We study a basic auction design problem with online supply. There are two unit-demand bidders and two types of items. The first item type will arrive first for sure, and the second item type may or may not arrive. The auctioneer has to decide the allocation of an item immediately after each item arrives, but is allowed to compute payments after knowing how many items arrived. For this problem w...

A universal KP-like equation in 2+1 dimensions, which models general nonlinear wave phenomena exhibiting p-power nonlinearity, dispersion, and small transversality, is studied. Special cases include the integrable KP (Kadomtsev-Petviashvili) its modified version, as well their generalizations. Two main results are obtained. First, all low-order conservation laws derived, including ones that ari...

Given a set of integers with no three in arithmetic progression, we construct a Stanley sequence by adding integers greedily so that no arithmetic progression is formed. This paper offers two main contributions to the theory of Stanley sequences. First, we characterize well-structured Stanley sequences as solutions to constraints in modular arithmetic, defining the modular Stanley sequences. Se...

Abstract The major problem associated with production of transgenic proteins in plant expression systems is the low level their accumulation. Transplastomic plants a transgene incorporated not nuclear but plastid genome (plastome) some cases ensure elevation yield desired protein dozens times and more. However, two problems arise this case: frequency integration transgenes into difficulties hom...