This study evaluates the oxidation states of formulations comprising styrene-butadiene-styrene (SBS), styrene-ethylene-butadiene-styrene (SEBS), and styrene-isoprene-styrene (SIS). The implementation of two chemiluminescence methods, isothermal and nonisothermal, allows depiction of the evolution of oxidation states as a function of the inorganic filler, BaTiO3, added at three concentrations: 1, 3, and 5 wt%. The conversion of hydroperoxides into stable oxygenated products reveals the filler's protective activity. This feature, the improvement of durability, recommends the studied formulation as an appropriate product for medical engineering.
The contamination of water sources intended for human consumption with heavy metals is a global concern due to their toxicity and potential carcinogenicity. In recent decades, research into heavy metal concentrations in major sources of drinking water, such as groundwater, spring water, and surface water, has increased in Romania, although most studies have been sporadic and limited in scope. In this study, 294 water samples were collected from 14 springs and wells in two regions of Romania. The quality of these waters, their level of contamination, and the associated health risks were then analysed. This research aims to evaluate the carcinogenic health risks primarily associated with chromium (Cr), nickel (Ni), cadmium (Cd), lead (Pb), cobalt (Co), manganese (Mn) and copper (Cu) in adults and children, depending on the ingestion pathway of these heavy metals in spring and well waters, or through dermal exposure when they are used for sanitation and hygiene purposes. The assessment of the risk to human health associated with consuming water contaminated with heavy metals indicated that, among the 14 sampling points from which water intended for human consumption was collected, some showed heavy metal concentrations exceeding the limits set by national legislation. Therefore, long-term consumption of this water may pose an increased risk to human health. This research found that exposure to chromium, nickel, and cadmium through ingesting water posed a carcinogenic health risk to both children and adults. Children were found to be more susceptible than adults. Regarding the potential carcinogenic risk associated with the aforementioned metals, the risk was highest in spring water, followed by well water.
In this paper, we study non-null osculating curves of type (n-3) in Lorentzian n-space 1 . EWe obtain necessary and sufficient conditions for non-null curves to be n osculating curves of type (n-3) in E1. We analyze these curves in terms of their curvature n functions and derive the necessary relations between the curvatures for a curve to be congruent to an osculating curve of type (n-3) in E1. Moreover, we re-characterize non-null n osculating curves of type (n-3) using harmonic curvature functions in terms of Bn_2.
This research examines a glazed inkwell from the Umayyad era preserved in the Rosetta store of antiquities. It was discovered during excavations at Tell Abu Mandour in the 2022-2023 season. The study also seeks to characterise the artefact's chemical composition, identify its components in both the glaze layer and the fired clay body, and diagnose signs of deterioration. Therefore, the inkwell was documented using AutoCAD, and a multi-analytical approach was used to investigate the inkwell through stereomicroscopy, polarised light microscopy (PLM), scanning electron microscopy coupled with energy dispersive X-ray spectroscopy (SEM-EDX), X-ray diffraction (XRD), thermal analysis, and Fourier transform infrared spectroscopy (FTIR). The results of microscopic examination revealed that the surface of the glaze layer had cracks, missing parts, accumulated dirt, peeling, and flaking. The polarised microscope indicated that the glazed inkwell consisted of three layers: the glaze, slip, and fired clay body. EDX confirmed the presence of a lead-based glaze containing manganese, copper, and iron colouring agents. XRD revealed the presence of quartz, gehlenite, and diopside, thereby confirming a calcareous clay body. FTIR spectroscopy indicated that gum Arabic was used to fix the decorations within the glaze layer. In addition, thermal analysis revealed that the clay body's firing temperature ranged from 850 degrees C to 900 degrees C. Finally, the treatment and restoration processes were carried out, comprising cleaning, completion, and consolidation to preserve its artistic and archaeological value and protect it from further damage and deterioration.
This paper extends the notion of interpolation from the quaternionic framework to the octonionic setting. By establishing a well-adapted algebraic basis, we examine how replacing the quaternion space with octonions influences the generated curves. The obtained curves in the octonionic space are not only differentiable but also display smoother behavior compared to those generated by corresponding methods in the quaternionic case. Moreover, the convergence is achieved with less iteration.
Nowadays, as information security is gaining vital importance, we aim to contribute to the development of coding/ decoding algorithms. To this end, we will apply innovative coding/decoding techniques using 2x2 matrices for Gauss-Fibonacci and GaussLucas numbers, and 3x3 matrices for Leonardo and Gauss-Leonardo numbers. We will also strengthen our system by integrating the mixed model to maximise information security. These new algorithms will improve information security while providing high accuracy.
Microplastics pose a significant risk to human health and the environment. This research examines microplastics in oral care products, particularly mouthwash, using morphological and chemical characterisation. A robust isolation protocol ensured the sample matrix was representative. Evaluation of digestion methods found that weak acids were ineffective and that strong oxidants were damaging to polymers. While alkaline treatment is feasible, the peroxide-based method proved optimal. Comprehensive characterisation is required to combine optical microscopy with micro-FTIR screening to ensure reliable data. A health risk assessment found that polypropylene and amorphous acrylate polymers in mouthwash pose a moderate to high risk for both adults and children.
This paper applies a wrapped exponential distribution to the axial domain for arcs of arbitrary lengths. Furthermore, we provide a closed-form expression for the characteristic function of the l-axial wrapped exponential distribution. We conduct a comprehensive analysis of population characteristics, parameter estimation techniques, and simulation studies, focusing primarily on the semicircular exponential distribution. Additionally, we discuss the practical applicability of this distribution to real-world datasets.
The Differential Transform Method (DTM) is a semi-analytical approach used to approximate solutions to various differential equations (DEs) and systems of DEs, typically yielding solutions in series form. In this paper, DTM is used to approximate solutions of some systems of DEs. To assess the accuracy and precision of the method, the responses obtained by the DTM are compared with those from the exact solutions for selected examples.
In this survey, we aim to present historical turning points and recent insightful results on the analysis of the Euler-Mascheroni constant.
The study of the geometric properties of analytic functions and their numerous applications across a variety of mathematical fields, including fractional calculus, probability distributions, and special functions, has drawn significant attention to Geometric Function Theory (GFT), one of the most prominent branches of complex analysis, in recent years. In this paper, we introduce a new subclass of uniformly convex functions with negative coefficients, defined in terms of the Hurwitz-Zeta function. We obtain the coefficient bounds, convex linear combinations, radii of close-to-convexity, starlikeness and integral means inequality for functions belonging to the class. Furthermore, we obtain neighbourhood results for this class.
Fibonacci polynomials are special cases of Chebyshev polynomials and have been studied on a more advanced level by many mathematicians. Fibonacci polynomials are defined by f(n+1)(x) = xf(n)(x)+f(n-1)(x), n >= 1 with f(0)(x)=0, f(1)(x)=1. The Fibonacci polynomials are of great importance in the study of many subjects, such as algebra, geometry, and number theory itself. Obviously, they have a deep relationship with the famous Fibonacci sequence. That is f(n)(1)=F-n, where F-n is a Fibonacci number. In this paper, we introduce the generalization of Fibonacci polynomials by changing the initial terms with preservation of recurrence relation. Furthermore, some properties and identities of generalized Fibonacci polynomials are established and derived by standard methods.
The Landau constants are defined by & sum; ( ) {} { } These constants play an important role in complex analysis. In this paper, we establish new asymptotic expansions and inequalities for the Landau constants.
Glycogen synthase kinase-3 is a fascinating enzyme involved in a series of physiological processes, and its activity is associated with the pathological features of various diseases, such as type 2 diabetes, Alzheimer's disease, chronic inflammation, cancer, and bipolar affective disorder. GSK-3 inhibitors are currently being tested for their therapeutic effects on these diseases. In this work, the inhibition of GSK-3/3 by aloisines is investigated by structure-activity correlation studies, the best model obtained being characterized by R2 = 0.8865. The identification of the molecular fragments that contribute most to the formation of biological activity is carried out using fingerprint descriptors, such as the electronegativity of the OMO/UMO quantum molecular states. For an even better understanding of the relationship between chemical structure and observed biological activity, an aloisine/GSK-3/3 complex structure was obtained using molecular docking. The two types of studies (correlation and docking) are in good and complementary agreement. Therefore, our study suggests that the aloisine molecules are potent and selective for GSK-3/3.
Four-dimensional number systems are of great importance in physics, robotics, and computer-aided engineering. The quaternions give a chance to make examinations on-dimensional structures and also-dimensional calculations as spatial quaternions. The major goal of this research is to extend the Frenet elements for the Frenet-Serret-vectors for spatial quaternionic and quaternionic curves constructed in using real variable quaternion-valued vector functions. For this, the mathematical formulations of the Frenet elements in are evaluated, and the results in are presented by using them. Finally, exemplifications of spatial quaternion and quaternion curves with-vectors are to the conclusions.
In this study, the concept of statistical convergence in real number series is examined. Definitions, theorems, and specific examples related to statistical convergence of series are given. The statistical convergence of the real number series, which has been studied very little, is introduced by using the natural density function. Taking advantage of this relationship, new features are examined. Theorems written on this subject are included. The grouping and the rearrangement of the terms of statistical convergent series are examined. Concepts known for Cauchy convergence, such as the Cauchy criterion and the general term test, are considered for statistical convergence. Original theorems are written on this subject, and new examples are found. Furthermore, the statistical convergence of the series is examined using tests such as the Abel and Dirichlet tests. These tests are developed, and some examples are included. Lastly, the Leibniz test and the Mertens test used in the Cauchy product series were developed for statistical convergence.
This study examines the optimization of the curvature energy of epicycloid and helical curves. The mathematical and computational aspects of optimization are explored, with a focus on its applications to curves in the existing literature. To minimize the curvature energy, the Gradient Descent and L-BFGS-B algorithms are employed, and their principles and implementation processes are explained. The optimization results are compared, highlighting the advantages and limitations of each algorithm. Finally, the effectiveness of the optimization methods is evaluated, and suggestions for future research are provided.
In this paper, we present numerical solutions of Abel's Fredholm and Abel's Volterra integral equations. This method is based on modifying the cubic spline function to approximate the unknown function; this approximation cancels the singularities in Abel's kernels and transforms the equation into a linear system of algebraic equations. With comparisons to other methods, using illustrative examples, we demonstrate the efficiency of this new method.
This study introduces a new bounded distribution defined on the (0,1) interval. Various statistical properties of the proposed distribution, including moments, coefficients of skewness and kurtosis, order statistics, and stochastic ordering, are investigated. The two unknown parameters of the distribution are estimated using twelve different estimation methods, including maximum likelihood, Cram & eacute;r-von Mises, Anderson-Darling, least squares, weighted least squares, maximum product of spacings, minimum spacing absolute distance, minimum spacing absolute log distance, Anderson-Darling left tail, Anderson-Darling left tail second-order, Anderson-Darling right tail and Kolmogorov method. The performance of these estimators is evaluated using a Monte Carlo simulation with 10,000 replications across various scenarios. Furthermore, to demonstrate the superiority of the proposed distribution over well-known competing bounded distributions such as the beta and Kumaraswamy distributions, it is analyzed and assessed on two real datasets.
In this article, the authors introduced pre-Lorentz sequence spaces with bicomplex terms and studied their properties. They encountered difficulty when they considered applying the known properties of pre-Lorentz function spaces to sequence spaces with bicomplex terms. They managed to overcome these difficulties by using idempotent representations of bicomplex numbers. After comprehensively examining the distribution and rearrangement functions in the space of sequences with bicomplex terms in their first study, presented in the references, it was time to examine pre-Lorentz spaces, and this study emerged.
