Compact surfaces with no Bonnet mate

This note gives sufficient conditions (isothermic or totally nonisothermic) for an immersion of a compact surface to have no Bonnet mate.Comment: 7 pages, LaTeX2

Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

Theory and Practice of Metro Network Design

Most transit networks are designed empirically. For bus net­works this process 1s often satisfactory because bus routes and networks are very dependent on local conditions, and they can be easily modified, allowing easy corrections of problems which line design may cause in operations. However, with transit systems which have extensive infrastructure, most typically metro lines and networks, corrections are ex­tremely difficult to make. Develop­ment of an optimal network and avoidance of design features which result in operational pro­blems are therefore of great im­portance. Yet, the experiences from the design and operation of such large older metro systems as London, Moscow, New York, Pan\u27s and Tokyo, or from numerous recently built medium-size metro systems, such as Hong Kong, San Francisco, Sao Paulo and Washington, remain largely unknown to the designers of new metro networks. This paper presents a theoretical analysis of transit lines and networks and its applications. The focus is on network geometry and operational characteristics. The basic design and operational elements, such as geometric forms of lines, headways, schedules, etc., are discussed in general terms, valid for any mode; however, the main focus is on metro systems because of the par­ticular importance of these analyses for fixed, permanent systems

Increasing Potential of Road Pricing for Improved Efficiency of Urban Transportation

There are a number of factors which contribute to the continuous pressure for driving in different cities. However most serious, but often overlooked is the problem that the structure of costs of driving stimulates excessive car use. This paper presents the structure of driving costs and classifies then into user, social and environmental costs. The incidence of all these costs is discussed. The importance of using road pricing for a more effective control of the demand for car travel is shown. The paper reviews objectives of road pricing and actions for their implementation and concludes that the need for road pricing and opportunities for its applications will greatly increased in the foreseeable future

Role and Organization of Transfers in Transit Networks

Passenger transfers among transit lines involve certain resistance , because they cause some delay and require passenger orientation and walking between vehicles on different lines. Therefore it is sometimes believed that transfers are undesirable and that they should be avoided whenever possible. The fact is, however, that transit networks with many transfer opportunities offer passengers much greater selection of travel paths than networks with disconnected lines which involve no transferring. In addition, the more transferring is performed, the greater is network efficiency, because each line can be designed optimally for its physical conditions, volume and character of demand. Consequently, when transfers are planned correctly, the resistance for passengers can be easily outweighed by the benefits transfers bring with respect to line alignments, schedules and, eventually, in better services offered. Passenger transfers among lines thus represent an important element of transit travel

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde

4-Quinolone fused heterocyclic ring systems by intramolecular reactions of 4-quinolone-2-carboxamides

A versatile synthetic route to new 4-quinolone-based polycyclic systems is described. TFA-catalyzed intramolecular reaction of N-unsubstituted quinolone-2-carboxylic acid amides gives structurally diverse compounds, depending on the length of the chain. Acid treatment of \u3b2-oxoamides furnishes 3H-pyrazino[1,2-a]quinoline-4,6-diones, due to the nucleophilic attack of N-1 to the carbonyl group, whereas TFA treatment of \u3b4- and \u3b5-oxoamides leads to the formation of tetracyclic compounds by a tandem heteroannulation reaction

Excursion Sets and Non-Gaussian Void Statistics

Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the distribution of collapsed objects (i.e. dark matter halos and the galaxies and galaxy clusters that reside in them) to probe primordial NG. An equally interesting and complementary probe however is the abundance of extended underdense regions or voids in the LSS. The calculation of the abundance of voids using the excursion set formalism in the presence of primordial NG is subject to the same technical issues as the one for halos, which were discussed e.g. in arXiv:1005.1203. However, unlike the excursion set problem for halos which involved random walks in the presence of one barrier $\delta_c$, the void excursion set problem involves two barriers $\delta_v$ and $\delta_c$. This leads to a new complication introduced by what is called the "void-in-cloud" effect discussed in the literature, which is unique to the case of voids. We explore a path integral approach which allows us to carefully account for all these issues, leading to a rigorous derivation of the effects of primordial NG on void abundances. The void-in-cloud issue in particular makes the calculation conceptually rather different from the one for halos. However, we show that its final effect can be described by a simple yet accurate approximation. Our final void abundance function is valid on larger scales than the expressions of other authors, while being broadly in agreement with those expressions on smaller scales.Comment: 28 pages (18+appendices), 7 figures; v2 -- minor changes in sec 3.2, version published in PR