Let (K, +, * ) be an odd order presemifield with commutative multiplication. We show that the set of nonzero squares of (K, * ) is a skew Hadamard difference set or a Paley type partial difference set in (K, +) according as q is congruent to 3 modulo 4 or q is congruent to 1 modulo 4. Applying this result to the Coulter-Matthews presemifield and the Ding-Yuan variation of it, we recover a recent construction of skew Hadamard difference sets by Ding and Yuan [7]. On the other hand, applying this result to the known presemifields with commutative multiplication and having order q congruent to 1 modulo 4, we construct several families of pseudo-Paley graphs. We compute the p-ranks of these pseudo-Paley graphs when q = 3 4 , 3 6 , 3 8 , 3 10 , 5 4 , and 7 4 . The p-rank results indicate that these graphs seem to be new. Along the way, we also disprove a conjecture of René Peeters [17, p. 47] which says that the Paley graphs Dedicated to Dan Hughes on the occasion of his 80th birthday. 50 Des. Codes Cryptogr. (2007) 44:49-62of nonprime order are uniquely determined by their parameters and the minimality of their relevant p-ranks.
Currently, cell membrane is always utilized for the construction of biomimetic nanoparticles. By contrast, mimicking the intracellular activity seems more meaningful. Inspired by the specific killing mechanism of deoxy‐hemoglobin (Hb) dependent drug (RRx‐001) in hypoxic red blood cells (RBC), this work aims to develop an inner and outer RBC‐biomimetic antitumor nanoplatform that replicates both membrane surface properties and intracellularly certain therapeutic mechanisms of RRx‐001 in hypoxic RBC. Herein, RRx‐001 and Hb are introduced into RBC membrane camouflaged TiO2 nanoparticles. Upon arrival at hypoxic tumor microenvironment (TME), the biomimetic nanoplatform (R@HTR) is activated and triggers a series of reactions to generate reactive nitrogen species (RNS). More importantly, the potent antitumor immunity and immunomodulatory function of RNS in TME are demonstrated. Such an idea would transfer the battlefield of RRx‐001 from hypoxic RBC to hypoxic TME, enhancing its combat capability. As a proof of concept, this biomimetic nanoreactor of RNS exhibits efficient tumor regression and metastasis prevention. The battlefield transfer strategy would not only present meaningful insights for immunotherapy, but also realize substantial breakthroughs in biomimetic nanotechnology.
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