Canonical connections of Finsler metrics and Finslerian connections on Riemannian metrics

A concept of canonical connection of a Finsler metric is developed. Connections that are compatible with Finsler metrics are compared with the canonical connection itself. They are also compared with the corresponding Cartan connection. A necessary and sufficient condition on metric Finsler connections is given for the metric to be Riemannian. This study unearths different ways in which Finsler geometry could be used to generalize the theory of general relativity.     

The emergence of a Kaluza-Klein microgenometry from the invariants of optimally Euclidean Lorentzian spaces

It is shown that relativistic spacetimes can be viewed as Finslerian spaces endowed with a positive definite distance (ω⁰, mod ωⁱ) rather than as pariah, pseudo-Riemannian spaces. Since the pursuit of better implementations of “Euclidicity in the small” advocates absolute parallelism, teleparallel nonlinear Euclidean (i.e., Finslerian) connections are scrutinized. The fact that (ω^μ, ω₀ ⁱ) is the set of horizontal fundamental 1-forms in the Finslerian fibration implies that it can be used in principle for obtainingcompatible new structures. If the connection is teleparallel, a Kaluza-Klein space (KKS) indeed emerges from (ω^μ, ω₀ ⁱ), endowed ab initio with intertwined tangent and cotangent Clifford algebras. A deeper level of Kähler calculus, i.e., the language of Dirac equations, thus emerges. This makes the existance of an intimate relationship between classical differential geometry and quantum theory become ever more plausible. The issue of a geometric canonical Dirac equation is also raised.     

The construction of teleparallel finsler connections and the emergence of an alternative concept of metric compatibility

The issue of whether teleparallel nonlinear connections exist is resolved by their explicit construction on Finslerian metrics that arise in the Robertson test theory of special relativity (RTTSR), and on the Minkowski metric in particular. The method is an adaptation to the Finsler bundle of a similar construction for teleparallel linear connections. It suggests the existence of a concept of metric compatibility alternative toω _μλ +ω _λμ = 0 for teleparallel nonlinear connections. A sophisticated system of partial differential equations whose solutions have been discussed in the computing literature is interpreted in geometric terms. The characteristics of the solutions are checked against compliance with the conditionω _μλ +ω _λμ = 0, an issue whose relevance for this theory derives from the fact that nonantisymmetric connections repeatedly appear in teleparallel geometry.     

Erratum to ``Real bounds, ergodicity and negative Schwarzian for multimodal maps'

A technical assumption in Part 1 of Theorem C of the authors' article Real bounds, ergodicity and negative Schwarzian for multimodal maps, J. Amer. Math. Soc. 17 (2004), 749-782, was, by mistake, omitted. Here we explain that the conclusion of the theorem holds if the interval we pullback is ``nice'.

     

An optimization-based approach for the design of Bayesian networks

Bayesian networks model conditional dependencies among the domain variables, and provide a way to deduce their interrelationships as well as a method for the classification of new instances. One of the most challenging problems in using Bayesian networks, in the absence of a domain expert who can dictate the model, is inducing the structure of the network from a large, multivariate data set. We propose a new methodology for the design of the structure of a Bayesian network based on concepts of graph theory and nonlinear integer optimization techniques.     

烟草(Nicotiana tabacum)原生质体再生成植株及影响植株分化的某些因素

从烟草(品种革新一号)单倍体花粉植株的叶和茎产生的愈伤组织,结合悬浮培养,获得的细胞分离出原生质体。在液体培养基中静置培养,12小时后原生质体开始变为卵圆形,细胞壁明显可见,24小时后完成第一次细胞分裂。以后继续分裂形成浅黄色的愈伤组织,在培养四星期后可达1毫米大小,再放到转床上进行旋转培养18天左右,愈伤组织可达3—4毫米大小。当转移到分化培养基后,分别分化出苗及根,长成完整的植株。 原生质体再生细胞的分裂与分化,不仅受不同器官来源的愈伤组织及其年龄的影响;还受分化培养基的基本成份及所用细胞分裂素的类型等的影响。     

MR and CT imaging of ethanol-treated liver tumors in an animal model

To characterize the radiographic appearance of liver lesions over time following ethanol injection, seven New Zealand white rabbits underwent surgical implantation of small fragments of VX-2 carcinoma within the liver. Upon reaching 1 cm in diameter, a tumor nodule was directly injected with absolute ethanol. Another nodule in the same animal was injected with saline as a control. Imaging was performed 6-24 days after the injections by high resolution CT and MRI, and correlation obtained with the pathologic specimens. Long TR spin-echo MR sequences were found to characterize the ethanol-treated regions of liver most accurately. Liver tissue infarcted by alcohol could be differentiated from tumor and necrosis by virtue of its short T2 relaxation value. There were no distinguishing features by other imaging techniques between the ethanol-treated and control tumor nodules. Peripheral contrast enhancement was demonstrated in both, corresponding to fibrous tissue around the ethanol-injected regions, and to viable tumor in the case of controls.     

叶轮机械设计自变数在内外环壁面上的限制条件及轴流式叶轮机械S1流面的翘曲

本文利用中心流面法的概念,指出叶轮机械的设计白变数在内、外环壁面上应有附加的限制条件,并导得其具体简明方程。同时,还定性地分析了S₁流面的翘曲情况。