Crystal and molecular structure of 5-diazo-2,2-dimethyl-4,6-dioxo-1,3-dioxane and 5-diazo-1,3-dimethylpyrimidin-2,4,6-trione

C₆N₂O₄H₆: M_r = 170.12, orthorhombic space group Pbca, a = 6.751(2), b = 13.669(4), c = = 16.845(4) Å, V = 1555(1) ų, D_x = 1.248 Mgm⁻³, Z = 8, F(000) = 704, λ(moKα) = 0.71069 Å, μ = 1.1 mm⁻¹. The crystal structure was determined by direct methods and refined by least-squares procedure to the discrepancy factor R = 0.039. C₆N₄O₃H₆: M_r = 182.14, monoclinic space group C2/c, a = 17.726(8), b = 6.191(12), c = 16.062(6) Å, β = 117.59 (3)°, V = 1562 (1) ų, D_x = 1.549 Mgm⁻³, Z = 8, F(000) = 752, λ(MoKα) = 0.71069 Å, μ = 1.2 mm⁻¹. The crystal structure was determined by direct methods and refined by least-squares procedure to the discrepancy factor R = 0.056.     

An Inverse Scattering Problem with Part of the Fixed-Energy Phase Shifts

Assume that q(r) is a real-valued, compactly supported potential, q(r)=0 for , . Let be an arbitrary fixed subset of non-negative integers such that , and be fixed-energy phase shifts corresponding to q(r). The main result is: Theorem. The data determine q(r) uniquely. Received: 3 March 1999 / Accepted: 27 April 1999     

A new approach to the inverse scattering and spectral problems for the Sturm-Liouville equation

New proofs of the known uniqueness theorems for the one-dimensional inverse spectral and scattering problems are given. Proof of the invertibility of all of the steps in the inversion procedures of Gelfand-Levitan and Marchenko is given. The proposed method of investigation yields some new results, for example, a Marchenko-type equation at x = 0 which holds on the whole axis, rather than on a half-axis, as usual for the scattering theory on half-axis. It also yields a new method, shorter and simpler than earlier published, for proving that the potential in the class L_1,1, obtained by the Marchenko reconstruction procedure, generates the scattering data from which it was reconstructed.     

Stability estimates in inverse scattering

An algorithm is given for calculating the solution to the 3D inverse scattering problem with noisy discrete fixed energy data. The error estimates for the calculated solution are derived. The methods developed are of a general nature and can be used in many applications: in nondestructive evaluation and remote sensing, in geophysical exploration, medical diagnostics, and technology.     

Nichtlineare Stabilitätsuntersuchungen mit der Methode der Finiten Elemente

Übersicht Ziel der Arbeit ist die exakte und genäherte Bestimmung der kritischen Last von elastischen Systemen mit nichtlinearem Vorbeulverhalten. Grundlage ist die Verschiebungsformulierung der Methode der finiten Elemente in inkrementell/iterativer Darstellung. Im ersten Hauptteil werden begleitende Stabilitätsuntersuchungen bei der exakten Auswertung der nichtlinearen Gleichungen behandelt. Hierzu gehören die Determinantenbeobachtung sowie Eigenwertuntersuchungen für den Lastparameter und die Eigenfrequenz. Im zweiten Hauptteil werden zwei verbesserte Anfangsstabilitätsanalysen zur genäherten Bestimmung der kritischen Last vorgestellt, die auf Reihenlösungen der Gleichgewichts- und Stabilitätsgleichungen basieren. In beiden Teilen bestätigen zahlreiche Beispiele die Brauchbarkeit der behandelten Verfahren.

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Nonlinear stability analysis in finite element formulation

Summary Exact and approximate solutions for the critical load of elastic structures exhibiting a nonlinear prebuckling response are described. The incremental iterative displacement finite element formulation is used. Two main aspects are covered. First different supplementary procedures evaluating the stability citerion parallel to the nonlinear analysis are investigated. Among these are the function of the determinant, and eigenvalue formulations for the load parameter and the frequency. In the second part two improved initial stability analyses are proposed to determine an approximate solution of the final critical load. They are based on the perturbation method in which the equilibrium and stability equations are expanded in series solutions. In both parts several numerical examples are given.