n−n-absorbing I−I-prime hyperideals in multiplicative hyperrings

In this paper, we define the concept $I-$prime hyperideal in a multiplicative hyperring $R$. A proper hyperideal $P$ of $R$ is an $I-$prime hyperideal if for $a, b \in R$ with $ab \subseteq P-IP$ implies $a \in P$ or $b \in P$. We provide some characterizations of $I-$prime hyperideals. Also we conceptualize and study the notions $2-$absorbing $I-$prime and $n-$absorbing $I-$prime hyperideals into multiplicative hyperrings as generalizations of prime ideals. A proper hyperideal $P$ of a hyperring $R$ is an $n-$absorbing $I-$prime hyperideal if for $x_1, \cdots,x_{n+1} \in R$ such that $x_1 \cdots x_{n+1} \subseteq P-IP$, then $x_1 \cdots x_{i-1} x_{i+1} \cdots x_{n+1} \subseteq P$ for some $i \in \{1, \cdots ,n+1\}$. We study some properties of such generalizations. We prove that if $P$ is an $I-$prime hyperideal of a hyperring $R$, then each of $\frac{P}{J}$, $S^{-1} P$, $f(P)$, $f^{-1}(P)$, $\sqrt{P}$ and $P[x]$ are $I-$prime hyperideals under suitable conditions and suitable hyperideal $I$, where $J$ is a hyperideal contains in $P$. Also, we characterize $I-$prime hyperideals in the decomposite hyperrings. Moreover, we show that the hyperring with finite number of maximal hyperideals in which every proper hyperideal is $n-$absorbing $I-$prime is a finite product of hyperfields.Comment: Journal of algebraic system

Bound state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry

The energy spectra and the corresponding two- component spinor wavefunctions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The $s-$wave ($\kappa = 0$ state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wavefunctions for this potential and other special types of this potential are obtained. Extension of this result to $\kappa \neq 0$ state is suggested.Comment: 18 page

Treatment delays and in-hospital outcomes in acute myocardial infarction during the COVID-19 pandemic: A nationwide study

Objective: Delayed admission of myocardial infarction (MI) patients is an important prognostic factor. In the present nationwide registry (TURKMI-2), we evaluated the treatment delays and outcomes of patients with acute MI during the Covid-19 pandemic and compaired with a recent pre-pandemic registry (TURKMI-1). Methods: The pandemic and pre-pandemic studies were conducted prospectively as 15-day snapshot registries in the same 48 centers. The inclusion criteria for both registries were aged ≥18 years and a final diagnosis of acute MI (AMI) with positive troponin levels. The only difference between the 2 registries was that the pre-pandemic (TURKMI-1) registry (n=1872) included only patients presenting within the first 48 hours after symptom-onset. TURKMI-2 enrolled all consecutive patients (n=1113) presenting with AMI during the pandemic period. Results: A comparison of the patients with acute MI presenting within the 48-hour of symptom-onset in the pre-pandemic and pandemic registries revealed an overall 47.1% decrease in acute MI admissions during the pandemic. Median time from symptom-onset to hospital-arrival increased from 150 min to 185 min in patients with ST elevation MI (STEMI) and 295 min to 419 min in patients presenting with non-STEMI (NSTEMI) (p-values <0.001). Door-to-balloon time was similar in the two periods (37 vs. 40 min, p=0.448). In the pandemic period, percutaneous coronary intervention (PCI) decreased, especially in the NSTEMI group (60.3% vs. 47.4% in NSTEMI, p<0.001; 94.8% vs. 91.1% in STEMI, p=0.013) but the decrease was not significant in STEMI patients admitted within 12 hours of symptom-onset (94.9% vs. 92.1%; p=0.075). In-hospital major adverse cardiac events (MACE) were significantly increased during the pandemic period [4.8% vs. 8.9%; p<0.001; age- and sex-adjusted Odds ratio (95% CI) 1.96 (1.20-3.22) for NSTEMI, p=0.007; and 2.08 (1.38-3.13) for STEMI, p<0.001]. Conclusion: The present comparison of 2 nationwide registries showed a significant delay in treatment of patients presenting with acute MI during the COVID-19 pandemic. Although PCI was performed in a timely fashion, an increase in treatment delay might be responsible for the increased risk of MACE. Public education and establishing COVID-free hospitals are necessary to overcome patients' fear of using healthcare services and mitigate the potential complications of AMI during the pandemic. © 2020 by Turkish Society of Cardiology