A note on higher-order nondifferentiable symmetric duality in multiobjective programming

AbstractIn this work, we establish a strong duality theorem for Mond–Weir type multiobjective higher-order nondifferentiable symmetric dual programs. This fills some gaps in the work of Chen [X. Chen, Higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290 (2004) 423–435]

Corrigendum: COVID-19 Confinement and Health Risk Behaviors in Spain

In the original article, the reference for Chen et al. (2009) was incorrectly written as “Chen, P., Mao, L., Nassis, G. P., Harmer, P., Ainsworth, B. E., and Li, F. (2009). Wuhan coronavirus (2019-nCoV): the need to maintain regular physical activity while taking precautions. J. Sport Health Sci. 9, 103–104. doi: 10.1016/j.jshs.2020.02.001”. It should be “Chen, P., Mao, L., Nassis, G. P., Harmer, P., Ainsworth, B. E., and Li, F. (2020). Coronavirus disease (COVID-19): The need to maintain regular physical activity while taking precautions. J. Sport Health Sci. 9, 103–104. doi: 10.1016/j.jshs.2020.02.001”. The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated

Sharp Threshold Asymptotics for the Emergence of Additive Bases

A subset A of {0,1,...,n} is said to be a 2-additive basis for {1,2,...,n} if each j in {1,2,...,n} can be written as j=x+y, x,y in A, x<=y. If we pick each integer in {0,1,...,n} independently with probability p=p_n tending to 0, thus getting a random set A, what is the probability that we have obtained a 2-additive basis? We address this question when the target sum-set is [(1-alpha)n,(1+alpha)n] (or equivalently [alpha n, (2-alpha) n]) for some 0<alpha<1. Under either model, the Stein-Chen method of Poisson approximation is used, in conjunction with Janson's inequalities, to tease out a very sharp threshold for the emergence of a 2-additive basis. Generalizations to k-additive bases are then given.Comment: 22 page