The -theory of toric manifolds

Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an -dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the -theory of all toric manifolds and certain singular toric varieties.

     

Use of Transmission Electron Microscopy in Combinatorial Studies of Functional Oxides

Summary: The principles of combinatorial methodology are based on high‐throughput properties measurements (HTPM) of multiple compositions in combinatorial libraries, and are recently being increasingly applied in materials research. Nevertheless, the authors' view is that the involvement of detailed but time‐consuming investigation using transmission electron microscopy (TEM) should be an important part of combinatorial materials research. In this paper we present three examples from our combinatorial studies where the TEM investigation was essential in obtaining a detailed picture of microstructures and their relationship with the physical properties. In the study of microwave dielectrics such as BaTiO₃‐SrTiO₃, TEM provides essential information on the type and distribution of defects in the deposited films. In the case of the wide‐band semiconductor ZnO‐MgO, the distribution and morphology of the phases were studied and related to the measured electronic properties. Study of the manganates LaMnO₃‐CaMnO₃ with colossal magneto‐resistive properties showed an anisotropic distribution of the structural domains and the morphology of the film. The distribution of the domains and the absence of epitaxial stresses found are essential in the interpretation of magnetic measurements.

Cross‐sectional TEM (dark field) micrograph taken with the reflection of h‐(Zn,Mg)O at x = 0.5.     

Transmission electron microscopy study of Ruddlesden-Popper Can+1MnnO3n+1n=2 and 3 compounds

Two Ruddlesden-Popper compounds Ca_n+1Mn_nO_3n+1 with n=2 and 3 synthesized by a citrate gel technique have been studied by TEM. The structure of Ca₄Mn₃O₁₀ is consistent with the previously determined structure having the space group Pbca and a⁻ a⁻ c⁺/a⁻ a⁻ c⁺ tilt system. The presence of defects suggests the possible high-temperature phase transition from untilted I4/mmm to Pbca. The structure of Ca₃Mn₂O₇ was found to be different from the previously suggested I4/mmm symmetry. Ca₃Mn₂O₇ forms with an orthorhombic structure with either Cmcm or Cmc2₁ space group. A structural model for Cmc2₁ based on the tilting of almost-rigid octahedra with a⁺ c⁻ c⁻/a⁺ c⁻ c⁻ tilt system is proposed. The lamellar defects were shown to be twin variants of the Cmc2₁ structure with the (001)_t interfaces, which suggests the possible tilting phase transition from the ideal I4/mmm to Cmc2₁ following the maximal group-subgroup symmetry tree: I4/mmm→Fmmm→Bbmm(Cmcm)→Bb2₁m(Cmc2₁).     

Combinatorial study of thin film metal hydride by prompt gamma activation analysis

Cold neutron prompt gamma activation analysis (PGAA) was used to determine the mass of hydrogen in Mg hydride thin films with varying hydrogenation times. The results suggest that hydrogenation of the Mg thin films remains unsaturated even after 48 h of treatment, contrary to the indications of inferential hydrogen measurement methods. To demonstrate PGAA as an effective combinatorial methodology for hydride thin films, a continuously varying composition gradient of thin Mg_yTi_(1−y) hydride film with y ranging from 0.65 to 0.94 was prepared and analyzed by both PGAA and instrumental neutron activation analysis (INAA). The variation in the molar ratio of Mg, Ti, and H was obtained for nine 5 mm wide segments of the film.     

Selective and efficient quantum process tomography without ancilla

Several methods, known as quantum process tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present a new method for quantum process tomography. We describe a new algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.     

The full-information best-choice problem with uniform or gamma horizons

A decision-maker has to choose one from among a Poisson stream of i.i.d. bids, with no recall. The stream stops at a random time with a uniform (in the first case) or Erlang (in the second case) distribution. We solve the problem explicitly for maximal expected gain for bids that may take on any finite number of values. A fast procedure to solve the problem for fixed horizon is presented as well.     

High-resolution identification of ½⟨110⟩ stacking faults in epitaxial Ba0.3Sr0.7TiO3 thin films

The near-interface region of an epitaxial Ba_0.3Sr_0.7TiO₃ thin film grown on LaAlO₃ (001) was found to consist of a high density of ½?110? stacking faults bounded by partial dislocations. The stacking faults can extend over large distances (greater than 50 nm). Various possible atomic configurations of the faults were considered. The atomic structures of the faults were identified using high-resolution electron microscopy and simulation as well as energy-filtered imaging. The ½[101] and faults (where [001] is normal to the film plane) were found to lie predominately on the {100} and {110} planes. The ½lsqb;101] faults on (010), (110) or (1&1tilde;0) have never been observed before in perovskites. The stacking faults on [100] have a structure consisting of a double layer of edge-sharing TiO₆ octahedra. The excess of Ti was detected by energy-filtered imaging. The formation of the extended stacking faults is probably related to a small amount of excess Ti during the film deposition, which may originate from the non-stoichiometry of the ceramic targets BaTiO₃ and SrTiO₃. It is also enhanced by the misfit-induced compressive strain in the early stages of the film growth.