A system of simultaneous multi-variable nonlinear equations can be solved by the Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superlinear convergence give solutions by approximating the Jacobian in some way. Unfortunately, the quasi-Newton condition (secant equation) doesn’t completely specify the Jacobian approximate in multi-dimensional case, so its full-rank update is not possible with classic variants of methods. The suggested new iteration strategy (“T-Secant”) allows full-rank update of the Jacobian approximate in each iteration by determining two independent approximates for the solution. They are used to generate a set of new independent trial approximates, then the Jacobian approximate can fully be updated. It is shown, that the T-Secant approximate is in the vicinity of the classic quasi-Newton approximate, providing that the solution is evenly surrounded by the new trial approximates. The suggested procedure increases the super-linear convergence of the secant method (φS = 1.618...) to super-quadratic (φT = φS + 1 = 2.618...) and the quadratic convergence of the Newton-method (φN = 2) to cubic (φT = φN + 1 = 3) in one dimensional case. The Broyden-type efficiency (mean convergence rate) of the suggested method in multi-dimensional case is an order higher than the efficiency of other classic low-rank update quasi-Newton methods as shown by numerical examples on a Rosenbrock-type test-function with up to 1000 variables. The geometrical representation (hyperbolic approximation) in single variable case helps explaining the basic operations and a vector-space description is also given in multi-variable case.

Keywords: liquid alloys, microstratification, dispersed particles, spontaneous dispersion, criteria for true (entropic) spontaneous dispersion, mechanisms of quasi-spontaneous dispersion, methods and results for assessing size of dispersed particles.

This paper introduces an innovative Particle Swarm Optimization (PSO) Algorithm in-corporating Sobol and Halton Random number samplings. It evaluates the enhanced PSO's performance against conventional PSO employing Monte Carlo Random Number Samplings. The comparison involves assessing the algorithms across nine benchmark problems and the renowned Travelling Salesman Problem (TSP). The re-sults reveal consistent enhancements achieved by the enhanced PSO utilizing Sob-ol/Halton samplings across the benchmark problems. Particularly noteworthy are the substantial improvements demonstrated by the enhanced PSO in solving the Travel-ling Salesman Problem. These findings underscore the efficacy of employing Sobol and Halton random number generation methods in enhancing algorithm efficiency.

We prove a quasi-pseudometric version of the strong Ekeland principle proved by P. Georgiev and T. Suzuki.

In this paper, a class of coupled competitive neural networks, which subject to disturbance and discontinuous activation functions, is concerned. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results.

The paper examines common elements between Lévai’s and Milson’s potentials obtained by Liouville transformations of two rational canonical Sturm-Liouville equations (RCSLEs) with even density functions which are exactly solvable via Jacobi polynomials in a real or accordingly imaginary argument. We refer to the polynomial numerators of the given rational density function as ‘tangent polynomial’ (TP) and thereby term the aforementioned potentials as ‘e-TP’ A special attention is given to the overlap between the two potentials along symmetric curves which represent two different forms of the Ginocchio potential exactly quantized via Gegenbauer and Masjed-Jamei polynomials respectively. Our analysis reveals that the actual interconnection between Lévai’s parameters for these two rational realizations of the Ginocchio potential is much more complicated than one could expect based on the striking resemblance between two quartic equations derived by Lévai for ‘averaged’ Jacobi indexes.

In this paper we provide some important and significant observations on invo-regular rings appeared in Ann. Univ. Mariae Curie-Sklodowska Sect. A Mathematica (2018). In addition we exhibit that strongly invo-regular rings, invo-regular rings and quasi invo-regular rings all coincide with the well known and well characterized tripotent rings and all these rings further coincide with the well known unit regular rings.

The school food environment is a suitable place to promote healthy habits, as it is a space for learning and constant social interaction, where children spend at least a third of their day, and have one to two meals. This study aimed to analyze the sale of food in the canteens of private schools in a capital in the Northeast of Brazil and verify the influence of it on students’ eating behavior. A cross-sectional, quantitative, multicenter study was carried out, taking place simultaneously in twenty capitals in Brazil. A checklist with 87 questions was applied to those responsible for the canteens in a representative sample of schools in each city. Frequencies and associations were performed using Pearson's Chi-Square test. The analysis of the foods sold, was based on the NOVA food classification from the Dietary Guidelines for the Brazilian Population, regarding the degree and extent of processing. Latent Class Analysis was carried out to group the canteens into similar response patterns, modeled with covariates, and the association was calculated with the Kruskal-Wallis and Duun tests or Fisher's Exact test. The results showed that students were very frequently offered ultra-processed, sugar-rich foods with low nutritional value; 88.7% of such foods had been chosen by managers as part of the menu because they are “students’ food preferences”. There is an average of 2.3 fresh foods in canteens compared to 7.5 varieties of ultra-processed foods. There must be stricter control over what is sold, to minimize student’s exposure to unhealthy foods.

Quasi-interpolation is a powerful tool for approximating functions using radial basis functions (RBFs) such as Gaussian kernels. This avoids solving large systems of equations as in RBF interpolation. However, quasi-interpolation with Gaussian kernels on compact intervals can have significant errors near the boundaries. This paper proposes a quasi-interpolation method with Gaussian kernels using Chebyshev points and boundary corrections to improve the approximation near the boundaries. The boundary corrections use a linear approximation of the function beyond the interval to estimate the truncation error and add correction terms. Numerical studies on test functions show that the proposed method reduces errors significantly near boundaries compared to quasi-interpolation without corrections, for both equally spaced and Chebyshev points. The convergence and accuracy with the boundary corrections are generally better with Chebyshev points compared to equally spaced points. The proposed method provides an efficient way to perform quasi-interpolation on compact intervals while controlling the boundary errors.

This narrative review critically evaluates the multidimensional impacts of team sports on student wellness through the Wellness Wheel framework, encompassing physical, emotional, intellectual, social, spiritual, occupational, and environmental well-being. Methodologically, the review synthesizes empirical studies, systematic reviews, and meta-analyses from the last 20 years, extracted from databases such as PubMed, PsycINFO, Scopus, Web of Science, and Google Scholar, to construct a comprehensive understanding of how team sports contribute to holistic student development. Our findings highlight team sports as a vital component of educational and wellness programs, significantly enhancing not just physical health but also emotional stability, cognitive performance, social skills, spiritual enrichment, and environmental awareness. The review underscores the necessity of integrating team sports into educational curricula to promote a balanced and comprehensive approach to student well-being. It also identifies existing gaps in literature, particularly the need for further research on enhancing inclusivity and accessibility in team sports, ensuring that all students can benefit from their wide-ranging impacts. This study advocates for strategic initiatives to incorporate team sports in educational settings, emphasizing their essential role in cultivating a well-rounded, healthy, and inclusive student body.

For many disciplines of science, all conceivable collisional cross sections and reactions must be precisely known. Although the recent decades were a trial of large-scale research to give these data, many essential atomic and molecular cross section data still missing, and the reliability of the existing cross sections has to be validated. In this paper, we present electron stripping, electron capture, and system breakdown cross sections in carbon (C5+) ions and lithium (Li2+) ions collisions with atomic hydrogen based on the Monte Carlo models of classical and quasi-classical trajectories. According to our expectation, the QCTMC results show higher results in comparison to standard CTMC data, emphasizing the role of Heisenberg correction constraint, especially in the low energy regime. On the Other hand, at high energy, the Heisenberg correction term has less influence as a projectile momentum increase. We present the total cross sections of electron stripping, electron capture, and system breakdown in C5+ ions and Li2+ ions collisions with atomic hydrogen in the impact energy range from 10 keV to 160 keV, which is of interest in astrophysical plasmas, atmospheric sciences, plasma laboratories, and fusion research.

The menace of human papillomavirus (HPV) infections among low- and middle-income countries with no access to free HPV vaccine is a public health concern. HPV is one of the most common Sexually Transmitted Infections (STIs) in Nigeria with high-risk HPV-16 and 18 genotypes. In this study, we explored the predictors of self-reported HPV infections and HPV genital warts infection among a population of students, non-academic staff, and academic staff of Ibrahim Badamasi Babangida (IBB) university located in Lapai, Nigeria. We also assessed their knowledge about HPV infections and genotypes, and sexual behaviors. An online cross-sectional study was conducted by setting up a structured questionnaire on google form and it was distributed to the University community via Facebook and other social media platforms of the university. The form captured questions on HPV infection, knowledge about HPV infection and genotypes, as well as sexual health of the participants. All variables were described using frequencies and percentage distribution, chi-squared test statistics was used to explore the association between HPV infection (medical records of HPV infection) and the participants’ profile, and logistic regression analysis was performed to examine the factors associated with HPV genital warts infection among the population. This study reveals those participants between the ages of 26 – 40 years (81.3%) and those currently not in a union (26.4%) who have self-reported having HPV-16 and -18 genotypes. Also, participants between 26 – 40 years of age (OR: 0.45, 95%CI: 0.22 – 0.89) reported to be carriers of HPV genital warts. Therefore, this study reveals the factors associated with HPV infection and genital warts peculiar to IBB university students and staff. Hence, we suggest the need for HPV awareness programs and free HPV vaccine availability at IBB university.