Generalized-hypergeometric solutions of the biconfluent Heun equation

The Ramanujan Journal - Infinitely many cases for which two independent fundamental solutions of the biconfluent Heun equation can each be presented as an irreducible linear combination of two...     

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.     

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     

Quantization of Poisson pencils and generalized lie algebras

We describe two types of Poisson pencils generated by a linear bracket and a quadratic one arising from a classical R-matrix. A quantization scheme is discussed for each. The quantum algebras are represented as the enveloping algebras of generalized Lie algebras.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 3, pp. 476–488, June, 1995.     

Self-dual Yang-Mills fields ind=4 and integrable systems in 1≤d≤3

The Ward correspondence between self-dual Yang-Mills fields and holomorphic vector bundles is used to develop a method for reducing the Lax pair for the self-duality equations of the Yang-Mills model ind=4 with respect to the action of continuous symmetry groups. It is well known that reductions of the self-duality equations lead to systems of nonlinear differential equations in dimension 1d3. For the integration of the reduced equations, it is necessary to find a Lax pair whose compatibility conditions is these equations. The method makes it possible to obtain systematically a Lax representation for the reduced self-duality equations. This is illustrated by a large number of examples.N. N. Bogolyubov Theoretical Physics Laboratory, JINR, 141980 Dubna, Russia. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 3, pp. 384–419, March, 1995.     

Boundary-value problem for the two-dimensional stationary heisenberg magnet with nontrivial background. II

The investigation of the boundary-value problem on a half-plane for the two-dimensional stationary Heisenberg magnet is continued. The asymptotic behavior of N-soliton solutions is discussed. The asymptotic contribution of the continuous spectrum is calculated. The gauge equivalence of the boundary-value problems for the models of a magnet and the elliptic equation represented by the sinh—Gordon equation is considered.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 3, pp. 513–529, September, 1995.     

A Ramification Formula for Poincare Series, and a Hyperplane Formula for Modular Invariants

Let (A) be the coefficient of the second term in the Laurentexpansion about T 1 of the Poincare series p(A, t) of a gradedring A. For a finite extension of integrally closed domains,we prove a formula relating if (B), if (A) and the differentialexponent of B over A. As an application, we prove a conjectureof Carlisle and Kropholler which computes for rings of modularinvariants of finite groups in terms of stabilizers of hyperplanes.     

On some boundary value problems with integral conditions for functional differential equations

For the functional differential equationu ⁽ⁿ⁾ (t)=f(u)(t) we have established the sufficient conditions for solvability and unique solvability of the boundary value problems $$u^{(i)} (0) = c_i (i = 0,...,m - 1), \smallint _0^{ + \infty } |u^{(m)} (t)|^2 dt< + \infty $$ and $$\begin{gathered} u^{(i)} (0) = c_i (i = 0),...,m - 1, \hfill \\ \smallint _0^{ + \infty } t^{2j} |u^{(j)} (t)|^2 dt< + \infty (j = 0,...,m), \hfill \\ \end{gathered} $$ wheren≥2,m is the integer part of $\tfrac{n}{2}$ ,c _i ∈R, andf is the continuous operator acting from the space of (n?1)-times continuously differentiable functions given on an interval [0,+∞] into the space of locally Lebesgue integrable functions.