Riemannian geometry of quantum computation

A review is given of some recent developments in the differential geometry of quantum computation for which the quantum evolution is described by the special unitary unimodular group, SU(2ⁿ). Using the Lie algebra su(2ⁿ), detailed derivations are given of a useful Riemannian geometry of SU(2ⁿ), including the connection and the geodesic equation for minimal complexity quantum computations.     

A practical algorithm for decomposing polygonal domains into convex polygons by diagonals

We present algorithms for decomposing a polygon (with holes) into convex polygons by diagonals. The methods are computationally quick, and although the partitions that they produce may not have minimal cardinality they usually have a low number of convex pieces. Thus, the methods are suitable for being used when achieving a modest load on the CPU time is more important than finding optimal decompositions as, for instance, in location problems. Part of the results in this paper are from Fernández (1999), and were presented in Fernández et al. (1998). This work has been supported by the Ministry of Science and Technology of Spain under the research projects BEC2002-01026, SEJ2005-06273/ECON (J. Fernández, B. Tóth and B. Pelegrín) and TIC2003-05982-C05-03 (L. Cánovas), in part financed by the European Regional Development Fund (ERDF).     

Realization of a unique time evolution unitary operator in Klein Gordon theory

The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hubert spaceL ²(R ³) and the Einstein’s relativistic equation in the spaceL ²(R ³, dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hubert spaceL ²(R ³) with the help of unique symmetric symplectic operator, the time evolution unitary operatorU(t) has been fixed for the Klein Gordon equation, incorporating either the positive or negative frequencies, in the infinite dimensional Hubert spaceL ²(R ³).     

Synthesis of 2,6-Disubstituted Fluorenones

Various 2,6-disubstituted fluorenones 1a-1g were synthesized by the dry salt decomposition of 5,4′ -disubstituted 2-diazoniobenzophenone tetrafluoroborates 8a-8g via Pschorr cyclization in reasonable yields.     

The population-sample decomposition approach to multivariate estimation methods

In this paper it is argued that all multivariate estimation methods, such as OLS regression, simultaneous linear equations systems and, more widely, what are known as LISREL methods, have merit as geometric approximation methods, even if the observations are not drawn from a multivariate normal parent distribution and consequently cannot be viewed as ML estimators. It is shown that for large samples the asymptotical distribution of any estimator, being a totally differentiable covariance function, may be assessed by the δ method. Finally, we stress that the design of the sample and a priori knowledge about the parent distribution may be incorporated to obtain more specific results. It turns out that some fairly traditional assumptions, such as assuming some variables to be non-random, fixed over repeated samples, or the existence of a parent normal distribution, may have dramatic effects on the assessment of standard deviations and confidence bounds, if such assumptions are not realistic. The method elaborated by us does not make use of such assumptions.     

N-策略单重休假M/G/1排队系统的队长分布

本文考虑N-策略单重休假M/G/1排队系统,通过引进"服务员忙期"和使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态分布和稳态分布,首次导出了在任意时刻t瞬态队长分布的L变换的递推表达式和稳态队长分布的递推表达式,以及平稳队长的随机分解.特别地,通过本文可直接获得一些特殊排队系统相应的结果.     

Geometric aspects of transversal Killing spinors on Riemannian flows

We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those flows carrying non-trivial solutions.      

All regular Landsberg metrics are Berwald

This article negatively answers the long standing problem concerning the existence of non-Berwald Landsberg metrics.