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This note outlines some connections between projective geometry and some designs used in clinical trials in the health sciences. The connections are not immediately obvious but they widen the scope for enrichment work at both the senior high school level and for capstone subjects at the undergraduate level.

In this paper, we define the Pell-Pell p-sequence and then we discuss the connection of the Pell-Pell p-sequence with Pell and Pell p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Pell-Pell p-numbers by the aid of the nth power of the generating matrix the Pell-Pell p-sequence. Furthermore, we obtain an exponential representation of the Pell-Pell p-numbers and we develop relationships between the Pell-Pell p-numbers and their permanent, determinant and sums of certain matrices.

The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings.

Medically complex infants experiencing NICU stays can be difficult to manage, exhibiting refractory agitation, disengagement, or both—all signs of delirium, which can present in a hypoactive, hyperactive, or mixed form. Though documented in other settings, delirium is under-recognized in NICUs. Pediatric studies show that a high percentage of patients with delirium are under the age of 12 months. Delirium is associated with increased ventilation days, hospital days, and costs. It negatively affects neurodevelopment and social interaction. Studies show that pediatric nurses are unprepared to recognize delirium. Our nurse-led multidisciplinary group created a best practice recommendation (BPR) focused on detecting delirium and minimizing risk through thoughtful sedation management, promotion of sleep hygiene and mobility, and facilitation of meaningful caregiver presence. Occasionally, medications, including melatonin and risperidone, are helpful. In 2019, we introduced this BPR to reduce delirium risk in our NICU. Practice changes tied to this initiative correlate with a significant reduction in delirium scores and risk including exposure to deliriogenic medications. A multidisciplinary care bundle correlates with decreased delirium screening scores in NICU patients. [ABSTRACT FROM AUTHOR]

This article re-considers some interrelations among Pythagorean triads and various Fibonacci identities and their generalizations, with some accompanying questions to provoke further development by interested readers or their students. (Contains 3 tables.)