On the spectral sequence constructors of Guichardet and Stefan

The concept of a spectral sequence constructor is generalised to Hopf Galois extensions. The spectral sequence constructions that are given by Guichardet for crossed product algebras are also generalised and shown to provide examples. It is shown that all spectral sequence constructors for Hopf Galois extensions construct the same spectral sequence.     

Pulsed reactive crossed beam laser ablation of La0.6Ca0.4CoO3 using O: Where does the oxygen come from?

The composition of thin perovskite films, especially the oxygen content, is a crucial parameter which influences many physical properties, such as conductivity and catalytic activity. Films produced by pulsed laser deposition are normally annealed in an oxygen atmosphere after deposition to achieve a desired oxygen content. In pulsed reactive crossed beam laser ablation, no annealing step is necessary, but a fundamental question regarding this deposition technique is still open: where does the oxygen in the films come from?There are three possibilities, i.e. from the target, from the gas background, or from the gas pulse. To answer this question two experiments were performed: ¹⁸O₂ was used during the deposition process as background gas with ¹⁶O anions in the target and ¹⁶O₂ gas pulse, and a ¹⁸O₂ gas pulse with ¹⁶O from the target and background. These experiments revealed that the quantification of the oxygen origin is only possible, when no oxygen exchange occurs at the deposition temperature. The films are characterized after deposition by elastic recoil detection analysis (ERDA) to determine the ¹⁶O/¹⁸O ratio. Experiments with different oxidizing species in the gas pulse (N₂O and O₂) confirm that the oxidizing potential (N₂O > O₂) as well as the number of molecules are important.     

A remark on Mansfield's imprimitivity theorem

We show that the Morita equivalence part of Mansfield's Imprimitivity Theory can be obtained by Green's Imprimitivity Theorem (and duality theory).

     

Parameterized approximations for the two-sided assortment optimization

We consider the problem faced by an online service platform that matches suppliers with consumers. Unlike traditional matching models, which treat them as passive participants, we allow both sides of the market to exercise their choices. To model this setting, we introduce a two-sided assortment optimization model wherein each participant's choice is modeled using a multinomial logit choice function, and the platform's objective is to maximize its expected revenue. We first show that the problem is NP-hard even when the number of suppliers is limited to two and provide a mixed-integer linear programming formulation. Next, we discuss two simple greedy heuristics and argue that these can lead to arbitrarily bad solutions. We then develop relaxations that provide upper and lower bounds and investigate the tightness of these relaxations by obtaining parametric approximation guarantees. Finally, we present numerical results on synthetic data demonstrating the practical utility of these relaxations.     

A Crossed Immunoelectrophoretic Technique for the Detection of the Down's Syndrome Protein

Abstract

The sera of seventy-one women and twenty-six men of various ages were examined by a two dimensional (crossed) immunoelectrophoresis technique which was modified to detect a protein (the Down's Syndrome protein) originally found in the sera of mothers of trisomy 21 children. The sensitivity of the method is reported to be 0.1 to 1.0 mg/L. Modifications included use of a Tris-Tricine buffer, high voltage in the second dimension, and relatively low antibody concentration to allow easy detection of the Down's Syndrome (DS) protein.

Of twenty-eight mothers and twelve fathers of trisomy 21 children, eighteen mothers and five fathers were positive, while of forty-three women and fourteen men having unaffected or no children, only seven women and two men were positive for the DS protein.

Since the presence of the Down's Syndrome protein may indicate a propensity for giving birth to a trisomy 21 affected child, this crossed immunoelectrophoretic technique may be used as a screening procedure for the DS protein and, therefore, as a tool in genetic counseling.     

Constructing the Co cyclic Structures for Crossed Copro duct Coalgebras

In this paper, we construct a cocylindrical object associated to two coal-gebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduct c...     

A combined crossed molecular beam and quasiclassical trajectory study of the Titan-relevant N(2D) + D2O reaction

Following a recent investigation on the N(²D) + H₂O reaction [Homayoon et al., J. Phys. Chem. Lett. 5, 3508 (2014)], we report on an experimental and theoretical study of the isotopologue N(²D) + D₂O reaction. Crossed molecular beam (CMB) experiments were conducted at a collision energy of 10.3 kcal mol^–1. Quasiclassical trajectory calculations were performed on a recent potential energy surface to derive the centre-of-mass functions necessary to simulate the CMB laboratory distributions. Excellent agreement was found. The importance of the channel leading to HON/DON was confirmed. The inclusion of this channel, in addition to that leading to the isomer HNO/DNO, can affect the models considering the coupling between nitrogen and oxygen chemistry in the upper atmosphere of Titan.     

The global dimensions of crossed products and crossed coproducts

In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H^＊ are semisimple, then gl.dim（A#σH）=gl.dim（A）, where a is a convolution invertible cocycle. We also discuss the relationship of global dimensions between the crossed product A^#σH and the algebra A, where A is coacted by H. Dually, we give a sufficient condition for a finite dimensional coalgebra C and a finite dimensional semisimple Hopf algebra H such that gl.dim（C α H）=gl.dim（C）.     

Oriented O(3P2), Ne(3P2), and He(3S1) atoms emerging from a bent magnetic guide

We describe our observation of strongly oriented total electronic angular momentum J in O(³P₂), Ne(³P₂), and He(³S₁) atoms emerging from a bent magnetic multipole guide, as measured by resonant multiphoton ionisation. This was contrary to our expectation because no additional (uniform) magnetic fields were applied to orient the atoms behind the exit of the guide. Two- and three-photon ionisation techniques were employed to determine the degree of J polarisation, from which we infer that atoms become oriented as a result of a combination of weak fringe fields, possible stray fields, and the fact that molecular beam packets do not oscillate around the geometric center of the bent multipole guide. We conclude that similar effects may exist in other, related experiments and that a detailed characterisation of the degree of orientation is required prior to any study of chemical dynamics or spectroscopy. This paper should serve as a warning for anybody using similar devices not to assume isotropic angular momentum distributions of atoms and molecules emerging from a magnetic guide or a decelerator, particularly when it is bent; whenever possible, the possibility for a J anisotropy should be experimentally checked.     

Cyclic Cohomology of étale Groupoids: The General Case

We give a general method for computing the cyclic cohomology of crossed products by étale groupoids, extending the Feigin–Tsygan–Nistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea, Connes, Feigin, Karoubi, Nistor, and Tsygan for the convolution algebra C _c (G) of an étale groupoid, removing the Hausdorffness condition and including the computation of hyperbolic components. Examples like group actions on manifolds and foliations are considered.