Vibro-acoustic noise control treatments for payload bays of launch vehicles: Discrete to fuzzy solutions

Sound transmitted through an enclosing structure into a cavity has been minimised by optimising the locations, numbers and properties of tuned mass dampers placed on the structure and Helmholtz resonators placed in the cavity. Most of the results presented in the literature show the effect of a few well selected acoustic or vibration absorbers on simple vibro-acoustic systems, whereas the results presented here indicate the trends that occur when a few absorbers are replaced by a large number. The results indicate that for low numbers of absorbers, the result of the optimal configuration is to reduce the response of discrete modes, and for a large number of absorbers the result of the optimal configuration is a tendency for the vibro-acoustic energy to be smeared over a range of frequencies, which is similar to the results seen in fuzzy structures. The enormous computational task was achieved using a distributed computing network and an asynchronous parallel genetic algorithm.     

Consistency of field equations in “Self-Creation” cosmologies

It is pointed out that the field equations in one of Barber's two self-creation cosmologies are not only in disagreement with experiment, but are actually inconsistent, in general. The construction of consistent general relativistic field equations involving field variables, such as, without invoking Lagrangian techniques, requires careful checking that sufficient functional freedom has been provided so as to produce a consistent set of equations.     

Magneto-optical study of shallow donors in transmutation-doped GaAs

Lineshapes and peak positions of 1s→2p^?1, donor transitions in epitaxial GaAs samples of relatively low compensation have been studied as functions of magnetic field by use of photoconductivity measurements. Some of these samples were produced by transmutation doping using thermal neutrons—a method which is useful for the controlled introduction of donor impurities in GaAs. Two new effects, tentatively attributed to van der Waals interactions between neutral donor atoms, are observed: (1) although both Se and Ge donors are introduced by thermal neutron transmutation, the Se line is much broader than the Ge line, and (2) deviations from isolated-donor behavior occur in the magnetic field dependence of the chemical shift of the shallowest donor present. The separation of lines from two deeper donors, Ge and Si, verified the simple phenomenological theory of the magnetic field dependence of central cell corrections of isolated donors up to at least 10T.     

Macrolide antibiotics—VIII The absolute configuration of certain centers in neomethymycin, erythromycin and related antibiotics

Neomethymycin (I) has been transformed into “anhydrocycloneomethynolide” (V) which could be degraded via (−)--methyllevulinic acid to (−)--methylsuccinic acid, thus establishing the absolute configuration of positions 4 and 6 in the lactonic acid (XIII). This acid is a common degradation product of methymycin, neomethymycin, pikromycin and narbomycin and there is thus available a standard of absolute configuration for these macrolide antibiotics. By a different sequence of reactions, erythromycin (XXIII) has been converted into (+)--methyllevulinic acid and (+)--methylsuccinic acid. Coupled with earlier results reported in the literature, it is now possible to assign absolute configurations to positions 10 (R) and 8 (R) of erythromycin and this applies most likely also to positions 4 (R) and 2 (S). Attention is called to the biogenetic significance of these observations.     

Aortic elastin fluorescence afterin vivo labeling with Congo red

Congo red (CR) is an azo dye which not only preferentially binds to elastin, an extracellular matrix protein found in the media of arterial vessel walls, but also fluoresces when it binds to this protein. Protein solubilization data following laser irradiation of elastin:CR suspensions determined that the amount of elastin solubilized by laser irradiation increased with the increase in CR. The saturation point of CR to elastin was attained when 400 g CR was added to 20 mg elastin suspension. When 20 ml of a 5% CR solution in 5% dextrose was administered intravenously, the CR was absorbed in levels sufficient to produce fluorescence of the main arteries in rabbits. Layers of tissue both in the media of the vessels and at the endothelial/intimal interface were clearly differentiated. Therefore, the elastin:CR complex appears to be an ideal system in which the elastin fluorescence could aid in distinguishing between normal and diseased tissue in certain pathological conditions, such as atherosclerosis and some types of breast tumors.     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

Fourier analysis of the approximation power of principal shift-invariant spaces

The approximation order provided by a directed set {S _h } _h>0 of spaces, each spanned by thehZ ^d -translates of one function, is analyzed. The nearoptimal approximants of [R2] from eachs _h to the exponential functions are used to establish upper bounds on the approximation order. These approximants are also used on the Fourier transform domain to yield approximations for other smooth functions, and thereby provide lower bounds on the approximation order. As a special case, the classical Strang-Fix conditions are extended to bounded summable generating functions.The second part of the paper consists of a detailed account of various applications of these general results to spline and radial function theory. Emphasis is given to the case when the scale {s _h } is obtained froms ₁ by means other than dilation. This includes the derivation of spectral approximation orders associated with smooth positive definite generating functions.     

Orbits of arcs in PG(N,K) under projectivities

The symmetric group on k symbols is made to operate on a certain set of matrices in such a way that its orbits are in one-to-one correspondence with the orbits of the k-arcs of an N-dimensional projective space under the group of projectivities. This leads to a formula for the number of such orbits.     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Transportation problems which can be solved by the use of hirsch-paths for the dual problems

Balinski uses his signature method for the proof of the Hirsch-conjecture for dual transportation polyhedra to obtain an efficient algorithm for the assignment problem. We will show how to extend this method to other primal transportation problems, including transportation problems with unit demands. We then prove that Balinski's assignment algorithm is equivalent, cycle by cycle, to that of Hung and Rom. We demonstrate that, under some assumptions for our probability model, a modification of the latter algorithm has an average complexity of O(n ²logn) and present some computational results confirming this. We also present results that indicate that this modification compares favorably with Balinski's algorithm and other codes. Research of both authors supported, in part, by grants of the Alexander von Humboldt-Stiftung. Supported, in part, by NSF grant DMS-8504050.