Majorization of regular measures and weights with finite and positive critical exponent

For the sets , 1?p<∞, of positive finite Borel measures μ on the real axis with the set of algebraic polynomials P dense in Lp(R,dμ), we establish a majorization principle of their “boundaries,” i.e. for every there exists such that dμ/dν?1. A corresponding principle holds for the sets , p>0, of non-negative upper semi-continuous on R functions (weights) w such that P is dense in the space : For every there exists such that w?ω.     

Application of the virial theorem to the study of molecular electronic wave functions

With aid of the virial theorem formulated for the energy differences of two electronic states some theorems on the wave functions of diatomic molecules have been proven. It is shown how proper Rydberg states can be distinguished from other electronic states with a diffuse outer orbital by virtue of the virial theorem and that a singlet-triplet pair of excited states cannot have the same equilibrium geometry and identical orbitals simultaneously. Furthermore if the two states have the same dissociation limit a theorem on the differences of the kinetic and the potential energy can be derived which allows an understanding of the shape of the electronic wave functions. As an application the wave functions and the ordering of the lowest states of H ₂ ⁺ and H₂ have been discussed.This work is part of the project Nr. SR 2.159.74 of the 802nv/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">Schweizerischer Nationalfonds802nv/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0">.     

Self-assemblies of Ni(II) with phenanthroline and maleate anions: [Ni(H2O)3(phen)L] ⋅ H2O (1) and [Ni(H2O)2(phen)L] ⋅ 2H2O (2) with H2L = maleic acid

The complex [Ni(H₂O)₃(phen)(C₄H₂O₄)] 802v219q2/xxlarge8901.gif" alt="sdot" align="BASELINE" BORDER="0"> H₂O (1), which was obtained by reaction of phenanthroline, Ni(NO₃)₂ 802v219q2/xxlarge8901.gif" alt="sdot" align="BASELINE" BORDER="0"> 6H₂O, and maleic acid in CH₃OH/H₂O at pH = 7.05, crystallized in the monoclinic space group P2₁ (no. 4) with cell dimensions: a = 9.350(1) Å, b = 7.631(1) Å, c = 12.821(1) Å, 802v219q2/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = 106.25(1), and D _calc = 1.607 g/cm³ for Z = 2. The Ni atoms are each octahe drally coordinated by one chelating phen ligand, three H₂O molecules and one monodentate maleato ligand to form [Ni(H₂O)₃(phen)(C₄H₂O₄)] complex molecules with d(Ni–O) = 2.038–2.090 Å, d(Ni–N) = 2.066, 2.089 Å. The formed complex molecules are, via the intermolecular hydrogen bonds, assembled into columnar 1D chains. Interdigitation of the chelating phen ligands of the neighboring chains leads to 2D layers and the crystal H₂O molecules are hydrogen bonded to the oxygen atoms of the maleate not coordinated to the Ni atom. However, reaction of NiCO₃, phen, and maleic acid in CH₃OH/H₂O at pH = 6.33 afforded [Ni(H₂O)₂(phen)(C₄H₂O₄)] 802v219q2/xxlarge8901.gif" alt="sdot" align="BASELINE" BORDER="0"> 2H₂O (2), which crystallized in the triclinic space group 802v219q2/10870_2004_Article_378503_TeX2GIFIE1.gif" alt=" $$P\bar 1$$ " align="middle" border="0"> (no. 2) with cell dimensions: a = 7.971(1) Å, b = 8.237(1) Å, c = 13.304(1) Å, 802v219q2/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> = 81.005(6)°, 802v219q2/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = 87.877(8)°, 802v219q2/xxlarge947.gif" alt="gamma" align="MIDDLE" BORDER="0"> = 78.322(8)°, and D _calc = 1.671 g/cm³ for Z = 2. The Ni atoms are each octahedrally coordinated by two N atoms of one phen ligand and four O atoms of two H₂O molecules and two bis–monodentate maleato ligands with d(Ni–O) = 2.041–2.120 Å and d(Ni–N) = 2.095 Å. The Ni atoms are bridged by the maleato ligands to generate 1D _{802v219q2/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0">} ¹ [Ni(H₂O)₂(phen)(C₄H₂O₄)_2/2] chains along [100]. The supramolecular assemblies of the 1D chains via 802v219q2/xxlarge960.gif" alt="pgr" align="BASELINE" BORDER="0">–802v219q2/xxlarge960.gif" alt="pgr" align="BASELINE" BORDER="0"> stacking inter- actions result in thick 2D layers parallel to (001), between which the noncoordinating H₂O molecules are sandwiched. The paramagnetic [Ni(H₂O)₂(phen)(C₄H₂O₄)_2/2] 802v219q2/xxlarge8901.gif" alt="sdot" align="BASELINE" BORDER="0"> 2H₂O (2) obeys the Curie–Weiss law 802v219q2/xxlarge967.gif" alt="chi" align="MIDDLE" BORDER="0">_m(T-802v219q2/xxlarge952.gif" alt="theta" align="BASELINE" BORDER="0">) = 1.139cm³ 802v219q2/xxlarge8901.gif" alt="sdot" align="BASELINE" BORDER="0"> mol^–1 802v219q2/xxlarge8901.gif" alt="sdot" align="BASELINE" BORDER="0"> K with the Weiss constant 802v219q2/xxlarge952.gif" alt="theta" align="BASELINE" BORDER="0"> = –0.95 K.     

Soft x-ray PHA measurement of the long pulse discharge in HT-7 tokamak

By analyzing the soft x-ray energy spectrum measured by the soft x-ray pulse height analysis (PHA) system, the electron temperature (Te) and the effective charge number (Zeff) of the ultra-long pulse discharge driven by lower hybrid wave (LHW) were obtained in the HT-7 tokamak. Moreover, the information of medium-Z impurities such as Ti, Cr, Fe, and Ni intrinsic to HT-7 tokamak can also be inspected. The accuracy of the electron temperature derived from the soft x-ray energy spectrum measurements is verified by comparing with the temperature measured by the Thomson scattering system for various plasmas and electron cyclotron emission diagnostic system for ohmic plasmas. The bulk electron temperature of about 1 keV and Zeff≈2 were achieved for long pulse plasma. The appreciable Kα lines of Ti, Cr, Fe and Ni metallic impurities released from the antennas of radio frequency wave and/or the first wall and Ar injected into plasma can be observed, and they kept stable during the long duration discharges. As a result, the longest pulse discharge with relatively high temperature of Te(0)∼1 keV, and ne(0)∼0.5×¹⁰¹⁹ m−3 has been achieved with a duration of 400 s in the HT-7 experimental campaign in 2008.     

Anticipatory Standards and the Commercialization of Nanotechnology

Standardization will play an increasing role in creating a smooth transition from the laboratory to the marketplace as products based on nanotechnology are developed and move into broad use. Traditionally, standards have evolved out of a need to achieve interoperability among existing products, create order in markets, simplify production and ensure safety. This view does not account for the escalating trend in standardization, especially in emerging technology sectors, in which standards working groups anticipate the evolution of a technology and facilitate its rapid development and entrée to the market place. It is important that the nanotechnology community views standards as a vital tool to promote progress along the nanotechnology value chain – from nanoscale materials that form the building blocks for components and devices to the integration of these devices into functional systems.This paper describes the need for and benefits derived from developing consensus standards in nanotechnology, and how standards are created. Anticipatory standards can nurture the growth of nanotechnology by drawing on the lessons learned from a standards effort that has and continues to revolutionize the telecommunications industry. Also, a brief review is presented on current efforts in the US to create nanotechnology standards.     

Zero location and asymptotic behavior for extremal polynomials with non-diagonal Sobolev norms

In this paper we are going to study the zero location and asymptotic behavior of extremal polynomials with respect to a non-diagonal Sobolev norm in the worst case, i.e., when the quadratic form is allowed to degenerate. The orthogonal polynomials with respect to this Sobolev norm are a particular case of those extremal polynomials. The multiplication operator by the independent variable is the main tool in order to obtain our results.     

Study on Interactions of Several Psychopharmaceutical Drugs with β-Cyclodextrin by Affinity Capillary Electrophoresis and their Application in Separation

The binding of psychopharmaceutical drugs by 802uqqtec8yvg/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin (802uqqtec8yvg/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD) changed their effective electrophoretic mobilities. Based on this phenomenon the interactions between some psychopharmaceutical drugs and 802uqqtec8yvg/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin were studied and the binding constants of 802uqqtec8yvg/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD with tiapride, imipramine, clomipramine, amitriptyline, trifluoperazine, perphenazine and carbamazepine were determined by affinity capillary electrophoresis. The presence of 802uqqtec8yvg/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD improved the separation of these psychopharmaceutical drugs. Organic modifier was used as another kind of additive to be added in the running buffer to improve further the separation. 70 mM pH 7.2 phosphate buffer solution containing 12 mM 802uqqtec8yvg/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin and 15% (v/v) acetone was selected as optimal running buffer for separation by capillary electrophoresis.