A faster 2-approximation algorithm for the minmax p-traveling salesmen problem on a tree

Given an edge-weighted tree T and an integer p1, the minmax p-traveling salesmen problem on a tree T asks to find p tours such that the union of the p tours covers all the vertices. The objective is to minimize the maximum of length of the p tours. It is known that the problem is NP-hard and has a (2−2/(p+1))-approximation algorithm which runs in O(p^p−1n^p−1) time for a tree with n vertices. In this paper, we consider an extension of the problem in which the set of vertices to be covered now can be chosen as a subset S of vertices and weights to process vertices in S are also introduced in the tour length. For the problem, we give an approximation algorithm that has the same performance guarantee, but runs in O((p−1)!·n) time.     

The covering number and the uniformity of the ideal ℐf

Let f, g ∈ ^ω ω . We will denote by g ? f that for every k < ω, f (n ^k ) ≤ g (n ) except for finitely many n . The ideal ?_f on ^ω 2 is the collection of sets X such that, for some g ? f and τ ∈ ∏_{n <ω} ^{g (n )}2, every x ∈ X satisfies τ (n ) ? x for infinitely many n . In the present paper, we will prove the consistency of cov(?_f ) < ?? and non(?_f ) < ??. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

k-Subdomination in graphs

For a positive integer k, a k-subdominating function of a graph G=(V,E) is a function f : V→{−1,1} such that ∑_uNG[v]f(u)1 for at least k vertices v of G. The k-subdomination number of G, denoted by γ_ks(G), is the minimum of ∑_vVf(v) taken over all k-subdominating functions f of G. In this article, we prove a conjecture for k-subdomination on trees proposed by Cockayne and Mynhardt. We also give a lower bound for γ_ks(G) in terms of the degree sequence of G. This generalizes some known results on the k-subdomination number γ_ks(G), the signed domination number γ_s(G) and the majority domination number γ_maj(G).     

Sweet &; sour and other flavours of ccc forcing notions

We continue developing the general theory of forcing notions built with the use of norms on possibilities, this time concentrating on ccc forcing notions and classifying them.The first author thanks the Hebrew University of Jerusalem for its hospitality during his visits to Jerusalem. His research was also partially supported by a grant from the University Committee on Research of UNOThe research of the second author was partially supported by the Israel Science Foundation. Publication 672Mathematics Subject Classification (2000): Primary 03E35 Secondary; 03E40, 03E05Revised version: 30 September 2003     

Radiative forcing of aerosols and gases over tropical ocean and its impact on the global atmospheric environment: GCM investigations during INDOEX campaigns

Radiative forcings due to aerosols and the pollutant gases accumulated as haze which are transported from nearby continent to the tropical ocean are essentially important elements of the world climate system. Vertical transport of aerosols and gaseous species takes place within the deep convective cloud clusters of the inter-tropical convergence zone and subsequently these are distributed by the upper atmospheric zonal wind flow, thereby have impact on the global atmospheric environment. The comprehensive global atmospheric models have shown capability of simulating the climate of the atmosphere with proper forcing. We have deduced the radiative forcing, optical depth and the global energy balance components by a global atmospheric model. The results are validated well with INDOEX and other available observational findings.     

A hybrid immersed‐boundary and multi‐block lattice Boltzmann method for simulating fluid and moving‐boundaries interactions

A numerical method is developed for modelling the interactions between incompressible viscous fluid and moving boundaries. The principle of this method is introducing the immersed‐boundary concept in the framework of the lattice Boltzmann method, and improving the accuracy and efficiency of the simulation by refining the mesh near moving boundaries. Besides elastic boundary with a constitutive law, the method can also efficiently simulate solid moving‐boundary interacting with fluid by employing the direct forcing technique. The method is validated by the simulations of flow past a circular cylinder, two cylinders moving with respect to each other and flow around a hovering wing. The versatility of the method is demonstrated by the numerical studies including elastic filament flapping in the wake of a cylinder and fish‐like bodies swimming in quiescent fluid. Copyright © 2006 John Wiley & Sons, Ltd.     

Environmental pollution due to black carbon aerosols and its impacts in a tropical urban city

Black carbon (BC) has become the subject of interest in the recent years for a variety of reasons. BC aerosol may cause environmental as well as harmful health effects in densely inhabited regions. BC is a strong absorber of radiation in the visible and near-infrared part of the spectrum, where most of the solar energy is distributed. Black carbon is emitted into the atmosphere as a byproduct of all combustion processes, viz., vegetation burning, industrial effluents, motor vehicle exhausts, etc. In this paper, we present results from our measurements on BC aerosols, total aerosol mass concentration, and aerosol optical depth over an urban environment, namely Hyderabad during January-May, 2003. Diurnal variations of BC suggest that high BC concentrations are observed during 6:00-9:00 h and 19:00-23:00 h. Weekday variations of BC suggest that the day average BC concentrations increases gradually from Monday to Wednesday and gradually decreases from Thursday to Sunday. Fraction of BC to total mass concentration has been observed to be 7%. BC showed positive correlation with total mass concentration and aerosol optical depth at 500 nm. Radiative transfer calculations suggest that during January-May, diurnal averaged aerosol forcing at the surface was calculated to be −33 Wm⁻² and at the top of the atmosphere (TOA) it is to be +9 Wm⁻².     

每个点都是链回归点的树映射

设f是端点数为n的树T上的连续自映射且T上的每一点都是f的链回归点.本文证明了: (1)如果T的某个端点是f的不动点,那么,T上的每个点都是f的周期为r≤n-1的周期点,或存在自然数r ≤ n-1,使得fr含有湍流; (2)如果f的不动点都在T的内部,那么,T上的每个点都是f的周期为r≤n的周期点,或存在自然数r≤n,使得,fr含有湍流.     

Removing Laver functions from supercompactness arguments

We show how the use of a Laver function in the proof of the consistency, relative to the existence of a supercompact cardinal, of both the Proper Forcing Axiom and the Semiproper Forcing Axiom can be eliminated via the use of lottery sums of the appropriate partial orderings. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multidimensional bipartite trees

We introduce a bipartite version of k-trees and establish characterizations of bipartite 2- and 3-trees.