Zur maassanalytischen Bestimmung der Phosphors?ure mit Uranl?sung

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The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 2¹⁶⁹⁴ scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.     

Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two‐dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time‐dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd.     

Controlling the water content of never dried and reswollen bacterial cellulose by the addition of water-soluble polymers to the culture medium

For the modification of medically useful biomaterials from bacterially synthesized cellulose, fleeces of Acetobacter xylinum have been produced in the presence of 0.5, 1.0, and 2.0% (m/v) carboxymethylcellulose (CMC), methylcellulose (MC), and poly(vinyl alcohol) (PVA), respectively, in the Hestrin-Schramm culture medium. The incorporation of the water-soluble polymers into cellulose and their influence on the structure, crystal modifications, and material properties are described. With IR and solid-state ¹³C NMR spectroscopy of the fleeces, the presence of the cellulose ethers and an increase in the amorphous parts of the cellulose modifications (NMR results) have been detected. The incorporation is represented by a higher product yield, too. As demonstrated by scanning electron microscopy, a porelike cellulose network structure forms in the presence of CMC and MC. This modified structure increases the water retention ability (expressed as the water content), the ion absorption capacity, and the remaining nitrogen-containing residues from the culture medium or bacteria cells. The water content of bacterial cellulose (BC) in the never dried state and the freeze-dried, reswollen state can be controlled by the CMC concentration in the culture solution. The freeze-dried, reswollen BC-CMC (2.0%) contains 96% water after centrifugation, whereas standard BC has only 73%. About 98% water is included in a BC-MC composite in the wet state, and about 93% is included in the reswollen state synthesized in the presence of 0.5, 1.0, or 2.0% MC. These biomaterial composites can be stored in the dried state and reswollen before use, reaching a higher water absorption than pure, never dried BC. The copper ion capacity of BC-CMC composites increases proportionally with the added amount of CMC. BC-CMC (0.5%) can absorb 3 times more copper ions than original BC. In the case of 0.5 and 1.0% PVA additions to the culture solution, this polymer cannot be detected in the cellulose fleeces after they are washed. Nevertheless the presence of PVA in the culture medium effects a decreased product yield, a retention of nitrogen-containing residues in the material during purification, a reduced water absorption ability, and a slightly higher copper ion capacity in comparison with original BC. The water content of freeze-dried, reswollen BC-PVA (0.5%) is only 62%. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 463–470, 2004     

Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit

We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method.     

Vacations in GI X/M Y/1 systems and Riemann boundary value problems

We consider systems of GI/M/1 type with bulk arrivals, bulk service and exponential server vacations. The generating functions of the steady-state probabilities of the embedded Markov chain are found in terms of Riemann boundary value problems, a necessary and sufficient condition of ergodicity is proved. Explicit formulas are obtained for the case where the generating function of the arrival group size is rational. Resonance between the vacation rate and the system is studied. Complete formulas are given for the cases of single and geometric arrivals. This revised version was published online in June 2006 with corrections to the Cover Date.