Problem 1. Infinite Products and Coproducts in Ab. We have seen that finite products and coproducts agree in Ab. However, the same is not true for infinite products and coproducts. Let I be a set and let {Ai}i∈I be a family of abelian groups, each equal to some fixed group A. (a) Show that the set AI := HomSet(I, A) is an abelian group. Furthermore, show that we can think of this group as the i...

Abstract: It is difficult to weigh the light objects by weighing balance accurately when measured individually. If several light objects are weighed in groups rather than individually then the precision of the estimates increases quite considerably. There are two types of balances one is chemical balance and other is spring balance. Spring balance is similar when only one pan of chemical balanc...

We would like to welcome our readers to the twenty-eighth issue of 49 th Parallel and our second of 2012. In the last few months there have been some exciting developments at the journal and we hope that 49 th Parallel will continue to flourish in the future. We would like to welcome our new Articles Editor, Galateia Demetriou, to the 49 th Parallel team. Galateia is a second year doctoral rese...

THE RESPONSE of hitherto known practical forms of seismographs depends upon the relative motion of a pendulum and the moving ground to which ~ts supporting structure is fastened. The various kinds of seismographs differ in the type of pendulum used, such as gravity, spring, torsion, and/or they differ in the type of magnifying and recording elements which they employ. They all measure or indica...

Beijing’s mountainous areas have an important ecological significance because they are ecological conservation and water source protection areas of Beijing. The impact of precipitation on the vegetation coverage of Beijing’s mountainous areas is qualitatively analyzed using multi-temporal Landsat images obtained during the last 20 years. Firstly, the influence of external factors, such as pheno...

3 Simulation Phase: Three Models for Simulation 9 3.1 3D ChainMail . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Mass Spring Models . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.1 Classical Mass Spring Model . . . . . . . . . . . . . . . 13 3.2.2 Fast Tetrahedral Mass Spring Model . . . . . . . . . . 15 3.3 Finite Element Models . . . . . . . . . . . . . . . . . . . . . . 1...

evaluation of weed population and their interference on lentil varieties at different sowing date was investigated in a field experiment in khorramabad during 2005-06 growing season. the experimental design was a randomized complete block in factorial arrangement with 4 replications. the experiment had 3 factors including: planting date at three levels (autumn, winter, and spring) weed interfer...