Formally smooth bimodules

The notion of a formally smooth bimodule is introduced and its basic properties are analyzed. In particular it is proven that a B-A bimodule M which is a generator left B-module is formally smooth if and only if the M-Hochschild dimension of B is at most one. It is also shown that modules M which are generators in the category σ[M] of M-subgenerated modules provide natural examples of formally smooth bimodules.     

Internal normality and internal compactness

This text contains an example which presents a way to modify any Dowker space to get a normal space X such that X×[0,1] is not κ-normal, and a theorem implying the existence of a non-Tychonoff space which is internally compact in a larger regular space. It gives answers to several questions by Arhangel'skii [A.V. Arhangel'skii, Relative normality and dense subspaces, Topology Appl. 123 (2002) 27-36].     

Extremum principles for a general class of saddle functionals

The usual notion of a saddle functional in the calculus of variations assumes a vex/concave structure over the product space of two inner product spaces. Here the ideas extended to include some convexity in both spaces whilst still retaining an overall saddle property. Dual extremum principles are established for these functionals. Examples include periodic solutions of Duffing's equation, an iterative scheme and a pair of simultaneous partial differential equations which arise in magnetohydrodynamics.     

Phase composition-dependent physical and mechanical properties of YbxZr1−xO2−x/2 solid solutions

The paper represents a detailed insight into the correlation between changes of the phase composition of crystalline Yb_xZr_1−xO_2−x/2 solid solutions and their structural, electrical, mechanical and optical properties. Particularly, the effect of the crystal growth conditions and stabilizer amount in the range of 1.5–13.8 mol% of Yb₂O₃ are studied in terms of Rietveld analysis of powder X-ray diffraction data, electrical conductivity measured by impedance spectroscopy, absorption coefficient and refractive index measurements, Vickers microhardness (classical technique) as well as the plastic microhardness and effective elastic modulus (DSI—depth-sensing indentation technique). Potential applications of the investigated systems are discussed in view of the results obtained.     

A size-width inequality for distributive lattices

We show that every collection ofw sets such that none contains any other generates at least 3w-2 sets under the operations of taking intersections and unions. In particular, we prove that if the finite distributive lattice ? contains an antichain of sizew, then |?| ≧3w, forw≠1, 2, 3, 6, where the minimal exceptional cases arise from the Boolean algebras ?_n withn=0, 1, 2, 3, 4 atoms.     

Characterization of Cu(In,Ga)Se2 thin films prepared by evaporationfrom ternary compounds

Thin films of Cu(In,Ga)Se₂ were fabricated by evaporation from ternary CuGaSe₂ and CuInSe₂ compounds for photovoltaic device applications and their properties were investigated. From XRF analysis, the Cu:(In+Ga):Se atomic ratio in all thin films was approximately 1:1:2. The Ga/(In+Ga) atomic ratio in the thin films changed linearly from 0 to 1.0 with increasing the [CGS]/([CGS]+[CIS]) mole ratio in the evaporating materials. However, for thin films prepared at the [CGS]/([CGS]+[CIS]) mole ratio above 0.4, the composition by EPMA analysis was not consistent with that by XRF analysis. The result of EPMA analysis showed that the surface of a thin film was Cu-rich. XRD studies demonstrated that the thin films prepared at the [CGS]/([CGS]+[CIS]) mole ratio under 0.2 had a chalcopyrite Cu(In,Ga)Se₂ structure and the preferred orientation to the 112 plane. On the other hand, XRD patterns of the thin films produced at the [CGS]/([CGS]+[CIS]) mole ratio above 0.6 showed the diffraction lines from a chalcopyrite Cu(In,Ga)Se₂ and a foreign phase. The separation of a peak was observed near 2θ=27°, indicative the graded Ga concentration in Cu(In,Ga)Se₂ thin film.     

Positive Galois coverings of self-injective algebras

In the article, we study the structure of Galois coverings of self-injective artin algebras with infinite cyclic Galois groups. In particular, we characterize all basic, connected, self-injective artin algebras having Galois coverings by the repetitive algebras of basic connected artin algebras and with the Galois groups generated by positive automorphisms of the repetitive algebras.     

The influence of aliovalent impurities on the oxidation kinetics of nickel at high temperatures

The influence of chromium and sodium on the nickel oxidation kinetics has been studied as a function of temperature (1373-1673 K) and oxygen activity (10−10⁵ Pa O₂), using microthermogravimetric techniques. It has been shown that the oxidation of Ni-Cr and Ni-Na alloys, like that of pure nickel, follows strictly the parabolic rate law being thus diffusion controlled. In agreement with the defect model of Ni_1−yO, it has been found that the oxidation rate of the Ni-Cr alloy is higher than that of pure nickel, the reaction rate is pressure independent and the activation energy of this process is lower. This implies that the concentration of double ionized cation vacancies in a Ni_1−yO-Cr₂O₃ solid solution is fixed on a constant level by trivalent chromium ions, substitutionally incorporated into the cation sublattice of this oxide. In the case of the Ni-Na alloy, on the other hand, the oxidation rate is lower than that of pure nickel, the activation energy is higher and the oxidation rate increases more rapidly with oxygen pressure. These results can again be explained in terms of the doping effect, by assuming that univalent sodium ions dissolve substitutionally in the cation sublattice of nickel oxide.     

New hierarchies of knot polynomials from topological Chern-Simons gauge theory

In this Letter, we report on a study of the expectation values of Wilson loops in D=3 topological Chern-Simons theory associated with the fundamental representation of the simple Lie algebras SO(n) and Sp(n). The skein relations satisfied by these expectation values are derived by conformal field-theory techniques. New hierarchies of invariant polynomials for knots in S ³ can be derived from these relations (at least) up to ten crossings. The N=3 Akutsu-Wadati polynomials are a special case with G=SO(3). The expectation value of the Wilson loops for a couple of simple unknotted circles is identified to the Weyl character.Work supported in part by U.S. National Science Foundation Grant PHY8706501.Work supported in party by Chinese National Science Foundation through Nankai University.