Sphere orders

Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P _i } of ordered sets such that eachP _i is ann-sphere order only forni; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.Research supported by ONR grant N00014 85-K-0769.     

Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, ). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

Algorithms for non-linear huber estimation

The Huber criterion for data fitting is a combination of thel ₁ and thel ₂ criteria which is robust in the sense that the influence of wild data points can be reduced. We present a trust region and a Marquardt algorithm for Huber estimation in the case where the functions used in the fit are non-linear. It is demonstrated that the algorithms converge under the usual conditions.     

Comparison theorems forL-monosplines of minimal norm

Summary LetLM _N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x _i } ₁ ⁿ ,a <x ₁ < ... <x _n <b and an incidence matrixE = (e _ij ) _i=1 ⁿ , _r-1 ^j=0 with Denote byLM _N ^O the subset ofLM _N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL _p-norms inLM _N belong toLM _N ^O .The results are reformulated as comparison theorems for quadrature formulae.     

Convolution quadrature and discretized operational calculus. I

Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integrals

The absorption of pulsed CO2-laser radiation by ethylene at total pressures from 25 to 3000 Torr

The absorption of pulsed CO₂-laser radiation by ethylene has been measured at total pressures from 25 to 3000 Torr, using the P(12) and P(14) lines in the 10.6 m band, with incident fluences from 0.1 to 0.7 J/cm². Marked deviations from the Beer-Lambert absorption law were observed, with the effective absorption coefficient varying with pressure, fluence, absorption path-length and the addition of non-absorbing gas. Pressure broadening of the rotational lines of the ethylene absorption spectrum was shown to be the major cause of these deviations, together with lesser effects which can be attributed to the rise in temperature of the absorbing gas during the laser pulse.     

Accurate determination of wavenumbers for iodine molecular lines in the red spectral region

The hyperfine structure of various absorption lines of molecular iodine with wavenumbers between 12980 and 13890 cm^–1 has been resolved using Doppler-free polarization spectroscopy. The wavenumbers of theo-component of 17 rovibrational lines of I₂ due to the transitionB ³ _ou ⁺ –X¹ _g ⁺ with even rotational quantum numbers have been determined with an accuracy of 0.001 cm^–1. A comparison of the centers of gravity of these 17 lines with the values of the iodine atlas of Gerstenkorn et al. yields a difference of thus corroborating the data of the iodine atlas in the red region within limits of error.     

Optimization of sucrose ethanol fermentation for K,Na, Ca,and cu metal contents

The effect of the trace metals Cu, K, Na, and Ca, separately or in mixture, on fermentation time, ethanol production rate, and cell growth in the fermentation of synthetic media containing sucrose is discussed. The results are related to the range of contents found in raw materials, molasses and raisins, in order to determine their optimum concentrations for alcohol production.     

Peptides-XXXXVI: Studies in the synthesis of an analogue of hen egg white lysozyme

The previously synthesised (1–37), (38–75), (76–93), (94–104), (105–117) and (118–129) fragments of the analogue were combined making extensive use of the DCCI/HONSu method. The final coupling involved the (1–75) and (76–129) sub-fragments. Aggregation of the latter fragment caused problems in purification by routine gel filtration methods employing Enzacryl K2 or Sephadex LH60. The fully protected (1–129) product was partially purified by washing, then deprotectcd and purified by gel filtration and ion exchange chromatography. Satisfactory removal of the acetamidomethyl group used for cysteine protection could not be achieved.