Bisoptic curves of hyperbolas

Given a hyperbola, we study its bisoptic curves, i.e. the geometric locus of points through which passes a pair of tangents making a fixed angle θ or 180° ? θ. This question has been addressed in a previous paper for parabolas and for ellipses, showing hyperbolas and spiric curves, respectively. Here the requested geometric locus can be empty. If not, it is a punctured spiric curve, and two cases occur: the curve can have either one loop or two loops. Finally, we reconstruct explicitly the spiric curve as the intersection of a plane with a self-intersecting torus.     

Optimal Parametric Search on Graphs of Bounded Tree-Width

We give linear-time algorithms for a class of parametric search problems on weighted graphs of bounded tree-width. We also discuss the implications of our results to approximate parametric search on planar graphs.     

Difluoro complexes of platinum(II) and -(IV) with monodentate phosphine ligands: an exceptional stability of d6 octahedral organometallic fluorides

Complexes (R3P)2PtF2 were prepared by reaction of the corresponding diiodo precursors with AgF in dichloromethane. The intermediate formation of trans- and cis-(R3P)2Pt(I)F was also observed. All fluoro complexes demonstrate a strong preference for the cis-configuration (R = Ph or Et) unless a bulky phosphine ligand is used (R = i-Pr), in which case the trans complex was observed. The Pt(IV) difluoro compounds (R3P)2Ar2PtF2 were obtained by reacting the Pt(II) diaryl precursors with XeF2. The fluoro ligands are located in the trans-position relative to the aryl groups in the overall octahedral environment. The representative Pt(II) and Pt(IV) difluoro complexes were characterized by X-ray crystallography. All fluoro compounds react rapidly with chlorotrimethylsilane to give the corresponding chloro complexes. The Pt(IV) difluorides are remarkably stable in the C-C reductive elimination reaction, relative to their dichloro analogs which reductively eliminate diaryl within several hours at 45 degrees C in N-methylpyrrolidone. It was found that phosphine dissociation from the octahedral Pt(IV) complex is essential for the reductive elimination reaction to take place, the difluoro complex being kinetically stable even at 60 degrees C.     

Polarized and Unpolarized Emission from a Single Emitter in a Bullseye Resonator

Polarized , and unpolarized emission from a single emitter embedded in a single, cylindrically symmetric device design is presented. The polarization stems from a position offset of the single emitter with respect to the cavity center, which breaks the cylindrical symmetry, and a position-dependent coupling to the frequency degenerate eigenmodes of the resonator structure is shown. The experimental results are interpreted by using numerical simulations and by experimental mapping of the polarization-resolved far-field emission patterns. The findings can be generalized to any nanophotonic structure where two orthogonal eigenmodes are not fully spatially overlapping.     

The journey to engaged customer community: Evidential social CRM maturity model in Twitter

We investigate the company use of Twitter as a platform for social customer relations management (SCRM) to find that message type and follower growth follow an identifiable maturity model. Studying longitudinal Twitter data from 73 Standard and Poor's companies, we find that companies map into one of two distinct maturity stages as reflected in the content of company‐generated messages. The first maturity stage consists of branding, where the focus is on customer acquisition up to a certain volume, at the expense of their engagement. The second is social care, where the focus is on retaining customers and increased engagement. We further find that companies have relatively little control over their maturity stage and that investing in social care in the first stage, aiming to increase engagement, is not effective. Proper understanding and recognition of the Twitter SCRM maturity model will allow companies to assess their methods and processes according to SCRM best practices.     

Finding a Hamilton cycle fast on average using rotations and extensions

We present an algorithm CRE, which either finds a Hamilton cycle in a graph G or determines that there is no such cycle in the graph. The algorithm's expected running time over input distribution G～G(n,p) is (1+o(1))n/p, the optimal possible expected time, for . This improves upon previous results on this problem due to Gurevich and Shelah, and to Thomason.     

Disturbing,but not surprising: Did Gödel surprise Einstein with a rotating universe and time travel?

The question is raised as to the kind of methodology required to deal with foundational issues. A comparative study of the methodologies of Gödel and Einstein reveals some similar traits which reflect a concern with foundational problems. It is claimed that the interest in foundational problems stipulates a certain methodology, namely, the methodology of limiting cases.In honor of Professor Max Jammer on the occasion of his 80th birthday.This paper was completed while I was a DAAD (Deutscher Akademischer Austauschdienst) fellow at the Zentrum Philosophie und Wissenschaftstheorie, Universität Konstanz, Germany. I gratefully acknowledge the generous assistance of the DAAD. Special thanks are due to Martin Carrier, Olivier Darrigol, and Gereon Wolters.     

Some contributions to the asymptotic theory of Bayes solutions

Summary This paper deals with the asymptotic theory of Bayes solutions in (i) Estimation (ii) Testing when hypothesis and alternative are separated at least by an indifference region, under the assumption that the observations are independent and indentically distributed. The estimation results which are partial generalizations of results of LeCam begin with a proof of the convergence of the normalized posterior density to the appropriate normal density in a strong sense. From this result we derive the asymptotic efficiency of Bayes estimates obtained from smooth loss functions and in particular of the posterior mean. The last two theorems of this section deal with asymptotic expansions for the posterior risk in such estimation problems. The section on testing contains a limit theorem for the n-th root of the posterior risk under weak conditions on the prior and the loss function. Finally we discuss generalizations and some open problems.Part of this research was done while P. J. Bickel was on leave at Imperial College, London. — This research was partially supported by National Science Foundation Grant GP-5059.This research was partially supported by National Science Foundation Grant GP-5705. Part of this research was done while J. A. Yahav was visiting the department of Statistics at Stanford University.     

Unpredicted electron injection in CdS/CdSe quantum dot sensitized ZrO2 solar cells

A quantum dot sensitized solar cell based on a porous ZrO(2) film, sensitized with CdSe quantum dots using CdS as an intermediate layer is presented. We observe electron injection from photo-excited quantum dots into the ZrO(2), which is unexpected due to the much higher conduction band edge (closer to the vacuum level) of bulk ZrO(2) compared to TiO(2).     

Synthesis of the elusive (R3P)2MF2 (M = Pd, Pt) complexes

The synthesis and characterization of previously unknown palladium(II) and platinum(II) difluoro phosphine complexes are described. These complexes can be obtained either via a halide metathesis reaction with AgF in dichloromethane or by reacting the corresponding dimethyl complexes with XeF2. While the Pt(II) complexes can be prepared with both aryl- and alkyl-phosphine ligands, the stability of the Pd(II) complexes is limited to those having cis-oriented trialkyl phosphine ligands.