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We introduce center-like subsets Z ∘ * (A , d) , Z ∘ * * (A , d) , where A is the ring and d is the multiplicative derivation. In the following, we take a new derivation for the center-like subsets existing in the literature and establish the relations between these sets. In addition to these new sets, the theorems are generalized as multiplicative derivations instead of the derivations found in previous studies. Additionally, different proofs are provided for different center-like sets. Finally, we enrich this article with examples demonstrating that the hypotheses we use are necessary. [ABSTRACT FROM AUTHOR]

Fractional order differential equations often possess inherent symmetries that play a crucial role in governing their dynamics in a variety of scientific fields. In this work, we consider numerical solutions for fractional-order linear delay differential equations. The numerical solution is obtained via the Laplace transform technique. The quadrature approximation of the Bromwich integral provides the foundation for several commonly employed strategies for inverting the Laplace transform. The key factor for quadrature approximation is the contour deformation, and numerous contours have been proposed. However, the highly convergent trapezoidal rule has always been the most common quadrature rule. In this work, the Gauss–Hermite quadrature rule is used as a substitute for the trapezoidal rule. Plotting figures of absolute error and comparing results to other methods from the literature illustrate how effectively the suggested approach works. Functional analysis was used to examine the existence of the solution and the Ulam–Hyers (UH) stability of the considered equation. [ABSTRACT FROM AUTHOR]

Purpose: To evaluate the dispensing and administration processes in hospital settings in Jeddah city, Saudi Arabia. Method: A questionnaire based on the annual ASHP national survey was distributed among 35 hospitals. The response rate was 60%. After a follow-up period of 6 months, the final questionnaire was collected in November 2019. Result : The survey had a 60% response rate. Most surveyed hospitals have centralized pharmacies (76.2%). Few hospitals reported the use of the Bar Code Medication Administration BCMA system (19.0%) to verify doses during dispensing, and only 28.6% use automated dispensing cabinets. The main method to check unit doses in pharmacies is the "technician fills/pharmacist checks" method, as reported by 76.2% of hospitals. Conclusion: The new technologies in the field of healthcare are impacting the practice of medication distribution. Hospital pharmacies in Jeddah, Saudi Arabia are implementing many changes to improve the medication-use system. However, more work has to be done to follow the leaders in the area of pharmacy practice. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this study was to evaluate the prescription and transcription processes in hospital settings in Jeddah city, Saudi Arabia. Method: A customized version of the original American Society of Health-System Pharmacists (ASHP) survey was distributed to a total of 26 hospitals in Jeddah city that fits our criteria starting from December 2017. Hospitals' names were adopted from the Ministry of Health and Jeddah Municipality websites. All questionnaires were collected in June 2018. After that, they were classified according to the type of care provided by the hospital, size, ownership, teaching affiliation, and accreditation. Data were entered electronically using Google forms, and then Microsoft Excel was used to conduct descriptive statistics. Results: The survey had a response rate of 57%. A strict formulary system was adopted in 53.3% of hospitals, and clinical practice guidelines were used to optimize medication use in 86.7% of hospitals. Pharmacists do not have the authority to write medication orders in about 86.7% of hospitals and only 40.0% of hospitals have pharmacists routinely assigned to patient care units. However, Pharmacists actively provided consultation, mostly in drug information (80.0%). Computerized prescriber order entry (CPOE) is used to receive medication orders electronically in 80.0% of hospitals, and electronic health record (EHR) is used in about 53.3% of hospitals and 50.0% of those hospitals have pharmacists who document their clinical intervention in EHR. Conclusion: Survey results suggest that pharmacists in hospital settings have not yet been positioned to improve the prescribing and transcribing components of the medication-use process. [ABSTRACT FROM AUTHOR]

Introduction: The effectiveness of nicotine replacement therapy (NRT) in critically ill patients remains uncertain, as conflicting research results have been reported. Despite potential side effects and inconsistent data on safety and efficacy, NRT is still prescribed in intensive care units (ICUs) to prevent withdrawal symptoms and manage agitation in patients who are smokers. This meta-analysis aimed to assess the effectiveness of nicotine replacement therapy in critically ill smoking patients., Methods: A systematic review and meta-analysis of randomized controlled trials investigated the outcomes of smokers admitted to ICUs and were randomized either to receive or not receive nicotine replacement therapy (NRT) during their ICU stay. The MEDLINE and Embase databases were searched from inception through 13 February 2023 using OVID. The primary outcome was ICU length of stay (LOS) for this systematic review and meta-analysis. Meta-analysis was conducted using both random-effects and fixed-effect models; the latter is recommended when meta-analysis is restricted to just a few studies. The study was registered in the Prospective International Register of Systematic Reviews (PROSPERO) under reference number CRD42023407804., Results: Of 28 studies initially identified, three, with 67 patients on NRT and 72 controls, were deemed eligible for pooled analysis. Patients who received NRT experienced a shorter LOS (mean difference, MD= -3.06; 95% CI: -5.88 - -0.25, p=0.0, I 2 =0%). The mechanical ventilation (MV) duration was also shorter in the NRT group, but this difference was not statistically significant (MD= -1.24; 95% CI: -3.21-0.72, p=0.22, I 2 =12.69%). Delirium duration was reported by two studies, from which pooled analysis revealed an MD of -0.50 (95% CI: -1.63-0.62, I 2 =0%). The vasopressor duration was assessed in two studies, and the overall MD for vasopressor duration was not statistically different between NRT patients and controls in the fixed-effects model (MD=0.11; 95% CI: -0.75-0.96, I 2 =0%)., Conclusions: Critically ill smoker patients who received NRT experienced a significantly shorter ICU LOS but no significant differences in the durations of MV, vasopressor use, or delirium., Competing Interests: The authors have completed and submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest and none was reported., (© 2024 Aljuhani O. et al.)