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Power series solution for fractal differential equations
No full textIn this paper, we provide an overview of fractal calculus as applied to fractal sets. We introduce the concept of power series defined on fractal sets and explore series solutions for second α-order fractal linear differential equations, particularly focusing on solutions near ordinary points. We also investigate the radius of convergence for these fractal series, elucidating the region where these series representations are valid. Furthermore, we employ the fractal Frobenius method to derive series solutions for second α-order linear fractal differential equations near regular singular points. By utilizing this method, we obtain analytical expressions that are applicable in the vicinity of such singularities, enhancing our understanding of fractal differential equations. To illustrate our findings, we graphically represent these solutions, providing visual demonstrations of the outcomes. These graphs serve to complement our analytical results and offer insights into the behavior of solutions within the context of fractal calculus and differential equations on fractal sets
Coğrafi Bilgi Sistemleri ve Analitik Hiyerarşi Süreci (AHP) ile Çaldıran (Van) İlçe Merkezi Deprem Risk Haritasının Oluşturulması
No full textVan Gölü’nün kuzeydoğusunda yer alan Çaldıran ilçesi önemli aktif tektonik hatlara oldukça yakın bir konumdadır. Yakın geçmişte meydana gelen yıkıcı depremler ilçenin deprem tehlikesini açık bir şekilde ortaya koymaktadır. Özellikle ilçede Çaldıran Fayı’nın 1976 yılında ürettiği Mw:7.3 büyüklüğündeki depremde 3840 kişi hayatını kaybetmiş, 9232 bina hasar görmüş olup 2000 km2’lik bir alandaki evlerin %80’i ağır hasar görmüştür. Ayrıca çalışma alanı tarihte önemli yerleşim merkezlerine ev sahipliği yaptığı için, bölgedeki yıkıcı tarihsel deprem kayıtları da bulunmaktadır. Çaldıran ilçesinde ilk tehlike deprem olmakla birlikte, zemin özellikleri, karbondioksit gazı çıkışı ve yapı stoğu verileri de tehlike ve risk boyutunu arttırmaktadır. Çalışmanın ilk etabında Çaldıran ilçesi ile ilgili yapılan çalışmalar derlenmiş ve coğrafi bilgi sistemleri tabanına eklenerek bir veri grubu oluşturulmuştur. Sonraki süreçte Çaldıran İlçesi’nde saha çalışması gerçekleştirilmiştir. Elde edilen tüm veriler altı adet veri grubu ile Analitik Hiyerarşik Süreç (AHS) ile analize tabi tutulmuştur. Sonuç olarak Çaldıran ilçe merkezi içerisinde yer alan yapıların yaklaşık %77’si uygun olmayan alan, yapı kalitesi, yapı kat adedi, aletsel ve tarihsel deprem verileri ve faya uzaklık kriterlerine bağlı olarak yüksek risk içermektedir. The Çaldıran District, located in the northeast of Lake Van, is situated in close proximity to significant active tectonic faults. Recent destructive earthquakes have clearly highlighted the seismic hazard of the district. Notably, the 7.5 magnitude earthquake generated by the Çaldıran Fault in 1976 resulted in 3,840 fatalities, with 9,232 buildings damaged, and approximately 80% of the houses within a 2,000 km² area sustained severe damage. Furthermore, due to its historical role as a major settlement area, the study region also contains records of destructive historical earthquakes. While the Çaldıran District's primary hazard is related to seismic activity, factors such as soil properties, carbon dioxide emissions, and building stock data further exacerbate the hazard and risk levels. In the initial phase of the study, existing research on the Çaldıran District was compiled and integrated into a Geographic Information Systems (GIS) database to create a comprehensive dataset. Subsequently, fieldwork was conducted in the Çaldıran District. All collected data were analyzed using the Analytic Hierarchy Process (AHP) with six distinct data sets. As a result, approximately 77% of the structures within the Çaldıran District center are classified as high risk based on criteria such as unsuitable land, building quality, number of building floors, instrumental and historical earthquake data, and distance from fault lines. </p
Association of Proximal Vessel Tortuosity with Technical Success and Clinical Outcomes: Analysis From the Progress-CTO Registry
No full textBackground: Proximal vessel tortuosity can hinder wiring and equipment delivery during chronic total occlusion (CTO) percutaneous coronary intervention (PCI). Aims: We sought to examine the association of proximal vessel tortuosity with the short and long-term outcomes of patients undergoing CTO PCI. Methods: We examined the association of proximal vessel tortuosity with clinical outcomes in patients who underwent CTO PCI at 50 US and non-US centers between 2012 and 2024. Results: Of 14,141 patients, 3,974 (28.1%) had moderate or severe proximal vessel tortuosity. Patients with moderate or severe proximal vessel tortuosity had more comorbidities and more complex angiographic characteristics, such as longer lesion length and higher prevalence of side branch at the proximal cap. Lesions with moderate or severe proximal tortuosity required greater procedure and fluoroscopy time. On unadjusted analyses, moderate/severe proximal vessel tortuosity was associated with lower technical success and higher incidence of major adverse cardiac events (MACE). In multivariable analysis, moderate/severe proximal vessel tortuosity was associated with lower technical success (odds ratio [OR]: 0.77; 95% confidence intervals [CI]: 0.67, 0.89) but similar MACE (OR: 1.26; 95% CI: 0.91, 1.73). Higher operator volume (≥ 30 CTO PCI cases per year) was associated with higher technical (85.2% vs. 75.6%, p < 0.001) and procedural success (83.6% vs. 74.5%, p < 0.001) but also higher risk of perforation (6.49% vs. 3.57%, p < 0.001) but not pericardiocentesis, in lesions with moderate/severe proximal vessel tortuosity. Conclusions: Moderate or severe proximal vessel tortuosity is independently associated with lower technical success in CTO PCI but not with MACE. High-volume operators are more likely to successfully perform CTO PCI in lesions with moderate/severe tortuosity at the cost of higher risk of perforation, without higher MACE
Evaluation of metal-organic framework/layered double hydroxide-embedded sodium alginate beads for effective removal of tartrazine dye: A comparative analysis of RSM and ANN
No full textComprehensive Survey of Common Potato Viruses in Eastern Anatolia Region of Turkey: New Isolates and Phylogenetic Insights
No full textPotatoes (Solanumtuberosum L.) are a vital crop in Turkey, contributing significantly to the country’s economy. However, they are susceptible to various viral infections, causing substantial yield losses if left unmanaged. This study aimed to conduct a comprehensive survey of economically significant viruses affecting potatoes in the Eastern Anatolia Region, Turkey, including the identification of new isolates and the inference of their phylogenetic relationships. A total of 1130 fresh leaf samples, including asymptomatic and symptomatic plant samples, were tested using the multiplex RT-PCR (m-RT-PCR) method to determine the prevalence of five viral pathogens. The test results revealed the presence of four viral pathogens, with an overall infection incidence of 37.08%. PVY was found in 35% of the samples, PVS in 8.5%, PVX in 1.8%, and PLRV in 1%. However, PVA was not detected. In addition, 74 of the 98 samples tested were positive for PVY + PVS, 13 for PVY + PVX, 2 for PVY + PLRV, 8 for PVY + PVS + PVX, and 1 for PVY + PVS + PLRV. From each sample that tested positive, two isolates were selected, and the complete coat protein (CP) gene regions of these isolates were cloned and sequenced. The sequences of the new potato virus isolates were deposited in the GenBank. Nucleic acid sequence comparisons revealed a consensus of over 99% among all available isolates and those from other regions of the world. However, this similarity is not specific to any particular host or region. In support of the similarities in nucleic acid, phylogenetic analyses also provided information on the evolutionary relatedness of these isolates from various origins and hosts. This finding suggests that the genetic makeup of these isolates is highly conserved across different populations and environments. This study, conducted in the Eastern Anatolia Region of Turkey, is the first comprehensive report on the presence and molecular phylogeny of four viral pathogens of economic importance in potato crops
