Recent technological advancements in produced water for the oil and gas industry have a long history that spreads over centuries and has roots with many mathematicians, physicists, engineers, and inventors. Working to understand the many ideas and questions has helped to bring the produced water technologies to where we are today. Fluid mechanics is an essential factor in the world of engineering because it comes with significant benefits when designing the necessary equipment to overcome the challenging endeavors of daily operations. Many of us believe certain ideas or products were developed within a specific year not fully understanding the idea or concept might be hundreds of years old. For example, when we think of fluid mechanics, we do not think of Archimedes' immersing King Hiero II crown in water. Archimedes did this to determine the displacement of the water as he knew gold was denser than silver. Archimedes was one of the pioneers who was part of the beginning of fluid mechanics. Another interesting fact is the first valve invented was in 1 AD by Heron of Alexandria. This valve can be described as the very first hydraulic valve. The evolution of technology over hundreds of years has made considerable innovations benefiting engineers all over the world. These innovations come in the form of PLCs, RTUs, PIDs, mathematical formulas, processing methods, and SCADA systems.

Aims: This study aimed at examining coach-athlete violence based on the retrospective reports of adults who had been athletes as children and adolescents; predict variables that contribute to the existence of such violence; describe difficulties that the participants encountered as young athletes following such violence; and reveal the outcomes of such violence on their emotions and behaviors, in the past and present. Methodology: The applied mixed-methods comprised quantitative self-reporting questionnaires and qualitative interviews. The former included 440 participants (mean age 27.6) who had trained for at least one year in a sports union youth department; the latter included 14 participants (aged 23-37). These competitive athletes came from eight branches of sports. The interviews were analyzed based on the Narrative Approach. Results: According to the quantitative study, all participants had experienced coach violence at least once during their career, mainly psychological violence and neglect, followed by physical violence. Sexual violence was least reported. The age of their retirement from sports and the number of coaches that they had had were significant predictors of violence. Thematic analysis of the qualitative interviews resulted in six types of coach-athlete violence: (1) psychological violence; (2) verbal violence; (3) starvation and food fattening; (4) non-proportional punishing; (5) physical violence; and (6) sexual violence. Conclusions: It is vital that coach-athlete violence is addressed in public discourse, that the topic of of young athletes’ safety is introduced into coaching education, and that a position holder is nominated to be in charge of such safety in all sports organizations.

Modification of electrode surface with a selective layer gives the possibility to detect target ana-lytes of forensic interest. 3-(4-trifluoromethyl)-phenyl)-thiophene (ThPhCF3) was deposited on a graphite (G) electrode by electrochemical oxidation and characterized as a receptor for the recognition of synthetic stimulants (2-aminoindane, buphedrone, naphyrone). First, the structural characterization of the polymeric layer were obtained from Raman spectroscopy. Second, the electrochemical profiles of selected synthetic stimulants and their affinity to ThPhCF3/G-modified electrodes were studied using square wave voltammetry and electrochemical impedance spec-troscopy. The values of the adsorption constant show the importance of – PhCF3 groups in the interaction with synthetic stimulants, namely recognition by the formation of hydrogen bonds (Kads (buphedrone) < Kads (2-AI)) and interaction with aromatic H atoms (Kads (buphedrone) < Kads (naphyrone)). It was demonstrated that the polymeric layer derived from thiophene with – PhCF3 group is capable to increase the intensity of the electrochemical signal.

In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method based on the weakly singular boundary integral equation, the quadrature techniques, dedicated for the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take the full advantage of the multi-patch technique. The generated collo-cation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by the simple examples with analytical solutions. The feature of the present multi-patch WSIGABEM is investigated by the comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner and the arch bridge are verified to be effective.

Optical communications are described and analyzed by shaped beams; we challenge the ‎effects of parameters that impact the profile of a Flat Top Gaussian (FTG) beam. When ‎the laser beam propagates throughout the atmosphere, it can be influenced by different ‎optical phenomena including scattering, absorption, and turbulence due to changes in the ‎scintillation index and the forms of intensity that are displayed in the source and receiver ‎planes. In this project, the FTG laser beam that propagates through a weak turbulent ‎region is numerically investigated using open-source software. This simulation will be ‎performed according to a mathematical model based on the split-step beam propagation ‎method. Intensity distributions at the source plane and the received average intensity in ‎atmospheric turbulence are calculated, and additional contour is in the transducer plane. ‎The scintillation index, structure constant, source size, and other parameters, are applied ‎in the Rytov method to quantify the weak turbulent model. Moreover, these parameters ‎are analyzed in near-field propagation. Also, the effects of the beam’s scintillation and ‎beam wander are determined. All results simulated are discussed and compared with the ‎TEM00 Gaussian beam. Finally, these results are compared to measurements in the ‎experimental part of the work.

The Polyurethane (PU) mixture is a high−performance engineering material with different dynamic properties compared to a hot−mixed asphalt mixture (HMA). This paper analyzed whether the Kramers−Kronig (K−K) relation and thermo−rheological simple properties were applicable to the PU mixture. Based on the result discussion, the PU mixture exhibited thermo−rheological simple properties within the test conditions. The time−temperature superposition principle (TTSP) was applicable for the PU mixture to construct the dynamic modulus master curve using the standard logistic Sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak−Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The Core−Core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K−K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results. The phase angle of the PU mixture cannot be derived from the dynamic modulus data and currently needs to be derived from the laboratory measurement.

Metal-organic frameworks (MOFs) have been subject of extensive scientific investigation in the last three decades and, currently, are one of the type of compounds most studied to be potentially applied in a wide range of distinct catalytic processes. Pristine MOF compounds provide several intriguing benefits for catalytic applications, including high interior surface areas and densities of active sites, allowing high catalytic reaction rates per volume, post-synthesis modified with com-plementary catalytic groups, enabling multiple functional groups to catalyze the reaction. Most of large-scale catalytic applications, including those in fuel processing, gas emission reduction and chemical synthesis, nevertheless the pristine MOFs often reveal limited stabilities and opportuni-ties for regeneration at high temperatures. As a result, the real applications of MOFs in these tech-nologies are likely to be constrained, and their controlled thermal modification aiming the prepa-ration of MOF-derivative compounds has been applied to induce crystalline structural changes and increase their structural stability, enhancing its potential applicability in more severe catalytic processes. Recent advances concerning the use of this strategy to boost the catalytic potential of the MOF-derivative compounds are outlined in this short-review article.

Body-centered cubic bismuth (Bi) is considered an enticing pressure marker, and therefore it is highly desirable to command its accurate equation of state (EOS). However, significant discrepancies are noted among the previous experimental EOSs. In the present work, the EOS up to 300 GPa is theoretically obtained by direct solving the partition function via a direct integral approach (DIA). The calculated results nearly reproduce the hydrostatic experimental measurements below 75 GPa, and the deviations from the measurements gradually get larger with increasing pressure. Based on the ensemble theory of equilibrium state, DIA works with high precision particularly in high-pressure conditions, so the hydrostatic EOS presented in this work is expected to be a reliable pressure standard.

The fungus Xylaria sp. Z184, harvested from the leaves of Fallopia convolvulus (L.) Á. Löve, has been isolated for the first time. Chemical investigation of the methanol extract of this strain’s culture broth led to the discovery of three new pyranone derivatives fallopiaxylaresters A-C (1–3) and a new bisabolane-type sesquiterpenoid named fallopiaxylarol A (4), along with the first complete set of spectroscopic data for the previously-reported pestalotiopyrone M (5). Known pyranone derivatives (6–11), sesquiterpenoids (12–14), isocoumarin derivatives (15–17), and an aromatic allenic ether (18) were co-isolated. Their structures were elucidated by the interpretation of HRESIMS, 1D, 2D NMR spectroscopy and quantum chemical computation method. The antimicrobial, anti-inflammatory, and α-glucosidase inhibitory activities of selected compounds and crude extract were evaluated in vitro. The extract inhibited nitric oxide (NO) production induced by lipopolysaccharide (LPS) in murine RAW264.7 macrophage cells, with an inhibition rate of 77.28 ± 0.82% at a concentration of 50 μg/mL. The compounds 5, 7 and 8 displayed weak antibacterial activity against Staphylococcus areus subsp. aureus at a concentration of 100 μM.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

This paper presents two control design strategies for voltage regulation in a single inductor dual output (SIDO) DC-DC Buck converter system. Based on a nominal multiple input multiple output (MIMO) plant model and performance requirements, both an LQR and a decoupled PI control laws are designed to control the power converter system, under parametric uncertainties such as voltage source variation, CPL power variation, and load resistance variation. Therefore, the SIDO converter can cascade operating, which may cause the undesired effects of voltage oscillation and reduce the system's stability margin. The control performance was assessed under both uncertainties resistive loading and power variation of a constant power load (CPL). A SIDO DC-DC Buck converter board has been developed for experimental tests. The experimental results show that the LQR strategy, compared to the PI strategy, presented a robust performance in the presence of parametric uncertainties in the resistive loads being, however, sensitive to uncertainties due to the presence of CPL loads.

The design of a mixed-mode proportional-integral-derivative (PID) controller circuit using current-feedback operational amplifiers (CFOAs) as active components is proposed. With the same circuit topology, the proposed configuration of three CFOAs, four resistors, and two capacitors is capable of performing the PID controller in all four operation modes: namely voltage mode, trans-admittance mode, current mode, and trans-impedance mode. Numerous mathematical analyses are conducted to determine the controller performance under ideal and non-ideal conditions. Additionally, the mixed-mode second-order lowpass filter is suggested, and also used to examine the workability of the proposed mixed-mode PID controller in a feedback control structure. The proposed PID controller is implemented with the commercially available IC-type CFOA AD844, and the simulation results are presented to illustrate the functionality of the controller and its closed-loop control system.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

The Fourier Continuous Derivative ($D_C$) offers a unique perspective on fractional differentiation grounded in the theory of Fourier series. This approach has the potential to address problems across various disciplines, including physics, engineering, and mathematics. The primary insight underpinning this approach is that a convex function defined on $\mathbb{Z}$ retains its convexity on $\mathbb{R}$. This paper delves into the Fourier Continuous Derivative, compares it with traditional fractional derivatives, and outlines its possible real-world applications, such as modeling viscoelastic materials, solving wave equations, and financial data analysis.

The article is devoted to the research of economic cycles and crises, which are studied within the framework of the theory of long waves by N. D. Kondratiev (K-waves) using the mathematical apparatus of fractional calculus. The object of the study is the mathematical model of S.V. Dubovsky 3 and some of its modifications, which describe the dynamics of the economic system, characterizing the interaction between the efficiency of new technologies and the efficiency of capital productivity. Modifications in the model are determined by the following points: the mathematical model takes into account the dependence of the rate of accumulation on capital productivity, there is an external harmonic influence - the influx of investments and new technological solutions, the economic system has heredity, including time-dependent, which leads to a delayed effect - the system’s response to impact. The property of heredity in the mathematical model is taken into account using fractional derivatives of constant and variable orders. Mathematical model S.V. Dubovsky and its modifications are studied numerically using the Adams-Bashforth-Moulton algorithm. Oscillograms and phase trajectories are constructed, and an interpretation of the simulation results is given.

The polysaccharide-based chiral stationary phase (CSP) columns for high-performance liquid chromatography (HPLC) were applied in the separation of liquid crystalline racemic mixtures obtained based on (R,S)-2-octanol and were found to be highly effective in recognizing isomers of minor structural differences. The mobile phase (MP), which consists of acetonitrile (ACN)/water (H2O) at different volume ratios, was used. All measurements were made at room temperature. The order of the elution was also determined. The chromatographic parameters such as resolution - (Rs), selectivity - (α), and the number of theoretical plates, i.e., column efficiency - (N), were determined. The polysaccharide-based CSP columns have unique advantages in separation technology, and this study has shown the potential usefulness of the CSP columns in separating liquid crystalline racemic mixtures belonging to the same homologous series.

Ensuring precise electric locomotive stopping is pivotal for achieving intelligent and unmanned auxiliary transportation systems. Currently, human drivers' expertise plays a central role in the stopping process, posing challenges for automation and cargo location accuracy, particularly in coal mining. This paper focuses on achieving accurate electric locomotive stopping under diverse conditions by utilizing permanent magnet synchronous motor-driven locomotives. This technique introduces a novel stopping control method that combines a fuzzy Proportional-Integral-Derivative (F-PID) controller and a vector control model for permanent magnet synchronous motors (PMSM). After this, we design the F-PID using the PMSM technique based on the new fuzzy rules for each sub-system. In the end, extensive simulations and real-world experiments are conducted on an electric locomotive stopping test bed, which demonstrate the effectiveness of the proposed control method. From the simulation results, it confirming that the ability to achieve precise stopping under various working conditions.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.

Digital twins are an emerging technology that could be harnessed for the digitalization of the industry. Steel industry systems contain a large number of electro-hydraulic components, as proportional valves. An input-output model for a novel water proportional cartridge valve is derived from physical modelling based on fluid mechanics, dynamics, and electrical principles. The valve is a two-stage valve with two 2/2-way water proportional valves as the pilot stage and a marginally stable poppet-type cartridge valve as the main valve. The orifice equation, which is based on Bernoulli principles, is approximated by a polynomial which makes parameter estimation easier and makes modelling possible without measuring pressure of the varying control volume situated in the pilot stage part of the valve. Data were collected when the valve was operating as a component in a closed-loop system as part of a press-mill machine in a steel manufacturing plant. Parameter estimation was made by convex optimization with physical constraints to overcome problems caused by poor system excitation. For comparison, a simple linear model was derived and the least squares method used for parameter estimation. A thorough estimation of the parameters relative errors is presented. The model contains 5 parameters related to the design parameters of the valve. The modelled position output is in good agreement with experimental data for training and test data. The model can be used for real time monitoring of the valve’s status by the model parameters. One of the model parameters varies linearly with production cycles. Thus, aging of the valve can be monitored.

In contemporary construction, the prevalence of vibration serviceability issues in lightweight and slender structures has become increasingly common, owing to advancements in building materials and construction methods. While these structures often meet the criteria for ultimate limit states, they can still elicit complaints due to excessive vibrations induced by human activity. To address this challenge, the Integral Resonant Control (IRC) technique has emerged as a favored approach for actively damping vibrations in various systems. This study introduces a fresh perspective on implementing a multi-input multi-output (MIMO) IRC scheme for active vibration control (AVC) specifically tailored for pedestrian structures utilizing inertial mass actuators. Building upon a common framework and design methodology outlined in previous research, this work presents a novel application of MIMO IRC for AVC. The designed controller is rigorously tested and implemented on a laboratory floor structure to validate its efficacy.

In the paper, a study of the performance of unmanned ground vehicle (UGV), establishes numerical simulation model of the chassis system by three-dimensional software and finite element analysis software. Based on the numerical modelling and analysis, the work focuses on study of the strength and stiffness of the vehicle's chassis and researched the distribution of stress and deformation under the extremal condition. The paper also presents an autopilot design with new cascade control system for an autonomous motion of an unmanned ground vehicle based on Proportional-Integral-Derivative (PID) and Feed-Forward (FF) control. The PID-FF controller is a part of dedicated for presented UGV used in a hybrid control system for precise control and stabilization, necessary to increase the vehicle motion stability and maneuvers precision. The hybrid PID-FF control system proposed for the ground vehicle model gives a satisfactory quality of control, while maintaining the simplicity of the control system. Presented tests performed in area of mechanical design and control analysis gives good results and proves usefulness of designed unmanned device.

In the full load operating range, wind turbines typically use pitch control to maintain rotor speed and output power at their rated values to guarantee the whole system’s safety. Blade pitch actuators are subject to physical limitations and safety requirements, which imposes strict constraints on pitch angle’s amplitude and rate of change. These constraints will bring windup problem to the integral part of the pitch controller. It leads to deterioration of the pitch control system’s performance or even the instability problem, especially for large-scale turbines operating in extreme uncertain wind conditions or suffering from cyber attacks. This paper designs an anti-windup robust pitch angle control strategy to deal with pitch rate constraint issue to enhance the security of control system. First, to facilitate controller design, a filtered tracking error technique is employed to transform the nonaffine form into an affine one. Subsequently, a feedback robust controller based on UDE is developed to handle the model’s uncertainty and external disturbances. To address the issue of integral saturation in the pitch system and guarantee its safety, an elliptical bounded constraint is integrated into the designed UDE strategy. This bounded UDE controller can improve the stability of power generation quality, reduces the mechanical loads on components and enhance the whole system’s safety. Finally, the effectiveness of the proposed scheme is verified on the Wind Turbine Blockset platform in Matlab/Simulink. It can achieve better performance than the traditional method.

The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

In the article, the authors presented the problem of the transition effect in bridge engineering, its causes, negative consequences, and suggested a solution involving the use of integral bridges with the embankment through a spatial bars structure using reinforced composite polymer material. Integral bridges are designed to collaborate with road or railway embankments in bearing loads. Additionally, their application minimizes maintenance and construction costs while enhancing durability. Current solutions in bridge engineering were described. It is predicted that the presented concept will reduce the amount of plastic waste and contribute to the long-term use of materials. The article emphasized the importance of sustainable development, recycling, and the potential application of substitute materials.

We show succinctly a natural origin of the beautiful Gamma function in light of the WJ distribution, linking to quite distinct fields.

Recently, Shehata et al. [37] introduced the r+1Rs(B;C; z) matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, dierential properties, new integral representations, k- Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the k-Riemann{Liouville and k-Weyl fractional integral and derivative operators an extended version of r+1Rs;k matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leer matrix function, k- Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.

In option pricing, we often deal with options whose payoffs depend on multiple factors such as foreign exchange rates, stocks, etc. Usually, it leads to a knowledge of the joint distributions and complicated integration procedures. The paper develops an alternative approach that converts the option pricing problem to a dual one and presents a solution to the problem in the optional semimartingale setting. The paper contains several examples which illustrate results in terms of the parameters of models and options.

We study the tight focusing properties of generic bright and dark HyOPS beams in the presence of primary coma. The role of the polarization singularity index and handedness of the polarization of the HyOPS beams on the focused structure has been discussed. Results have been presented for the total intensity, component intensities, and component phase distributions for left-, and right-handed bright and dark star and lemon types singularities. The presence of primary coma distorted the focal plane intensity distributions for both positive and negative index generic C-points. Coma is known to disturb the circular symmetry of the focal plane intensity distribution. Similarly in tight focusing polarization is known to disturb the symmetry. Therefore, a beam with structured and inhomogeneous polarization distribution tightly focused under the influence of coma is a fit case to study. It is found that the presence of primary coma aberration in the focusing system produces a positional shift of the high-intensity peaks and a reduction of the intensity on one side of the center. As the strength of the primary coma increases, the focal plane intensity distributions shift more and more toward the right from the initial position. Unlike the scalar vortex case, in the case of HyOPS beams, the focal plane intensity distribution undergoes rotation, as the helicity of the HyOPS beams is inverted, in addition to shifting. All the component phase distributions are found to be embedded with phase vortices of charge ±1.

Amplitudes of quantum transitions containing time zigzags are considered. The discussion is carried out in the framework of the Minkowski metric and the standard quantum mechanics without adding new postulates. We argue that time zigzags are not suppressed at the quantum level, but their contribution to the amplitude is zero. The result is valid for a single particle and a non-interacting scalar field.

We propose a new hierarchy of the vector derivative nonlinear Schr{\"o}dinger equations and consider the simplest multiphase solutions of this hierarchy. The study of the simplest solutions of these equations led to the following results. First, the three-leaf spectral curves $\Gamma=\{(\mu,\lambda)\}$ of the simplest multiphase solutions have a quite simple symmetry. They are invariant with respect to holomorphic involution $\tau$. The type of this involution depends on the genus of the spectral curve. Or the involution has the form $\tau:(\mu,\lambda)\to(\mu,-\lambda)$, or $\tau:(\mu,\lambda)\to(-\mu,-\lambda)$. The presence of symmetry leads to the fact that the dynamics of the solution is determined not by the entire spectral curve $\Gamma$, but by its factor $\Gamma/\tau$, which has a smaller genus. Secondly, it turned out that the dynamics of the two-component vector $\bp=(p_1,p_2)^t$ is determined, first of all, by the dynamics of its length $\abs{\bp}$. Independent equations determine the dependence of the direction of the vector $\bp$ from its length. In cases where the direction of the vector $\bp$ is fixed, the corresponding spectral curve splits into separate components. In conclusion, we note that, as in the case of the Manakov system, the equation of the spectral curve is invariant with respect to the orthogonal transformation of the vector solutions. I.e., the solution can be found from the spectral curve up to the orthogonal transformation. This fact indicates that the spectral curve does not depend on the individual components of the solution, but on their symmetric functions. Thus, the spectral data of multiphase solutions have two symmetries. These symmetries make it difficult to reconstruct signals from their spectral data. The work contains examples illustrating these statements.

An advanced driver-assistance system (ADAS) is critical to driver-vehicle-interaction systems. Driving behaviour modelling and control significantly improves the global performance of ADAS. A haptic assistive system assists the driver by providing a specific torque on the steering wheel according to the driving-vehicle-road profile to improve the steering control. However, the main problem is designing a compensator dealing with the high-level uncertainties in different driving scenarios with haptic driver assistance, where different personalities and diverse perceptions of drivers are considered. If not properly accounted for, these differences can lead to poor driving performance. This paper focuses on designing a data-driven model-free compensator considering various driving behaviours with a haptic feedback system. A back propagation neural network (BPNN) models driving behaviour based on real driving data (speed, acceleration, vehicle orientation, and current steering angle). Then using the genetic algorithm (GA) and the integral time absolute error (ITEA) criterion to optimize multiple PID compensation parameters for various driving behaviour (such as speeding/braking, lane-keeping and turning), which are then be combined by the fuzzy logic to provide different driving commands. An experiment was conducted with 5 participants in a driving simulator. During the second experiment, seven participants drove in the simulator to evaluate the robustness of the proposed combined GA-PID offline and the Fuzzy-PID controller applied online. The experiment results evaluated the ITAE of lateral displacement and yaw angle, during various driving behaviour. The results validated the proposed method by significantly enhancing the driving performance.

This paper introduces new improvements to the modified version of the BIRECT (BI secting RECTangles) algorithm referred to as BIRECTv. We explore various approaches, by first including a grouping strategy for hyper-rectangles having almost the same sizes by categorizing them into different classes. Therefore constraining them not to exceed a certain pre-defined threshold (a small positive value to define the tolerance level). This approach allows for more efficient computation and can be particularly useful when dealing with a large number of hyper-rectangles with varying sizes. To avoid over-sampling, and preventing redundant or excessive sampling, at some shared vertices in descendant subregions, a particular vertex database is used to limit the number of samples taken within each subregion to two. The experimental investigation shows that these improvements have a positive impact on the performance of the BIRECTv(imp.) algorithm and the proposal is a promising global optimization algorithm compared to the original BIRECTv algorithm and its variants. Additionally, the BIRECTv(imp.) algorithm showed particular efficacy in solving high-dimensional problems.

Background: Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data (Ingber, 2018). Adaptive Simulated Annealing (ASA) was used for all fits to data. A numerical path-integral for quantum systems, qPATHINT, was used. Objective: The quantum path-integral for Calcium ions was used to derive a closed-form analytic solution at arbitrary time. The quantum effects is parameterized here, whereas the previous 2018 paper applied a nominal ratio of 1/2 to these effects. Method: Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used. The quantum path-integral is used to derive a closed-form analytic solution at arbitrary time, and is used to calculate interactions with classical-physics SMNI interactions among scales. Results: The mathematical-physics and computer parts of the study are successful, in that three cases with Subjects (blind to this author) after 1,000,000 visits to the cost function gave: Subject-07 = 0.04, Subject-08 = 0.55, and Subject-09 = 1.00. All other 9 Subjects gave 0.

In our previous published papers, considering 3 large atomic gravitational constants assumed to be associated with weak, strong and electromagnetic interactions, we have proposed the existence of a nuclear charge of magnitude, e_n=2.95e and developed a nuclear mass formula associated with strong and weak interactions having 4 simple terms and only one energy coefficient. Two important assumptions are, there exists a weak fermion of rest energy 585 GeV and strong coupling constant is the squared ratio of electromagnetic charge and nuclear charge. The aim of this paper is associated with understanding the mystery of quantum of magnetic flux, Planck’s quantum radiation constant and Reduced Planck’s constant. Proceeding further, quark charges, strong coupling constant, nuclear stability, nuclear binding energy, medium and heavy atomic X-ray levels and celestial magnetic moments can be understood in a unified approach. It may also be noted that, by considering integral nature of elementary particle masses, it seems possible to understand the discreteness of angular momentum. Considering our proposed e_n=2.95e=3e as a characteristic nuclear charge, it seems possible to understand the integral nature of quarks electromagnetic charge. With this idea, neutron, proton and pions decay can be understood very easily. In all the cases, up quark of charge (±2e) seems to play a crucial role with the internal transformation of down quark of charge (±e) and external observable elementary basic elementary particles. It needs further study at fundamental level.

This article is a study on the (k,s)-Riemann-Liouville fractional integral, a generalization of the Riemann-Liouville fractional integral. Firstly, we introduce several properties of the extended integral of continuous functions. Furthermore, we make the estimation of the Box dimension of the graph of continuous functions after the extended integral. It presents that the upper Box dimension of the (k,s)-Riemann-Liouville fractional integral for any continuous functions is no more than the upper Box dimension of the functions on the unit interval I=[0,1], which indicates that the upper Box dimension of the integrand f(x) will not be increased by the σ-order (k,s)-Riemann-Liouville fractional integral ksD−σf(x) where σ&gt;0 on I. Additionally, we prove that the fractal dimension of ksD−σf(x) of one-dimensional continuous functions f(x) is still one.

This study investigates the therapeutic potential of new compound, potassium 2-[2-(2-oxo-4-phenylpyrrolidin-1-yl) acetamido]ethanesulfonate (Compound I), in depression. Willner's chronic unpredictable mild stress model of depression in 48 male Wistar rats was used a depression model. The rats were randomized into four groups, including an intact group, a Compound I group, a Fluoxetine group, and a control group receiving saline. Behavioral tests, such as the Porsolt forced swim test, hole-board test, elevated plus maze test, and light-dark box, were used to assess the animals' conditions. Our results demonstrated that Compound I effectively reduced the immobilization time of rats in the forced swim test, increased orientation and exploratory behavior, and decreased the latency period of going into the dark compartment compared to the control group. Hippocampal and striatal serotonin concentrations were increased in the Compound I group, and the compound also reduced the level of corticosterone in the blood plasma of rats compared to intact animals. These results suggest that Compound I has a reliable antidepressant activity, comparable to that of the reference antidepressant Fluoxetine.

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially we develop a binary data matrix to record variables' values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle oriented coordinate and generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar field in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of cumulative probability function defined on Riemannian manifold also gives the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and gives the formal definition of joint probabilities by partial derivatives of cumulative distribution function. The equivalence between symmetrized covariant derivative and generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

In this paper, existence and stability results of non-local integro-differential equation with Hilfer derivative of order ω∈(1,2) have been investigated. In this derivative is applied in RLC circuit equation of various fractional order. To proposed problem the existence solutions are derived using Schaefer’s fixed point theorem and the Banach contraction principle is using for uniqueness results. To demonstrate the effectiveness and applicability of our theoretical conclusions and two-step Lagrange polynomial interpolation were used to solve four numerical results.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

Ship wave is of great interest for wave drag, coastal erosion and ship detection. In this paper, a highly-paralleled numerical scheme is proposed for simulating three-dimensional (3-D) nonlinear Kelvin ship waves effectively. First, a numerical model for nonlinear ship waves is established based on potential flow theory, boundary integral method and Jacobian-free Newton-Krylov (JFNK) method. In order to improve computational efficiency and reduce data storage of JFNK method, a banded preconditioner method is then developed by formulating the optimal bandwidth selection rule. After that, a Graphics Process Unit (GPU) based parallel computing framework is designed, and a GPU solver is developed by using Compute Unified Device Architecture (CUDA) language. Finally, numerical simulations of 3-D nonlinear ship waves under multiple scales are performed by using the GPU and CPU solvers. Simulation results show that the proposed GPU solver is more efficient than the CPU solver with the same accuracy. More than 66% GPU memory can be saved and the computational speed can be accelerated up to 20 times. Hence, the computation time for Kelvin ship waves simulation can be significantly reduced by applying the GPU parallel numerical scheme, which lays a solid foundation for practical ocean engineering.

The duality is one of the most interesting properties of the Laplace and Fourier transforms associated to the integer order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier transforms. The scale and nabla derivatives are used.

Abstract: — management of the Continuous Stirred Tank Reactor (CSTR) operation has proven to be a difficult undertaking due to the complex and ever-changing nature of its behavior, which is both nonlinear and dynamic, which is further compounded by its instability. Attempts have been made to use Proportional-Integral-Derivative (PID) controllers for such processes, but the performance is often poor due to the inherent limitations of the controllers. In contrast, heuristic algorithms have been employed to tune the controllers, but these methods can only provide optimal performance for a restricted range of parameter variations. This paper presents a novel approach that involves using a conventional gain scheduling PID controller in combination with a fuzzy gain scheduling (FGS) controller method to calibrate set-point weighted PID controllers for the CSTR process. The paper outlines the design of the controllers and evaluates their performance by subjecting them to varying input signals within the given bandwidth.

We consider a classial case of irrational integrals containing a square root of a quadratic polynomial. It is well known that they can be expressed in terms of elementary functions by one of three Euler’s substitutions. It is less known that the Euler substittutions have a beautiful geometric interpretation. In the framework of this interpretation one can see that the number 3 is not the most suitable. We show that it is natural to introduce the fourth Euler substitution. By the way, it is not clear who was the first to attribute these three substitutions to Euler. In his original treatise Leonhard Euler uses two substitutions which are sufficient to cover all cases.

In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained.

The resonance spectrum of surface resistance derivative in quasi-two dimensional layered organic conductors has been calculated numerically for the out-of-plane and in-plane magnetic field. Not all but some of the resonances in a given series of transitions are present in the spectra. They are observed at the positions corresponding to the maxima in the surface resistance derivative curve and are in a good agreement with previously calculated magnetic field resonance positions. For tilted magnetic fields, there are more resonances present in the spectrum than in the case of a non-tilted field. Apart from the resonances corresponding to the transitions between the adjacent surface states there also appear resonances involving the transitions between the more distant surface states. This is correlated with the specific topology of Fermi surface of the organic conductors. The presented calculations will allow correct interpretation of the experimental curves for the resonance spectrum, and also to obtain information on the surface properties of these materials for their possible implementation in fabrication of devices based on organic molecular conductors.

In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $\beta=\frac{2\alpha}{2\alpha - 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $\omega_{X} \in [0,1]$, the order belongs to the interval $1\leq \beta \leq 2$, and when $\omega_{X}\in[-1,0)$, the order belongs to the interval $0<\beta \leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\Omega,\phi)$ and its corresponding momenta $(\Pi_\Omega, \Pi_\phi)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(\tau)$, however in the dust era we found a closed solution in the gauge time $\tau$.

In this study, we investigate the existence of positive solutions within a system of Riemann-Liouville fractional differential equations that incorporate the (r1,r2,r3)-Laplacian operator while being subject to three-point boundary conditions. These equations incorporate various fractional derivatives and are influenced by parameters represented as (ψ1,ψ2,ψ3). Our approach involves employing techniques such as cone expansion and compression of the functional type, in conjunction with the Leggett-Williams fixed point theorem, to establish the existence of positive solutions. To emphasize the practical significance of our findings in the realm of fractional differential equations, we provide two illustrative examples.

Ballasted railway tracks can be modelled using reduced/simplified models composed of several layers of discrete components. This paper deals with the two-layer model, which is very popular due to its computational efficiency. In order to provide some recommendations for track design, it is necessary to identify which set of parameters leads to some irregular/unexpected behavior. Such irregularity is investigated at three levels, such as: (i) critical velocity of moving constant force; (ii) instability of a single moving mass; (iii) instability of two moving masses. All results are presented in dimensionless form to cover a wide range of real parameters. Irregular cases are identified by sets of parameters leading to them and then general conclusions are drawn. Regarding the method, all results are obtained analytically or semianalytically, where “semi” refers to solving the roots of a given polynomial by predefined numerical procedures in symbolic software. No numerical integration is involved in all results presented. This means that the results are highly accurate and refer to exact values, so any kind of parametric or sensitivity analyses is readily possible.

In this paper for every number field K generated by a root α of a trinomial x⁷ + ax + b ∈ Z[x] and for every prime integer p, we calculate ν_p(i(K)), the highest power of p dividing the index i(K) of the field K. In particular, we calculate the index i(K). As application, when the index of K is not trivial, then K is not monogenic.

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.

In this paper, the new optical wave solutions of truncated M-fractional perturbed Kundu-Eckhaus model with full non-linearity are obtained by utilizing the expa function technique and modified extended tanh expansion function technique. The solutions are in the form of dark soliton, bright soliton, singular solitons and other form of solutions. The gained solutions are helpful for the further development of concerned model. The obtained results have also been presented graphically in both two-dimensional and three-dimensional formats to discuss the dynamical features as well as the parametric dependence of the constructed solutions. The study offers a highly spectacular and acceptable techniques to combine various intriguing wave demonstrations for more sophisticated models of the modern day.

We obtain some generalised Minkowski-type integral formulas for compact Riemannian (resp. spacelike) hypersurfaces in Riemannian (resp. Lorentzian) manifolds admitting an arbitrary vector field that we assume to be timelike in the case where the ambient space is Lorentzian. Some of these formulas generalize existing formulas in the case of conformal and Killing vector fields. We apply these integral formulas to obtain interesting results concerning the characterization of such hypersurfaces in some particular cases such as when the ambient space is Einstein admitting an arbitrary (in particular, conformal or Killing) vector field, and when the hypersurface has constant mean curvature.

In this study, long-term mortality effects associated with exposure to PM10, PM2.5, BC (black carbon), and NOx were analyzed in a cohort in southern Sweden during the period from 1991‒2016. Participants (those residing in Malmö, Sweden, born between 1923‒1950) were randomly recruited from 1991‒1996. At enrollment, 30,438 participants underwent a health screening, which consisted of questionnaires about lifestyle and diet, a clinical examination, and blood sampling. Mortality data were retrieved from the Swedish national cause of death register. The modeled concentrations of PM10 (particles with an aerodynamic diameter smaller than or equal to 10 µm), PM2.5 (particles with an aerodynamic diameter smaller than or equal to 2.5 µm), BC (black carbon), and NOx (nitrogen oxides) at the cohort participants' home addresses were used to assess air pollution exposure. Cox proportional hazard models were used to estimate the associations between long-term exposure to PM10, PM2.5, BC, and NOx and the time until death among the participants during the period from 1991‒2016. The hazard ratios (HRs) associated with an interquartile range (IQR) increase in each air pollutant were calculated based on the exposure lag windows of the same year (lag0), 1‒5 years (lag1‒5), and 6‒10 years (lag6‒10). Three models were used with varying adjustments for possible confounders including both single-pollutant estimates and two-pollutant estimates. With adjustments for all covariates, the HRs for PM10, PM2.5, BC, and NOx in the single-pollutant models at lag1‒5 were 1.06 (95% CI: 1.02‒1.11), 1.01 (95% CI: 0.95‒1.08), 1.07 (95% CI: 1.04‒1.11), and 1.11 (95% CI: 1.07‒1.16) per IQR increase, respectively. The HRs were in most cases decreased by the inclusion of a larger number of covariates in the models. The most robust associations were shown for NOx, with statistically significant positive HRs in all models. An overall conclusion is that road traffic-related pollutants had a significant association with mortality in the cohort.

Covariant integral quantization with rotational symmetry SO(3) is established for the quantum motion on this group manifold, or, alternatively, for Gabor signal analysis on this group. We revisit the action of the related (non-unitary) Weyl-Gabor operator on the Hilbert space of square integrable functions on SO(3) and disclose a set of various properties. By selecting weight functions on the corresponding discrete-continuous phase space, one derives related coherent states and Wigner transform.

Sirtuins are a family of Class III epigenetic modifying enzymes involved in regulating cellular processes through the removal of acetyl groups from proteins. They rely on NAD+ as a coenzyme in contrast with classical HDACs (Class I, II, and IV) that depends on Zn+ for their activation, linking their function to cellular energy levels. There are seven mammalian sirtuin isoforms (SIRT1-7), each located in different subcellular compartments. Sirtuins act as master regulators of cellular homeostasis, responding to changes in nutrient availability and energy status. They play vital roles in diverse physiological and pathological conditions, making them promising therapeutic targets for various diseases, including cancer, neurodegenerative disorders, and metabolic diseases. High levels of SIRT6 are involved in the cancer progression of many tumor types and our previous studies revealed that sirtuin 6 was highly expressed in NSCLC cells and its inhibition potentially favored apoptosis and cell cycle arrest. Sirt6 emerged as a promising target and inhibitors of natural and synthetic sources are highly warranted. Imidazole derivatives are often investigated as sirtuin regulators due to their ability to interact with the binding site and modulate their activity. Imidazole bestows many possible substitutions on its ring and neighboring atoms, to design and synthesize derivatives with specific target selectivity and improved pharmacokinetic properties, optimizing drug development. We recently developed imidazole-based derivatives that potentially inhibited classical HDAC enzymes. Therefore, we evaluated the Sirtuin inhibition activity of our in-house compound comprised of imidazole derivatives and the strongest inhibition was observed with Ethyl 2-[5-(4-chlorophenyl)-2-methyl-1-H-Imidazole-4-yl) acetate against Sirt6 by in-silico and protein expression studies. Our results suggested that Ethyl 2-[5-(4-chlorophenyl)-2-methyl-1-H-Imidazole-4-yl) acetate could be a potential novel sirt6 inhibitor.

In this paper, we consider a pursuit-evasion game of inertial players, where pursuer’s control is subject to integral constraint, and evader’s control is subject to geometric constraint. In the pursuit problem, the main tool is the strategy of parallel pursuit. Sufficient conditions are obtained for the solvability of pursuit-evasion problems. Also, the main lemma describing the monotonicity of an attainability domain of the evader is proved and an explicit analytical formula for this domain is given. As one of the important results of our paper, the Isaacs Life-line game is solved for a special case.

TThis paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann-Liouville fractional integral and fractional Caputo derivatives, enabling a comprehensive understanding of these functions. Additionally, we introduce a secondary characterization based on the Bernstein characterization of completely monotone functions. The practical significance of our study is showcased through an examination of the positivity of the fundamental solution of the space-fractional Bessel diffusion equation, highlighting the real-world applicability of the developed concepts. Through this work, we contribute to the broader understanding of radial positive definite functions and their utility in diverse mathematical and applied contexts.

In this study, we construct a new Atangana-Baleanu fractional model for whooping cough disease to predict future dynamics of the disease, as well as to suggest strategies to eliminate the disease in an optimal way. We prove that the proposed model has a unique solution which is positive and bounded. To measure contagiousness of the disease, we determine the reproduction number R0 and use it to examine the local and global stability at equilibrium points that have symmetry. Through sensitivity analysis, we determine parameters of the model that are most sensitive to R0. The ultimate aim of this research is to analyze different disease prevention approaches in order to find the most suitable one. For this, we include the vaccination and quarantine compartments in the proposed model and formulate an optimal control problem to assess the effect of vaccination and quarantine rates on disease control in three distinct scenarios. Firstly, we study the impact of vaccination strategy and conclude findings with presentation of graphical results. Secondly, we examine the impact of quarantine strategy on whooping cough infection with possible elimination from the society. Lastly, we implement vaccination and quarantine strategies together to visualize their combine effect on infection control. In addition to the study of an optimal control problem, we examine the effect of fractional order on disease dynamics as well as the impact of constant vaccination and quarantine rates on disease transmission and control. We determine that the optimal control strategy with the three controls is more effective in reducing the spread of whooping cough infection. Implementation of Toufik-Atangana type numercial scheme both for the state and adjoint equations is another contribution of this article.

Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated. Usually, such two-component integrable nonlinear evolutionary equations are considered, the form of which does not depend on the replacement of one component with another. In this paper, we propose for consideration and usage a new hierarchy of two-component integrable nonlinear equations, which have an important difference from the already known equations. Among the hierarchy equations there are analogues of the two-component nonlinear Schrödinger equation (second equation from hierarchy) and the two-component modified Korteweg-de Vries equation (fourth equation from hierarchy). The third equation of the hierarchy is a combination of the nonlinear Schrödinger equation for one component and the modified Korteweg-de Vries equation for the second component. The equations for the individual components are very different from each other, even if they have the same order. Let us note that even hierarchy equations can be reduced to well-known variants of the scalar derivative nonlinear Schrödinger equations, and odd equations can’t be reduced. To construct the hierarchy equations, we use the monodromy matrix method, first proposed by B.A. Dubrovin. Knowledge of the monodromy matrix makes it possible to construct spectral curves of multiphase solutions, as well as to find stationary equations that these solutions satisfy. The last section presents the simplest solutions in the form of solitons and periodic one-phase waves, as well as spectral curves corresponding to these solutions.

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

This paper focuses on a joint model to analyse longitudinal proportion and survival data. After transforming the longitudinal proportional data by a logit function, we adopt a partially linear mixed-effect model for it, in which nonlinear function of time is fitted via using B-splines technique and a centered Dirichlet Process Mixture Model (CDPMM) is specified for a general distribution of random effects. The survival data is assumed to a Cox proportional hazard model, the sharing random effects joint model is developed for the two types of data. Combining the Gibbs sampler and the Metropolis-Hastings algorithm, we propose a Bayesian Lasso (BLasso) method to simultaneously estimate unknown parameters and select important covariates. Simulation studies are conducted to investigate the finite sample performance of the proposed methods. An example from the MA.5 research experiment is used to illustrate the proposed methodologies.

The continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection) has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and management breakout poses a new kind of global hazard. The good news is that there is currently enough knowledge about the epidemic process to allow for the creation of mathematical forecasting models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although many US states and other nations around the world followed lockdown and reopening processes, we perform some analysis on using some techniques of the epidemic course. A new perspective of fractional calculus known as piecewise derivatives of fractional order is used to study the proposed model. Sufficient conditions are established to show the existence theory. In addition, a numerical scheme based on Newton’s polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Some real data results are also shown with comparison of the numerical results.

NAD⁺ is known classically as a metabolite that participates in catabolic and anabolic pathways throughout the metabolism that is taught to students in introductory biochemistry courses. However, non-classical studies starting over a decade ago found that NAD⁺ is also involved in higher order functions, in part because of its involvement in the activation of SIRTs and the support of the mitochondrial unfolded protein response. Many studies since have suggested that NAD⁺ is involved in an extensive spectrum of human pathologies, including neurodegenerative disorders, cardiomyopathy, obesity, and diabetes, Further, healthy aging and longevity appear to be closely related to NAD⁺ and its related metabolites, including NAR and NMN. Together, these studies show that this system has value as a dietary supplement to improve general health overall, as well as mitigating specific disease conditions. Accordingly, many are now recommending the consumption of materials in this system as dietary supplements. Nicotinamide riboside (NAR) appears to have special value in this regard. It appears to be better tolerated than other molecules in this system, as well as better pharmacodynamics and greater potency. Unfortunately, NAR is a reactive molecule, often unstable during its manufacturing, transport, and storage. Indeed, HPLC analyses of many commercial samples of NAR shows that they contain substantial amounts of material that are not, in fact, NAR. In some of these commercial preparations, NAR is a minority component. Therefore, more stable derivatives of NAR that are easily converted upon consumption into NAR are therefore desired. Recently work related to prebiotic chemistry provided the borate derivative of NAR. NARB is considerably more stable than NAR itself. However, immediately upon consumption, the borate dissociates from NARB, and is lost in the body through dilution and binding to other species, notably carbohydrates such as fructose and glucose. The NAR left behind is expected to behave pharmacologically in ways identical to NAR itself. This review provides a comprehensive summary (through Q1 of 2023) of literature that makes the case for the consumption of NAR as a dietary supplement. It then summarizes the challenges of delivering quality NAR to consumers using standard synthesis, manufacture, shipping, and storage approaches. It concludes by outlining the advantages of NAR-borate in these processes.

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

As an option to deal with the insulin-dependent disease, a recent commuted PD control strategy is designed and carefully analyzed for different clinic diabetic patients. This controller approach is mainly conceived to stabilize the glucose blood concentration in a diabetic patient around its basal value, hence avoiding extreme situations such as hypoglycemia and hyperglycemia. This control strategy receives two inputs carefully tuned to actuate when the measured variable is out of a prescribed healthy zone. Therefore, one of these variables is invoked to decrease the glucose concentration to insulin injection, and the other is employed to increase the glucose absorption, both by using a proper PD controller. According to our numerical experiments, our controller approach performs well, even when there is an external disturbance in the controlled system.

Epilepsy is a neurological disorder that affects approximately 1% of the world's population. To diagnose and estimate the occurrence of epilepsy, the analysis of recorded brain activity is performed by a neurologist, which is not only time-consuming and tedious but also occasionally accompanied by human error. Therefore, in recent decades, researchers have aimed to unravel an approach for designing and building an automated method for diagnosing and estimating the occurrence of epilepsy. Accordingly, the present study proposed two new-fangled ways based on brain signals and a convolutional neural network (CNN). Moreover, this research implements a CNN with a sequential three-layer structure. Numerous experiments were performed, and the accuracy of estimating epilepsy using the developed methods was achieved at 95% without feedback and 97% with feedback. The proposed methods were proven to be more accurate than the previous techniques and can be employed as a physician's assistant once entering the field of operation.

When undertaking wind assessment around buildings using large eddy simulation (LES), the implementation of the integral length scale at the inlet for inflow generation is controversial, as real atmospheric length scales require huge computational domains. While length scales significantly influence inflow generation in the domain, their effect on the downstream flow field has not yet, been investigated. In this paper, we validate the effectiveness and accuracy of implementing a reduced turbulence integral length scale for inflow generation in LES results at the rooftop of low-rise buildings and develop a technique to estimate the real local length scales using simulation results. We measure the wind locally and calculate the turbulence length scales from the energy spectrum of the wind data and simulation data. According to these results, there is an excellent agreement between the length scale from simulation and measurement when they are scaled with their corresponding freestream/inlet value. These results indicate that a reduced integral length scale can be safely used for LES to provide a reliable prediction of the energy spectrum as well as the length scales around complex geometries. The simulation results were confidently employed to obtain the best location for a wind turbine installation on low-rise buildings.

Diversified techniques have been applied in many research papers for the optimization of rehabilitation robotic movements in order to maintain smoothness and accuracy. Smooth and precise control is needed necessarily for upper limb rehabilitation robotic applications having five degree of freedom. The preferred parameters which are used for the controlling were validated by mathematical model and these tuning parameters were optimized. Designing optimization algorithms to control complex physical robots has been a challenging task. In this study, a number of optimization techniques will be analyzed to determine the optimal parameters of a PID controller with a dynamic model of the upper limb rehabilitation system. For determining optimal control parameters for PID, there exists a number of tuning methods such as Zeigler Nichols and fuzzy logic which are classical methods. Swarm intelligence-based optimization algorithms are inspired by the behaviors of living things in nature. Several researchers have reported the optimal design of PID controller parameters using optimization techniques. The proposed control technique has been implemented on a 5-DOF RAX hardware and before any clinical trials, six healthy subjects went for trials under strict protocol. It has been discovered that the proposed control technique rejects the external unwanted disturbances as well as keeps the system stable under extreme perturbed and harsh conditions. In this research paper mathematical models have been validated to determine the PID parameters for the optimization. The comparative study is carried out with four different cost functions since a well-designed objective function leads to better performance of the system and indicates control design expectations. These objective functions are an integral squared error (ISE) and integral absolute error (IAE). In this research work, the effects of different cost functions on optimization techniques for controller parameters were analyzed. The performance of the controller with different cost functions has examined for robustness analysis. The cost function of particle swarm optimization, Firefly, Ant Bee Colony and Ant Colony optimization were developed for the better optimization results.

Improper lifting measures of long-span spatial steel structures during construction process may delay the construction period and even cause safety accidents. Few studies on long-span spatial steel structures considered time-varying mechanical characteristic during construction process. In order to achieve safe and efficient installation in a long-span spatial steel structure, this research presents a time-varying mechanical analysis of the synchronous and asynchronous integral lifting and a single and interlaced point’s asynchronous integral lifting analysis method of a long-span spatial steel structure. The results showed that in the case of asynchronous lifting of single point, the displacement influence on other members is related to the distance. The closer the distance from the lifting point, the greater the influence. In asynchronous integral lifting, the lifting point with large lifting force is first installed to the specified position, and the lifting point with small lifting force is installed to the specified position.

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.

The main goal of the paper is to use a generalized proportional Riemann-Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved such as the fractional derivative of a squared function. Also some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given illustrating the meaning of the equilibrium as well as its stability properties.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

Bio-based packaging materials and efficient drug delivery systems are gaining attention, carboxymethyl cellulose (CMC) is one of the most soluble cellulose derivatives, is a good candidate material due to its biocompatibility, biodegradability, and reproducibility. However, CMC-based films are lack of sufficient mechanical properties, limiting its widespread application. In this paper, the molecular interactions between CMC and additives with different molecular structures have been studied with rheological method. The additives are chitosan and cellulose derivatives including O-carboxymethylated chitosan (O-CMCh), N-2-hydroxypropyl-3-trimethylammonium-O-carboxymethyl chitosan (HTCMCh), hydroxypropyltrimethyl ammonium chloride chitosan (HACC), cellulose nanofibers (CNC), and cellulose nanofibers (CNF). The influencing factors, such as molecular structure, concentration of additives and temperature on the rheological properties were studied, which results revealed the information intermolecular interactions. Based on the rheological properties, several systems were selected to prepare films, which show very good transparency, wettability, mechanical properties, biodegradability, and cytotoxicity. These good characteristics of the selected films also proved the good biocompatibility of CMC and chitosan and cellulose derivatives. This work will provide an idea to prepare CMC-based food packaging and effective drug delivery materials with specific properties.

Chronoamperometric curves of the oxidation of a ferrocenyl derivative by the potential step showed diffusion controlled-like currents less than the Cottrell's equation at a platinum wire electrode. The lower deviation cannot be explained by the Butler-Volmer heterogeneous kinetics, but was ascribed to the negatively capacitive current associated with the redox reaction. The deviation at the fully oxidized potential corresponds to the non-zero concentration at the electrode surface, which cannot be predicted from the Nernst equation. The Nernst equation expresses the relationship of the potential with the activity at the electrode surface rather than the concentration. The diffusion equation provides the relation of the current with the surface concentration rather than the activity. The negative capacitance or the non-zero concentration may arise from structure formation on the electrode owing to the dipole-dipole interaction, which is similar to the generation of the double layer capacitance including frequency dispersion. On this concept, we derive here expressions for the lowered diffusion-controlled current and the time-dependent surface concentration. The negatively capacitive current shows the time-dependence of t-0.9, which is similar to the decay of the double layer capacitive currents. The surface concentration decays with the t-0.4-dependence.

This paper aims to unify q-derivative/q-integral and h-derivative/h-integral in a single definition, this will be called q−h-derivative/q−h-integral. These notions are further extended on finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities are studied for q−h-integrals which are directly connected with well known results. In diverse fields of science and engineering the theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified by using the concept of q−h-derivative/q−h-integral.

In this article, the multitouch option, also called the n  touch option (or the “baseball” option when n  3 ) is analyzed and valued in closed form. This is a kind of barrier option that sets a gradual knockout / knock-in mechanism based on the number of times the underlying asset has crossed a predefined barrier in various time intervals before expiry. The higher the number of predefined time intervals during which the barrier has been touched, the lower the value of a knock-out contract at expiry, and conversely for a knock-in one. Multitouch options can be viewed as an extension of step barrier options, preserving the ability of the latter to adjust the exposure to risk over time, while eliminating the notorious danger of “sudden death” that holders of step barrier options are faced with. Unlike occupation time derivatives, the payoff at expiry does not depend on the amount of time spent outside the authorized range, but on the number of passages beyond the authorized range.

This study presents the solution of the second type of a two-dimensional nonlinear integral equation in Banach space. Also, the existence and uniqueness of this equation’s solution are discussed. We utilize a numerical approach involving hybrid and block-pulse functions to obtain the approximate solution of a two-dimensional nonlinear integral equation. Nonlinear integral equation in two dimensions is reduced numerically to a system of nonlinear algebraic equations that can be solved using numerical methods. This study focuses on showing the convergence analysis for the numerical approach and obtaining an error estimate. Some numerical examples have been provided to demonstrate the approach’s viability and efficacy

The article considers an internal boundary value problem of the distribution of an electrostatic field in a lens formed by two identical semi-infinite circular cylinders coaxially located inside an infinite external cylinder. The problem is reduced to solving a system of singular Wiener-Hopf integral equations, which is further solved by the Wiener-Hopf method using factorized Bessel functions. Solutions to the problem for each region inside the infinite outer cylinder are presented as exponentially converging series in terms of eigenfunctions and eigenvalues.

Based on the marine natural products piperafizine B, X334 and our previously reported compound 4m, fourteen novel 3,6-diunsaturated 2,5-diketopiperazine (2,5-DPK) derivatives (1-2, 4-6, 8-16), together with two known ones (3 and 7), were designed and synthesized as anticancer agents against cell lines A549 and Hela. The MTT assay results showed that the derivatives 6, 8-12 and 15 had moderate to good anticancer capacities with the IC50 values ranging from 0.7 to 8.9 μM. Among them, compound 11 with naphthalen-1-ylmethylene and 2-methoxybenzylidene functions at the 3- and 6-positions of 2,5-DPK ring, respectively, displayed good inhibitory activities to both cancer cells A549 (IC50 = 1.2 μM) and Hela (IC50 = 0.7 μM). It could also induce apoptosis and obviously block the cell cycle progression at G2/M phase in both cells at 1.0 μM. The electron withdrawing functions might not be favorable for the derivatives with high anticancer activities. Additionally, compared to piperafizine B and X334, these semi-N-alkylated derivatives have high liposolubilities (&gt; 1.0 mg•mL-1). Compound 11 can be further developed aiming to the discovery of novel anticancer candidate.

We prove Lp estimates of a class of generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these estimates along with an extrapolation argument we obtain the boundedness of our operators under very weak conditions on the kernel functions. Our results in this paper improve and extend several known results on both generalized Marcinkiewicz integrals and parabolic Marcinkiewicz integrals on product domains.

The use of logistic regression models in data analysis and machine learning has expanded in recent years and has become the primary preference of researchers in risk assessment studies across a wide range of scientific fields. From the assessment of credit risk in financial institutions to the estimation of risk factors for traffic accidents or the identification of etiological factors for chronic diseases. All logistic models are natural extensions of the simple binary model, and their interpretation is based on it. Using the data of a cross-sectional study on the risk factors of traffic collisions, the two main extended models of logistic techniques, multinomial and ordinal logistic regression, are presented in the article in detail. Emphasis is placed on the use of ordinal regression since the outcome variable of the collision data is defined as ordinal measurement reflecting a latent continuous scale.

It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Although quantum mechanics correctly predicts what it is possible to observe (the emissions) it ignores the other half of natural phenomena, what cannot be observed (the absorptions), thereby violating the conservation laws. By describing only one-half of radiation processes conceptual difficulties such as wave function collapse, infinite paths, and inscrutable mathematics seem to be insoluble mysteries. The deficiencies are corrected by introducing Hamilton’s principle S = ∫ Ldt and applying the methods of quantum field theory to derive relativistic equations of motion. The calculus of variations is used to show that the wave function represents an incomplete equation of motion because it equals twice the allowable action minimum.

The time interval set approach depends on results for radiation propagation from star sources, ie spherically symmetric, where properties relate to propagation sphere surfaces, finite for any realistic event and measurement. In contrast the usual vector and one moment time set approach from Newton’s laws, applies to stationary parallel radiation. A time interval only description necessarily has to start from it's own definitions, and properties for time intervals have to be defined with time intervals. This paper is devoted to deriving time interval only set properties commutation, addition and multiplication and derivative, and to define how these can correspond consistently to one moment time set properties. Time development within the time interval description equilibrium depends on the well-known ‘mean velocity theorem’ (MVT) and the time interval version of the Legendre transform, defined in earlier papers. Radiation propagation ‘away from’ and gravitation ‘towards’ the star source can be part of the description. In the discussion parts these properties are applied within astrophysics. Included is a integral derivation of star source radiation energy for both zero and non zero wave particle mass. The time interval set is not one of the usual sets encountered. However it’s non-linearity or non-commutativity property can be related to Noether charges and structure constants, that equal the radiation wave group-velocity, for photons the light velocity c, and, different from the usual derivative to one moment time, to specifics of the time interval only set derivative to time intervals.

Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.

Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

In this paper, the 1st level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and then specify a set of the kernels that satisfy this condition and posses an integrable singularity of power law type at the origin. The 1st level general fractional derivatives of arbitrary order are integro-differential operators of convolution type with the kernels from this set. They contain both the general fractional derivatives of arbitrary order of the Riemann-Liouville type and the regularized general fractional derivatives of arbitrary order considered in the literature so far. For the 1st level general fractional derivatives of arbitrary order, some important properties including the 1st and the 2nd fundamental theorems of Fractional Calculus are formulated and proved.

Discretization is the process of converting a continuous function or model or equation into discrete steps. In this work, adaptive and learning methods are implemented to control DC motors that are used for actuating control surfaces of unmanned underwater vehicles. Adaptive control is a method in which the controller is designed to adapt the system with parameters which vary or are uncertain. Parameter estimation is the process of computing the parameters of a system using a model &amp; measured data. Adaptive methods have been used in conjunction with different parameter estimation techniques. Deterministic artificial intelligence, a learning-based approach that uses the process dynamics defined by physics, is also applied to control the output of the DC motor to track a specified trajectory. This work goes further to evaluate the performance of the adaptive &amp; learning techniques based on different discretization methods. The results are evaluated based on the absolute error mean between the output &amp; the reference trajectory and the standard deviation of the error. The first order-hold method of discretization and surprisingly large sample time of seven tenths of a second yields over sixty percent improvement over the results presented in the prequel literature.

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning &amp; fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three dimensional space defined by energy, temperature and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of large fermion systems with numerical simulation. As an example, we present energies for up to 50 noninteracting fermions and up to 20 interacting fermions at all temperatures and show good agreement with the analytical result for noninteracting case.

This paper explores ballot split by type and introduces universal measures of democratic power flow and accountable local representation. These measures allow definitive comparison of electoral systems between countries, and choice of a new electoral system within a country based on existing data and with minimum assumptions.

Enterococcus faecalis is a bacterium that can develop a multidrug resistance profile associated with the community as well as nosocomial-acquired infections. Among the treatment options for these infections are aminoglycosides combined with bacterial cell wall inhibitors such as beta-lactams, since E. faecalis is intrinsically resistant to aminoglycosides. One of its most representative resistance mechanisms is the expression of aminoglycoside-modifying enzymes, such as the aminoglycoside phosphotransferase type IIIa of E. faecalis (EfAPH(3')-IIIa). This enzyme acts by phosphorylating aminoglycosides in an ATP-dependent reaction, modifying the 3' position of hydroxyl groups of these antibiotics. Considering this scenario, 3,092 natural products obtained from the ZINC22 database were analyzed to select molecules with the highest affinity for the nucleotide-binding pocket of EfAPH(3')-IIIa, which could be potential aminoglycoside adjuvants. The molecules that showed the best-score results obtained from ensemble docking-based virtual screening were ZINC000000952700 (BS-1), ZINC000014793040 (BS-2) and ZINC000015498603 (BS-3). The most promising results were for BS-2, a flavone derivative, due to its improved stability profile in molecular dynamics simulation (average values of RMSD of 0.23 nm, and Rg of 1.94 nm), binding free energy calculations (average ΔG total of -35.3 nm), as well as better toxicological profile (lower probability of hepatotoxicity, carcinogenic, immunotoxicity, mutagenicity, and cytotoxicity effects), compared to BS-1 and BS-3. These results allow us to propose that a flavone derivative may act as an adjuvant to aminoglycosides in the treatment of E. faecalis infections, acting as an inhibitor in the nucleotide-binding pocket of EfAPH(3')-IIIa.

Polyhedral oligomeric silsesquioxane (POSS) is a suitable nanoscale reinforcement for thermosetting polymers, such as epoxy resin systems in order to modify its mechanical, thermal, and chemical properties. The inclusion of POSS in the epoxy resin at higher loading (greater than 1 wt.%), however, introduces the ductility during the fracture behavior of these nanocomposites. Consequently, the J-integral is used to quantify the fracture behavior of these materials and characterize the crack growth resistance curve against stable crack growth. A range of nanocomposites is prepared by adding 0.5, 1, 3, 5, and 8 wt.% of glycidyl POSS into DGEBF epoxy resin cured with an amine-based curing agent. From the fracture toughness experiment the load-displacement result confirms that when the POSS reinforcement is greater than 1 wt.%, the fracture behavior of the nanocomposite changes from brittle to ductile. For both brittle and ductile nanocomposites, the addition of POSS molecules improves the crack initiation toughness. The development of POSS–POSS compliant domains are reported previously, is attributed for this change in the failure behavior. The fractured images of POSS–epoxy nanocomposites, obtained using scanning electron microscopy, show that the increase in fracture resistance at higher values of POSS loading occurs due to the extensive shear yielding. Meanwhile, the increased fracture toughness at lower values of POSS loading occurs due to crack pinning and crack deflection.

In this paper, we introduced a generalized ∆-implicit locally contractive condition and give some examples to support it and to show its significance in fixed point theory. We prove that the mappings satisfying generalized ∆-implicit locally contractive condition admits a common fixed point, where, the ordered multiplicative GM−metric space is chosen as underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show existence of solutions to a system of nonlinear -Volterra type- integral equations.

In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

This paper focuses on the so-called proportional intensity-based software reliability models (PI-SRMs), which are extensions of the common non homogeneous Poisson process (NHPP)-based SRMs, and describe the probabilistic behavior of software fault-detection process by incorporating the time-dependent software metrics data observed in the development process. Especially we generalize the seminal PI-SRM in Rinsaka, Shibata and Dohi (2006) by introducing eleven well-known fault-detection time distributions, and investigate their goodness-of-fit and predictive performances. In numerical illustrations with four data sets collected in real software development projects, we utilize the maximum likelihood estimation to estimate model parameters with three time-dependent covariates; test execution time, failure identification work and computer time-failure identification, and examine the performances of our PI SRMs in comparison with the existing NHPP-based SRMs without covariates. It is shown that our PI-STMs could give better goodness-of-fit and predictive performances in many cases.

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

A quantitative description of the second law of thermodynamics in small scale systems and over short time scales comes from various fluctuation theorems. The applicability of the transient fluctuation theorem in particular to small scale systems perturbed from an initial equilibrium steady-state distribution has been demonstrated both theoretically and experimentally in several works over the past few decades. In addition, some experimental works in the past have also made successful attempts to demonstrate the applicability of the fluctuation theorem to small scale systems evolving from a certain nonequilibrium steady-state distribution over relatively long time scales. To this end, this paper seeks to demonstrate the transient fluctuation theorem for a Brownian particle confined within a power-law trapping potential by following the trajectory of the particle that itself is translating linearly along one dimension with constant acceleration in a viscous fluid. Considered herein is an idealized version of this model, in that it is assumed that the force of the trapping potential is only felt by the translating Brownian particle confined within the trap, and that this Brownian particle moves relative to the fluid molecules that are held stationary. The results presented herein show that the transient fluctuation theorem applies not only to equilibrium steady-state distributions but also to nonequilibrium steady-state distributions of an ideal colloidal system in an accelerated frame of reference in the asymptotic (long-time) limit.

The quest for accurate and more efficient methods for solving periodic/oscillatory problems is gaining more attention in recent time. This paper presents the construction and implementation of a family of exponentially–fitted Obrechkoff methods. A single–step Obrechkoff method involving terms up to the fourth derivatives was used as the base method. We also present the stability and convergence properties of the constructed family of methods. Two numerical examples were use to illustrate the performance of the constructed methods.