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This study proposes a nabla discrete fractional-order system of differential equations to model lung cancer and its interactions with lung epithelial cells, mutated cells, oncogenes, tumor suppressor genes, immune cells, cytokines, growth factors, angiogenic factors, and extracellular matrix. The proposed model can help predict cancer growth, metastasis, and response to treatment. Analytical results show the system is stable with a unique solution, and the model predicts that the immune system responds to cancer cells but eventually becomes overpowered. The numerical analysis employed the forward and backward Euler method and demonstrated that changes in parameter values have significant effects on the steady-state solution. The findings show that the growth of lung epithelial cells or their interaction with immune cells can cause an increase in the number of lung cancer cells. Conversely, an increase in cell death or a reduction in the interaction between lung epithelial cells and immune cells can decrease the number of lung cancer cells. The study highlights the usefulness of the nabla discrete fractional model in studying lung cancer dynamics.

The theory of convexity pertaining to fractional calculus is a well-established concept that has attracted significant attention in mathematics and various scientific disciplines for over a century. In the realm of applied mathematics, convexity, particularly in relation to fractional analysis, finds extensive and remarkable applications. In this manuscript, we establish new fractional identities. Employing these identities, some extensions of the fractional H-H type inequality via generalized preinvexities are explored. Finally, we discuss some applications to the q-digamma and Bessel functions via the established results. We believe that the methodologies and approaches presented in this work will intrigue and spark the researcher's interest even more. [ABSTRACT FROM AUTHOR]

Objective: The Mediterranean island of Cyprus has a high rate of human transit as a result of tourism, human trafficking, and migration, which could contribute to the rate of HIV infection. The island is divided into 2 states - the northern portion is mainly populated by Turkish-Cypriots, and the southern portion is populated by Greek-Cypriots. The aim of this study was to assess the dynamics of HIV infection in both segments of Cyprus using a mathematical model. Materials and Methods: Data of HIV-positive individuals diagnosed during the period 1997-2018 in northern Cyprus were obtained from the Turkish Republic of Northern Cyprus Ministry of Health database, yielding a total of 129 cases, and data for the southern region, the Republic of Cyprus, were retrieved from a European Centre for Disease Prevention and Control (ECDC) 2013 report and ECDC/World Health Organization 2017 data. The total number of reported HIV infections was 1057. A mathematical model was used to evaluate the current and future HIV infection rate. Results: Stability analysis of the equilibrium point - disease-free or endemic - was conducted using the Lyapunov function. The basic reproduction number, represented as R0, is a measure of the potential for disease spread and serves as a threshold for stability. The R0 value was 0.83 in northern Cyprus and 0.040 in southern Cyprus. An R0 indicated a disease-free equilibrium. Conclusion: The calculations suggest that there is no current HIV epidemic on either part of the island; however, the model predicted a significant increase in the near future. [ABSTRACT FROM AUTHOR]

Solving stiff, singular, and singularly perturbed initial value problems (IVPs) has always been challenging for researchers working in different fields of science and engineering. In this research work, an attempt is made to devise a family of nonlinear methods among which second‐ to fourth‐order methods are not only 풜− stable but 풜− acceptable as well under order stars' conditions. These features make them more suitable for solving stiff and singular systems in ordinary differential equations. Methods with remaining orders are either zero‐ or conditionally stable. The theoretical analysis contains local truncation error, consistency, and order of accuracy of the proposed nonlinear methods. Furthermore, both fixed and variable stepsize approaches are introduced wherein the latter improves the performance of the devised methods. The applicability of the methods for solving the system of IVPs is also described. When used to solve problems from physical and real‐life applications, including nonlinear logistic growth and stiff model for flame propagation, the proposed methods are found to have good results. [ABSTRACT FROM AUTHOR]

Introduction: Regular skin self-examination (SSE) is very important for the early diagnosis of malignant melanoma (MM). Since sun exposure is the most important trigger factor for the development of skin cancers, effective and regular sun protection is the main preventive method. Aim: To investigate the awareness of SSE, risky nevus and sun protection of the adolescents in the Turkish Republic of Northern Cyprus (TRNC). Material and methods: The data used within this research were obtained from questionnaires administered to volunteer high school students in the TRNC. Results: 39.8% of the participants included in the study stated that they conducted SSE. All the participants who said they conducted SSE reported that they performed a face exam. The body regions that the participants did not examine were the scalp (47.7%), foot (36.9%), back (35.4%) and genital area (35.4%). The features of the nevus perceived by the participants as risk factors included rapid growth, bleeding and itching. While 74% of respondents said they used sunscreen products, only 9% of users reported using them every day. Conclusions: In the TRNC where the exposure to the sun is high, young people perform skin examinations at high rates in order to monitor their nevi. Nevertheless, the results of this research show that hard-to-reach areas are neglected. [ABSTRACT FROM AUTHOR]

One common negative side effect of orthodontic treatment with fixed appliances is the development of white spot lesions (WSLs) around brackets. This study is aimed at comparing the efficacy of various oral hygiene practices in preventing enamel demineralization around orthodontic brackets under similar in vitro conditions. The study included 90 extracted bovine incisors, which were randomized into six groups: fluoride toothpaste (FT), nonfluoride toothpaste (NFT), fluoride varnish plus fluoride toothpaste (FV+FT), CPP-ACP varnish plus fluoride toothpaste (CPP-ACP+FT), medical minerals gel plus nonfluoride toothpaste (MMG+NFT), and no intervention (control). All groups were subjected to demineralization and remineralization cycles. Visual appraisals were used to evaluate the changes in the enamel surface appearance at the beginning and end of the experiment. The changes in the demineralization degree were evaluated by measuring the Ca+2 concentration in the demineralization solution at different time points. The majority of teeth in the CPP-ACP+FT group exhibited no shift in appearance, whereas in the other groups, a slight change in enamel translucency was observed. At all the time points, the Ca+2 concentration in the demineralization solution in the CPP-ACP+FT group was the least among all other groups. At day 5, MMG+NFT's preventive efficacy was significantly higher than FV+FT's, but at days 10, 15, and 19, their efficacy was similar. However, at all the time points, MMG+NFT's efficacy was significantly higher than that of control, whereas FV+FT's efficacy was decreased at days 10, 15, and 19 and was close to the efficacy of control. To fight WSLs, early diagnosis was of great importance and examination of the tooth surface after air-drying for 5 s was recommended. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for mappings satisfying expansive conditions in non-normal cone pentagonal metric spaces. Our results extend and improve the recent results announced by Patil and Salunke [Fixed point theorems for expansion mappings in cone rectangular metric spaces, Gen. Math. Notes 29 (1) (2015), 30-39], Shatanawi and Awawdeh [Some fixed and coincidence point theorems for expansive maps in cone metric spaces, Fixed Point Theory and Applications 1 (2012), 1-10], Huang, Zhu and Wen [Fixed point theorems for expanding mappings in cone metric spaces, Math. Reports 14 (64) (2) (2012), 141-148], Kadelburg, Murthy and Radenovic [Common fixed points for expansive mappings in cone metric spaces, Int. J. Math. Anal. 5 (27) (2011), 1309-1319], Aage and Salunke [Some fixed point theorems for expansion onto mappings on cone metric spaces, Acta Mathematica Sinica 27 (6) (2011), 1101-1106], Kumar and Garg [Common fixed points for expansion mappings theorems in metric spaces, Int. J. Contemp. Math. Sciences 4 (36) (2009), 1749-1758], and many others in the literature. [ABSTRACT FROM AUTHOR]

Objective: The aim of this study was to figure out the oral and dental health status and also to elucidate the relationships between clinical conditions and some socio-demographic characteristics in Lapta region of Turkish Republic of Northern Cyprus (TRNC) Methods: The study was done by the support and assistance of TRNC Lapta Municipality between May 2011 and May 2012 which was based on a survey and intra-oral examinations of the volunteers who were agreed to participate the study and living in in Lapta, Kayalar, Sadrazamköy, Mediterranean, Çamlıbel, Kozanköy, Alemdağ, Taşkent, Tepebaşı, Hisarköy, Koruçam, Kozan, TRNC. In order to conduct intra-oral examinations; gloves, mask, mirror, sond, wet wipes and gauze sterilized instruments, were used which was sterilized and prepared on a daily basis. Results were statistically evaluated. Results: A total of 735 patients were examined and questionnaire was filled. Results indicated that most of the participants consume sugary foods between meal courses. Of all participants, 85% of the population had toothbrush, however 8.31% never brush their teeth. Almost six percent of the people have never visited a dental clinic. There was a considerable teeth loss in the participants' mouth. More than seventy percent of the individuals had decayed teeth, whereas half of them had fillings in the mouth. Conclusion: The main oral health problem is the dental caries in Lapta region. It is suggested that the preventive dental applications, the importance of encouraging people to go to the dentist for a routine checkup and dental treatment is crucial to improve the oral and health status in this region. [ABSTRACT FROM AUTHOR]

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The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This difference scheme is built on the Taylor's decomposition method on three and two points. The theorem on the stability of the presented difference scheme is proven. In practice, stability estimates for the solutions of three-step difference schemes for different types of delay partial differential equations are obtained. Finally, in order to ensure the coincidence between experimental and theoretical results and to clarify how efficient the proposed scheme is, some numerical experiments are tested. [ABSTRACT FROM AUTHOR]