In this paper, we pursue and investigate the solutions for fractional kinetic equations, involving Bessel-Struve function by means of their Sumudu transforms. In the process, one Important special case is then revealed, and analyzed. The results obtained in terms of Bessel-Struve function are rather general in nature and can easily construct various known and new fractional kinetic equations.

Among the various types of gas sensors, the chemoresistive gas sensors based on metal oxides are considered the most attractive ones due to their simple operation, low costs and miniaturization. Thin films of V2O5 undoped and doped with TiO2 were studied as nitrogen dioxide, methane and hydrogen sensors. The experimental kinetics of the electrical conductivity changes due to introduction and removal of gas on metal oxide gas sensors were successfully explained in terms of the Langmuir adsorption theory.

Recently, representation formulae and monotonicity properties of generalized k-Bessel functions, Wk v,c., were established and studied by SR Mondal [24]. In this paper, we pursue and investigate some of their image formulae. We then extract solutions for fractional kinetic equations, involving Wk v,c, by means of their Sumudu transforms. In the process, Important special cases are then revealed, and analyzed.

A comprehensive kinetic model of the Fischer-Tropsch synthesis (FTS) is developed in a fixed bed reactor under operating conditions (temperature, 230–235°C, pressure, 20–25 bar, gas hourly space velocity, 4000–5000 cm³(STP)/h/g_catalyst ,H₂/CO feed molar ratio, 2.1) over a Co based catalyst. Reaction rate equations based on Eley-Rideal (ER) type model for initiation step and Langmuir-Hinshelwood-Hougen-Watson (LHHW) type model for propagation and termination steps of the FTS reactions have been considered and the readsorption of olefins were taken into account. The model that was reported in the literature was modified in order to explain many significant deviations from the ASF distribution. Optimum parameters have been obtained by Genetic Algorithms (GA). The calculated activation energies to produce n-paraffins and 1-olefins were in the range of 82.24 to 90.68 kJ/mol and 100.66 to 105.24 kJ/mol, respectively. The hydrocarbon distribution in FTS reactions was satisfactorily predicted particularly for paraffins.

Despite the recognized influence of maximum or acceleration strength on combat techniques and countermovement jump (CMJ) performance, the relationship between body segment weights and combat techniques remains unexplored. This study aimed to examine the impact of body segment weights, including striking arm weight (SAW), kicking leg weight (KLW), and trunk weight (TW), on the dynamics of direct punches (DP), palm strikes (PS), elbow strikes (ES), front kicks (FK), and CMJ performance. Sixteen male military cadets (22.3±1.8 years, 181.4±7.0 cm, 83.0±8.1 kg) performed combat techniques, with performance measured by using a force plate and body segment weights assessed by Dual-energy X-ray absorptiometry. Spearman's correlation analysis was applied. Results indicated a strong correlation between KLW and FK impulse (r = 0.64, p ≤ 0.01) and CMJ impact force (r = 0.80, p ≤ 0.01). SAW showed moderate correlations with DP impulse (r = 0.53, p ≤ 0.05) and ES impulse (r = 0.54, p ≤ 0.05). Additionally, FK peak and impact forces were strongly correlated with CMJ jump height (r = 0.74, p ≤ 0.01; r = 0.77, p ≤ 0.01), and FK peak force moderately correlated with CMJ peak velocity (r = 0.63, p ≤ 0.05). These findings suggest targeted arm strength training could enhance striking abilities, while improvements in leg acceleration strength may directly boost kicking performance and vertical jump capabilities, which are crucial in combat scenarios.

In this paper, we study the semilinear pseudo-parabolic equations $\displaystyle u_{t} - \triangle_{\mathbb{B}}u - \triangle_{\mathbb{B}}u_{t} = \left|u\right|^{p-1}u$ on a manifold with conical singularity, where $\triangle _{\mathbb{B}}$ is Fuchsian type Laplace operator investigated with totally characteristic degeneracy on the boundary $x_{1} = 0$. Firstly, we discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence and nonexistence of global weak solution: for the low initial energy $J(u_{0})<d$, the solution is global in time with $I(u_{0}) >0$ or $\displaystyle\Vert \nabla_{\mathbb{B}}u_{0}\Vert_{L_{2}^{\frac{n}{2}}(\mathbb{B})} = 0$ and blows up in finite time with $I(u_{0}) < 0$; for the critical initial energy $J(u_{0}) = d$, the solution is global in time with $I(u_{0}) \geq0$ and blows up in finite time with $I(u_{0}) < 0$. The decay estimate of the energy functional for the global solution and the estimates of the lifespan of local solution are also given.

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. To illustrate our main findings, we present two numerical algorithms and examples in this paper.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

Conversion of electromagnetic energy into magnetohydrodynamic energy occurs when the electric conductivity changes from negligible to finite values. This process is relevant during the epoch of reheating of the early Universe at the end of inflation and before the emergence of the radiation-dominated era. We find that conversion into kinetic and thermal energies is primarily the result of electric energy dissipation and that the magnetic energy plays only a secondary role in this process. This means that, since electric energy dominates over magnetic energy during inflation and reheating, significant amounts of electric energy can be converted into magnetohydrodynamic energy when conductivity emerges early enough, before the relevant length scales become stable.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

Proteins in biological systems function at the interface of single molecule and bulk chemistry and thus provide novel insights into the basic physical chemistry of scaling and emergent phenomena. For example, a binary mechanical model based on the chemistry of muscle contraction unifies molecular mechanics and thermodynamics and provides an explicit solution to the Gibbs paradox. Using the same model system, here I show that chemical activities of molecular states have no effect on chemical kinetics or energetics. Specifically, while the concentration or number of molecules in a molecular state is widely thought to contribute to reaction free energies, here I show that it is not the physical presence of molecules that pushes a reaction forward but the number of microstates, , accessible in a chemical state that pulls a reaction toward equilibrium with an entropic force down an entropic funnel. With the derivation of an entropic contribution to chemical kinetics, I develop a novel chemical kinetic formulation that fully describes the chemical thermodynamics of both equilibrium and non-equilibrium reactions in terms of an a priori system reaction energy landscape.

Sewage sludge was utilized into biochar using the slow pyrolysis method. The biochar was then being used for ammonium removal. The sewage sludge biochar was produced at temperature of 550°C, 600°C, 650°C, 700°C and 750°C. A few characterization tests were carried out to study about the physical and chemical properties of the biochar. For instance, moisture and ash content analysis, FTIR spectroscopy, pH Zero Point Charge, biochar yield and SEM. As the pyrolysis temperature increased, the moisture content of SSB decreased while the ash content increased. The FTIR spectra of sewage sludge biochar showed that there were various organic functional groups on the surface of the biochar which were responsible for ammonium adsorption. Furthermore, through pH Zero Point Charge analysis, pH 7.0 was the most optimum pH for the adsorption test of ammonium. The optimum adsorbent dosage was 0.01g while optimum contact time was 150 minutes. Furthermore, 1.2ppm was the most optimum concentration for adsorption process. Based on the result of the characterization tests, SSB700 was the most effective biochar for ammonium adsorption. Based on the result of kinetic and isotherm analysis, the adsorption of ammonium ions usign sewage sludge biochar was a monolayer chemisorption process.

There are many pollution and environment problem in the human ecosystem. There are different methods are used to removal of sulfur from sour gases for example Basic Claus process and Modified Claus process . There are different chemical software are used for simulation and optimization of Claus process for example Aspen Plus and Chemcad ECT. The Gibbs free energy method is introduced and model of Claus process. There are new parameter are introduced in reaction furnace to reduce the error from 33% to 7 %. The waste heat boiler is installed at the reaction furnace in which high pressure stream is produced and study the decomposition the hydrogen sulphide. The new rate of reaction is introduced of the enhancement of H2 production in chemical process. The simulation of reaction furnace in Aspen plus software is the maximum utilization of process. Due to suitable operating condition of reaction furnace is caused the maximum destruction of ammonia gas in the reactor. When we are increasing the oxygen concentration and temperature of feed is causing decreasing the ammonia production in reaction furnace. It is below than acceptance value of ammonia is 150 ppm in the reaction furnace. The presence of oxygen components, Sulfur oxide, hydroxide components are effect on decreasing the amount of ammonia in furnace and temperature is about at 1350⁰C. It is noted that when the production of sulfur recovery is decrease in Claus process and the production of carbon monoxide is increase in the thermal section at the existence. Now we are work on parametric studies of furnace that could be causes the production of ammonia destruction and CO emission in the Claus process. Due to optimize the reaction furnace parameter are help to get large of sulfur production, ammonia gas destruction, increased the catalyst life and decreased of dangerous gases.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

The second article in the series presents the application of the Smoothed Particle Hydrodynamics (SPH) method to modelling of batch crystallisation in stirred tanks. A methodology to integrate the population balance equations (PBE) in parallel and independently from the Navier-Stokes equations is demonstrated. The benefits of the proposed methodology in terms of computational requirements, accuracy and availability of the crystal size distribution are discussed. The specific formulation of the SPH equations where the resulting system of ordinary differential equations is solved using the weighted contributions rather than numerically by solving a linear system of equations allows for massive parallelisation and a very loose coupling of the population balance and the fluid dynamics. It has been demonstrated, that the population balance equations can be solved on a Shared Memory Architecture (SMA) system using the OpenMP interface while the fluid dynamics equations being computed independently on a General Purpose Graphics Processing Unit (GPGPU) using the NVidia CUDA technology. This way, a significant portion of the computational overhead due to the large number of additional transport equations resulting from the discretisation of the population balance was removed: the SPH simulation coupled with 200 population balance equations was only 40% slower compared to SPH-only simulation. Two methods for the solution of population balance equations that preserve full crystal size distribution were implemented: discretised population balance (DPB) and method of characteristics (MOCH). The DPB equations are solved using the high-resolution finite-volume method with flux limiter and the effect of a large number of different flux limiters have been investigated. Both methods were validated using the case studies from the literature where an analytical solution can be derived. The developed models were applied to a numerical solution of coupled computational fluid dynamics and population balance equations to model a batch crystallization process. The effect of the hydrodynamics on the local temperature/supersaturation and the resulting crystal size distribution was captured and compared to the ideal mixing case. The simulation results from the DPB and MOCH methods were compared in terms of computational requirements and accuracy and MOCH selected as computationally more efficient and accurate.

The study aims to explain the different effects between the multiplication, addition, division and subtraction equations. In this sense, multiplication and addition equations develop a new element or fact, meanwhile, division equations express information within the element or fact, subtraction is the selection of element or fact. Furthermore, for a multiplication and addition equation results in the new element or fact, it is necessary to depend on specific physical concepts, without extreme alteration, as it would result in the alteration of the element or fact. It is worth highlighting the importance of fixed values ​​in the equation to describe the specific nature of the element or fact. The study makes it possible to understand open equations (without solutions) in mathematics and physics, in addition to understanding existing equations. The study makes reference to the theory of obligatory necessity and the theory of differences between elements.

In this paper, we study the problem of controllability of impulsive neutral evolution integrodifferential equations with state dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskii's fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory.

The well-known equations for the process of powder compaction (PCP) in a rigid die published over the period from the beginning of the last century to the present are considered. Most of the considered equations are converted into the dependence of the densification pressure on the relative density. The equations were analyzed and their ability to describe PCP was assessed by determining the coefficient of determination when approximating experimental data on the compaction of various powders. It is shown that most of the equations contain two constants, the values of which are determined by fitting the mathematical dependence to the experimental curve. Such equations are able to describe PCP with high accuracy in the case of compaction of powders up to a relative density of 0.9-0.95. It is also shown that different equations can describe PCP in the range of density change from the initial to 0.9 with the same and sufficiently high accuracy, but when the process of compaction is extrapolated to higher values of density, the curves diverge. This indicates the importance of equations that can unambiguously describe PCP to a relative density equal to or close to 1.0. For an adequate description of PCP to a relative density greater than 0.95, equations containing three or four constants have proven themselves well.

The paper is considering of the basic differential equations of hydrodynamics: the equation of continuity and motion. On the simplest example, it is shown that the equation of continuity in a system with the equation of motion leads to contradictions and erroneous results of modeling. A more correct form of the continuity equation is described. It is shown that the equations of motion can be written in the form of complete differentials. Three possible integral forms of the equations of motion are presented. As a conclusion, the existence and smoothness of the solution of the Navier-Stokes equations are considered.

Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. This involves the expression for the Laurent coefficients including the residue, the Kronecker limit formulas and higher order coefficients as well as the difference formed to cancel the inaccessible part, typically the Clausen functions. We also state Abelian results which yield asymptotic formulas for weighted summatory function from that for the original summatory function

Maxwell’s equations are valid only for a stationary observation point, therefore, to adequately describe real processes so far we have had to move to a moving reference frame. This paper presents the equations of electrodynamics for the moving observation point, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward, which cannot be said about Maxwell’s equations. The fields of uniformly moving charges are also solutions of the equations. Now there is no need to move to a moving reference frame, to use four-dimensional space and covariant form of equations. The question of finding a universal form of the equations that allows a solution in the form of the field of an arbitrarily moving charge remains open. This raises the question of the existence of a two-parameter group of transformations of electromagnetic fields along with the known one-parameter group has been posed. The phenomena derived from the equations, which make an additional contribution to the phase overrun in the Aharonov-Bohm effect are considered. The equation of motion of a charged particle in an electromagnetic field without simplifying approximations is considered, which allows us to take into account the radiation effects. It is shown that the fields in a moving observation point depend on its velocity and acceleration. In particular, although in a constant uniform electric field a force qE acts on a motionless charged particle, but on the same motionless but not fixed particle the force 4/3qE acts already, because it has a nonzero acceleration and the electric field at this point is larger. As the speed increases, the field decreases, and when it reaches the speed of light, when the particle stops accelerating, the force again becomes equal to qE The principle of operation of an unconventional alternator in a constant electric field and its corresponding engine, as well as new types of direct and impulse current generators, predicted by the equations, are described.

In this study, the Bohler K 190 steel was used. The steel was manufactured by the powder metallurgy (PM) process. The boronizing process was carried out in the range of 1173 to 1323 K, for 1-10 h. The samples were boronized in solid medium, called the Durborid powder mixture. For the microstructural observations, the scanning electron microscopy was utilized for determining the morphology of interfaces and measuring the layers’ thicknesses. The phase composition of boride layers was also determined with X-ray diffraction analysis. To investigate the redistribution of chemical elements redistribution during the boronizing process, the EDS mapping and EDS point analysis were used. The boride layers were constituted by FeB and Fe2B phases except for 1173 K for 1 h. The values of Vickers microhardness of Fe2B, FeB and transition zone were estimated. Finally, to assess the boron activation energies in FeB and Fe2B, the so-called integral method was applied and the results in terms of activation energies were confronted with the literature data.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

In this study, we have focused on studying the heterogenous degradation kinetics of regarding the decomposition of emergency contraceptive agent levonorgestrel (LNG), which is a second-generation synthetic progestogen that is the active component of the racemic mixture of norgestrel. The degradation processes of the active pharmaceutical ingredient (API) were compared with the ones obtained from model system containing the API along with the excipients that are found in a commercialized pharmaceutical formulation in a mass ratio of 1:1 (LNGMIX), in order to observe if the excipients have a stabilizing or destabilizing effect for the degradation of this progestogen. To achieve this, the following investigational methods were used: FTIR (Fourier transform infrared) spectroscopy and thermal analysis (TG/DTG/DSC analysis). For the kinetic analysis the data obtained from two main decomposition processes observed on the DTG curves were used and processed with a preliminary method, namely ASTM E698 and two isoconversional methods: Friedman and Flynn-Wall-Ozawa. The isoconversional study revealed that the decomposition mechanism of both LNG and LNGMIX are complex, and the excipients have a stabilizing effect over decomposition of API in tablet.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

The ordinary continuity equation relating the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The horizontal and transverse currents and the densities associated with them are found to be coupled to each other. Each of these quantities are found to obey a wave equation traveling at the velocity of light in vacuum. London's equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London's equations are symmetric and are shown to be dual to each other. It is shown that London's equations are Maxwell's equations with massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

We suggest a deep learning based sensor signal processing method to remove chemical, kinetic and electrical artifacts from ion selective electrodes’ measured values. An ISE is used to investigate the concentration of a specific ion from aqueous solution, by measuring the Nernst potential along the glass membrane. However, application of ISE on a mixture of multiple ion has some problem. First problem is a chemical artifact which is called ion interference effect. Electrically charged particles interact with each other and flows through the glass membrane of different ISEs. Second problem is the kinetic artifact caused by the movement of the liquid. Water molecules collide with the glass membrane causing abnormal peak values of voltage. The last artifact is the interference of ISEs. When multiple ISEs are dipped into same solution, one electrode’s signal emission interference voltage measurement of other electrodes. Therefore, an ISE is recommended to be applied on single-ion solution, without any other sensors applied at the same time. Deep learning approach can remove both 3 artifacts at the same time. The proposed method used 5 layers of artificial neural networks to regress correct signal to remove complex artifacts with one-shot calculation. Its MAPE was less than 1.8% and R² of regression was 0.997. A randomly chosen value of AI-processed data has MAPE less than 5% (p-value 0.016).

This study presents a new kinetic scheme for the mass yield prediction of waste lignocellulosic biomasses treated by Hydrothermal Carbonization (HTC). The proposed reactions are based on the decomposition, solubilization, and polymerization of each main fraction of the biomass: cellulose, hemicellulose, and lignin. The ash content was assumed to be inert. The kinetic parameters have been obtained by non-linear adjustment using a data set with 220 experimental runs collected from the literature. The results indicate that the pre-exponential factors range was from 7.33 x10¹ to 1.412x10⁵ min^-1, and activation energies were between 33.75 y 225.3 kJ/mol. A good fit is achieved between the observed and predicted data with an R² of 0.81 and an RMSE of 7.7 %. The proposed scheme was validated with the experimental data obtained by the HTC of sawdust (Pinus radiata) and rapeseed (Brassica napus). The experiments were carried out at temperatures of 190, 220, and 250 ºC and reaction times of 0, 30, 60, 90, and 120 min. The predicted values showed an average error of 2.3 and 3.5 %, respectively. Therefore, the kinetic scheme is a useful tool in the conversion analysis of waste biomass treated by HTC.

Purposely slow velocity resistance exercise (i.e., 10 s concentric and eccentric phases) is a popular training method, but limits the loads that can be lifted (e.g., <50% 1 RM). This study compared the biomechanical properties of purposely slow velocity (SLOW) and traditional resistance exercise (TRAD) that uses maximal lifting velocities. Healthy resistance-trained men (n=5) performed two testing sessions (barbell squat and bench press) in random-order; a SLOW session (1 set x 10 repetitions at 28% 1 RM, 10 s concentric & eccentric), and a TRAD session (3 x 10 at 70% 1 RM, controlled eccentric and maximal concentric). A force plate and linear position transducer were used to collect kinetic and kinematic data for every repetition of both protocols (α = 0.05). For both exercises, both concentric and eccentric mean force (N) and power (W) for each repetition was greater for TRAD. When the entire training session (squat + bench press) was examined, SLOW exhibited greater time under tension, while TRAD produced greater work (J) and impulse (N·s). Contrary to suggestions in both the lay and scientific literature, purposely slow resistance exercise produced less force, power, and work than traditional velocity resistance exercise.

Research abounds in the literature on kinetic analyses using thermogravimetric (TG) runs. Many of these studies use approximations of integral or derivative forms of the kinetic law and all of them use programmed temperature, not the actual temperature measured by thermocouples close to the sample. In addition, it is common to conduct a single run in order to perform the calculation. Nevertheless, many authors consider that numerical methods should be used to analyse the kinetics of decomposition. In such cases, the actual temperature is used and, generally, several runs are fitted using the same kinetic parameters, giving robustness to the results. In the present work, a numerical integration procedure was discussed and applied to different examples. We focused on materials presenting a single decomposition curve as well as other materials with more complex processes. Different examples were explored, and the methodology was applied to a number of wastes such as coffee husks, polystyrene and polyethylene.

After 40 years of the discovery of metallocene catalysts, there are still several aspects that remain unresolved, especially when the “conventional” alkylaluminum activators are not used. Herein, we systematically investigate the synthesis of PE via three different zirconocene catalysts, with different alkyl substituents, activated via different organoboron compounds. The polymerization behavior, as well as the properties of the materials, are evaluated. The results demonstrate that the highest catalytic activity is shown by Bis(cyclopentadienyl)dimethylzirconium activated by trityl tetra(pentafluorophenyl)borate. Also finding that toluene is the optimum solvent for these systems and at these reaction conditions. Moreover, to validate our experimental results, a comprehensive mathematical model is developed on the basis of thermodynamic and kinetic principles. The concentration of ethylene transferred to the solvent phase (toluene) in a liquid-vapor equilibrium (LVE) system is estimated based on the Duhem’s theorem. Arrhenius expressions for the kinetic rate constants of a proposed kinetic mechanism are estimated by a kinetic model, in which the rate of polymerization is fitted by a least-square optimization procedure and the molecular weight averages by the method of moments. The simulations of the coordination polymerization suggest the presence of two types of active sites, principally at low temperatures, and the reactivation of the deactivated sites via a boron-based activator. However, the effect of the temperature on the reactivation step is no clear; a deeper understanding via designed experiments is required.

The research paper provides a mathematical framework for understanding phase shift in wave phenomena, bridging theoretical foundations with real-world applications. It emphasizes the importance of phase shift in physics and engineering, particularly in fields like telecommunications and acoustics. Key equations are introduced to explain phase angle, time delay, frequency, and wavelength relationships. The study also introduces the concept of time distortion due to a 1° phase shift, crucial for precise time measurements in precision instruments. The research also addresses infinitesimal wave energy loss related to phase shift, enriching our understanding of wave behavior, and impacting scientific and engineering disciplines.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

The retrospective noninterventional study investigated the kinetic energy of video images of 18 fertilized eggs (7 were normal and 11 were abnormal) recorded by a time-lapse device leading up to the beginning of the first cleavage. The norm values of cytoplasmic particles were measured by the optical flow method. Three phases profile for normal cases were found regarding the kinetic energy that were 2.199×10⁻²⁴±2.076×10⁻²⁴, 2.369×10⁻²⁴±1.255×10⁻²⁴, and 1.078×10⁻²⁴±4.720×10⁻²⁵ (J) for the phases 1, 2, and 3, respectively. In phase 2, the energies were 2.369 × 10⁻²⁴ ± 1.255 × 10⁻²⁴ and 4.694 × 10⁻²⁴ ± 2.996 × 10⁻²⁴ (J) (mean ± SD, P = 0.0372), and the time required was 8.114 ± 2.937 and 6.018 ± 5.685 (H) (P = 0.0413) for the normal and abnormal cases, respectively. The kinetic energy change was considered a condition for applying the free energy principle that states that, for any self-organized system to be in equilibrium in its environment, it must minimize its informational free energy. The kinetic energy while interpreting it in terms of the free energy principle suggesting clinical usefulness would further our understanding of the phenomenon of fertilized egg development with respect to the birth of human life.

We study in this work a dilute granular gas immersed in a thermal bath made of smaller particles with nonnegligible masses as compared with the granular ones. The kinetic theory for this system is developed and described by an Enskog--Fokker--Planck equation for the one-particle velocity distribution function. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is based on a nonlinear drag force plus a white-noise stochastic force. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects like Mpemba and Kovacs-like ones.

In this study, we introduce a novel framework for the estimation of residual renal function (RRF), based on the population compartmental kinetic behavior of Beta 2 Microglobulin (B2M) and its dialytic removal. Using this model, we simulated a large cohort of patients with various levels of RRF receiving either conventional high-flux hemodialysis or on-line hemodiafiltration. These simulations were used to estimate a novel population kinetic (PK) equation for RRF (PK-RRF) that was validated in an external public dataset of real patients. We assessed the performance of the resulting equation(s) against their ability to estimate urea clearance using cross-validation. Our equations derived entirely from computer simulations and advanced statistical modeling, and had extremely high discrimination (AUC 0.808 – 0.909) when applied to a human dataset of measurements of RRF. A clearance-based equation that utilized pre and post dialysis B2M measurements, patient weight, treatment duration and ultrafiltration had higher discrimination than an equation previously derived in humans. Furthermore, the derived equations appeared to have higher clinical usefulness as assessed by Decision Curve Analysis, potentially supporting decisions that for individualizing dialysis frequency in patients with preserved RRF.

The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

The paper considers the physical consequences of bimetric geodesically (pro jectively) invariant equations of gravitation. The correct expression for the energy- impulse tensor of the gravitational field is obtained and with its help the key role of the gravitational defect of mass-energy for the energy of the newborn universe is shown..

Most fully developed galaxies have vivid spiral structure, but the formation and evolution of spiral structure is still a mystery that is not fully understood in astrophysics. We find that the currently used equations of galactic dynamics contain some unreasonable components. In this paper, the following three working assumptions are introduced to simplify the galactic structural equations. 1. In the research of large-scale structure, the retarded potential of the gravitational field should be taken into account. The propagating time of the gravitational field from center to border is longer than the revolution periods of the stars near the center of galaxy. Newton's gravitational potential is unreasonable for such case, and the weak field and low velocity approximation of Einstein's field equation should be adopted. 2. The stars in a fully developed galaxy should be zero-pressure and inviscid fluid, and the equation of motion is different from that of ordinary continuum mechanics. Stars move along geodesics. 3. The structure of the galaxy is only related to the total mass density distribution. The equation of state of dark halo is different from that of ordinary luminous interstellar matter, so their trajectories are also very different. Dark halo and ordinary matter in galaxy are automatically separated. The total mass density distribution can be presupposed according to the observation data, and then it can be determined by comparing the solution of the equations with the observed data. These assumptions and treatments are supported by theory and observation. The variables of the equations of simplified galactic dynamics are separated from each other, and the equations are well-posed and can be solved according to a definite procedure. Therefore, this simplified dynamic equation system provides a more reasonable and practical framework for the further study of galactic structure, and can solve many practical problems. Besides, it is closely related to the study of dark energy and dark matter.

The feasibility of using full ion kinetics, instead of gyrokinetics, in simulating low-frequency Ion-Temperature-Gradient (ITG) instabilities in tokamaks has recently been demonstrated by Sturdevant et al. [Physics of Plasmas 24, 081207 (2017)]. In that work, a variational integrator was developed to integrate the full orbits of ions in toroidal geometry, which proved to be accurate in capturing both the short-time scale cyclotron motion and long time scale drift motion. The present work extends that work in three aspects. First, we implement a relatively simple full orbit integrator, the Boris integrator, and demonstrate that the accuracy of this integrator is also sufficient for simulation of ITG instabilities. Second, the equilibrium magnetic configuration is extended to general toroidal configuration specified numerically, enabling simulation of realistic equilibria reconstructed from tokamak experiments. Third, we extend that work to the nonlinear regime and investigate the nonlinear saturation of ITG instabilities. To verify the new numerical implementation of the orbit integrator and magnetic configuration, the linear electrostatic ITG frequency and growth rate are compared with those given in Sturdevant's work and good agreement is found.

Background: Depending on the phase of the menstrual cycle the athlete is in, some kinetic, physiological and fatigue variables will show differences. The aim of this study is to analyze whether there are changes in these variables over the course of the menstrual cycle. Methods: Eight regular female runners and triathletes performed a maximal treadmill test, as well as a submaximal test (6’ stages at 50%, 60% and 80% of maximal aerobic speed) in each of the phases of the menstrual cycle: bleeding phase (day 2.4 ± 0.7), follicular phase (day 10.4 ± 2.2) and luteal phase (day 21.8 ± 2.1). Running dynamics were measured (using RunScribe) at the end of each test, as were lactate concentration, heart rate and fatigue (evaluated on a scale of 0 to 5). Results: Higher shock (G) values were recorded in the bleeding phase and higher vertical spring stiffness (kN/m) in the follicular phase. The phase of the menstrual cycle had a significant effect on average and peak heart rate, which was significantly higher in the follicular phase. Conclusions: Higher vertical spring stiffness was observed in the follicular phase, as well as higher peak and average heart rate.

This study evaluated eight herbal and fruit teas to produce kombucha beverages. Besides, the effect of initial sucrose concentration (10, 40, and 70% w/v) on kombucha fermentation from tea extracts was investigated. Kinetic characterization and modeling of kombucha fermentation were also performed. Results showed that kombucha beverages' characteristics and chemical content changed according to tea type and initial sucrose concentration. It was determined that as initial sucrose concentration increased, the consumed substrate concentration increased. The highest total biomass values were determined when green tea and pomegranate tea were supplemented with 70 g/L sucrose. The highest total phenolic content and antioxidant activity were achieved with green tea samples. The total acidity and phenolic substance concentration increased as fermentation progressed in general. The kinetic parameters including maximum consumption rate, sugar utilization, yield, biomass yield, maximum biomass, total acidity, phenolic production rate, and the phenolic result were computed depending on changing substrate concentration. Concerning kinetic modeling, proposed models (Logistic and Luedeking-Piret models) estimated satisfactorily experimental substrate consumption and total acidity values. Besides, total acidity was associated with the substrate consumption.

We consider a Cauchy problem for differential equations in a Hilbert space $X$. The problem is stated in a time interval $I$, which can be finite or infinite. Weuse a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we state and prove convergence criteria for both a general fixed point problem and thecorresponding Cauchy problem. These criteria provide necessary and sufficient conditions on a sequence $\{u_n\}$ which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.

The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of a cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wear. This paper presents an alternative mechanism that is functionally equivalent to a classical flywheel while relying exclusively on limited-stroke flexure-joints. This novel 1-degrees-of-freedom zero-stiffness mechanism has no wear and requires no lubrication: it is thus compatible with extreme environments, such as vacuum, cryogenics, or ionizing radiation. The mechanism is composed of two coupled pivoting rigid bodies whose individual angular momenta vary during motion but whose sum is constant at all times when the pivoting rate is constant. The quantitative comparison of the flexure-based flywheel to classical ones based on a hollow cylinder as inertia shows that the former stores typically 6 times less angular momentum and kinetic energy for the same mass while occupying typically 10 times more volume. The freedom of design of the shape of the rigid bodies offers the possibility of modifying the ratio of the kinetic energy stored versus angular momentum, which is not possible with classical flywheels. For example, a flexure-based flywheel with rigid pivoting bodies in the shape of thin discs stores 100 times more kinetic energy than a classical flywheel with the same angular momentum. A proof-of-concept prototype was successfully built and characterized in terms of reaction moment generation, which validates the presented analytical model.

Gold nanoparticles, were deposited in titanium oxide (TiO2) Degussa-P25 with the Photodeposition method in the presence of UV light at different concentrations. It was determined by diffuse reflectance (DF), Scanning electron microscopy (SEM), that the Photodeposition method is effective for the inclusion of gold particles on the surface. The catalyst band gap showed a reduction to 2.9 e.V, as well as it was observed that the gold-doped catalyst shows absorption in the visible light range around 500 to 600 nm. The percentage of deposited gold nanoparticles was determined by energy dispersive spectroscopy (EDS). The experimental data were analyzed using different analytical techniques (UV-Vis spectrophotometry, TOC total organic carbon), with these results a carbon-based mass balance and reaction kinetics were generated using the Langmuir-Hinshelwood (LH-HW) heterogeneous catalysis model. For the estimation of the kinetic constants, the non-linear regression of the Levengerd Marquad algorithm was used, with these results, kinetic models of the degradation of the molecule and the generation and consumption of Organic Intermediate Products (OIP) were generated.

Kinetic estimation of glomerular filtration rate (KeGFR) proved its utility in predicting acute kidney injury (AKI) in both adults and children. Our objective is to assess the clinical utility of KeGFR in predicting AKI severity and progression to acute kidney disease (AKD) in patients already diagnosed with AKI and to examine major adverse kidney events at 30 days (MAKE30). We retrospectively calculated the KeGFR in the first 24 hours of identified AKI (KeGFR1) and in the 24 hours prior to AKD (KeGFR2) in all admitted children under 18 years old. The cohort consisted of 803 patients with AKI. We proposed a new classification of KeGFR stages, from 1 to 5, and assessed the predictive value of KeGFR stages for AKD development and MAKE30. AKI severity was associated with lower KeGFRs. KeGFR1 and KeGFR2 predicted AKD with AUC values between 0.777 and 0.841 respectively, p<0.001. KeGFR2 had the best performance in predicting MAKE30 (AUC of 0.819) with a sensitivity of 66.67% and specificity 87.7%. KeGFR1 stage 3, 4 and 5 increased the risk of AKD by 3.07, 6.56 and 28.07 times respectively while KeGFR2 stage 2, 3, 4 and 5 increased the risk of AKD 2.79, 3.58, 32.75 and 80.14 times fold. Stage 5 KeGFR1 and KeGFR2 stages 3, 4 and 5 increased the risk of MAKE30 by 7.77, 4.23. 5.89 and 69.42 times in the adjusted models. KeGFR proved to be a useful tool in AKI settings. KeGFR dynamics can predict AKI severity, duration and outcomes.

Ofloxacin is a highly efficient and widely used antibiotic drug. It is classified as a refractory pollutant due to its poor biodegradability. Consequently, it is commonly found in water sources, requiring efficient methods for its removal. Advanced Oxidation Processes (AOPs) offer efficient alternatives since those yield complete degradation not achieved in adsorption or membrane processes. Previous studies suggest ofloxacin degradation follows a pseudo-first or -second order processes, whereas for full removal of refractory pollutants – lower pseudo-orders are required. Monitoring the actual “pseudo-order” degradation kinetics of ofloxacin is needed to evaluate any proposed AOP process. This study presents a simple procedure to evaluate pseudo-orders of AOPs. Photolysis of 20 mM ofloxacin solutions follow pseudo-zero order kinetics, with half-life times (t_1/2) of approx. 60 min. TiO₂ heterogenous catalyst show to have no influence at low concentration (0.2 mg L^-1) but a significant reduction of half-life time (t_1/2 = 20 min) and increase in pseudo-order (0.8) is measured at 2.0 mg L^-1. Similar results are obtained with homogenous catalysis by 2.0 mg L^-1 H₂O₂. The combination of H₂O₂ and TiO₂ catalysts shows additional reduction in half-time life with increase in the pseudo-order to 1.2. The conclusions are (1) heterogenous and homogenous photocatalysis can effectively degrade ofloxacin, (2) combined photocatalysis yields higher pseudo-order, being less prone to achieve full removal, (3) analysis of specific pseudo-orders in AOPs of refractory pollutants helps to further elucidate the efficiency of the processes.

Vanadium titano-magnetite is a significant resource in China, and in this study, we characterize its isothermal reduction mechanisms in the mixture of H₂, CO, and N₂ where the variables considered here include reduction time, reduction temperature, gas composition, and pellet size. The kinetics of the reduction process are mainly studied, which follows a shrinking core model. The results indicate that the reduction degree of oxidized VTM pellets increases with the increase of reduction time, reduction temperature but decreases with the increase of pellet size. Moreover, we found that an increase of H₂/(H₂+CO) ratio induces an increase of the reduction degree. Then the transformation of main Ti-bearing mineral phases is discussed, and the most probable reaction mechanism is revealed. In the whole reduction process, the kinetic results confirm the existence of an early stage and a latter stage, which are controlled by interface chemical reaction and diffusion, respectively. Furthermore, the results show that the diffusion-control step can be observably shortened with the decrease of pellet size because a thinner product layer is formed during the reduction process. Our study thus provides a valuable technical basis on the VTM industrial application.

We explore the field equations in a 4-d complex space-time, in the same way, that general relativity does for our usual 4-d real space-time, forming this way, a new "general relativity" in C⁴ space-time, free of sources. Afterwards, by embedding our usual 4-d real space-time in C⁴ space-time, we describe geometrically the energy-momentum tensor T_μν as the lost geometric information of this embedding. We further give possible explanation of dark eld and dark energy.

When discussing the Diophantine quintic equation $p(a^5 + b^5) = q(c^5 + d^5)$ where p is a prime and q is an integer, there is a clear gap between the mathematical literature and online forums. Because of the intrinsic complexity of parameterizing fifth-degree equations, this equation re- mains largely unexplored. In this work, we approach this quintic problem through algebraic methods with the goal of providing numerical solutions that illuminate its properties and behaviors.Our research uncovers in- triguing patterns and connections that shed light on the enigmatic nature of Diophantine quintic equations in this particular form.

Abstract: The YF3: (Eu3+, Nd3+) nanoparticles (orthorhombic phase, D ~ 130 nm)) were synthesized via the co-precipitation method with subsequent hydrothermal treatment and annealing. The Eu3+ τdecay linearly descends with the increase of temperature in the 80 - 320 K range. The τdecay (T) slope values of the annealed YF3: Eu3+ (2.5 and 5.0 mol. %) nanoparticles were the highest (110·10-4 and 67·10-4, μs/K in the whole 80 – 320 K range, respectively. Thus, these samples were chosen for further doping with Nd3+. The maximum Sa and Sr values based on the LIR (IEu/INd) function were 0.67 K-1 (at 80 K) and 0.86 %·K-1 (at 154 K), respectively. As it was mentioned above, the sin-gle-doped YF3: Eu3+ (2.5. %) nanoparticles showed the linearly decreasing τdecay (T) function (5D0 – 7F1 emission). The main idea of Nd3+ co-doping was to increase this slope value (as well as the sensitivity) by increasing the rate of τdecay (T) descent via the addition of one more tempera-ture-dependent channel of 5D0 excited state depopulation. Indeed, we managed to increase the slope (Sa) up to 180·10-4 K-1 at 80 K. This result is one of the highest compared to the world analogs.

Water pollution is regarded as a dangerous problem that needs to be resolved right away. This is largely due to the positive correlation between the increase in global population and waste production, especially food waste. Hydrogel beads based on sodium alginate (Alg) and pomegranate fruit peels (PP) were developed for the adsorption of Safranin O dye (SO) in aqueous solutions. The obtained Alg-PP beads were widely characterized. The effects of the contact time (0-180 min) and initial concentration (10-300 mg/l), the initial pH (2-10), the adsorbent dosage (1-40 g/l) and the temperature (293-333 K) were investigated through batch tests. The data proved that the adsorption kinetics of SO reached equilibrium within 30 min and up to 180 min. The adsorption data of SO onto synthesized beads follow the pseudo second-order model. The experimental data fitted very well to both Freundlich and Langmuir models. The maximum adsorption capacity of Alg-PP could reach 8.99 mg/g at 293 K. Calculation of Gibbs free energy and enthalpy indicated that adsorption of SO onto Alg-PP is spontaneous and endothermic. Finally, analysis of diffusion and mass transport phenomena were presented. The reported results revealed that the Alg-PP beads could be used as a novel natural adsorbent for the removal of cationic dye pollutants from aqueous environments.

To realize the energy recovery of wheat straw, the pyrolysis behavior of wheat straw was studied at three heating rates (10, 20, and 30 K/min) based on thermogravimetric analysis (TG–DTG). Kinetics and thermodynamics were analyzed using Flynn–Wall–Ozawa (FWO) and Kissinger–Akahira–Sunose (KAS) model-free methods, and reaction mechanism was determined using Coats–Redfern (CR) model-fitting method. The results show that there are three weightlessness stages in the pyrolysis process, of which the second stage was the main weightlessness stage and two distinct peaks of weightlessness were observed in this stage. With increasing heating rate, the main pyrolytic weightlessness peaks of DTG curve shifts to higher temperature. The pyrolysis activation energy calculated by FWO and KAS methods are 165.17–440.02 kJ/mol and 163.72–452.07 kJ/mol, and the pre-exponential factor vary in the range of 2.58×1012–7.45×1036 s-1 and 1.91×1012–8.66×1037 s-1, respectively. The thermodynamic parameters indicates that wheat straw has the favorable conditions for product formation and containes potential energy to be utilized for bioenergy production, its pyrolysis reaction was non-spontaneous and the energy output is stable. CR method analysis shows that the A1/3 random nucleation model is the most suitable mechanism to characterize the pyrolysis process, and random nucleation may be in charge of the main pyrolysis stage. This study can provide a theoretical basis for the thermochemical conversion and utilization of wheat straw.

Background: Little is known about potential confounding factors influencing the humoral response in individuals having received the BNT162b2 vaccine. Methods: Blood samples from 231 subjects were collected before and 14, 28 and 42 days following COVID-19 vaccination with BNT162b2. Anti-Spike Receptor-Binding-Domain protein (anti-Spike/RBD) immunoglobulin G (IgG) antibodies were measured at each time-point. Impact of age, sex, childbearing age status, hormonal therapy, blood group, body mass index and past-history of SARS-CoV-2 infection were assessed by multivariable analyses. Results and Conclusions: In naïve subjects, the level of anti-Spike/RBD antibodies gradually increased following administration of the first dose to reach the maximal response at day 28 and then plateauing at day 42. In vaccinated subjects with previous SARS-CoV-2 infection, the plateau was reached sooner (i.e. at day 14). In the naïve population, age had a significant negative impact on anti-Spike/RBD titers at day 14 and 28 while lower levels were observed for males at day 42, when corrected for other confounding factors. BMI as well as B and AB blood groups had a significant impact in various subgroups on the early response at day 14 but no longer after. No significant confounding factors were highlighted in the previously infected group.

A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N. Zubarev. Generalized transfer equations for a consistent description of kinetics and hydrodynamics of the dense quantum-field system with strongly coupled states are derived.

We present three reduced integrable hierarchies of nonlocal integrable NLS type equations from a vector integrable hierarchy associated with a matrix Lie algebra, not being A type. Three similarity transformations are taken to keep the invariance of the transformed zero curvature equations. The key step is to formulate a solution to a reduced stationary zero curvature equation so that the zero curvature formulation works for a reduced case.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

In this paper, we investigate the equilibrium points of following a system of difference equations x_n+1 = x_n 2y_n−1, y _n+1 = y_n 2x_n−1. We also study the asymptotic stability of related system of difference equations. Further we examine the periodic solutions of related system with period two. Additionally, we find out the invariant interval and periodic cycles of related system of difference equations.

We have shown that the use of evolutionary gravitational constants G, the speed of light c, and cosmological constant Λ in the Einstein’s field equations leads to a very simple model that fits the supernovae Ia data with a single parameter as well as the standard ΛCDM model with two parameters, and has the predictive capability superior to the latter. We have shown that at the current time G and c both increase as dG/dt = 5.4GH₀ and dc/dt = 1.8cH₀ with H₀ as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH₀. Negative finding on the variation of G with time derived from the analysis of lunar laser ranging data in several studies has been attributed to the fact that these studies did not consider the variation of c simultaneously with G.

We prove general stability theorems for $n$-dimensional quartic-cubic-quadratic-additive type functional equations of the form \begin{eqnarray*} \sum_{i=1}^\ell c_i f \big( a_{i1}x_1 + a_{i2}x_2 + \cdots + a_{in}x_n \big) = 0 \end{eqnarray*} by applying the direct method. These stability theorems can save us much trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

Remote patient monitoring systems are helpful since they can provide timely and effective healthcare facilities. Such online telemedicine are usually achieved with the help of sophisticated and advanced wearable sensor technologies. The modern type of wearable connected devices enables the monitoring of vital sign parameters such as: heart rate variability (HRV) also known as electrocardiogram (ECG), blood pressure (BLP), Respiratory rate and body temperature. The ubiquitous problem of wearable devices is power demand for signal transmission, such devices require frequent battery charge which causes serious limitations to the continuous monitoring of vital data. To overcome this, the current study provides a primary report for collecting kinetic energy from human daily activities for monitoring Human vital signs, the harvested energy is used to sustain the battery autonomy of wearable devices, which enables longer monitoring time of vital data. A thorough review of available commercial ECG devices is first provided, and different methods evaluated in other literature to improve the monitoring time of wearable IOT devices. Besides, a novel type of Stress or exercise ECG monitoring device based on Microcontroller PIC18F4550 and Wi-Fi device ESP8266 is proposed in this study, which is cost effective and enables real time monitoring of heart rate on cloud during normal daily activities. In order to achieve both portability and maximum power, the harvester has smallest structure and low friction. Neodymium magnets are chosen for their highest magnetic force. Due to nonlinear magnetic force interaction of the magnets, the nonlinear part of the dynamic equation has inverse quadratic form. Electromechanical damping is considered in this study and the quadratic non linearity is approximated using MacLaurin expansion, which enables to find the law of motion for general case of studies using classical methods for dynamic equations and find the suitable parameters for the harvester. The oscillations are enabled by applying an initial force and there is loss of energy due to the electromechanical damping. A typical numerical application is computed with Matlab software and ODE45 solver is used to verify the accuracy of the method.

Kinetic modeling is an essential tool in systems biology research, enabling the quantitative analysis of biological systems and predicting their behavior. However, the development of kinetic models is a complex and time-consuming process. In this article, we propose a novel approach called KinModGPT, which generates kinetic models directly from natural language text. KinModGPT employs GPT-3 as a natural language interpreter and Tellurium as an SBML generator. We demonstrate the effectiveness of KinModGPT in creating SBML models from complex natural language descriptions of biochemical reactions. KinModGPT successfully generates valid SBML models from a range of natural language model descriptions of metabolic pathways, protein-protein interaction networks, and heat shock response. This article demonstrates the potential of KinModGPT in kinetic modeling automation.

Our starting point is the covariant coordinate transformation equation of a relativistic positioning system in Minkowski space-time, which maps the receiver’s emission coordinates (proper times broadcast by the emitters) to its coordinates in some inertial reference frame. Bancroft’s analytical (closed-form) solution to the basic pseudorange navigation equations with four emitters is recovered and the subjacent elements are geometrically interpreted. The case of four static beacons is analized as a clarifying situation.

In this study, we focus on an abstract form of summation equations, which can be regarded as a particular class of nonlinear difference equations. We investigate sufficient conditions for the existence of discrete almost automorphic solutions by appealing to the fixed point theory and establish a linkage between the existence of discrete almost automorphic solutions and the existence of bounded solutions for the nonlinear difference equations in the spotlight. Consequentially, we propose a discrete counterpart of the Bohr-Neugebauer theorem for the qualitative theory of difference equations.

It is universally accepted that Maxwell equations do not remain invariant under the Galilean transformation. This conflicts the principle of relativity which states that the physical law must remain invariant in the mathematical form in all inertial frames of reference. For this reason, the Lorentz transformation is invented, and the Galilean transformation is nowadays superseded by the Lorentz transformation. However, this paper challenges this widely held belief that the Maxwell equations are not invariant under the Galilean transformation. By applying the Galilean transformation to Lienard-Wiechert electromagnetic fields it is mathematically proven that the Maxwell equations indeed remain invariant under the Galilean transformation. In addition, the critical error in Lorentz's proof of Galilean non-invariance of Maxwell equations is pointed out, and it turns out that Lorentz's conclusion that Maxwell equations are not invariant under the Galilean transformation is the result of a mathematical error.

We establish certain modular equations of degree three based on some results of Ramanujan's theta functions.

Considerable efforts have been devoted to modifying gravity, which aim to elucidate the possible existence or nature of dark matter and energy, describe observational data more effectively, and formulate quantum gravity. In addition, despite the immense success of the quantum field theory, the framework requires renormalization techniques and breaks down at high energies. Recently, the Planck legacy 2018 release has confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level higher than 99%. This study considers the implied curvature of the early Universe as the curvature of “the background or 4D conformal bulk as a manifestation of vacuum energy” and distinguishes it from the localized curvature that is induced in the bulk by the presence of celestial objects that are regarded as ”4D relativistic cloud-worlds.” Analogously, because gravity appears to emerge owing to spacetime curvature and does not exhibit critical characteristics shared by other fields, it has been incorporated as the local curvature of the bulk affecting the embedded quantum fields that are regarded as propagating “4D relativistic quantum clouds.” To consider the effects of the bulk on embedded clouds, this paper presents interaction field equations in terms of brane-world modified gravity and the perspective of geometrization of the quantum mechanics wherein gravity is manifested by the curvature of 4D conformal bulk as an indicator of the field strength of vacuum energy on the embedded 4D relativistic clouds in addition to the boundary interactions, which could remove the singularities and satisfy a conformal invariance theory. A visualization of the evolution of the 4D relativistic cloud-worlds over the conformal spacetime of the 4D bulk is presented, whereas the standard said theories can be recovered from the interaction field equations.

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

The Maxwell equations of electrodynamics describe electrical and magnetic forces with great accuracy in the vacuum of space. But the equations of electrodynamics applied to material systems are usually written in a way that obscures their accuracy. The usual formulation of the Maxwell equations includes a dielectric constant as a single real number that grossly over-approximates the actual properties of matter, particularly liquid matter so important in applications of electrodynamics to biology and chemistry. We rewrite two Maxwell equations here to make clear the precision of the Maxwell equations in the presence or absence of matter. We discuss and derive two well known corollaries that are as universal and precise as the Maxwell equations themselves: (1) a continuity equation that relates charge and flux and (2) a conservation equation in which total current never accumulates at all. The total current is the right hand side of the Ampere-Maxwell law. Total current is perfectly incompressible. It is conserved exactly, everywhere and at every time, independent of the microphysics of charge conduction. The total current combines the flux of charges and the ethereal current. The ethereal current \varepsilon_{o\ }\sfrac{\partial\mathbf{E}}{\partial t}\ exists everywhere, including the interior of atoms, because it is a property of space, not matter. The ethereal current exists, and thus flows, in a vacuum devoid of mass. The ethereal current is a consequence of the relativistic (Lorentz) invariance of charge. Charge does not change even if it moves at speeds approaching the velocity of light. Total current has properties quite distinct from flux of mass because of the ethereal current. Most strikingly, in the one dimensional unbranched systems of electronic circuits and biological ion channels, the total current is independent of location, even if the flux of charges varies a great deal. Indeed, the Maxwell equations—and thus conservation of total current—act as a perfect low pass spatial filter, converting the infinite variation of (the Brownian model of) thermal motion of charges to the zero variation of the total current.

This paper attempts to clarify an long-standing issue about the number of unknowns in the Reynolds-Averaged Navier-Stokes equations (RANS). This study shows that all perspectives regarding the numbers of unknowns in the RANS stem from the misinterpretation of the Reynolds stress tensor. The current literature consider that the Reynolds stress tensor has six unknown components; however, this study shows that the Reynolds stress tensor actually has only three unknown components, namely the three components of fluctuation velocity. This understanding might shed a light to understand the well-known closure problem of turbulence.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

Smoked cigarette butts (SCB) can be used as precursors to obtain activated carbon (AC) due to their high carbon content related to the presence of cellulose acetate and components that are retained in the tobacco combustion process. In this way, it was analyzed how the process of pyrolysis or formation of char from this residue occurs, for this a study of the kinetics of formation of char is carried out by thermogravimetry, using three heating speeds 5, 10 and 15 °C/min. Based on the data obtained, mathematical models such as Kissenger - Akahira - Sunose (KAS), Starink (STK) and Ozawa - Flynn - Wall (OFW) were used in order to identify thermodynamic parameters through the energy of activation. The char obtained was subjected to an activation treatment with KOH in order to increase the surface area and pore volume, obtaining values of 433 m2/g of BET area and 0.25 cm3/g of micropore volume. Finally, the adsorbent was applied in the removal of Cr (VI) obtaining a Qmax capacity determined by the Langmuir model of 55.8 mg/g.

In this study, considering the peroxidase-like activity of the SiO₂@AuNPs nanocomposite, their biochemical properties including, pH stability, cycling stability, shelf stability, and kinetic parameters were investigated. The results revealed that the as-mentioned SiO₂@AuNPs nanocomposite reveal its maximal activity at pH=4.0 along with saving 83.3% of its maximal activity at pH=5.0. Besides, the reusability and shelf-storage studies exhibited that the SiO₂@AuNPs nanocomposite retained 90% and 100% of its initial activity after 5 operational cycles and 30 days of storage, in order. The kinetic parameters of the as-prepared nanozymes were calculated using Menten kinetic model, revealing a V_max of 1.35 µM min^-1 and a K_m as low as 0.06 mM for the SiO₂@AuNPs nanocomposite. Based on the results of this work, the as-prepared SiO₂@AuNPs nanocomposite with intrinsic peroxidase-like activity shows high substrate affinity and catalytic efficiency along with excellent cycling- and shelf-stability, making them suitable for application in peroxidase-mediated reactions instead of the native enzyme.

The presence of metal ions, in high concentrations, in the effluents results from industrial metal coating is a well-known fact. Most of time, such metal ions, once they reach the environment, contribute significantly to its degradation. Therefore, it is essential that before such effluents are discharged into the environment, the concentration of metal ions is reduced (as much as possible), to minimize the negative impact on the quality of ecosystems. Among all methods that can be used to reduce the concentration of metal ions, sorption is one of the most viable options, due to its high efficiency and low cost. Moreover, due to the fact that many of the industrial wastes have sorbent properties, this method is in accordance with the principles of circular economy. Based on these considerations, in this study, mustard waste biomass (resulting after oil extraction) was functionalized with an industrial polymeric thiocarbamate (METALSORB), and used as an sorbent to removal Cu(II), Zn(II) and Co(II) ions from aqueous media. The best conditions for the functionalization of mustard waste biomass were found to be: mixing ratio biomass : METASORB = 1g : 1.0 mL and temperature of 30 C. The experimental sorption capacities of functionalized sorbent (MET-MWB) were 0.42 mmol/g for Cu(II), 0.29 mmol/g for Zn(II) and 0.47 mmol/g for Co(II), and were obtained in the following conditions: pH of 5.0, 5.0 g sorbent/L and temperature of 21 C. Modeling of isotherms and kinetic curves, but also the analysis of the results obtained from desorption processes, demonstrates the usefulness of this sorbent in the treatment of effluents contaminated with metal ions. In addition, tests on real wastewater samples highlight the potential of MET-MWB for large-scale applications.

For the KdV-Burgers equations on cylindrical and spherical waves the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary is studied. The equations describe a medium which is both dissipative and dispersive. Symmetries, invariant solutions and conservation laws are investigated. For an appropriate combination of dispersion and dissipation the asymptotic profile looks like a periodical chain of shock fronts with a decreasing amplitude (sawtooth waves). The development of such a profile is preceded by a head shock of a constant height and equal velocity which depends on spatial dimension as well as on integral characteristics of boundary condition; an explicit asymptotic for this head shock and a median of the oscillating part is found.

The storm of November 12th-13th, 2019 provoked the displacements of boulders in a central Mediterranean rocky coast; with reference to a selected area, prone to the boulder production and geomorphologically monitored for years, a field-oriented study approach was applied for the phenomenon, by collating data concerning pre-storm locations and kinematics of these boulders. The number of displaced boulders is 11, that is, in terms of morphological imprint of a specific storm, one of the major study cases for the Mediterranean. In addition, based on widely used hydrodynamic equations, the minimum wave height required to displace the boulders is assessed. The values conform with the expected values for the wave climate dominating during the causative meteorological event and give a measure of the energy of the storm slamming the coast. Boulder dislodgements usually have plays a key role in determining the rate of the coastal recession, likely also in the investigated area. In view of an adverse climate evolution with a possible increase of energy and frequency of severe storms, the results deriving from the study of this morphodynamics should be considered for the hazard assessment and coastal management.

The prevalence of differential equations as a mathematical technique has refined the fields of control theory and constrained optimization due to the newfound ability to accurately model chaotic, unbalanced systems. However, in recent research, systems are increasingly more nonlinear and difficult to model using Differential Equations only. Thus, a newer technique is to use policy iteration and Reinforcement Learning, techniques that center around an action and reward sequence for a controller. Reinforcement Learning (RL) can be applied to control theory problems since a system can robustly apply RL in a dynamic environment such as the cartpole system (an inverted pendulum). This solution successfully avoids use of PID or other dynamics optimization systems, in favor of a more robust, reward-based control mechanism. This paper applies RL and Q-Learning to the classic cartpole problem, while also discussing the mathematical background and differential equations which are used to model the aforementioned system.

E-waste management (EWM) refers to the operation-management of discarded or unproductive electronic devices and components, a challenge exacerbated due to overindulgent urbanization. This article presents a multidimensional cost-function-based analysis of the EWM framework structured on three modules - environmental, economic, and social uncertainties - which contemplate the 3 pillars of sustainability in an e-waste recycling plant, including the production-delivery-utilization process. The framework incorporates material recovery from a single e-waste facility provisioning for chemical and mechanical recycling. Each module is ranked using independent Machine Learning (ML) protocols: a) Analytical Hierarchical Process (AHP) and b) combined AHP and Principal Component Analysis (PCA). From a long list of possible contributors, the model identifies and ranks two key sustainability contributors to the EWM supply chain: overall energy consumption and volume of carbon dioxide generated. Another key finding is a precise time window for policy resurrection, which for the data considered, happens to be 400-600 days from the start of operation. Another interesting outcome is the quality of prediction using a combination of AHP and PCA, which consistently produced better results than any of these ML methods individually implemented. Model outcomes have been verified using a case study to outline a future E-waste sustained roadmap.

Self-healing ceramic composites are promising smart materials for high-temperature applications. To better understand their behaviors under service conditions, numerous studies have been performed both experimentally and numerically, and kinetics parameters such as activation energy and frequency factor are reported to be indispensable for investigating healing phenomena. Here, we propose a method for determining the kinetic parameters of self-healing ceramic composites based on the oxidation kinetics model of strength recovery. These parameters are determined by an optimization method using experimental strength recovery data under various healing temperatures and times and microstructural features on the fractured surfaces. Alumina and mullite matrix-based self-healing ceramic composites, such as Al2O3/SiC, Al2O3/TiC, Al2O3/Ti2AlC (MAX phase), and mullite/SiC, were selected as target materials. The theoretical strength recovery behaviors of the cracked specimens obtained from the determined kinetic parameters were compared with the experimental results. The determined parameters are within the previously reported range, and the predicted strength recovery behaviors are reasonably agreed with the experimental values. The proposed method can also be applied to other self-healing ceramics with matrices reinforced with different healing agents to evaluate oxidation rate, crack healing rate, and theoretical strength recovery behaviors for designing self-healing materials used in high temperature applications. Furthermore, the healing ability of composites can be fairly discussed regardless of the type of strength recovery test.

An exact solution is obtained for the kinetic energy in the general case of the spatial motion of solids with arbitrary rotation, which differs from the Koenig formula by three additional terms with centrifugal moments of inertia. The description of motion in the Lagrange form and the superposition principle are used, which provides a geometric summation of the velocities and accelerations of the joint motions in the Lagrange form for any particle at any time. The integrand function in the equation for kinetic energy is represented by the sum of the identical velocity components of the joint plane-parallel motions. The moments of inertia in the Koenig formula do not change during movement and can be calculated from the current or initial state of the body. The centrifugal moments change and turn to 0 when rotating relative to the main central axes only for bodies with equal main moments of inertia, for example, for a ball. In other cases, the difference in the main moments of inertia leads to cyclic changes in the kinetic energy with the possible manifestation of precession and nutation, the amplitude of which depends on the angular velocities of rotation of the body. An example of using equations for a robot with one helical and two rotational kinematic pairs is given.

The kinetics of biogas production from biomass depends on several factors such as: carbon to nitrogen ratio (C/N), reactor temperature (T), and retention time (RT). The purpose of this study was to obtain a new model for predicting biogas production. Spent Mushroom Compost (SMC) was used to produce biogas in a batch type reactor. The experiments were carried out with different C/N ratios (12.1, 20, 30 and 40) and in both mesophilic (35°C) and thermophilic (55°C) temperatures. The results showed that the Maximum biogas production at 35°C, C/N=20 was equal to 41.9 mL/gVS and 55°C, C/N=30 was equal to 51.6 mL/gVS. By using experimental data, a new kinetic model was proposed to predict biogas production. Comparing the values of the results indicate that the total values of RMSE for Logistics, Gampartz and new kinetic models was 0.1906, 0.1830 and 0.1617, respectively. Therefore, the process of anaerobic digestion of biomass can be assumed to be just a chemical reaction, and the new kinetic model is an appropriate alternative to microbial growth models.

Multiple lines of evidence indicate that CD8$^+$ T cells are important in the control of HIV-1 (HIV) replication. However, CD8$^+$ T cells induced by natural infection cannot eliminate the virus or reduce viral loads to acceptably low levels in most infected individuals. Understanding the basic quantitative features of CD8$^+$ T-cell responses induced during the course of HIV infection may therefore inform us about the limits that HIV vaccines, which aim to induce protective CD8$^+$ T-cell responses, must exceed. Using previously published experimental data from a cohort of HIV-infected individuals with sampling times from acute to chronic infection we defined the quantitative properties of CD8$^+$ T-cell responses to the whole HIV proteome. In contrast with a commonly held view, we found that the relative number of HIV-specific CD8$^+$ T-cell responses (response breadth) changed little over the course of infection (first 400 days post-infection), with moderate but statistically significant changes occurring only during the first 35 symptomatic days. This challenges the idea that a change in the T-cell response breadth over time is responsible for the slow speed of viral escape from CD8$^+$ T cells in the chronic infection. The breadth of HIV-specific CD8$^+$ T-cell responses was not correlated with the average viral load for our small cohort of patients. Metrics of relative immunodominance of HIV-specific CD8$^+$ T-cell responses such as Shannon entropy or the Evenness index were also not significantly correlated with the average viral load. Our mathematical-model-driven analysis suggested extremely slow expansion kinetics for the majority of HIV-specific CD8$^+$ T-cell responses and the presence of intra- and interclonal competition between multiple CD8$^+$ T-cell responses; such competition may limit the magnitude of CD8$^+$ T-cell responses, specific to different epitopes, and the overall number of T-cell responses induced by vaccination. Further understanding of mechanisms underlying interactions between the virus and virus-specific CD8$^+$ T-cell response will be instrumental in determining which T-cell-based vaccines will induce T-cell responses providing durable protection against HIV infection.

Process simulation represents an important tool for plant design and optimisation, either applied to well established or to newly developed processes. Suitable thermodynamic packages should be selected in order to properly describe the behaviour of reactors and unit operations and to precisely define phase equilibria. Moreover, a detailed and representative kinetic scheme should be available to predict correctly the dependence of the process on its main variables. This review points out some models and methods for kinetic analysis specifically applied to the simulation of catalytic processes, as a basis for process design and optimisation. Attention is paid also to microkinetic modelling and to the methods based on first principles, to elucidate mechanisms and calculate thermodynamic and kinetic parameters. Different case histories support the discussion. At first, we have selected two basic examples from the industrial chemistry practice, e.g. ammonia and methanol synthesis, which may be described through a relatively simple reaction pathway. Then, a more complex reaction network is deeply discussed to define the conversion of bioethanol into syngas/hydrogen or into building blocks, such as ethylene.

Biodiesel has several drawbacks, such as being prone to oxidation, having reduced stability, and having limited storage time. Antioxidants compatible with biodiesel are being used to address its drawbacks. The use of antioxidants in biodiesel has a significant impact on the environment and economy, especially in promoting sustainable energy. The study used blends consisting of 20% biodiesel and 80% diesel fuel. Isatin-thiosemicarbazones were tested as additives in blends at a concentration of 3000 parts per million (ppm) using an oxifast device. Comparing them to the chemical antioxidant Trolox. FT-IR, DSC, and TGA were used to characterize these samples. DSC measured sample crystallization temperatures (Tc). Samples with antioxidants showed decreased values compared to the non-antioxidant diesel sample D100. Several DSC tests were conducted to determine the antioxidant strengths of various samples. The results showed that the FT-IR spectrum's antioxidant effect regions grow clearer with antioxidants. The extra antioxidant is effective. Biodiesel's oxidative stability improves with isatin-thiosemicarbazones at varying concentrations. The kinetics of thermal decomposition of isatin-thiosemicarbazones under non-isothermal conditions have been determined using the Kissinger, Ozawa, and Boswell techniques. The activation energies of compounds 1 and 2 were calculated 137–147 kJ mol-1 and 173–183 kJ mol-1, respectively.

Intensive development of many industries, including textile, paper or plastic, which consume large amounts of water and generate huge amounts of wastewaters containing toxic dyes, contribute to pollution of the aquatic environment. Among many known methods of wastewater treatment, adsorption techniques are considered as the most effective. In the present study the weakly basic anion exchangers such as Amberlyst A21, Amberlyst A23 and Amberlyst A24 of the polystyrene, phenol-formaldehyde and polyacrylic matrices were used for C.I. Direct Yellow 50 removal from aqueous solutions. The equilibrium adsorption data were well fitted to the Langmuir adsorption isotherm. Kinetic studies were described by the pseudo-second order model. The pseudo-second order rate constants were in the range of 0.0609-0.0128 g/mg·min for Amberlyst A24, 0.0038-0.0015 g/mg·min for Amberlyst A21 and 1.1945-0.0032 g/mg·min for Amberlyst A23, and decreased with the increasing initial concentration of dye from 100-500 mg/L, respectively. There were observed auxiliaries (Na2CO3, Na2SO4, anionic and non-ionic surfactants) impact on the dye uptake. The polyacrylic resin Amberlyst A24 can be promising sorbent for C.I. Direct Yellow 50 removal as it is able to uptake 666.5 mg/g of the dye compared to the phenol-formaldehyde Amberlyst A23 of the 284.3 mg/g capacity.

Curcumin has restrained clinical applications due to poor bioavailability. This study aimed to synthesize cockle shell-derived calcium carbonate (aragonite) nanoparticles (CSCaCO3NP) for delivery of curcumin and to evaluate its kinetic release in vitro. CSCaCO3NP was synthesized and conjugated with curcumin (Cur-CSCaCO3NP) using a simple top down approach and characterized for its physicochemical properties as a potential curcumin carrier. In vitro release profile was assessed using dialysis bag membrane method. The release data were fitted to Korsmeyer-Peppas, Zero order and Higuchi models to evaluate the mechanism of release pattern. A spherical shaped CSCaCO3NP with a surface area of 14.48±0.1 m2/g, average mean diameter size of 21.38±2.7 nm and a zeta potential of -18.7 mV was synthesized which has a high loading content and encapsulation efficiency. The FT-IR and XRD revealed less observable changes on the peaks after conjugation. In vitro kinetic release profile demonstrated sustained release and best fitted to the Higuchi equation model. The results of this study showed the capacity of the synthesized CSCaCO3NP to encapsulate curcumin efficiently with a stable release in vitro. This could give an insight and supportive ideas on the potentials of CSCaCO3NP for curcumin delivery. Therefore, CSCaCO3NP holds future prospects in preclinical framework to enhance curcumin efficacy for oral therapeutic applications.

In this study, functionalized-MWCNTs with 3-aminopropyltriethoxysilane (APTES) loaded titania nanoparticles (MWCNTs-APTES-TiO₂) were prepared to investigate their physicochemical properties and photocatalytic activity for methyl orange (MO) degradation. The TiO₂ nanoparticles, functionalized-MNCNT and composite powders were characterized by XRD, raman, and TEM. The results obtained proved that titania (TiO₂) nanoparticles was successfully loaded on APTES-MWCNTs. The best photocatalytic degradation of methyl orange solution under UV light irradiation was recorded over MWCNTs-APTES-TiO₂ (1:2), with 87% after 180 min. Kinetic analysis indicated that photocatalytic degradation of MO solution by MWCNTs-APTES-TiO₂ obeyed second-order kinetic model (R² > 0.95), supported by half-life equations and graph. The presence of carbon nanotubes accelerated the degradation of methyl orange due to inhibition of electron-hole recombination, the formation of additional hydroxyl radicals and functional groups of the latter had an inhibitory effect on the degradation of methyl orange. This study shows that the MWCNTs-APTES-TiO₂ nanocomposites exhibit promising photocatalytic degradation against methyl orange.

Recently several papers have been published on the Liénard equation x'' +L x+m x^3+n x^5=0, where the authors studied their explicit solutions and their applications. Here we describe the complete dynamics of these differential equations in the Poincar\'e disc. The Poincar\'e disc is the closed disc centered at the origin of coordinates of radius one, the whole plane R^2 is identified with the interior of this disc, and its boundary, the circle $\sss^1$ is identified with the infinity of R^2.

We explore the relationship between the exact renormalization group (RG) equation and quantum mechanics. The central idea is to rewrite the exact Wilsonian RG equation as a Schrödinger-type equation, opening avenues for analysis. By introducing a functional transformation, the RG equation takes on a form analogous to a quantum mechanical Schrödinger equation. The study investigates solutions to this equation and draws parallels with quantum mechanics, paving the way for understanding the infrared behavior of quantum field theories. Furthermore, we extends its insights to a one-dimensional toy model, providing illustrative examples. The discussion encompasses the implications of these findings in multiple dimensions and quantum field theory, with a brief exploration of their relevance in the context of inflationary cosmology.

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables’ trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system’s mean CFL number agrees with the full model’s.

Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

A new type of ordinary differential equation is introduced and discussed, namely, the time-dependent order ordinary differential equations. These equations can be solved via fractional calculus and are mapped into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equations smoothly deforms solutions of the classical integer order ordinary differential equations into one-another, and can generate or remove singularities. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers was also proved.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

This manuscript presents a novel approach to estimating the potential within Schrödinger equations, with a particular focus on applications to the Navier-Stokes problem in fluid dynamics. By establishing new theoretical estimates, we delve into the intricate dynamics of fluid flow, aiming to unveil previously obscured aspects of the Navier-Stokes equations. Through a rigorous mathematical framework, we explore how these new potential estimates can provide a fresh perspective on fluid mechanics, contributing to the ongoing quest to solve some of its most persistent challenges.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: 1) Lax representation $[L,M]=0$; 2)~construction of fundamental analytic solutions (FAS); 3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) $\xi^+(x,t,\lambda) =\xi^-(x,t,\lambda) G(x,t\lambda)$ on a contour $\Gamma$ with sewing function $G(x,t,\lambda)$; 4) soliton solutions and possible applications.Step 1) involves several assumptions: the choice of the Lie algebra $\mathfrak{g}$ underlying $L$, as well as its dependence on the spectral parameter, typically linear or quadratic in $\lambda$. In the present paper we propose another approach which substantially extends the classes of integrable NLEE.Its first advantage is that one can effectively use any polynomial dependence in both $L$ and $M$. We use the following steps: A) Start with canonically normalized RHP with predefined contour $\Gamma$; B) Specify the $x$ and $t$ dependence of the sewing function defined on $\Gamma$; C) Introduce convenient parametrization for the solutions $ \xi^\pm(x,t,\lambda)$ of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); D) use Zakharov-Shabat dressing method to derive their soliton solutions. This needs correctly taking into account the symmetries of the RHP. E) Define the resolvent of the Lax operator and use it analyze its spectral properties.

In this paper we study solutions and drift homogenization for a class of viscous lake equations by using the method of semigroups of bounded operators. Suppose that the initial value i.e.,for some Hölder continuous function onwith smooth function value satisfying and Then the initial value problem (2) for viscous lake equations has a unique smooth local strong solution. Using this result we study the drift homogenization for three-dimensional stationary Stokes equation in the usual sense