Generalized Jordan derivations associated with Hochschild 2-cocycles of triangular algebras

In this paper, we investigate a new type of generalized derivations associated with Hochschild 2-cocycles which is introduced by A.Nakajima (Turk. J. Math. 30 (2006), 403–411). We show that if U is a triangular algebra, then every generalized Jordan derivation of above type from U into itself is a generalized derivation.     

Donald in Wonderland: The Many-Faceted Life of H. S. M. Coxeter

The Mathematical Intelligencer -     

Incidence-polytopes of type {6, 3, 3}

From the hyperbolic honeycomb {6, 3, 3} we derive a class of abstract polytopes whose cells are isomorphic to the toroidal maps {6, 3} _b,c and vertex figures to tetrahedra. We give a criterion on the finiteness of these incidence-polytopes in terms of the group PSL ^± (2, []), leading, among other things, to the explicit recognition of the groups in some interesting special cases.Research supported by NSERC Canada Grant A8857.     

Effects of laser irradiation energy density on the properties of pulsed laser deposited ITO thin films

The properties of indium tin oxide (ITO) thin films, deposited at room temperature by simultaneous pulsed laser deposition (PLD), and laser irradiation of the substrate are reported. The films were fabricated from different Sn-doped In₂O₃ pellets at an oxygen pressure of 10 mTorr. During growth, a laser beam with an energy density of 0, 40 or 70 mJ/cm² was directed at the middle part of the substrate, covering an area of ∼1 cm². The non-irradiated (0 mJ/cm²) films were amorphous; films irradiated with 40 mJ/cm² exhibited microcrystalline phases; and polycrystalline ITO films with a strong 〈111〉> preferred orientation was obtained for a laser irradiation density of 70 mJ/cm². The resistivity, carrier density, and Hall mobility of the ITO films were strongly dependent on the Sn doping concentration and the laser irradiation energy density. The smallest resistivity of ∼1×10^-4 Ω cm was achieved for a 5 wt % Sn doped ITO films grown with a substrate irradiation energy density of 70 mJ/cm². The carrier mobility diminished with increasing Sn doping concentration. Theoretical models show that the decrease in mobility with increasing Sn concentration is due to the scattering of electrons in the films by ionized centers. PACS 81.15.Fg; 73.61.-r; 73.50.-h     

Semisymmetric graphs from polytopes

Every finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which are edge- but not vertex-transitive). In particular, the Gray graph arises as the medial layer graph of a certain universal locally toroidal regular 4-polytope.     

Microdetermination of metals in organometallic compounds by the oxine method after oxygen flask combustion: IV. Neodymium,praseodymium, samarium,and yttrium

The oxine method after oxygen flask combustion was extended for the microdetermination of neodymium, praseodymium, samarium, and yttrium in their organometallic compounds. The metal content is determined gravimetrically (Method I) and volumetrically (Methods II and III) using a single sample weight. The method has the advantage of a favorable gravimetric factor, besides a sufficiently sharp endpoint with 12-fold amplification reaction in case of titrimetric finish. The average percent error for the determination is ±0.07, ±0.06, and ±0.07 for Methods I, II, and III, respectively.