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On some universal sums of generalized polygonal numbers
For those with are
called generalized -gonal numbers. Sun [13] studied for what values of
positive integers the sum is universal over (i.e., any has the form
with ). We prove that
and are universal over , as conjectured by Sun. Sun also conjectured that any can be
written as and with
; in contrast, we show that and
are universal over . Our proofs are essentially
elementary and hence suitable for general readers.Comment: Final published versio
Experimental investigation into amplitude-dependent modal properties of an eleven-span motorway bridge
The authors would like to thank their supporters. New Zealand Earthquake Commission (EQC) Research Foundation provided financial support for experimental work (Grant No. UNI/578). New Zealand Transport Agency (NZTA) provided access to the bridge. Piotr Omenzetterβs work within the LRF Centre for Safety and Reliability Engineering at the University of Aberdeen is supported by Lloydβs Register Foundation. The Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research. Ge-Wei Chenβs doctoral study is supported by China Scholarship Council (CSC) (Grant No. 2011637065).Peer reviewe
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