Velocity inversion: A case study in infinite-dimensional optimization

The goal of seismic velocity inversion is the estimation of seismic wave velocities inside the earth by attempting to predict, in a least-error sense, seismic waveforms measured at its surface. We present velocity inversion as a case study in the various infinite-dimensional pathologies which may afflict practically important problems of distributed parameter identification, treated as optimization problems in function spaces. These features differentiate various problem formulations far beyond the degree one would expect for finite- (small-) dimensional problems. We illustrate this differentiation by comparing the characteristics of three different least-squares formulations of velocity inversion.     

On the principal axes of diffusion in difference schemes for 2d transport problems

Via Taylor series, we associate with a difference stencil L^h approximating Lu := au_x + bu_y its modified equation:

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. By rotating axes to eliminate the 2Bu_xy term, the principle axes through which the diffusion in L^h acts is calculated. Interestingly, for many schemes proposed for 2D transport problems these axes have little to do with the “streamline” and ”crosswind” directions of the continuous problem. Several examples are considered from this point of view.     

Crystal and molecular structure of crenatine carbonate

The crystal and molecular structure of 1-ethyl-4-methoxy-9H-pyrido[3,4b]indole (crenatine) carbonate C₁₄H₁₄N₂O·H₂CO₃, (MS, m/z 226)M _R 288.3, a-carboline alkaloid, has been determined from X-ray diffraction data. The compound crystallizes in the space group Pbca with cell parameters:a=11.616(4),b=18.450(8),c=12.992(5)Å,V=2784(2)ų,Z=8,D _calc=1.375 g cm^–3, (MoK)=0.71069Å,(Mo K)=0.94 cm^–1,F(000)=1216,R/R _w =8.2/10.3% for 1099 reflections. The ring system of the-carboline nucleus is planar. The title compound shows a two center hydrogen bond between the indole N-H group and the oxygen atom of a carbonate group. The structure does not display hydrogen bonding between-carboline groups but rather a bonding network involving the carbonate group.     

Operator stable laws: Series representations and domains of normal attraction

LetX,X ₁,X ₂,... be i.i.d. random vectors in ^d. The limit laws that can arise by suitable affine normalizations of the partial sums,S _n=X ₁+...+X _n, are calledoperator-stable laws. These laws are a natural extension to ^d of the stable laws on. Thegeneralized domain of attraction of [GDOA()] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to . If the linear part of the affine transformation is restricted to take the formn ^–B for some exponent operatorB naturally associated to thenX is in thegeneralized domain of normal attraction of [GDONA()]. This paper extends the theory of operator-stable laws and their domains of attraction and normal attraction.     

Rings of regular functions on nilpotent orbits and their covers

Summary LetG be a complex semisimple algebraic group with Lie algebra . Let be a nilpotentG-orbit, its ring of regular functions. We derive a formula for as aG-module and prove some partial results on a cover of . We then relate this formula to various existing multiplicity formulas forK-types in Harish-Chandra bimodules ofG.Supported by National Science Foundation Grant DMS-8505550     

Crystal structures of dimethylsuccinate and dimethyloxalate: Carbonyl group orientation for C13 chemical shielding tensor studies

The crystal structures of dimethylsuccinate (DMS) and dimethyloxalate (DMO) have been determined to facilitate the determination of the C-13 chemical shielding tensors of the carbonyl carbon in esters. Crystals of DMS are monoclinic, space groupC2/c,Z=4,a=13.154(4),b=6.156(1),c=9.363(4)Å,=98.53(3)°. The structure was solved by direct methods and refined by leastsquares procedures to giveR=0.071 for 932 observed data. Crystals of DMO are monoclinic space group,P2₁/n,Z=2, witha=3.891(1),b=11.879(2),c=6.213(2) Å,=103.32(2)°. The structure is the same (within experimental error) as that reported by Dougill and Jeffrey (1953) and refined to giveR=0.074 for 395 observed data.     

Truncation error bounds for modified continued fractions with applications to special functions

Much recent work has been done to investigate convergence of modified continued fractions (MCF's), following the proof by Thron and Waadeland [35] in 1980 that a limit-periodic MCFK(a _n , 1;x ₁), with andnth approximant

Synthesis and molecular structure of [Al(CH3)2]2[C10H22N4] [Al(CH3)3]2: Condensation product of trimethylaluminum and a multidentate open-chain amine

The crystalline condensation product [Al(CH₃)₂]₂[C₁₀H₂₂N₄][Al(CH₃)₃]₂ is prepared from reaction of the multidentate open-chain amine 1,4-bis(3-aminopropyl)piperazine with trimethylaluminum in methylene chloride. The compound crystallized in the monoclinic space groupC2/c with unit cell parametersa=25.166(12),b=7.268(4),c=17.316(4) Å,=115.3(4)°, andD _c =1.06 g cm^–3 forZ=4. Least-squares refinement based on 1054 observed reflections with intensitiesI 3(I) in the range 2<2<45° led to a finalR factor of 0.053 (R _w =0.064). The title compound resides on a crystallographic center of symmetry with independent Al-N distances of 1.889(5), 2.058(5), and 2.030(5) Å.