Integrability of vector and multivector fields associated with interior point methods for linear programming

In the feasible region of a linear programming problem, a number of desirably good directions have been defined in connexion with various interior point methods. Each of them determines a contravariant vector field in the region whose only stable critical point is the optimum point. Some interior point methods incorporate a two- or higher-dimensional search, which naturally leads us to the introduction of the corresponding contravariant multivector field. We investigate the integrability of those multivector fields, i.e., whether a contravariantp-vector field isX _p -forming, is enveloped by a family ofX _q 's (q > p) or envelops a family ofX _q 's (q < p) (in J.A. Schouten's terminology), whereX _q is aq-dimensional manifold.Immediate consequences of known facts are: (1) The directions hitherto proposed areX ₁-forming with the optimum point of the linear programming problem as the stable accumulation point, and (2) there is anX ₂-forming contravariant bivector field for which the center path is the critical submanifold. Most of the meaningfulp-vector fields withp 3 are notX _p -forming in general, though they envelop that bivector field. This observation will add another circumstantial evidence that the bivector field has a kind of invariant significance in the geometry of interior point methods for linear programming.For a kind of appendix, it is noted that, if we have several objectives, i.e., in the case of multiobjective linear programs, extension to higher dimensions is easily obtained.     

Dependence Between Order Statistics in Samples from Finite Population and its Application to Ranked Set Sampling

Let X1, X2,..., Xm, Y1, Y2,..., Yn be a simple random sample without replacement from a finite population and let X(1) X(2) ... X(m) and Y(1) Y(2) ... Y(n) be the order statistics of X1, X2,..., Xm and Y1, Y2,..., Yn, respectively. It is shown that the joint distribution of X(i) and X(j) is positively likelihood ratio dependent and Y(j) is negatively regression dependent on X(i). Using these results, it is shown that when samples are drawn without replacement from a finite population, the relative precision of the ranked set sampling estimator of the population mean, relative to the simple random sample estimator with the same number of units quantified, is bounded below by 1.     

Magnetic Alignment in Solid State and Temperature Hysteresis in Aqueous Tetrahydrofuran Solution for Tetrathiafulvaleno[18]annulenes

Tris(tetrathiafulvaleno)dodecadehydro[18]annulene‐hexaesters have a multi‐functionality that is very sensitive to small differences in the ester side‐chain. Self‐aggregation of the [18]annulenes in amphiphilic media such as THF–H₂O (v/v, 1:1) either produce a fibrous structure or result in temperature hysteresis of the color and ¹H NMR signals. This temperature hysteresis in solution is due to both strong self‐aggregation behavior and unique cluster formation in a binary solution of THF and water.     

Harpagometabolins I and II,Two New Metabolites from Harpagoside by Human Intestinal Bacteria

Harpagoside,which is one main iridoid constituent of the dried roots of Scrophularia ningpoensis Hemsl.,was biotransformated by bacteria isolated from human fecal flora and three metabolites were obtained.The structures of the metabolites,including two new alkaloids,named harpagometabolins I(1)and II(2),and a known alkaloid acubinine B(3),were identified by chemi cal methods and the spectroscopic evidences.     

New Catalytic Functions of Pd and Pt Catalysts for Hydrogenolysis of Methyl Formate

The catalytic performance of supported Pd and Pt catalysts for the title reaction was greatly improved upon the formation of Pd and Pt alloys. Over Pd and Pt alloys, methyl formate was selectively hydrogenolyzed to methanol, while over metallic Pd and Pt, it was decarbonylated to methanol and carbon monoxide. This revised version was published online in June 2006 with corrections to the Cover Date.     

Dielectric relaxation behavior of poly(methyl methacrylate) under high‐pressure carbon dioxide

An in situ dielectric measurement for atactic poly(methyl methacrylate) (at‐PMMA) was performed under high‐pressure CO₂ under various pressures and temperatures. The at‐PMMA has the acetate side group with a large dipole moment. In the glassy state, a local relaxation process (β‐process) can be observed using dielectric measurement. In the rubbery state, the micro‐Brownian motion of main chain (α‐process) occurs, and the β‐process changes into αβ‐process coordinated with the α‐process. The dielectric loss (ε″) spectrum of at‐PMMA in the glassy state is asymmetric because of the density fluctuation for the amorphous structure. The loss peak frequency shifted to higher frequencies, and the relaxation strength increased with increasing CO₂ pressure. In the glassy state, the shape of ε″ spectrum became more symmetric with increasing CO₂ pressure. These show that the molecular mobility enhanced by the plasticization effect of CO₂ allows the dipolar side groups in the high‐density region to contribute to the relaxation process. We also found that the apparent activation energy decreased under high‐pressure CO₂. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2951–2962, 2005     

Polysulfonylated cyclodextrins. Part 13: Chemistry of cyclomaltoheptaose tetrasulfonates providing a complete 6-O-sulfonylated cyclomaltoheptaoses library

Five regioisomeric cyclomaltoheptaose (β-cyclodextrin) tetramesitylenesulfonates were prepared and each of them was isolated by a combination of reversed and ordinary phase chromatographic separations. The positions of the substituents on each regioisomer were unambiguously determined using interresidual NOEs. As a result of this study, an indexed library of sulfonylated β-cyclodextrins composed of 19 sulfonates has been established.     

Robust portfolio selection with uncertain exit time using worst-case VaR strategy

To deal with the robust portfolio selection problem where only partial information on the exit time distribution and on the conditional distribution of portfolio return is available, we extend the worst-case VaR approach and formulate the corresponding problems as semi-definite programs. Moreover, we present some numerical results with real market data.     

Band alignment of SiO2/Si structure formed with nitric acid vapor below 500 °C

A relatively thick (i.e., ∼9 nm) SiO₂ layer can be formed by oxidation of Si with nitric acid (HNO₃) vapor below 500 °C. In spite of the low temperature formation, the leakage current density flowing through the SiO₂ layer is considerably low, and it follows the Fowler-Nordheim mechanism. From the Fowler-Nordheim plots, the conduction band offset energy at the SiO₂/Si interface is determined to be 2.57 and 2.21 eV for HNO₃ vapor oxidation at 500 and 350 °C, respectively. From X-ray photoelectron spectroscopy measurements, the valence band offset energy is estimated to be 4.80 and 4.48 eV, respectively, for 500 and 350 °C oxidation. The band-gap energy of the SiO₂ layer formed at 500 °C (8.39 eV) is 0.68 eV larger than that formed at 350 °C. The higher band-gap energy for 500 °C oxidation is mainly attributable to the higher atomic density of the SiO₂ layer of 2.46 × 10²²/cm³. Another reason may be the absence of SiO₂ trap-states.