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The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ -Fibonacci statistical convergence, strong Δ -Fibonacci summability, and Δ -Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers. [ABSTRACT FROM AUTHOR]

The applications of a Fibonacci sequence in mathematics extend far beyond their initial discovery and theoretical significance. The Fibonacci sequence proves to be a versatile tool with real-world implications and the practical utility of manifests in various fields, including optimization algorithms, computer science and finance. In this research paper, we introduce new versions of convergence and summability of sequences in normed spaces with the help of the Fibonacci sequence called weak Fibonacci φ-lacunary statistical convergence and weak Fibonacci φ-lacunary summability, where φ is a modulus function under certain conditions. Furthermore, we obtain some relations related to these concepts in normed spaces. [ABSTRACT FROM AUTHOR]

Ephedra is the most widely and largest widespread genus in the Gnetopsida, a subgroup of the gymnosperms. This research was done to find out how gamma radiation affected the in vitro growth of callus and suspension cultures. In addition, the effect of gamma rays (γ-rays) on the ephedrine and pseudoephedrine concentrations was evaluated through HPLC analysis. The cell suspension and callus cultures were formed on Murashige and Skoog's basal medium (MS) supplemented with 0.5 mg/l kinetin (Kn), and 3 mg/l of 2, 4-dichlorophenoxy acetic acid (2,4-D) and exposed to variable gamma radiation doses (0, 5, 10, 15, 20, 25 and 30 Gray). Highly significant differences in both fresh and dry callus weights were recorded due to the effect of gamma rays (γ-rays). The findings demonstrated that in the cell suspension and callus cultures, 15 Gray achieved the highest fresh and dry weights when compared to the control. Similarly, the highest concentrations of ephedrine and pseudoephedrine were found in suspension and callus cultures compared to control at 15 Gray. [ABSTRACT FROM AUTHOR]

Background: The primary burden among severely ill COVID-19 cases allocated to ICUs is secondary bacterial and fungal infections. Antimicrobial resistance is aggravated more likely by empiric overusing of antimicrobials. This study aimed to assess the microbiological profile of fungal and bacterial superinfections in laboratory confirmed COVID-19 cases and their antimicrobial susceptibility pattern. Methods: Various clinical samples were obtained from 117 critically ill COVID-19 patients in the clinical suspicion of secondary infections for assessing the pathogens accountable for the superinfections and their antimicrobial susceptibility pattern according to standard microbiological procedures. Results: Among 117 COVID-19 patients allocated to ICU, 68 (58%) had secondary infections. The most prevalent infection was of the lower respiratory tract. Most infections were bacterial 85.8%. Gramnegative isolates were the most predominant strains, accounting for 71.7%. among them, Klebsiella pneumoniae 43.4 % and Acinetobacter baumannii 20.7% were the most predominant. Majority of the bacterial strains were multidrug-resistant, all gram-negative strains showed one hundred percent resistance rate to cephalosporins, amoxicillin, and amoxicillin-clavulanic. The lowest resistance was observed for tigecycline. All gram-positive strains were susceptible to linezolid and vancomycin. Additionally, all candida isolates were susceptible to the tested antifungals. Conclusions: In hospitalized severely ill COVID-19 patients, secondary infections are most frequently caused by Gram-negative pathogens exhibiting high rate of antibiotic resistance and are associated with poor outcomes. Strict adherence to infection control measures as well as regular microbiological surveillance are required. [ABSTRACT FROM AUTHOR]

This research paper focuses on defining the relationships between the sets of strongly lacunary summable and lacunary statistically convergent sequences of complex numbers by using different modulus functions f and g under certain conditions and different orders α, β ∈ (0, 1] such that α ≤ β. Furthermore, for some special modulus functions, we establish the relations between the sets of strongly f-lacunary summable sequences and strongly f-lacunary summable sequences of order α. [ABSTRACT FROM AUTHOR]

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RETRACTED ARTICLE: To date, no antiviral therapy has shown proven clinical effectiveness in treating patients with COVID-19. We assessed the efficacy of remdesivir in hospitalized Egyptian patients with COVID-19. Patients were randomly assigned at a 1:1 ratio to receive either remdesivir (200 mg on the first day followed by 100 mg daily for the next 9 days intravenously infused over 30-60 minutes) in addition to standard care or standard care alone. The primary outcomes were the length of hospital stay and mortality rate. The need for mechanical ventilation was assessed as a secondary outcome. Two hundred patients (100 in each group) completed the study and were included in the final analysis. The remdesivir group showed a significantly lower median duration of hospital stay (10 days) than the control group (16 days; P < 0.001). Eleven of the patients in the remdesivir group needed mechanical ventilation compared with eight patients in the control group (P = 0.469). The mortality rate was comparable between the two groups (P = 0.602). Mortality was significantly associated with older age, elevated C-reactive protein levels, elevated D-dimer, and the need for mechanical ventilation (P = 0.039, 0.003, 0.001, and < 0.001 respectively). Remdesivir had a positive influence on length of hospital stay, but it had no mortality benefit in Egyptian patients with COVID-19. Its use, in addition to standard care including dexamethasone, should be considered, particularly in low- and middle-income countries when other effective options are scarce.