The approximation characteristic of diagonal matrix in probabilistic setting

In this paper, the approximation characteristic of a diagonal matrix in probabilistic and average case settings is investigated. And the asymptotic degree of the probabilistic linear (n,δ)$(n,\mathrm{<font\; color="red">\delta </font>})$-width and p$p$-average linear n$n$-width of diagonal matrix M$M$ are determined.     

Influence of Nitrogen,Water and Competition on Carbon Isotope Ratios (δ13C) in a CAM Plant (Crassula argentea)

Abstract

Leaf carbon isotope ratios (δ¹³C), an indicator of long-term intercellular carbon dioxide concentration, and also stem and root carbon isotope ratios were measured on the obligate CAM species Crassula argentea cultivated in pure and mixed cultures with the succulent C₃ Peperomia obtusifolia in open-air conditions under two different levels of nitrogen and water supply.

As expected, a diminished water supply and a relatively dry and hot summer climate cause a shift of δ¹³C values to a less strong ¹³C discrimination (less negative δ¹³C values). A diminished nitrogen supply causes a shift of the δ¹³C values in direction of a higher ¹³C discrimination (more negative δ¹³C values), particularly in the leaves. Competition causes also an increased ¹³C discrimination, especially valid for shoot axes.

The shift of ¹³C/¹²C isotope ratios in case of nitrogen deficiency is discussed to be a result of a decreased PEPCase activity in the night.     

Clusters of bound particles in the derivative δ-function Bose gas

In this paper we discuss a novel procedure for constructing clusters of bound particles in the case of a quantum integrable derivative δ-function Bose gas in one dimension. It is shown that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. We also establish a connection between these special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles associated with the derivative δ-function Bose gas and allows us to study various properties of these clusters like their size and their stability under the variation of the coupling constant.     

An improved radio frequency heavy ion source

Abstract

An improved r.f. heavy ion source, which can operate with gases, liquids and solids is described. The operating temperature of the ion source may reach 1000°C. It can therefore, generate ion beams of a considerable number of elements. including metallic ions. At present, ion beams of S⁺, Al⁺, As⁺. Zn⁺, Mg⁺, Cd⁺, Ag⁺, Sm⁺, Te⁺, Se⁺, Sn⁺, In⁺, Hg⁺, etc. have been extracted. The extracted total beam current ranges from several hundred microamperes to the order of milliampere. The useful fraction of ion in the total beam is 70–90%. Life span of the source ranges from 40 hours to more than 100 hours. The emittance of the source is 3 × 10^?6 cm rad. Structure and operating characteristics of this ion source are discussed.     

Mass,momentum and energy conservation laws in zero-pressure gas dynamics and δ-shocks: II

We study δ-shocks in a one-dimensional system of zero-pressure gas dynamics. In contrast to well-known papers (see References) this system is considered in the form of mass, momentum and energy conservation laws. In order to define such singular solutions, special integral identities are introduced which extend the concept of classical weak solutions. Using these integral identities, the Rankine–Hugoniot conditions for δ-shocks are obtained. It is proved that the mass, momentum and energy transport processes between the area outside the of one-dimensional δ-shock wave front and this front are going on such that the total mass, momentum and energy are independent of time, while the mass and energy concentration processes onto the moving δ-shock wave front are going on. At the same time the total kinetic energy transforms into total internal energy.     

Ferroelastic detwinning of the high-temperature superconductor YBa2Cu3O7-δ

Crystals of YBa₂Cu₃O_7-δ (YBC) were prepared using a flux technique. The as-grown crystals were typically on the order of 200 μm × 200 μm × 50 μm, where the 50 μm dimension is in the c-direction. Ferroelastic behavior was observed by applying a uniaxial stress along the [100]_tet-direction using a specially-designed fixture which was mounted to a programmable hot/cold stage of a polarizing reflected-light microscope. Domain wall motion was observed for temperatures greater than 200°C, and complete poling was accomplished at stresses on the order of 50–100 MPa at temperatures of 350–400°C. An ionic diffusion-activated mechanism is suggested.     

Prime Lie Rings of Derivations of Commutative Rings

Let R be a 2-torsion free commutative ring with identity, and δ a nonzero derivation of R such that R is δ-prime. Then Rδ is a prime Lie ring and any nonzero ideal of Rδ contains an ideal of the form Jδ where J is a nonzero δ-ideal of R.     

Detailed Description of Pulse Isotopic Exchange Method for Analyzing Oxygen Surface Exchange Behavior on Oxide Ion Conductors

A novel pulse ¹⁸O-¹⁶O isotopic exchange (PIE) technique for measurement of the rate of oxygen surface exchange of oxide ion conductors was presented. The technique employs a continuous flow packed-bed micro-reactor loaded with the oxide powder. The isothermal response to an ¹⁸O-enriched pulse passing through the reactor, thereby maintaining chemical equilibrium, is measured by on-line mass spectrometry. Evaluation of the apparent exchange rate follows from the uptake of ¹⁸O by the oxide at given reactor residence time and surface area available for exchange. The developed PIE technique is rapid, simple and highly suitable for screening and systematic studies. No rapid heating/quenching steps are required to facilitate ¹⁸O tracer anneal or analysis, as in other commonly used techniques based upon oxygen isotopic exchange. Moreover, the relative distribution of the oxygen isotopologues ¹⁸O₂, ¹⁶O¹⁸O, and ¹⁶O₂ in the effluent pulse provides insight into the mechanism of the oxygen exchange reaction. The PIE technique has been demonstrated by measuring the exchange rate of selected oxides with enhanced oxide ionic conductivity in the range of 350?900 oC. Analysis of the experimental data in terms of a model with two consecutive, lumped steps for the isotopic exchange reaction shows that for mixed conductors Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3-δ(BSCF) and La₂NiO_4+δ the reaction is limited by the apparent rate of dissociative adsorption of O₂ molecules at the oxide surface. For yttria-stabilized zirconia (YSZ), a change-over takes place, from rate-limitations by oxygen incorporation below ∽800 oC to rate-limitations by O₂ dissociative adsorption above this temperature. Good agreement is obtained with exchange rates reported for these materials in literature.     

2-Isopropylbenzimidazole and 2-methylbenzimidazole as bulky proton sources: Stereoselective protonation and application to the synthesis of γ- and δ-lactones

2-Isopropylbenzimidazole and 2-methylbenzimidazole have been found to be effective bulky proton sources for stereoselective protonation of chiral enolate anions. 2-Isopropylbenzimidazole worked in the stereoselective protonation of the Birch reduction of chiral α,β-unsaturated imides. On the other hand, 2-methylbenzimidazole was found to be the best protonation reagent in the isomerization reaction of α,β-unsaturated imide into β,γ-unsaturated imide. The Birch reduction using 2-isopropylbenzimidazole realized a concise and stereoselective synthesis of δ-lactone 14, a sex pheromone of Macrocentrus grandii, while the isomerization reaction using 2-methylbenzimidazole was employed in the highly stereoselective synthesis of the γ-lactone intermediate in the synthesis of depsipeptide antibiotics. These bulky proton sources would be powerful tools to achieve a concise synthesis of natural products.