Integrated semigroups and their applications to the abstract Cauchy problem

This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u′(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x ∈ D(An). Investigating these operators we are led to the class of integrated semigroups . Among others, this class contains the classes of strongly continuous semigroups and cosine families and the class of exponentially bounded distribution semigroups. The given characterizations of the generators of these integrated semigroups unify and generalize the classical characterizations of generators of strongly continuous semigroups, cosine families or exponentially bounded distribution semigroups. We indicate how integrated semigroups can be used studying second order Cauchy problems u″(t) - A1u′(t) - A2u(t) = 0, operator valued equations U′(t) = A1U(t) + U(t)A2 and nonautonomous equations u′(t) = A(t)u(t). © 1988 by Pacific Journal of Mathematics

Logics and the Sorites Paradox

Renderings of the ancient Sorites paradox in classical first-order logic, Lukasiewicz’s three-valued first-order logic, and a Pavelka-style derivation system for Lukasiewicz’s fuzzy first-order logic are derived. It can be seen that only in the last logic mentioned is the conclusion of the Sorites paradox false while the premises are true thus resolving the paradox

INPUT: An academic–practice partnership to an underserved rural community

The INPUT project is a model partnership that changed the way health care was offered to the underserved in rural Western North Carolina. Grant funding provided a full‐time Family Nurse Practitioner (FNP) to a free clinic and created clinical placements for FNP students. Students had opportunities to learn about unique aspects of care for vulnerable, underserved populations to encourage them to consider working in rural communities. The clinic saw an increase in patient visits and offered more continuity in follow‐up care. This academic–practice partnership represents a successful example of how working together can benefit the collaborators and community

Redbird Buzz Episode 31: Judy Neubrander, August 15, 2023

Interview with Judy Neubrander, the dean of the Mennonite College of Nursing at Illinois State University. The interview was conducted by John Twork from University Marketing and Communications on August 15, 2023, for the Illinois State University Redbird Buzz podcast

ON SUBDIAGONAL RATIONAL PADE APPROXIMATIONS AND THE BRENNER-THOMEE APPROXIMATION THEOREM FOR OPERATOR SEMIGROUPS

The computational powers of Mathematica are used to prove polynomial identities that are essential to obtain growth estimates for subdiagonal rational Pade approximations of the exponential function and to obtain new estimates of the constants of the Brenner-Thomee Approximation Theorem of Semigroup Theory

Au38(SPh)24: Au38 Protected with Aromatic Thiolate Ligands

Au38(SR)24 is one of the most extensively investigated gold nanomolecules along with Au25(SR)18 and Au144(SR)60. However, so far it has only been prepared using aliphatic-like ligands, where R = 12SC6H13, 12SC12H25 and 12SCH2CH2Ph. Au38(SCH2CH2Ph)24 when reacted with HSPh undergoes core-size conversion to Au36(SPh)24, and existing literature suggests that Au38(SPh)24 cannot be synthesized. Here, contrary to prevailing knowledge, we demonstrate that Au38(SPh)24 can be prepared if the ligand exchanged conditions are optimized, under delicate conditions, without any formation of Au36(SPh)24. Conclusive evidence is presented in the form of matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS), electrospray ionization mass spectra (ESI-MS) characterization, and optical spectra of Au38(SPh)24 in a solid glass form showing distinct differences from that of Au38(S-aliphatic)24. Theoretical analysis confirms experimental assignment of the optical spectrum and shows that the stability of Au38(SPh)24 is not negligible with respect to that of its aliphatic analogous, and contains a significant component of ligand 12ligand attractive interactions. Thus, while Au38(SPh)24 is stable at RT, it converts to Au36(SPh)24 either on prolonged etching (longer than 2 hours) at RT or when etched at 80 \ub0C

A variational approach to strongly damped wave equations

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix--Haase, thus extending several known results and obtaining optimal analyticity angle.Comment: This is an extended version of an article appeared in \emph{Functional Analysis and Evolution Equations -- The G\"unter Lumer Volume}, edited by H. Amann et al., Birkh\"auser, Basel, 2008. In the latest submission to arXiv only some typos have been fixe

Hyperbaric treatment for children with autism: a multicenter, randomized, double-blind, controlled trial

<p>Abstract</p> <p>Background</p> <p>Several uncontrolled studies of hyperbaric treatment in children with autism have reported clinical improvements; however, this treatment has not been evaluated to date with a controlled study. We performed a multicenter, randomized, double-blind, controlled trial to assess the efficacy of hyperbaric treatment in children with autism.</p> <p>Methods</p> <p>62 children with autism recruited from 6 centers, ages 2–7 years (mean 4.92 ± 1.21), were randomly assigned to 40 hourly treatments of either hyperbaric treatment at 1.3 atmosphere (atm) and 24% oxygen ("treatment group", n = 33) or slightly pressurized room air at 1.03 atm and 21% oxygen ("control group", n = 29). Outcome measures included Clinical Global Impression (CGI) scale, Aberrant Behavior Checklist (ABC), and Autism Treatment Evaluation Checklist (ATEC).</p> <p>Results</p> <p>After 40 sessions, mean physician CGI scores significantly improved in the treatment group compared to controls in overall functioning (p = 0.0008), receptive language (p < 0.0001), social interaction (p = 0.0473), and eye contact (p = 0.0102); 9/30 children (30%) in the treatment group were rated as "very much improved" or "much improved" compared to 2/26 (8%) of controls (p = 0.0471); 24/30 (80%) in the treatment group improved compared to 10/26 (38%) of controls (p = 0.0024). Mean parental CGI scores significantly improved in the treatment group compared to controls in overall functioning (p = 0.0336), receptive language (p = 0.0168), and eye contact (p = 0.0322). On the ABC, significant improvements were observed in the treatment group in total score, irritability, stereotypy, hyperactivity, and speech (p < 0.03 for each), but not in the control group. In the treatment group compared to the control group, mean changes on the ABC total score and subscales were similar except a greater number of children improved in irritability (p = 0.0311). On the ATEC, sensory/cognitive awareness significantly improved (p = 0.0367) in the treatment group compared to the control group. Post-hoc analysis indicated that children over age 5 and children with lower initial autism severity had the most robust improvements. Hyperbaric treatment was safe and well-tolerated.</p> <p>Conclusion</p> <p>Children with autism who received hyperbaric treatment at 1.3 atm and 24% oxygen for 40 hourly sessions had significant improvements in overall functioning, receptive language, social interaction, eye contact, and sensory/cognitive awareness compared to children who received slightly pressurized room air.</p> <p>Trial Registration</p> <p>clinicaltrials.gov NCT00335790</p