifically developed in some detail in perturbation theory for the ground state of positronium.While the current work should be considered as a general examination of the properties of a large class of BS equations of the Coulomb-Dirac or Breit-type, two areas for specific applications immediately come to mind: the calculation of positronium energy levels to very high order and the study of quark-antiquark binding involving both like and unlike quarks.     

Thermal analysis of water at x- and a-type zeolites

The nature of the sorbed water has been examined by differential scanning calormetry and effluent gas analysis at the zeolites of the types X and A, with univalent and bivalent cations. p]The desorption heats depending on the coverage and the cation form of zeolite have been determined. All these experiments point to the existence of only one general desorption mechanism independent of the ion-exchanging cation. The nature of the sorbed water is discussed.