On polynomial nn-tuples of commuting isometries

We extend some of the results of Agler, Knese, and McCarthy [1] to $n$-tuples of commuting isometries for $n>2$. Let $\mathbb{V}=(V_1,\dots,V_n)$ be an $n$-tuple of a commuting isometries on a Hilbert space and let Ann$(\mathbb{V})$ denote the set of all $n$-variable polynomials $p$ such that $p(\mathbb{V})=0$. When Ann$(\mathbb{V})$ defines an affine algebraic variety of dimension 1 and $\mathbb{V}$ is completely non-unitary, we show that $\mathbb{V}$ decomposes as a direct sum of $n$-tuples $\mathbb{W}=(W_1,\dots,W_n)$ with the property that, for each $i=1,\dots,n$, $W_i$ is either a shift or a scalar multiple of the identity. If $\mathbb{V}$ is a cyclic $n$-tuple of commuting shifts, then we show that $\mathbb{V}$ is determined by Ann$(\mathbb{V})$ up to near unitary equivalence, as defined in [1].Comment: 29 pages. Ver. 2 : Fixed typos, added acknowledgements, removed some examples, fixed Lemma 7.13 (now 7.12

Rearrangement on Conditionally Convergent Integrals in Analogy to Series

Rearrangements on conditionally convergent series suggests the existence of a similar process for integrals, here also referred to as rearrangement. In this document, a general theorem concerning rearrangement for conditionally convergent integrals is presented, as well as supporting theorems and a corollary to the general theorem

Rearrangement on Conditionally Convergent Integrals in Analogy to Series

Rearrangements on conditionally convergent series suggests the existence of a similar process for integrals, here also referred to as rearrangement. In this document, a general theorem concerning rearrangement for conditionally convergent integrals is presented, as well as supporting theorems and a corollary to the general theorem

Early identification of the difficult airway from orbital deformity

"We report an adult patient presenting for surgery with hidden marked orbital exenteration (Figures 1, 2). The patient had history of resected left orbital neoplasm that remained concealed under an eye patch during preoperative physical examination and presentation to the operating room. Face mask ventilation proved impossible after anesthetic induction. Removal of the eye patch revealed a large facial orbital floor defect from exenteration of the orbit floor and the patient immediately underwent endotracheal intubation. Following the procedure, postoperative respiratory insufficiency required additional airway support. Emergent placement of a laryngeal mask airway provided adequate ventilation."--CaseJulie M. Marshall, Noah J. Timko (Department of Anesthesiology and Perioperative Medicine, University of Missouri)Includes bibliographical reference

Digilego for Peripartum Depression: A Novel Patient-Facing Digital Health Instantiation

Digital health technologies offer unique opportunities to improve health outcomes for mental health conditions such as peripartum depression (PPD), a disorder that affects approximately 10-15% of women in the U.S. every year. In this paper, we present the adaption of a digital technology development framework, Digilego, in the context of PPD. Methods include mapping of the Behavior Intervention Technology (BIT) model and the Patient Engagement Framework (PEF) to translate patient needs captured through focus groups. This informs formative development and implementation of digital health features for optimal patient engagement in PPD screening and management. Results show an array ofPPD-specific Digilego blocks ( My Diary , Mom Talk , My Care , Library , How am I doing today? ). Initial evaluation results from comparative market analysis indicate that our proposed platform offers advantageous technology aspects. Limitations and future work in areas of interdisciplinary care coordination and patient engagement optimization are discussed