Siirt Üniversitesi Kurumsal Akademik Arşivi
DSpace@Siirt, Siirt Üniversitesi tarafından doğrudan ve dolaylı olarak yayınlanan; kitap, makale, tez, bildiri, rapor, araştırma verisi gibi tüm akademik kaynakları uluslararası standartlarda dijital ortamda depolar, Üniversitenin akademik performansını izlemeye aracılık eder, kaynakları uzun süreli saklar ve telif haklarına uygun olarak Açık Erişime sunar.
Güncel Gönderiler
Piecewise derivatives versus short memory concept: analysis and application
(Amer Inst Mathematical Sciences-Aims, 2022) Atangana, Abdon; Araz, Seda Igret
We have provided a detailed analysis to show the fundamental difference between the concept of short memory and piecewise differential and integral operators. While the concept of short memory leads to different long tails in different intervals of time or space as a result of a power law with different fractional orders, the concept of piecewise helps to depict crossover behaviors of different patterns. We presented some examples with different numerical simulations. In some cases piecewise models led to transitional behavior from deterministic to stochastic, this is indeed the reason why this concept was introduced.
Deterministic-Stochastic modeling: A new direction in modeling real world problems with crossover effect
(Amer Inst Mathematical Sciences-Aims, 2022) Atangana, Abdon; Araz, Seda Igret
Many real world problems depict processes following crossover behaviours. Modelling processes following crossover behaviors have been a great challenge to mankind. Indeed real world problems following crossover from Markovian to randomness processes have been observed in many scenarios, for example in epidemiology with spread of infectious diseases and even some chaos. Deterministic and stochastic methods have been developed independently to develop the future state of the system and randomness respectively. Very recently, Atangana and Seda introduced a new concept called piecewise differentiation and integration, this approach helps to capture processes with crossover effects. In this paper, an example of piecewise modelling is presented with illustration to chaos problems. Some important analysis including a piecewise existence and uniqueness and piecewise numerical scheme are presented. Numerical simulations are performed for different cases.
The effect of Some Boron Derivatives on Kanamycin Resistance and Survival of E. coli and P. aeruginosa in Lake Water
(Chinese Center Disease Control & Prevention, 2012) Darcan, Cihan; Kahyaoglu, Mustafa
Objective To study MIC value of 7 boron derivatives namely [Boric acid (H3BO3), Anhydrous Borax (Na2B4O7), Sodium Borate (NaBO2), Diammonium Tetraborate (NH4)(2)B4O7, Sodium Perborate (NaBO3), Boron Trioxide (B2O3), Potassium Tetraborate (K2B4O7)] on E. coli and P. aeruginosa and their effects on survival of bacteria in lake water and resistance against kanamycin antibiotic. Methods MIC values of Boron derivatives and antibiotic were studied by broth microdilution method. The effect of boron derivatives on survival of bacteria in lake water were also determined with plate count. Results Sodium perborate was determined as the most effective substance among the studied substances. Effectiveness increased as temperature increased. E. coli was more affected from P. aeruginosa in 8 mg/mL sodium perborate concentration in lake water. Moreover, it was determined that MIC value of kanamycin antibiotic decreased 200 times by especially treating P. aeruginosa with sodium perborate in lake water. However, it can be stated that this change in resistance did not arise from microorganisms. Conclusion Sodium perborate solution can be used supportedly in kanamycin antibiotic applications for P. aeruginosa. Future studies are necessary to explore the relation between sodium perborate and kanamycin which is effective on P. aeruginosa in lake water.
Approximation of fixed point of generalized non-expansive mapping via new faster iterative scheme in metric domain
(Amer Inst Mathematical Sciences-Aims, 2023) Muhammad, Noor; Asghar, Ali; Irum, Samina; Akgul, Ali; Khalil, E. M.; Inc, Mustafa
In this paper, we establish a new iterative process for approximation of fixed points for contraction mappings in closed, convex metric space. We conclude that our iterative method is more accurate and has very fast results from previous remarkable iteration methods like Picard-S, Thakur new, Vatan Two-step and K-iterative process for contraction. Stability of our iteration method and data dependent results for contraction mappings are exact, correspondingly on testing our iterative method is advanced. Finally, we prove enquiring results for some weak and strong convergence theorems of a sequence which is generated from a new iterative method, Suzuki generalized non-expansive mappings with condition (C) in uniform convexity of metric space. Our results are addition, enlargement over and above generalization for some well-known conclusions with literature for theory of fixed point.
Rhythmic behaviors of the human heart with piecewise derivative
(Amer Inst Mathematical Sciences-Aims, 2022) Atangana, Abdon; Igret Araz, Seda
It has been noticed that heartbeats can display different patterns according to situations faced by a human. It has been indicated that, those passages from one pattern to another cannot be modelled using a single differential operator, either classical, fractional, or stochastic. In 2021, alternative concepts were introduced and called piecewise differentiation and integration, these concepts were applied in several complex problems with great insight. It is strongly believed that such will be leading concepts to modelling real-world problems with crossover behaviors. Crossover behaviors have been observed in heart rhythm, therefore, in this paper, the well-known van Der Pol equation will be subjected to piecewise analysis. Several simulations will be obtained using a numerical scheme based on Newton polynomial interpolation. Obtained figures show real world behaviors of heart rhythm with piecewise patterns.
