The crystal structure of eudesma-4(15),7(11)-dien-8α, 12-olide: a sesquiterpene lactone fromTrattinickia rhoifolia Willd

The title compound, formula C₁₅H₂₀O₂, is orthorhombic, P2₁2₁2₁ witha=8.747(2),b=12.025(3),c=12.554(3)Å,Z=4, andD _m =1.32(2)g/ml. The structural analysis shows that the compound corresponds to eudesma-4(15),7(11)-dien-8,12-olide, a sesquiterpene lactone previously isolated fromAster umbellatus but whose crystal structure was unknown.     

Equational compactness of bi-frames and projection algebras

We generalize D. Kelly's and K. A. Nauryzbaev's results of 1-variable and 2-variable equational compactness of complete distributive lattices satisfying the infinite distributive law and its dual (bi-frames) to objects similar to monadic algebras (which we will callprojection algebras). This will lead us in particular to an example of bi-frame that is not 3-variable equationally compact, even forcountable equation systems, thus solving a problem of G. Grätzer. This example is realized as a certain complete sublattice of the complete Boolean algebra of regular open subsets of some Polish space.Presented by M. Henriksen.     

An experimental investigation of the sources of propeller noise due to the ingestion of turbulence at low speeds

Noise radiation from a four bladed, 10 in. diameter propeller operating in air at a rotational speed of 3000 RPM and a freestream velocity of 33 ft/s was experimentally analyzed using hot-wire and microphone measurements in an anechoic wind tunnel. Turbulence levels from 0.2 to 5.5% at the propeller location were generated by square-mesh grids upstream of the propeller. Autobicoherence measurements behind the blade trailing edges near the hub and tip showed regions of high phase-coherence between the blade-passage harmonics and the broadband frequencies. Inflow turbulence reduced this coherence. By relating the fluctuation velocities in the propeller wake to the unsteady blade forces, the primary regions of tonal noise generation have been identified as the hub and tip regions, while the midspan has been identified as a region responsible for broadband noise generation. These measurements were complimented by cross-spectra between the propeller wake-flow and the measured sound. The effect of turbulence on the radiated noise level showed an overall increase of 2 dB in the broadband levels for every 1% increase in turbulence. This effect varied for different frequency bands in the acoustic spectrum.List of Symbols b ² (f _k, f _l) Bicoherence - B (k, l) Bispectrum - B Number of Blades - c Speed of Sound - C _T Thrust coefficient=T/n ²D⁴ - D Propeller diameter - E [ ] Expected value - f Frequency, Hz - G _xx (f) One sided autospectral density function. - G _xy (f) One sided cross-spectral density function - J Advance ratio, J=U/nD - j, k Fourier component indices - m Grid mesh length - M _o Rotational mach number at a radial location M _o =2nr/a _o - M _c Axial convection mach number - n Rotational speed, revolutions per second - r Propeller radial location - R Propeller radius - R _e Reynolds number - T Propeller thrust - U Freestream velocity - U _i Induced axial velocity from propeller - u, w RMS of fluctuating velocity, u=(U–u)² - X(f) Fourier transform of x(t) Symbols _xy ^/2 (f) Coherence function, - Observer angle, measured from propeller thrust direction - _f Longitudinal Eulerian dissipation length scale - _f Longitudinal Eulerian integral length scale - Air density - Blade azimuthal location This research was performed at the Hessert Center for Aerospace Research, Department of Aerospace and Mechanical Engineering, University of Notre Dame, and was sponsored by the U.S. Navy, Office of Naval Research, Arlington, Virginia under Contract No. N00014-89-J-1783. The authors would like to thank the program manager, and technical manager, Dr. E. P. Rood. The authors would also like to thank Dr. William Blake of the David Taylor Research Center and Dr. Flint O. Thomas and Dr. Huang-Chang Chu of Notre Dame for their help and comments at various stages of this research     

Recognition of partially overlapped particle images using the Kohonen neural network

A neural network is proposed for the recognition of partially overlapped particle images in the analysis of Particle Tracking Velocimetry (PTV) frames. The Kohonen neural network is an approximation to an optimum classifier. In this work it allows single particle images to be distinguished from overlapped particle images by shape analysis: it classifies 99.1% of the spots correctly (in test images). If a spot has an almost circular shape, the barycenter co-ordinates are extracted. If the spot shape is far from being circular, it is believed to be a particle overlap, and a procedure to find more centroids is activated.The particle recognizer based on the Kohonen neural network is tested on both multi-exposed and single-exposure images at high particle density, and compared to a particle recognizer that did not consider the partial overlap. The management of overlapped particles causes the neural network to produce a big improvement in the number of barycenters that can be extracted from these images. The practical consequence is that the seeding density in PTV can be increased, so as to improve the spatial resolution of the technique in the velocity field calculation.Marcello Sallusti and Paolo Monti produced the synthetic PTV images that were used in this project. Gianni Leuzzi helped clearing the statistic properties of the neural network through infinite discussions. We would like to thank them all, since we are aware that they all gave a decisive contribute to the project.     

Method for symmetrization and estimation of solutions of the Neumann problem for the equation of a porous medium in domains with noncompact boundary for infinitely increasing time

We consider the initial boundary-value Neumann problem for the equation of a porous medium in a domain with noncompact boundary. By using a symmetrization method, we obtain exactL _p-estimates, 1p, for solutions as t.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 147–157, February, 1995.     

Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes

Summary We introduce a new Skorohod topology for functions of several variables. Since ann-variable function may be viewed as a one-variable function with values in the set of (n–1)-variable functions, this topology is defined by induction from the classical Skorohod topology for one-variable functions. This allows us to define the notion of completen-parameter symmetric Markov processes: Such processes are, for any 1pn, rawp-parameter Markov processes (in the sense of our previous paper [17]) with values in the space of (n–p)-variable functions. We prove, for these processes and their Bochner subordinates, a maximal inequality which implies the continuity of additive functionals associated with finite energy measures. We finally present several important examples.     

Classification of polynomial translation hypersurfaces of finite type

In this paper we prove that any hypersurface in Eⁿ⁺¹ of the form where P ₁ is a polynomial of degree ≥2 and P ₂, ... , P _n are functions such that P _i ^′ P _i ^″ = 0 somewhere for all i = 2, ... , n, is of infinite type. As a consequence, we deduce that a polynomial translation hypersurface in Eⁿ⁺¹, i. e. a hypersurface of the above form where P ₁, ... , P _n are polynomials, is of finite type if and only if it is a hyperplane. This provides some partial solutions to a problem of B. Y. Chen [C3].     

Ground-state energy of a quantum chain with competing interactions

We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of =/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.