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H.B. Wen, T. Zeng and G.Z. Hu

Abstract

Laplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.

Open access

Robert P. Agans, Malcolm T. Jefferson, James M. Bowling, Donglin Zeng, Jenny Yang and Mark Silverbush

Abstract

To receive federal homeless funds, communities are required to produce statistically reliable, unduplicated counts or estimates of homeless persons in sheltered and unsheltered locations during a one-night period (within the last ten days of January) called a point-in-time (PIT) count. In Los Angeles, a general population telephone survey was implemented to estimate the number of unsheltered homeless adults who are hidden from view during the PIT count. Two estimation approaches were investigated: i) the number of homeless persons identified as living on private property, which employed a conventional household weight for the estimated total (Horvitz-Thompson approach); and ii) the number of homeless persons identified as living on a neighbor’s property, which employed an additional adjustment derived from the size of the neighborhood network to estimate the total (multiplicity-based approach). This article compares the results of these two methods and discusses the implications therein.