The paper considers the environmental aspects of water supply in the campus of Kyrgyz-Turkish “Manas” University, and evaluates them in the context of the indicators of the “UI GreenMetric World University Ranking – 2024” system: SI-infrastructure (70.33%); EC-energy and climate (37.62%); WR-water (70%); WS-waste (66.67%); TR-transport (77.78%); ED-education and research projects (66.67%). It was noted that within the campus, there is a centralized city water supply system, and in addition, four wells have been drilled, fed from the groundwater of the Chui Valley. The main consumers of water are educational, industrial, household and agricultural campus facilities. Part of the water from the springs is used for drinking purposes. Taking these circumstances into account, the chemical composition of the model water was established. Thermodynamic modeling of an aqueous solution was carried out at a minimum Gibbs energy and the concentration distribution of elements, cations and anions in the liquid phase was established. It has been shown that the pH value of water ranges from 7.3 to 7.62, and the redox potential is positive. Accordingly, the properties of water are restorative in nature and are quite suitable for drinking purposes, which means solving an important practical problem.

Finding the root is one of the most common problems in scientific disciplines. Due to their increasing importance in a wide variety of practical applications, nonlinear functions are utilized across the entire spectrum of various areas within mathematics, science, and engineering. Using computers to solve these functions is very important, especially in today's world. The most important things to think about when working out the roots of non-linear equations are how well the method works and how much it costs to do it. A better method is more effective and less expensive. Considering these facts, the main aim of this paper is to present a new method that doesn't involve derivatives and is more efficient. This paper presents an approach to solving nonlinear equations by extending the Lagrange method to find roots of polynomial curves. These equations can be solved using various iterative techniques, including the Secant, Newton-Raphson, Bisection, Regula Falsi, and others. The objective is to find the roots of such equations without considering any derivative operations. This is achieved by considering polynomial curves produced using Lagrange interpolation under specific initial circumstances. The effectiveness of the proposed approach is demonstrated by examining well-documented cases from the literature. It could also be used in mathematical modeling, optimization, and computational science, making it useful for solving many practical problems.

The effectiveness of generative artificial intelligence models in software development is determined not only by their ability to generate correct solutions but also by their adherence to quality metrics and their resilience to exceptional scenarios. In this context, a comparative evaluation was conducted on four models using 10 fundamental algorithm problems and 10 object-oriented programming problems in the C# programming language. The generated solutions were assessed in terms of time complexity, memory usage, lines of code, number of variables and methods, and execution time. In addition, meaningful edge-case scenarios were employed to measure error tolerance and exception handling performance. The findings indicate that all models produced functionally valid solutions, yet exhibited limitations in advanced software engineering practices such as modularity, comprehensive error management, performance measurement, and unit testing. The analysis revealed that ChatGPT and Gemini stood out in terms of structure and consistency, Claude demonstrated greater reliability in handling errors, while Copilot offered advantages in code simplicity. Overall, the results highlight the importance of evaluating generative AI models not only under ideal conditions but also in atypical scenarios to ensure software quality and reliability.

In the article, the minimization problem is investigated of piecewise linear functional in non-linear optimization of oscillation processes described by Fredholm integro-differential equations. An algorithm has been developed for constructing a generalized solution to boundary value problem that describes the oscillation process. Using the maximum principle for systems with distributed parameters, optimality conditions are determined in the form of equality and inequality.

This study investigates consecutive reactions in chemical kinetics. Consecutive reactions are irreversible, meaning that the products formed do not return to the original reactants, and this makes their modeling more complex compared to other reaction types. Examples of such reactions include polymerization, radioactive decay, hydrocarbon chlorination, the reaction of unabsorbed ethanol in the human body, and thermal cracking. For these consecutive reactions, a conformable kinetic model is considered and analytically solved by means of the conformable Laplace transform. The effects of different conformable orders α on the reaction dynamics are examined in detail. The obtained solutions are presented graphically and interpreted in terms of the temporal evolution of each species. The results indicate that the conformable model provides an effective and flexible representation of the behavior of consecutive reactions.

In this study, BIS/HEMA-based cryogels were synthesized as an environmentally friendly purification approach and functionalized with tannic acid to investigate their applicability for the removal of Pb(II) ions from aqueous solution. Two different modifications were performed by using 5 and 10 mg/100 µL of tannic acid, and the adsorption performance of the resulting cryogels was evaluated under parameters such as pH, contact time, adsorbent dose, and temperature. Based on batch adsorption experiments, the maximum Pb(II) removal for all cryogel types was observed at pH 6, and the highest adsorption capacity was achieved with the cryogel modified with 10 mg of tannic acid. Under optimum conditions (pH: 4; Time: 60 min; Dose: 0.05 g; Temperature: 25o C) maximum Pb(II) removal was determined to be approximately 99%. Kinetic analyses revealed that the adsorption process followed a pseudo-second-order kinetic model, indicating that chemical interactions were dominant. Isotherm modeling showed that the adsorption behavior fitted the Langmuir model, suggesting a monolayer and homogeneous surface structure. Thermodynamic data indicated that the adsorption process was spontaneous and endothermic. The obtained findings demonstrate that BIS/HEMA cryogels functionalized with tannic acid represent an effective and sustainable adsorbent alternative for heavy metal removal in wastewater treatment.

This paper focuses on utility voltage regulator using ac – dc – ac converter topology for single-phase resistive load applications. The power circuit converter has been presented, to solve the problem of undesired voltage supply to domestic and industrial equipment. The utility voltage regulator is commonly used in applications that require, the conversion of an AC fluctuating input voltage to maintain a constant AC output voltage value. Its main features are: high reduction in weight and volume, portable, noiseless, simple control strategy, and connection between input and output enabling the use of utility voltage regulator and bypass switch. The voltage regulator comprises of rectifier and inverter circuits with their descriptions, operations and control are discussed in detail. Single and sine pulse width modulation schemes are adopted as a means of regulating the voltage transformations. The ac – dc power switches are controlled by proportional integral (PI) using voltage closed loop feedback. In the proposed topology, simulations have been conducted using computer aided software package MATLAB/SIMULINK 2007(b) to verify its operations. A 1 kVA prototype of the transformerless type has been built and tested in the laboratory to validate the system performance. The performance of the rated prototype is evaluated and the result yielded 91.0% efficiency, 3.06% THD, reduced power losses due to less number of power electronic components count.

In this study, the simultaneous quantification of amlodipine and atorvastatin in pharmaceutical preparations was successfully accomplished without the need for a separation process by using chemometric calibration methods (principal component analysis method (PCA), principal component regression method (PCR), and partial least squares method (PLS). Additionally, chemometric evaluation was performed on the data obtained from UV visible field spectroscopy methods. 16 mixes containing the chemicals atorvastatin and amlodipine were created as a calibration (concentration) set to assess the validity of the designated chemometric procedures. The calibration set's absorption spectrum was captured between 200 and 500 nm. The link between the calibration set and the absorption data collected in the 215–355 nm region was used to produce three chemometric calibrations. Amlodipine and atorvastatin synthetic mixtures were analyzed to assess the validity of the PCA, PCR, and PLS approaches. The percentage (%) recovery average for atorvastatin and amlodipine was determined for both the drug sample and the synthetic mixture using the approach we used. It was discovered that the computed values were fairly high.The methodologies were controlled, and the ANOVA test was run using the results of the PLS and PCR calibration techniques. The enhanced technique might be suggested for the examination of medication samples containing atorvastatin and amlodipine since it is among the most sensitive, accurate, and repeatable techniques available.

The paper studies new ruled surfaces with the vectors of Bishop frame via Smarandache geometry. The fundamental forms and the corresponding curvatures are provided for each ruled surface to draw characteristics of the surfaces such as developability and minimality. Moreover, the properties of the base curve and the corresponding striction curves of each surface are also discussed through asymptoticity, geodesicity and principal line. It is found that a ruled surface designed by Bishop vectors of a slant helix-like curve apart from other special kinds of curves has a direct effect on the characteristics of some constructed ruled surfaces.

The generalized pathway fractional integral formulas for the newly extended multiindex Mittag-Leffler function defined by using two Fox-Wright functions as its kernel is studied. Moreover, the SUM integral transform of the composition formula for the pathway fractional integral and extended multi-index Mittag-Leffler function is also presented.