Oberflächen-Eigenschaften von Hydroxyapatiten. I. Eintauch-Enthalpie

Ohne Zusammenfassung     

Studies related to the synthesis of maytansinoids.

Two approaches to the partial synthesis of C₁–C₅ of a bis-nor maytansinoid $\text{1}$ have been investigated starting on the one hand with (S)-(?)-malic acid and on the other, with D-(+)-ribonolactone.     

A polynomial energy-gap model for molecular linewidths

A simple phenomenological model for predicting high-temperature linewidths is described. The rotationally inelastic relaxation time is calculated by using a polynomial inverse-energy-gap model. From this time, the linewidths may be calculated and ambient pressure linewidths may then be used to determine the polynomial coefficients and predict high-temperature linewidths. A detailed comparison with known nitrogen linewidths is given. The relaxation rates obtainable from the model may also be used to calculate pressure-narrowing effects for vibrational Q branches.     

Macropolyhedral boron-containing cluster chemistry. A synthetic approach via the auto-fusion of [6,9-(SMe2)2-arachno-B10H12

In an attempt to build up borane-based multicluster assemblies, thermolysis of [6,9-(SMe2)2-arachno-B10H12] 1 in inert hydrocarbon solution, followed by chromatographic separation, has resulted in the isolation not only of the previously established single-cluster product from this reaction, [5-(SMe2)-nido-B10H12] 2 (30%), but also the two two-cluster species [6,9-(SMe2)2-arachno-B10H11-1-(6-nido-B10H13)] 3 (20%) and [1,6-(nido-B10H13)2] 6 (ca. 0.5%) and the two three-cluster species [6,9-(SMe2)2-arachno-B10H10-1,5-(6-nido-B10H13)2] 4 (5%), characterized crystallographically, and [6,9-(SMe2)2-arachno-B10H10-1,3-(6-nido-B10H13)2] 5 (<1%), identified by NMR spectroscopy. An improved crystallographic investigation of [5-(SMe2)-nido-B10H12] 2 is also presented. The feasibility of the stability of species resulting from multiple adjacent substitution of nido-decaboranyl units on the [6,9-(SMe2)2-arachno-B10H12] skeleton is tested by DFT calculations. In an extension, to attempt the use of pre--linked two-cluster compounds as starting substrates, two-cluster [5-(SMe2)-4-(2-nido-B10H13)-nido-B10H11] 7 (0.6%) has been isolated from the reaction of SMe2 with [1,5-(nido-B10H13)2], other identified products being compound 1 (39%) and compound 3 (10.5%).     

Global dynamic optimization for parameter estimation in chemical kinetics

We present the first method guaranteed to find the best possible least-squares (chi2) fit of experimental data by a nonlinear kinetic model. Several important advantages of knowing with certainty the best possible fit rather than a locally optimum fit are discussed and demonstrated using data from the recent literature. This is particularly important when the model and the data appear to be inconsistent. With the new method, one can rigorously demonstrate that a nonlinear kinetic model with several adjustable rate parameters is inconsistent with measured experimental data. The numerical method presented is a valuable tool in evaluating the validity of a complex kinetics model.     

Decision-dependent probabilities in stochastic programs with recourse

Stochastic programming with recourse usually assumes uncertainty to be exogenous. Our work presents modelling and application of decision-dependent uncertainty in mathematical programming including a taxonomy of stochastic programming recourse models with decision-dependent uncertainty. The work includes several ways of incorporating direct or indirect manipulation of underlying probability distributions through decision variables in two-stage stochastic programming problems. Two-stage models are formulated where prior probabilities are distorted through an affine transformation or combined using a convex combination of several probability distributions. Additionally, we present models where the parameters of the probability distribution are first-stage decision variables. The probability distributions are either incorporated in the model using the exact expression or by using a rational approximation. Test instances for each formulation are solved with a commercial solver, BARON, using selective branching.     

Nonsmooth exclusion test for finding all solutions of nonlinear equations

A new approach is proposed for finding all real solutions of systems of nonlinear equations with bound constraints. The zero finding problem is converted to a global optimization problem whose global minima with zero objective value, if any, correspond to all solutions of the original problem. A branch-and-bound algorithm is used with McCormick’s nonsmooth convex relaxations to generate lower bounds. An inclusion relation between the solution set of the relaxed problem and that of the original nonconvex problem is established which motivates a method to generate automatically, starting points for a local Newton-type method. A damped-Newton method with natural level functions employing the restrictive monotonicity test is employed to find solutions robustly and rapidly. Due to the special structure of the objective function, the solution of the convex lower bounding problem yields a nonsmooth root exclusion test which is found to perform better than earlier interval-analysis based exclusion tests. Both the componentwise Krawczyk operator and interval-Newton operator with Gauss-Seidel based root inclusion and exclusion tests are also embedded in the proposed algorithm to refine the variable bounds for efficient fathoming of the search space. The performance of the algorithm on a variety of test problems from the literature is presented, and for most of them, the first solution is found at the first iteration of the algorithm due to the good starting point generation.     

Convex and Concave Relaxations for the Parametric Solutions of Semi-explicit Index-One Differential-Algebraic Equations

A method is presented for computing convex and concave relaxations of the parametric solutions of nonlinear, semi-explicit, index-one differential-algebraic equations (DAEs). These relaxations are central to the development of a deterministic global optimization algorithm for problems with DAEs embedded. The proposed method uses relaxations of the DAE equations to derive an auxiliary system of DAEs, the solutions of which are proven to provide the desired relaxations. The entire procedure is fully automatable.     

Interval bounds on the solutions of semi-explicit index-one DAEs. Part 1: analysis

This article presents two methods for computing interval bounds on the solutions of nonlinear, semi-explicit, index-one differential-algebraic equations (DAEs). Part 1 presents theoretical developments, while Part 2 discusses implementation and numerical examples. The primary theoretical contributions are (1) an interval inclusion test for existence and uniqueness of a solution, and (2) sufficient conditions, in terms of differential inequalities, for two functions to describe componentwise upper and lower bounds on this solution, point-wise in the independent variable. The first proposed method applies these results sequentially in a two-phase algorithm analogous to validated integration methods for ordinary differential equations. The second method unifies these steps to characterize bounds as the solutions of an auxiliary system of DAEs. Efficient implementations of both are described using interval computations and demonstrated on numerical examples.     

Interval bounds on the solutions of semi-explicit index-one DAEs. Part 2: computation

This article presents two methods for computing interval bounds on the solutions of nonlinear, semi-explicit, index-one differential-algebraic equations (DAEs). Part 1 presents theoretical developments, while Part 2 discusses implementation and numerical examples. The primary theoretical contributions are (1) an interval inclusion test for existence and uniqueness of a solution, and (2) sufficient conditions, in terms of differential inequalities, for two functions to describe componentwise upper and lower bounds on this solution, point-wise in the independent variable. The first proposed method applies these results sequentially in a two-phase algorithm analogous to validated integration methods for ordinary differential equations (ODEs). The second method unifies these steps to characterize bounds as the solutions of an auxiliary system of DAEs. Efficient implementations of both are described using interval computations and demonstrated on numerical examples.