Primal-dual interior point approach for computingl 1-solutions andl ∞-solutions of overdetermined linear systems

This paper concerns solving an overdetermined linear systemA ^T x=b in the leastl ₁-norm orl _{283/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0">}-norm sense, whereA283/xxlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0">283/xxlarge8477.gif" alt="Ropf" align="BASELINE" BORDER="0"> ^m×n ,m<n. We show that the primal-dual interior point approach for linear programming can be applied, in an effective manner, to linear programming versions of thel ₁ andl _{283/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0">}-problems. The resulting algorithms are simple to implement and can attain quadratic or superlinear convergence rate. At each iteration, the algorithms must solve a linear system with anm×m positive-definite coefficient matrix of the formADA ^T , whereD is a positive diagonal matrix. The preliminary numerical results indicate that the proposed algorithms offer considerable promise.This research was supported in part by Grants NSF DMS-91-02761 and DOE DE-FG05-91-ER25100.     

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This work is supported by the National Basic Research Program of China, the National Natural Science Foundation of China, and Chinese Academy of Sciences.     

Materialersparnis,zeitgewinn und erhöhte genauigkeit in der massanalyse durch “umkehrtitrationen”

If, in volumetric analysis, the solution, as well as the reagent, is measured by means of a burette (replacing the usual pipette), we are able, after reaching the first end-point, to add a small quantity of either solution, substance or reagent, to titrate for a second end-point and to repeat these operations as many times as are necessary to obtain an average value with the desired accuracy, which 'can be very high. The economy, both in tbc amount of solution required and time, is considerable. The procedure is very useful in theoretical .studies on controversial volumetric reactions and in calibrating burettes.     

Submillimeter measurements of N2 and air broadening of hypochlorous acid

The pressure induced broadening of a several pure rotational transitions of hypochlorous acid, HOCl, have been measured as a function of temperature. This set of rotational transitions is the dominant feature of the submillimeter spectrum in the range where several remote sensing instruments currently operate. Additional features throughout the submillimeter spectrum have been recorded at the full-resolution of the room temperature Doppler linewidth using multiplier chains in the 110- wavelengths.     

Lifting inequalities for polytopes

We present a method of lifting linear inequalities for the flag f-vector of polytopes to higher dimensions. Known inequalities that can be lifted using this technique are the non-negativity of the toric g-vector and that the simplex minimizes the cd-index. We obtain new inequalities for six-dimensional polytopes. In the last section we present the currently best known inequalities for dimensions 5 through 8.     

A Solution and Solid State Study on 2-Hydroxypropyl-β-Cyclodextrin Complexation with Hyodeoxycholic Acid

Hyodeoxycholic acid (HDCA) isa 6-283/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> dihydroxylated natural bile acid capable ofpreventing gallstone formation by reducing the bilecholesterol saturation. However, any attempt to enrichthe bile acid pool with HDCA have failed owing to thepoor solubility of the molecule. To resolve thebioavailability problems, the complexation of HDCAinto the HP283/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">CD cavity was studied in solution(solubility methods, ¹³C- and ¹H-NMRspectroscopy and circular dichroism) and in the solidstate (IR spectroscopy, X-ray diffractometry andthermal analysis). According to the results, the HDCAinclusion took place with 1 : 1 stoichiometry. Theinfluence of different preparation methods of thesolid complex was evaluated for its potential use inappropriate pharmaceutical formulations to improve thebioavailability of HDCA.     

Exact solution of the alternating XXZ spin chain with generic non-diagonal boundaries

The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K$K$-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused R$R$-matrices and K$K$-matrices, we obtain certain closed operator identities and conditions, which allow us to construct an inhomogeneous T−Q$T-Q$ relation and the associated Bethe Ansatz equations accounting for the eigenvalues of the transfer matrix.