Search Results (36)

The kinetics of the depolymerization of natural rubber (NR) to hydroxyl-terminated natural rubber (HTNR) by hydrogen peroxide (H₂O₂) in the presence of a Fenton catalyst within an acidic milieu and under ultraviolet radiation has been rigorously examined utilizing infrared spectroscopy to determine the alterations in molar mass and the functional characteristics. The kinetic model was analyzed in accordance with the elementary reaction, encompassing the following mechanisms: the interaction between hydroxyl radicals and NR, producing radical NR and hydroxylated NR; the reaction wherein radical NR and hydroxyl radicals yield hydroxylated NR; and the subsequent reaction of hydroxylated NR with hydroxyl radicals producing lower radical NR, hydroxylated terminated NR, radical NR, and hydroxylated NR. The conversion of the NR polymer and the total hydroxyl content were discerned at the absorption bands of the CH₂-CH₂ and OH groups located at 850 cm⁻¹ and 3400 cm⁻¹, respectively. The absorption peak at 1850 cm⁻¹ attributed to CH₃ was employed as the reference group for calibration. The influence of the temperature on the depolymerization process conformed to the Arrhenius equation, characterized by activation energies of 750 K and 1200 K. The impact of the H₂O₂/Fenton ratio on the depolymerization process follows a power law with power coefficients of 1.97 and 1.82. Full article

Phenylene-based bis-oxamate polydentate ligands offer a unique opportunity for creating a large variety of coordination compounds, in which paramagnetic metal ions are strongly magnetically coupled. The employment of imino nitroxyl (IN) radicals as supplementary ligands confers numerous benefits, including the strong ferromagnetic interaction between Ni and IN. Furthermore, the chelating IN can act as a capping ligand, thereby impeding the formation of coordination polymers. In this study, we present the molecular and crystal structure and experimental and theoretical magnetic behavior of an exceptional neutral trinuclear complex [Ni(L³⁻)₂(IN)₃]∙5CH₃OH (1) (L is N,N′-1,3-phenylenebis-oxamic acid; IN is [4,4,5,5-tetramethyl-2-(6-methylpyridin-2-yl)-4,5-dihydro-1H-imidazol-1-yl]oxidanyl radical) with a cyclic triangular arrangement. Moreover, in this compound three Ni²⁺ ions are linked by the two bis-oxamate ligands playing a rare tritopic function due to an unprecedented triple deprotonation of the related meta-phenylene-bis(oxamic acid). The main evidence of such a deprotonation of the ligand is the neutrality of the cluster, since there are no anions or cations compensating for its charge in the crystals of the compound. Despite the presence of six possible magnetic couplings in the trinuclear cluster 1, its behavior was reproduced with a high degree of accuracy using a three-J model and ZFS, under the assumption that the three different Ni-IN interactions are equal to each other, whereas only two equivalent-in-value Ni-Ni interactions were taken into account, with the third one being equated to zero. Our study indicates the presence of two opposite-in-nature types of magnetic interactions within the triangular core. DFT and CASSCF/NEVPT2 calculations were completed to support the experimental magnetic data simulation. Full article

In this work, we define the multi-radical quadratic and multi-radical quartic mappings as two systems of radical functional equations and then represent them as two equations. Then, we establish some results concerning the stability of multi-radical quadratic and multi-radical quartic mappings by applying a fixed-point based on Brzdȩk. As a direct consequence, we prove the Rassias and Hyers stability of the mentioned mappings. Full article

Zinc-imprinted polymer (ZnIP) and non-imprinted polymer (NIP) were synthesized by radical polymerization, and their properties were studied. The novelty of the work lies in the use of humic acids isolated from coals of the Shubarkol deposit (Karaganda, Kazakhstan) as a basis for the imprinted polymer matrix, with methacrylic acid and ethylene glycol dimethacrylate as a functional monomer and a cross-linking agent, respectively. The composition and structure of ZnIP and NIP were characterized using various physicochemical methods. The specific surface area of ZnIP determined by the BET method was 40.60 ± 0.4 m²/g, which is almost twice as high as the similar indicator for NIP (21.50 ± 0.3 m²/g). In sorption tests of solutions with bimetallic ions, ZnIP demonstrates higher adsorption: 96.15% for Zn²⁺ and 74.88% for Pb²⁺, while NIP adsorbs only 81.33% and 60.11%, respectively. Sorption on both polymers is described by a pseudo-first-order equation (r > 0.99). The distribution coefficients for ZnIP are higher than for NIP. ZnIP has a relative selectivity that exceeds NIP by 2.90 times. The research results indicate the promise of using ZnIP for the selective removal of zinc ions from solutions of multicomponent systems, including wastewater, making it a valuable material for solving environmental and technological problems. Full article

In this paper, we prove a superstability theorem for a general functional equation ${\sum }_{j=1}^{\infty }{a}_{j}f\left({\gamma }_j(t,s)\right)=h\left(t\right)g\left(s\right)$, with the unknown functions $g:T\to X$, $h:S\to \mathbb{K}$ and $f:S\to X$, such that the series ${\sum }_{j=1}^{\infty }f\left({\gamma }_j(t,s)\right)$ is convergent for every $(s,t)\in S\times T$, where S and T are nonempty sets, and X is a Banach space over a field $\mathbb{K}$, which is either the set of real numbers $\mathbb{R}$ or the set of complex numbers $\mathbb{C}$. Namely, we show that if h is unbounded, and the difference ${\sum }_{j=1}^{\infty }{a}_{j}f\left({\gamma }_j(t,s)\right)-h\left(t\right)g\left(s\right)$ is bounded, then h and g satisfy the equation ${\sum }_{j=1}^{\infty }{a}_{j}g\left({\gamma }_j(t,s)\right)=h\left(t\right)g\left(s\right)$. Next, we show that the superstability of pexiderizations and radical versions of several well-known functional equations (e.g., of Cauchy, d’Alembert, Wilson, Reynolds, and homogeneity) is a consequence of this simple outcome. In this way, we generalize several classical superstability results and, in particular, the first superstability outcome of J. Baker, J. Lawrence, and F. Zorzitto, which states that every unbounded mapping f, from a real vector space X into the set of real numbers $\mathbb{R}$, satisfying the inequality $\left|f\right(x+y)-f(x\left)f\right(y\left)\right|\le \delta$ for every $x,y\in X$, with some real $\delta >0$, is an exponential function, i.e., satisfies the equality $f(x+y)=f\left(x\right)f\left(y\right)$ for all $x,y\in X$. In order to make this publication more accessible to a wider range of readers, we limit various related information, avoid very abstract generalizations, and provide some simple examples. Full article

The problem of Ulam stability for equations can be stated in terms of how much the mappings satisfying the equations approximately (in a sense) differ from the exact solutions of these equations. One of the best known results in this area is the following: Let g be a mapping from a normed space V into a Banach space B. Let $\xi \ge 0$ and $t\ne 1$ be fixed real numbers and $g:V\to B$ satisfy the inequality $\parallel g(u+v)-g\left(u\right)-g\left(v\right)\parallel \le \xi (\parallel u{\parallel }^t+\parallel v{\parallel }^t)$ for $u,v\in V\setminus \left\{0\right\}$. Then, there exists a unique additive $f:V\to B$ fulfilling the inequality $\parallel g\left(u\right)-f\left(u\right)\parallel \le \xi |1-2^{t-1}{|}^{-1}{\parallel u\parallel }^t$ for $u\in V\setminus \left\{0\right\}$. There arises a natural problem if the constant, on the right hand side of the latter inequality, is the best possible. It is known as the problem of the best Ulam constant. We discuss this problem, as well as several related issues, show possible generalizations of the existing results, and indicate open problems. To make this publication more accessible to a wider audience, we limit the related information, avoid advanced generalizations, and mainly focus only on the additive Cauchy equation $f(x+y)=f\left(x\right)+f\left(y\right)$ and on the general linear difference equation $x_{n+p}=a_1{x}_{n+p-1}+\dots +a_p{x}_n+b_n$ (considered for sequences in a Banach space). In particular, we show that there is a significant symmetry between Ulam constants of several functional equations and of their inhomogeneous or radical forms. We hope that in this way we will stimulate further research in this area. Full article

Heavy metal ions in industrial wastewater pose significant environmental and ecological threats. In this work, a hydrogel featuring a double network structure was synthesized via radical polymerization and cross-linking of β-cyclodextrin (CD) and carboxymethylcellulose (CMC) with acrylic acid (AA). The hydrogel’s functional groups and microstructure were characterized using Fourier transform infrared spectroscopy (FTIR-ATR), X-ray diffraction (XRD), scanning electron microscopy (SEM), and thermogravimetric analysis (TGA). Mechanical properties were evaluated through rheological and compression tests. The study examined the impact of initial metal ion concentration, adsorbent-ion contact time, and solution pH on adsorption capacity. The maximum adsorption capacities of the functionalized CD/CMC-PAA-MBA hydrogel for Cu²⁺, Pb²⁺, and Cd²⁺ ions were 158.12, 393.56, and 290.12 mg/g, respectively. Notably, the hydrogel exhibited the highest selectivity for Pb²⁺ in mixed solutions. The adsorption kinetics of the metal ions were modeled using the pseudo-second-order rate equation and the Langmuir adsorption isotherm. Full article

Many authors have studied various functional equations of forms patterned on the equation expressed as $g\left(\sqrt{a^2+b^2}\right)=g\left(a\right)+g\left(b\right)$, which can be considered, e.g., for real functions. Such equations are usually referred to as radical functional equations or of the radical type. Authors mainly study the so-called Ulam stability of such equations, i.e., they investigate how much the mappings satisfying the equations approximately (in a sense) differ from the exact solutions of these equations. Quite often, information about the solutions of these equations is also provided, but unfortunately, sometimes, such information is given in a misleading or incomplete way. It seems, therefore, that there is a need for a publication containing simple descriptions of such solutions (with appropriate examples), which would help in easy correction of such information and avoidance of similar problems for future authors. This is the main motivation for this expository paper. We present a general approach to the topic and consider two general forms of such equations. Moreover, the results presented in this paper show significant symmetry between the solutions of numerous functional equations and the solutions of equations of the radical type that correspond to them. To make this publication accessible to a wider audience, we omit various related information, avoid advanced generalizations, and present several simple examples. Full article

The health-promoting properties of black elderberry are related to its high content of polyphenols (natural antioxidants), which eliminate free radicals and prevent the formation of oxidative stress responsible for many diseases. The aim of this work was to determine, the anti-radical effect of Sambucus nigra infusions based on the reaction with 2,2-diphenyl-1-picrylhydrazyl (DPPH) and galvinoxyl (Glv) radicals and to determine the function describing the disappearance curves of these radicals. The antioxidant properties of infusions obtained from the flowers and fruits of this plant were tested using the modified Brand-Williams method using DPPH and Glv radicals. Higher antioxidant activity towards both the DPPH and Glv radicals was found in flowers compared to fruits. In addition, it was found that the process of quenching radicals in the reaction with Sambucus nigra infusions proceeds in accordance with the assumptions of second-order reaction kinetics. The infusion obtained from flowers quenched radicals faster than fruit infusions. The applied second-order kinetics equation may enable estimation of antioxidants levels in natural sources of radicals. Full article

Background: Severe and rigid scoliosis represents a type of spinal deformity characterized by a Cobb angle exceeding 90° and a flexibility of less than 30%. Halo spinal traction remains the established standard for managing severe scoliosis, although alternative approaches such as temporary internal distraction rods and staged surgical correction exist. The primary objective of this investigation was to compare two cohorts of patients treated using these distinct methods to ascertain any divergences in terms of surgical and radiological outcomes, pulmonary function (PF), and quality of life (QoL). Methods: This study encompassed a total of 62 pediatric patients meeting the specified criteria, which included severe idiopathic scoliosis (major Cobb curve >90) and flexibility <30%. Group 1 (G1) underwent surgical intervention involving preoperative Halo gravity traction (HGT) succeeded by posterior spinal fusion (PSF). On the other hand, Group 2 (G2) underwent a two-stage procedure starting with a less invasive temporary internal distraction technique (LITID) prior to PSF. The radiological outcomes, PF, and QoL were documented and assessed over a monitoring period ranging from 2 to 5 years. Results: The average preoperative major curves (MCs) measured 124° and 122° in G1 and G2, respectively (p < 0.426). Initial flexibility, as observed in preoperative bending films, ranged from 18% in G1 to 21% in G2 (p < 0.001). Following the ultimate surgical intervention, the MCs were corrected to 45° and 37.4° in G1 and G2, respectively (p < 0.001). The percentage correction of the MCs was higher in G2 (63% vs. 70% in G1 and G2, respectively), with significant between-group disparities (p < 0.001). The mean preoperative thoracic kyphoses (TKs) were 96.5° in G1 and 92° in G2 (p = 0.782), which were rectified to 45.8° in G1 and 36.2° in G2 (p < 0.001), equating to correction rates of 55% and 60% in the respective groups. Initially, G2 exhibited lower values for the percentage of predicted lung volume (FVC) and predicted FEV1 compared with G1 (49% and 58% vs. 54.5% and 60.8%; N.S.). Nonetheless, both groups demonstrated enhancements in their FVC and FEV1 values over the follow-up period. Conclusions: The surgical management of severe and untreated spinal curvatures in the pediatric and adolescent population can be considered safe, with a tolerable incidence of minor complications. LITID emerges as a method offering improved QoL and pulmonary function, achieving notably substantial average corrections in deformity by 70% in the coronal plane and 60% in the sagittal plane, alongside a mean increase in trunk height of 10.8 cm. Furthermore, a typical reduction of 76% in rib humps and enhancements in respiratory function, as indicated by improvements in 1 s predicted forced expiratory volume (by 25–56%) and forced vital capacity (by 35–65%), were achieved, leading to a clinically and statistically significant enhancement in QoL when evaluated using SRS-22r, without resorting to more radical, high-risk procedures. Full article

What is striking about de Broglie’s foundational work on wave–particle dualism is the role played by pseudo-Riemannian geometry in his early thinking. While exploring a fully covariant description of the Klein–Gordon equation, he was led to the revolutionary idea that a variable rest mass was essential. DeWitt later explained that in order to obtain a covariant quantum Hamiltonian, one must supplement the classical Hamiltonian with an additional energy ${\hslash }^2\mathcal{Q}$ from which the quantum potential emerges, a potential that Berry has recently shown also arises in classical wave optics. In this paper, we show how these ideas emerge from an essentially geometric structure in which the information normally carried by the wave function is contained within the algebraic description of the geometry itself, within an element of a minimal left ideal. We establish the fundamental importance of conformal symmetry, in which rescaling of the rest mass plays a vital role. Thus, we have the basis for a radically new theory of quantum phenomena based on the process of mass-energy flow. Full article

Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We briefly review existing analytical results to highlight consequences of interactions between the channel nanopore and the translocating particles. These interactions are described within a minimalistic approach by lumping together multiple physical forces acting on the particle in the pore into a one-dimensional potential of mean force. Such radical simplification allows us to obtain transparent analytical results, often in a simple algebraic form. While most of our findings are quite intuitive, some of them may seem unexpected and even surprising at first glance. The focus is on five examples: (i) attractive interactions between the particles and the nanopore create a potential well and thus cause the particles to spend more time in the pore but, nevertheless, increase their net flux; (ii) if the potential well-describing particle-pore interaction occupies only a part of the pore length, the mean translocation time is a non-monotonic function of the well length, first increasing and then decreasing with the length; (iii) when a rectangular potential well occupies the entire nanopore, the mean particle residence time in the pore is independent of the particle diffusivity inside the pore and depends only on its diffusivity in the bulk; (iv) although in the presence of a potential bias applied to the nanopore the “downhill” particle flux is higher than the “uphill” one, the mean translocation times and their distributions are identical, i.e., independent of the translocation direction; and (v) fast spontaneous gating affects nanopore selectivity when its characteristic time is comparable to that of the particle transport through the pore. Full article

We investigated the physicochemical properties of Japanese rice wines, including their functional properties and carbohydrate and amino acid content in solution and solid state. Three samples were tested. The glucose, allose, and raffinose contents in samples (A, B, C) in g/100 g were (3.47, 3.45, 7.05), (1.60, 1.63, 1.61), and (2.14, 2.75, 1.49), respectively. The total amino acid in µmol/mL was (3.1, 3.5, 4.4). Glutamic acid, alanine, and arginine varied in content across the samples. The viscosity (10 °C) and activation energy (ΔE) calculated using the Andrade equation were (2.81 ± 0.03, 2.74 ± 0.06, 2.69 ± 0.03) mPa-s and (22.3 ± 1.1, 22.0 ± 0.2, 21.3 ± 0.5) kJ/mol, respectively. Principal component analysis using FT-IR spectra confirmed the separation of the samples into principal components 2 and 3. The IC₅₀ values from the DPPH radical scavenging test were (2364.7 ± 185.3, 3041.9 ± 355.1, 3842.7 ± 228.1) µg/mL. Thus, the three rice wines had different carbohydrate and amino acid contents, viscosities, and antioxidant capacities. Full article

The objectives of the study are to reveal the influence of multistage fuel-oxidation chemistry, thermal radiation of soot during the combustion of a small (submillimeter size) fuel droplet, and real gas effects on the operation process of compression ignition engines. The use of the multistage oxidation chemistry of iso-octane in the zero-dimensional approximation reveals the appearance of different combinations of cool, blue, and hot flames at different compression ratios and provides a kinetic interpretation of these phenomena that affect the heat release function. Cool flames are caused by the decomposition of alkyl hydroperoxide, during which a very reactive radical, OH, is formed. Blue flames are caused by the decomposition of H₂O₂ with the formation of OH. Hot flames are caused by the chain branching reaction between atomic hydrogen and molecular oxygen with the formation of OH and O. So-called “double” cool flames correspond to the sequential appearance of a separated cool flame and a low-intensity blue flame rather than two successive cool flames. The use of a one-dimensional model of fuel droplet heating, evaporation, autoignition, and combustion at temperatures and pressures relevant to compression ignition engines shows that the thermal radiation of soot during the combustion of small (submillimeter size) droplets is insignificant and can be neglected. The use of real gas caloric and thermal equations of state of the matter in a three-dimensional simulation of the operation process in a diesel engine demonstrates the significant effect of real gas properties on the engine pressure diagram and on the NO and soot emissions: real gas effects reduce the maximum pressure and mass-averaged temperature in the combustion chamber by about 6 and 9%, respectively, increases the autoignition delay time by a 1.6 crank angle degree, increase the maximum heat release rate by 20%, and reduce the yields of NO and soot by a factor of 2 and 4, respectively. Full article

An electrochemical sensor with high sensitivity for the detection of sodium nitrite was constructed based on the peroxidase-like activity of Au magnetic nanocomposites (Au@Fe₃O₄). The Au@Fe₃O₄ composite nanoparticles were green-synthesized via the reduction of gold nanoparticles (AuNPs) from waste chestnut skins combined with the sonochemical method. The nanoparticles have both the recoverability of Fe₃O₄ and the advantage of being able to amplify electrical signals. Furthermore, the synergistic effect of green reduction and sonochemical synthesis provides a functional approach for the preparation of Au@Fe₃O₄ with significant peroxidase-like activities. The physicochemical properties were characterized using transmission electron microscopy (TEM), energy dispersive X-ray spectroscopy (EDS), the Brunauer–Emmett–Teller (BET) method, and Fourier transform infrared spectroscopy (FT-IR). The electrochemical properties of sodium nitrite were determined with cyclic voltammetry (CV) and chronoamperometry (i-t). The results revealed that Au@Fe₃O₄ acted as a peroxidase mimic to decompose hydrogen peroxide to produce free radicals, while ·OH was the primary free radical that promoted the oxidation of sodium nitrite. With the optimal detection system, the constructed electrochemical sensor had a high sensitivity for sodium nitrite detection. In addition, the current response had a good linear relationship with the sodium nitrite concentration in the range of 0.01–100 mmol/L. The regression equation of the working curve was y = 1.0752x + 4.4728 (R² = 0.9949), and the LOD was 0.867 μmol/L (S/N = 3). Meanwhile, the constructed detection system was outstanding in terms of recovery and anti-interference and had a good detection stability of more than 96.59%. The sensor has been successfully applied to a variety of real samples. In view of this, the proposed novel electrochemical analysis method has great prospects for application in the fields of food quality and environmental testing. Full article