Model for superconducting current in HTSC: How to calculate the maximum intrinsic values

Summary In order to explain the HTSC electrical density values, the authors propose a new original model for these new superconductors, introducing the parameterSc, given by the ratio between the coherence distance ξ₀ and the lattice constant λ₁. The value ofSc is less than 1 in HTSC and higher than 1 in normal s.c. In HTSC the pair electron transport mechanism became different than in other s.c., in which a wave function linear coherence is established. A Josephson intrinsic electrical conduction mechanism is established. The HTSC behaves like a good diamagnetic material but a bad superconductor.     

Spurious Disambiguation Errors and How to Get Rid of Them

The disambiguation approach to the input of formulae enables users of mathematical assistants to type correct formulae in a terse syntax close to the usual ambiguous mathematical notation. When it comes to incorrect formulae however, far too many typing errors are generated; among them we want to present only errors related to the formula interpretation meant by the user, hiding errors related to other interpretations. We study disambiguation errors and how to classify them into the spurious and genuine error classes. To this end we give a general presentation of the classes of disambiguation algorithms and efficient disambiguation algorithms. We also quantitatively assess the quality of the presented error classification criteria benchmarking them in the setting of a formal development of constructive algebra. Partially supported by the Strategic Project “DAMA: Dimostrazione Assistita per la Matematica e l’Apprendimento” of the University of Bologna.     

XAS investigation of tantalum and niobium in nanostructured TiO2 anatase

Sol-gel routes were used to prepare Ta 10 at% and Nb 5 at% and 10 at% doped titania nanosized powders. When fired between 410°C and 850°C the doped titania powders are in the anatase phase; further heating up to 1050°C is required to obtain the rutile phase. The presence of dopant atoms delays the rate of transformation as compared with pure titania powders. Doping also affects the rate of grain growth and increases the conductance response to gas. To better understand the role played by dopant atoms in inhibiting both phase transformation to rutile and grain growth, X-ray Absorption Spectroscopy measurements were performed at the L_III-L_I absorption edges of Ta and Nb K absorption edge. Analysis was restricted to the anatase phase because the transformation to rutile phase, obtained by firing at 1050°C, is accompanied by the formation of undesired Ta and Nb oxides (Ta₂O₅ and Nb₂TiO₇, respectively). Extended X-ray Absorption Fine Structure and X-ray Absorption Near-Edge Spectroscopy analysis results indicate that in nanostructured anatase both tantalum and niobium atoms substitute Ti cations with +5 valence state.     

Sol-Gel Nanosized Semiconducting Titania-Based Powders for Thick-Film Gas Sensors

Pure, 5 at%, and 10 at% Ta- or Nb-doped TiO₂ nanosized powders were prepared by the sol-gel method. The powders heated to 400°C have the crystalline anatase structure. While the pure TiO₂ powder heated to 850°C has the rutile structure, the addition of Ta and Nb inhibited the anatase-to-rutile phase transformation at this temperature. Ta was soluble in the titania lattice up to the concentration of 10 at%, while the solubility of Nb was 5 at%. Thick films were fabricated with these powders by screen printing technology and then fired at 650°C and 850°C for 1 h. SEM observations showed that the anatase-to-rutile phase transformation induces a grain growth of about one order of magnitude for pure TiO₂. The addition of Ta and Nb is effective to keep the TiO₂ grain size at the nanometric level even at 850°C. Conductance measurements showed that a good gas response is observed only for the nanostructured titania-based films. The CO response of these materials is only slightly affected by humidity.     

Lebesgue’s dominated convergence theorem in Bishop’s style

We present a constructive proof in Bishop’s style of Lebesgue’s dominated convergence theorem in the abstract setting of ordered uniform spaces. The proof generalises to this setting a classical proof in the framework of uniform lattices presented by Hans Weber in [Uniform lattices. II: order continuity and exhaustivity, Annali di Matematica pura ed applicata, (IV) CLXV (1993) 133-158].     

Nachweis und Bestimmung des Mangans sowie seine Trennung von anderen Elementen

Ohne Zusammenfassung     

A Survey on Retrieval of Mathematical Knowledge

We present a survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 77 papers and tentative taxonomies of both retrieval problems and recurring techniques.