The Sanshui Basin (SSB) is located at the northern continental margin of the South China Sea and characterized by a continental rift basin. The bimodal volcanic rocks in SSB record the early Cenozoic magmatic activity in the South China Block, on the magmatic evolution process of bimodal volcanic rocks are poorly understood. Clinopyroxenes in bimodal volcanic rocks in the SSB provide an opportunity to investigate the magma process during magma ascent. We classified nine types of clinopyroxene phenocrysts according to the different compositions and textures types in cogenetic basalt-trachyandesite-comenditic trachyte, the composition of unzoned clinopyroxene have an evolution sequence of diopside- hedenbergite- aegirine with the decrease of Mg#, and the trace element contents of unzoned clinopyroxenes also increase systematically during magma evolution, indicating that the genesis of clinopyroxene dominated by fractional crystallization in a closed magma system; however, the clinopyroxenes with reverse zoning and multiple zoning record the process of magma mixing and recharge indicating an open magma system. Whilst fractional crystallization is the dominated process, magma mixing, recharge, and crystal settling complicate magma evolution. Thermobarometric calculations show that clinopyroxene phenocrysts in bimodal volcanic rocks of SSB are distributed in the whole crust during magma ascent. We have established a magma plumbing system, which provides a new constrain for the complex magmatic evolution history in the SSB by detailed mineral-scale analysis.

Sentinel-2 provides the opportunity to map the snow cover at unprecedented spatial and temporal resolution at global scale. Here we calibrate and evaluate a simple empirical function to estimate the fractional snow cover (FSC) in open terrain using the normalized difference snow index (NDSI) from 20 m resolution Sentinel-2 images. The NDSI is computed from flat surface reflectances after masking cloud and snow-free areas. The NDSI-FSC function is calibrated using Pléiades very high resolution images and evaluated using independent datasets including SPOT 6/7 satellite images, time lapse camera photographs, terrestrial lidar scans and crowd-sourced in situ measurements. The calibration results show that the FSC can be represented with a sigmoid-shaped function 0.5×tanh(a×NDSI+b)+0.5 where a = 2.65 and b = -1.42 yielding a root mean square error of 25%. Similar RMSE are obtained with different evaluation datasets with a high topographic variability. With this function, we estimate that the confidence interval on the FSC retrievals is 38% at the 95% confidence level.

Nanofluids are a novel class of heat transfer fluid that plays a vital role in industries. In mathematical investigations, these fluids are modeled in terms of traditional integer-order partial differential equations (PDEs). It is recognized that traditional PDEs cannot decode the complex behavior of physical flow parameters and memory effects. Therefore, this article intends to study the mixed convection heat transfer in nanofluid over an inclined vertical plate via fractional derivatives approach. The problem in hand is modeled in connection with Atangana-Baleanu fractional derivatives without singular and local kernel having strong memory. The human blood is considered as base fluid dispersing carbon nanotube (CNTs) (single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes(MWCNTs )) into it to form blood-CNTs nanofluid. The nanofluids are considered to flow in a saturated porous medium under the influence of an applied magnetic field. The exact analytical expressions for velocity and temperature profiles are acquired using the Laplace transform technique and plotted in various graphs. The empirical results indicate that the memory effect decreases with increasing fractional parameters in the case of both temperature and velocity profiles. Moreover, the temperature profile is higher for blood-SWCNTs by reason of higher thermal conductivity whereas, this trend is opposite in case of velocity profile due densities difference.

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

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

Based on the fractional order of nonlinear system for love model with a periodic function as an external force, analyzed the characteristics of the chaotic dynamic in this study. The relationship between the chaotic dynamic of the fractional-love model with the external force and the fractional-order system was analyzed when the parameters are fixed. Further, we also studied the relationship between the chaotic systemic dynamic and the parameters when the fractional-order system is fixed. The results show that when the parameters are fixed, the fractional-order system exhibited segmented chaotic states for the different fractional orders of the system. When fixed the fractional-order system, the system exhibited the periodic and chaotic states as parameter changes.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

In Einstein’s Special Relativity(SR), time is treated as one of the four dimensions within spacetime and is relative in nature. Typically, a photon clock serves as the illustrative device in the time dilation thought experiment, featuring a single photon bouncing between two mirrors. However, the present paper identifies a fundamental flaw in this thought experiment, hence challenging its validity. Contrary to SR, this paper asserts that time is a consequence of motion. Space and time should be treated differently as proposed by classical mechanics. Importantly, this stance does not challenge the concept of curved space in General Relativity (GR), but rather questions the idea of relative time, as employed in both SR and GR. The absence of time dilation also dispels the twin paradox, prompting a necessary reassessment of the second postulate of relativity to ensure a more precise depiction of relativistic effects.

In this paper, we investigate the Green measure for a class of non-Gaussian processes in $\mathbb{R}^{d}$. These measures are associated with the family of generalized grey Brownian motions $B_{\beta,\alpha}$, $0

In this paper, we prove the existence of three solutions for a $p$-Kirchhoff problem with $\psi$-Hilfer fractional derivative. To be more precise, we use the variational method and we prove that the associated functional energy admits a critical point in each of the three constructed sets, these critical points are weak solutions for a studied problem. Moreover, by definition of these sets, one of these solutions is positive, the second is negative, and the third one change sign. At the end of this work, we present an example to validate our main results.

Shigella and Salmonella have been implicated in neonatal sepsis, food poisoning, and bacteremia. Their increasing resistance to antibiotics has undermined treatment options, constituting a public health crisis. Also, the scarcity of new antibiotics in the development pipeline compounds multidrug-resistance (MDR). Hence, there is a need to potentiate antibiotics to mitigate resistance. This study leveraged riboflavin to re-sensitize fluoroquinolones and carbapenems against MDR Shigella and Salmonella spp. Disk diffusion, microbroth-dilution, chequerboard, and time-kill assays were used to determine resistance profiles and riboflavin-antibiotic activity. Biofilm-formation and bacterial viability (after riboflavin-antibiotic challenge) was determined with crystal-violet and Macrophage infection assays, respectively. Strains exhibited >80% resistance to fluoroquinolones and carbapenems, with 160–320 µg MIC ranges and 0.5–2 FIC, indicating no synergy. At 40–80 µg riboflavin, there was two-fold reduction in bacterial survival, with meropenem-riboflavin exhibiting significant reduction and FIC of 0.075 indicating high synergistic activity. Biofilm-formation was altered (from strong to weak phenotype) with 40 µg riboflavin-antibiotic treatment. There was a 40–70% reduction in bacterial survival in THP-1 cells treated with meropenem-riboflavin after 3 hours, and complete clearance between 24-48 hpi. Riboflavin potentiated fluoroquinolones and meropenem, leading to modulation of the host immune response for the clearance of the strains.

In this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover behavior of the operators, we divide the study interval into two subintervals. In the first interval, the classical derivative is employed to study the qualitative properties of the proposed system, while in the second interval, we utilize the ABC fractional differential operator. Consequently, the study is initiated using the piecewise Atangana-Baleanu derivative framework for the systems. The HBV model is then analyzed to determine the existence, Hyers-Ulam (HU) stability, and disease-free equilibrium point of the model. Moreover, we showcase the application of an Adams-type predictor-corrector (PC) technique for Atangana-Baleanu derivatives and an extended Adams-Bashforth-Moulton (ABM) method for Caputo derivatives through numerical results. Subsequently, we employ computational methods to numerically solve the models and visually present the obtained outcomes using different fractional-order values. This network is designed to provide more precise information for disease modeling, considering that communities often interact with one another, and the rate of disease spread is influenced by this factor.

Backgrounds Linear association has widely been assumed for prediction of aging-related fractional anisotropy (FA) decline in white matter of the brain. While useful for testing significance of the aging effect, it fails to identify a threshold age before and after which the age-FA association changes. Identification of such a threshold is often of clinical interest for timely intervention. Methods We employed a sigmoidal growth function to test a threshold effect in age triggering onset of cerebral decline in 21 white matter tracts, and compared its fitting performance to those of linear, and power regression. The study sample was a normal healthy cohort of 106 participants with ages in mid-life ranging from 18 to 60 years. Results Of the 21 white matter tracts analyzed, the posterior thalamic radiation showed better fit with sigmoidal curve model, compared to a linear or power regression. The estimated threshold age in years (95% confidence interval) were 47.2 (44.1-48.4). Conclusion While available evidence regarding the presence of a specific age threshold for cerebral decline in mid-life based on FA was limited, the posterior thalamic radiation exhibited a threshold age of 47.2. Beyond this age point, we observed a significant change in the FA risk pattern.

In this research, a computation algorithm is established for a fractional order 2D fuzzy heat equation. In this study, Elzaki transform and HPM fusion is produced. Computing the desired outcome in series yields a fast convergence on an appropriate response. Examples are provided to support the conclusions, which are then compared with a particular approach to show the effectiveness and potential of the suggested approach. Two crisp equations—one for the lower bound solution and one for the upper bound solution are constructed from the input fuzzy fractional heat equation. The contour and surface representations of the approximate and exact results are offered for the lower and upper-bound solutions. The l∞-error norm is used in this study to validate the numerical convergence aspect. Together with the absolute inaccuracy, the approximate and exact solutions are matched. It has been demonstrated that the proposed regime will make it feasible to work with fuzzy fractional partial differential equations in a wide range of dimensions.

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.

The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand-new and distinguished with the existing literature, which fill the gaps of studies for admissibility. These approaches are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). In addition, a method involved least real decision variables in terms of strict LMIs is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of proposed results.

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.

The quality of underground space information has become a major problem that endangers the safety of underground spaces. Currently, the main methods for the high-precision and long-distance transmission of detection information are radar and optical methods. However, in practical applications, we found that the radar method has the shortcomings of large energy loss and poor anti-jamming ability, which limit the accuracy of information data transmission and distance. The optical method has the shortcomings that the weather has a great impact on its accuracy and can only be applied to static objects above ground; therefore, it has the limitation of application objects and use environment. More importantly, the current high-precision information remote detection methods are limited to the detection of overground space objects and are not applicable to the detection of various information data in underground space. In this study, we analyze the spectral properties of the fractional differential operator and find that it is suitable for studying non-linear, non-causal, and non-stationary signals. The theory of fractional calculus is applied to the field of data processing, and a mathematical model of remote transmission and high-precision detection of information based on fractional difference is established, which realizes the functions of high-precision and remote detection of information. By fusing the information data to detect the mathematical model over a long distance and with high accuracy, a mathematical model for stratum data processing used to provide long-distance and high-accuracy data was established. Through application in engineering practice, the effectiveness of this method for underground space information data detection was verified.

Background. The treatment of coronary stenosis relies on invasive high risk surgical assessment to generate the fractional flow reserve diagnostics index, a ratio of distal to proximal pressures in respect of coronary atherosclerotic plaque causing stenosis. Non-invasive methods are therefore a need of the times. This study proposes an extensible mathematical description of the coronary vasculature that permits rapid estimation of the coronary fractional flow reserve. Methods. By adapting an existing closed loop model of human coronary blood flow, the effects of large vessel stenosis and microvascular disease on fractional flow reserve were quantified. Several simula-tions generated flow and pressure information which was used to compute fractional flow re-serve under a spectrum of conditions including focal stenosis, diffuse stenosis, and microvascular disease. Sensitivity analysis stratified the influence of model parameters on the index. The model was simulated as coupled non-linear ordinary differential equations and numerically solved us-ing an implicit higher order method. Results. Large vessel stenosis affected fractional flow re-serve. The model predicts that the presence, rather than severity, of microvascular disease affect coronary flow deleteriously. Sensitivity analysis revealed that heart rate may not affect the index. Conclusions. The model provides a computationally inexpensive instrument for future in silico coronary blood flow investigations as well as clinical-imaging decision making. A combination of focal and diffuse stenosis appears to be essential in reducing the index. In addition to pressure measurements in the large epicardial vessels, diagnosis of microvascular disease is essential. The independence of the index with respect to heart rate suggests that computationally inexpensive steady state simulations may provide sufficient information to reliably compute the index.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

In this work, we establish some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. Moreover, we show that through the conformable fractional integral we can find some new Hermite-Hadamard type inequalities for convex functions via the classical integrals.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

In this paper, we study the fractional pseudo-parabolic equations u_t + (−△)^s u + (−△)^s u_t = u log |u|. Firstly, we recall the relationship between the fractional Laplace operator (−△)^s and the fractional Sobolev space H^s and discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence of global weak solution: for the low initial energy J(u₀) < d, the solution is global in time with I(u₀) > 0 or ∥u₀∥X_0(Ω) = 0 and blows up +∞ with I(u₀) < 0; for the critical initial energy J(u₀) = d, the solution is global in time with I(u₀) ≥ 0 and blows up at +∞ with I(u₀) < 0. The decay estimate of the energy functional for the global solution is also given.

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

Time, traditionally viewed as a linear, non-dynamic parameter, is re-envisioned in this study as a Hyperdimensional concept. This paper conducts a cross-disciplinary examination, critically analysing the conceptualization of time in classical mechanics, quantum mechanics, and cosmology to propose a ground breaking reconceptualisation that extends beyond conventional frameworks. In classical mechanics, time is perceived as an absolute, continuously progressing backdrop, largely independent of events. Quantum mechanics treats time as a static parameter that does not influence quantum states but provides a framework for their evolution. In cosmology, time is considered a dimension that emerges from the Big Bang and serves as a measure for the universe's expansion, yet it does not interact with the structural dynamics of the cosmos. Challenging the transformative insights of Einstein’s relativity, which merges time with spatial dimensions under extreme conditions, we advocate for a perspective that views time as a Hyperdimensional and universal constant. This perspective posits that time, despite its unique and intrinsic properties, does not dynamically interact with or alter physical phenomena. Instead, it underpins our understanding of phenomena across different scales—from the minutiae of quantum states to the macroscopic dynamics of cosmology—without direct causation or change. A critical examination of time dilation and relativistic assumptions reveals significant discrepancies in traditional interpretations, particularly in how they are applied across different physical contexts. Our findings challenge the uniform applicability of time dilation, suggesting that observed phenomena often attributed to relativistic effects might better be explained through non-relativistic mechanisms such as phase shifts or changes in wavelength rather than temporal dilation. By synthesizing insights from various scientific domains, we advocate for a unified theory that recognizes time as a fundamental, universal dimension that is conceptual and non-interactive. Our goal is to bridge existing gaps between diverse scientific interpretations and promote a more integrated, profound understanding of time's autonomous and intrinsic nature.

The present investigation focuses on the impact of jet nozzle orientation on mixing time in a cylindrical tank. The aim is to identify nozzle positions that improve mixing performance and to elucidate the governing parameters that influence it. A water tank was employed for the experiment. The vertical inclination angle (α) and the horizontal inclination angle (β) of the jet nozzle determined the nozzle positions. Mixing time was determined using an inert tracer and spectrophotometry measurements. The findings show that the mixing time is significantly influenced by the position of the jet nozzle position. The accuracy of existing jet turbulence and the circulation models for the prediction of mixing time was evaluated for the different nozzle positions. Our results indicate that both models provide accurate predictions for the conventional centrally aligned (β = 0°), upward-pointing jet nozzle positions only (α > 0). For the other nozzle positions where β > 0° and at varying α, the data follow the same trends as the jet turbulence and circulation models, however, the proportionality constants vary. Shorter mixing times can be attributed principally to longer jet path lengths and therefore higher fluid entrainment and circulation, as well as higher dissipation rates per jet length squared. However, it is suspected that the 3-dimensional nature of the flow pattern generated in the tank also plays a non-negligible role since mixing is hindered when the nozzle points more towards the tank wall.

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 our increasingly urbanized world, precise and up-to-date maps of human settlements are essential for sustainable urban development policies. The availability of open-access Sentinel-2 data from the Copernicus program presents an opportunity to create a comprehensive global map of human settlements, offering a detailed view of built areas on a large scale. This study estimates large-scale built-up fractions using encoder-decoder deep learning architectures like U-net, Res-U-net, and Attention-U-net in the large and complex urban area of Delhi, India. Openly available datasets like Open Street Map (OSM) and Microsoft building footprint datasets are used to derive built-up fractions at 10×10m resolution cells for over 34,000 km2. Our results show that Attention-U-net with the Huber loss function performs the best in different built-up densities (i.e., urban, semi-urban or rural) with an R2 score of 0.631, while Res-U-net and U-net obtained an R2 score of 0.623 and 0.612, respectively. The investigated networks significantly improve the accuracy over the latest Global Human Settlement Layer product (GHSL-S2), which uses a deep-CNN and reaches an R2 of 0.387 in our case study area. The result of this study yields a valuable spatial layer for examining the spatial distribution of human settlements across the entire spectrum from rural to urban areas.

This study develops a new definition of fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels. Such developed definition encompasses many types of fractional derivatives, such as the Riemann-Liouville and Caputo fractional derivatives for singular kernel type as well as the Caputo-Fabrizio, the Atangana-Baleanu and the generalized Hattaf fractional derivatives for non-singular kernel type. The associate fractional integral of the new mixed fractional derivative is rigorously introduced. Furthermore, newly numerical scheme is developed to approximate the solutions of a class of fractional differential equations (FDEs) involving the mixed fractional derivative. Finally, an application to computational biology is presented.

About half of the transcatheter aortic valve replacement (TAVR) recipients exhibit some degree of coronary artery disease (CAD), and controversial results have been reported regarding the impact of the presence and severity of CAD on clinical outcomes post-TAVR. In addition to coronary angiography, promising data has been recently reported on the use of both cardiac computed tomography angiography and the functional invasive assessment of coronary lesions whether by FFR or iFR in the work-up pre-TAVR. Despite mitigated available data, percutaneous revascularization of significant coronary lesions has been the routine strategy in TAVR candidates with CAD. Also, scarce data exists on the incidence, characteristics and management of coronary events post-TAVR, and increasing interest exist on potential coronary access challenges in patients requiring coronary angiography/intervention post-TAVR. This review provides an updated overview of the knowledge of CAD in TAVR recipients, focusing on its prevalence, clinical impact, pre- and post-procedural evaluation and management.

This paper presents a numerical method for solving a two-dimensional subdiffusion equation with a Caputo fractional derivative. The problem considered assumes symmetry in both the equation’s solution domain and the boundary conditions, allowing for a reduction of the two-dimensional equation to a one-dimensional one. The proposed method is an extension of the fractional Crank-Nicolson method, based on the discretization of the equivalent integral-differential equation. To validate the method, the obtained results were compared with a solution obtained through Laplace transform. The analytical solution in the image of the Laplace transform was inverted using the Gaver-Wynn-Rho algorithm implemented in the specialized mathematical computing environment, Wolfram Mathematica. The results clearly show the mutual convergence of the solutions obtained by the two methods.

The paper's main goal is to introduce a novel type of interpolative convex contraction and build up some fresh findings for it using the interpolative convex contractions' progressive approach. We have established certain conclusions using orbitally S-complete and Suzuki type contractions in F-metric spaces. My research aims to examine the fixed point method's efficacy in solving fractional differential equation with boundary conditions.

The information data accuracy affects the working reliability of production management system directly. Mobile equipment is an important part of integrated manufacturing system, in the course of its works, due to the complex working environment and the dynamic change of its position, it lead to the important problem of information detection distortion. Because the application of fractional differential operator has the dual functions of enhancing signal strength and reducing data error, we puts forward a data processing method of obtaining production information data of various accuracy by changing the parameters of fractional differential operator. Establish a mobile equipment detection data fusion processing model based on fractional order partial differential equations and apply it in the processing experiment of mobile equipment testing information detection data in an integrated manufacturing system, the feasibility and effectiveness of the method are verified. We conclude that the fractional order partial differential equations used in the processing of mobile equipment monitoring information data of an integrated manufacturing system has the function of obtaining production information data of various accuracy, which are of great significance to improve the working reliability in integrated manufacturing system. which is of great significance to improve the working reliability and scientific decision of integrated manufacturing system.

Brazil, Russia, China, India, and the Republic of South Africa (BRICS) represent developing economies facing different energy and economic development challenges. The current study aims to forecast energy consumption in BRICS at aggregate and disaggregate levels using the annual time series data set from 1992 to 2019 and to compare results obtained from a set of models. The time-series data are from the British Petroleum (BP-2019) Statistical Review of World Energy. The forecasting methodology bases on a novel Fractional-order Grey Model (FGM) with different order parameters. This study contributes to the literature by comparing the forecasting accuracy and the forecasting ability of the FGM(1,1) with traditional ones, like standard GM(1,1) and ARIMA(1,1,1) models. Also, it illustrates the view of BRICS's nexus of energy consumption at aggregate and disaggregates levels using the latest available data set, which will provide a reliable and broader perspective. The Diebold-Mariano test results confirmed the equal predictive ability of FGM(1,1) for a specific range of order parameters and the ARIMA(1,1,1) model and the usefulness of both approaches for energy consumption efficient forecasting.

In this study, by using Least Square Method, the dataset for the Gross Domestic Product per capita is modeled as a function satisfying the fractional differential equation. The function itself is assumed to be the finite summation of its previous values and the derivatives with unknown coefficients. Then, the prediction for the upcoming years is done by having an approach dividing the dataset into 4 regions corresponding to four different tasks. The mathematical model of the Gross Domestic Product (GDP) per capita of the countries (and union) which are Brazil, China, European Union (EU), India, Italy, Japan, UK, the USA, Spain, and Turkey is constructed with a new methodology called as the deep assessment method which comes from the expressing an arbitrary function modeling the dataset as the finite summation of its previous values and the derivatives with unknown coefficient. The method uses the fractional calculus properties combining with Least Square Method and is compared to Long short-term memory (LSTM) algorithm which is a special type of neural network used for time sequences in general.

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

Permanent magnet synchronous motor (PMSM) AC servo system shows the characteristics of uncertainty, time-varying and non-linearity, which makes it difficult for traditional PID control to achieve ideal control effect. Fuzzy control has strong adaptability to the problems of parameter variation, non-linearity and model inaccuracy of the controlled object. Vector control strategy is used to study its control principle and the realization of SVPWM. Because the motor object has certain fractional order characteristics, the fuzzy parameter self-tuning PIλ control is chosen as the position regulator of servo motor. It combines the accuracy of fractional order PI control and the adaptability of fuzzy control. A simulation model of PMSM three-closed-loop system is built in MATLAB/Simulink environment. The results show that the control method is effective and can satisfy the trajectory tracking of servo control.

The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.

In this article, we establish the existence of and then compare smallest eigenvalues for nabla fractional boundary value problems involving a fractional difference boundary condition, using the theory of u0-positive operators with respect to a cone in a Banach space.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

Physicists have employed various approaches to solve the “paradox” and offered a consistent conclusion that the traveller twin is younger than the homebody twin. However, some authors attribute the cause of differential aging to acceleration, while others believe that acceleration should not be regarded as the source of differential aging, but frame switch is. So far there is no agreement on this issue. Actually, acceleration and frame switch should not be regarded as the source of differential aging. The author will introduce a thought experiment in which two very long spacecraft are moving in opposite directions at a speed close to the speed of light to discuss the real cause of differential aging. The author found that the real cause of differential aging in the twin “paradox” is because of the asymmetry of destination choice. People always choose their destinations in the universe rather than in spacecraft. The destinations are always stationary relative to the homebody twin and moving relative to the traveller twin. Once we choose a destination in a reference frame, the distance is the proper length in this reference frame, but the distance will contract in another moving reference frame, thus the recording time will be shorter.

This addendum contains clarifications and a sharpening of some of the results on the VIT transform framework developed in [1]. The focus is on the right-coefficient and left- coefficient forms of the transform, the extraction of a first-order term from a left polynomial fraction, and the application to linear time-varying systems.

We have introduced a sign operator of energy, analogous to the operator helicity, but in the direction of what we call energy vector. However, this energy vector needs a time vector. To give physical senses to the components of such a time vector, we try to explain the time dilation in special relativity and try to relate the components of the time vector to the tunneling times when an electron crosses a potential barrier.

Climate change such as sea level rise, change in temperature, precipitation, and storminess are expected to impact significantly coastal lagoons. The nature and magnitude of these impacts are uncertain. The objective of the research is to determine the climate change impacts on mixing and circulation at Songkhla lagoon, Thailand. Songkhla lagoon is the largest lagoonal water resource in Thailand and Southeast Asia. The lagoon is a combined freshwater and estuarine complex of high productivity which represents an extraordinary combination of environmental resources believed to be unique in the region. This work is part of a Climate Change impact assessment framework. It is the validation phase (step 5) of the framework applying a case study. Delft 3D was used to simulate CC scenarios in the climate downscaling models, part of the previous framework steps. These results were compared to the current conditions to determine the main changes in mixing and circulation in the coastal lagoon. Three indicators were applied to quantify the impacts: flushing time, salinity intrusion and stratification. The results suggest an increase in water velocities at the inlet in future scenarios and a decrease of flushing time. Salinity and stratification showed more complex changes in futures scenarios.

A number of experimental tests of time orientability are described as well as clear experimental signatures from non time orientability (time reversal). Some tests are well known, while others are based on more recent theoretical work. Surprisingly, the results all suggest that time is not orientable at a microscopic level; even definitive tests are positive. At a microscopic level the direction of time can reverse and a consistent forward time direction cannot be defined. That is the conclusion supported by a range of well-known experiments. The conflict between quantum theory and local realism; electrodynamics with electric charges; and spin half transformation properties of fermions; can all be interpreted as evidence of time reversal. While particle-antiparticle annihilation provides a definitive test. It offers both a new view of space-time and an novel interpretation of quantum theory with the potential to unify classical and quantum theories.

Can physical objects be in time-symmetry? Physical objects can only exist in a medium that has physical attributes, which means this medium is a type of energy. Is time energy? This article will show that time is not energy and there is no possibility that physical objects could be in time-symmetry. Physical objects only can be in symmetry in the time-invariant space in which they exist. In this perspective time measured with clocks is the result of the observer’s measurement in the time-invariant space. The time-symmetry model is flawed.

Capacity Expansion Models (CEMs) are optimization models used for long-term energy planning on national to continental scale. They are typically computationally demanding, thus in need of simplification, where one such simplification is to reduce the temporal representation. This paper investigates how using representative periods to reduce the temporal representation in CEMs distorts results compared to a benchmark model of a full chronological year. The test model is a generic CEM applied to Europe, equipped with a novel formulation for storage in model versions with reduced temporal representation. We test the performance of reduced models at penetration levels of wind and solar of 90%. Three measures for accuracy are used: (i) system cost, (ii) total capacity mix and (iii) regional capacity. We find that: (i) the system cost is well represented (~5% deviation from benchmark) with as few as ten representative days, (ii) the capacity mix is in general fairly well (~20% deviation) represented with 50 or more representative days, and (iii) the regional capacity mix displays large deviations (>50%) from benchmark for as many as 250 representative days. We conclude that modelers should be aware of the error margins when presenting results on these three aspects.

Today, due to recent developments in technology, children devote plenty of time for screen viewing. However, its harmful effects are not yet clear. The purpose of present study was to examine the associations among screen viewing and sleep duration, and body mass index (BMI) in under-five years old children. This cross-sectional study was conducted with 322 under-five healthy children that were selected using multistage stratified cluster sampling method in 2017. The data that were gathered by time-use diary method were analyzed using Kolmogorov-Smirnov test, Spearman correlation tests, multiple linear regression analysis, one-way ANCOVA, two-way ANCOVA. There was a negative correlation between screen time and sleep duration (rs = -0.42, p = 0.00), positive correlation between screen time and BMI (rs = 0.38, p = 0.00) and sleep duration negatively correlated with BMI (rs = -0.22, p = 0.00). screen viewing was a predictive factor for both sleep duration (β = -0.26, p = 0.00) and BMI (β = -0.26, p = 0.00). screen viewing had a significant impact on sleep duration (4, 314) = 5.02, P = 0.001) and BMI (F (4, 314) = 1.16, P=0.298). Results of this study indicated that screen viewing is related to sleep duration and BMI in under-five children. furthermore, screen time has an impact on sleep duration and BMI scores of children. findings of our study suggest that sleep duration negatively is associated with BMI in under-five-year-old children.

Nonlocal theories are gaining prominence because they can solve problems which lead to unphysical conclusions in standard models. This study presents a novel fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. This broad BEM solution combines two solutions: anisotropic fibrous polymer nanomaterials problem solution and nonlinear nonlocal thermoelasticity problem solution. The nonlinear nonlocal thermoelasticity problem solution divides the displacement field into complementary component and particular component. The overall displacement is generated using the boundary element technique, which is the solution to a Navier type problem, while the particular displacement is derived using local radial point. The New Modified Shift-Splitting (NMSS) approach, which reduces memory and processing time requirements, was used to solve linear systems created by BEM. Figures demonstrate the numerical findings, which show the effects of fractional and graded parameters on the thermal stresses of nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. The numerical results indicate the consistency and efficiency of the proposed methodology.

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.

: This paper presents a comparison between direct integer orders or classical model reference adaptive control (IO-DMRAC) versus its fractional orders counterpart (FO-DMRAC) applied to the F-16 aircraft longitudinal model pitch rate control. A substantial improvement is achieved when using fractional order adaptive control, since, in addition to performance indices, such as Integral Square-Error criterion (ISE) and Integral Square-Input criterion (ISU) being lower, the oscillations of the system output (pitch rate) in the transient period, are eliminated. Moreover, it is the first attempt in literature of adaptive control that a FO-DMRAC is applied to the pitch rate control of an aircraft. A F-16 short-period model, whose relative degree is equal to 1 (n^*=1) is analyzed by mean of simulations with good results. A FO-DMRAC is designed, for a specific operating flight conditions and compared with its IO-DMRAC counterpart. Furthermore, the boundedness of all signals, including the internal ones ω(t) are assured.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi univalent function defined in open unit disk connected with a linear q-convolution operator, which are associated with the quasi-subordination. We find coefficients estimate |h_2 |,|h_3 | for functions in these subclasses. Several known and new consequences of these results are also pointed out.

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 investigated whether export performance is correlated with innovation. We explicitly considered five types of innovation: a) process innovation; b) product innovation; c) process and product innovation; d) product innovation new to the firm; and e) product innovation new to the market. We en-larged the findings of R&D-export and R&D-investment relations using a vast sample of cross-European firms. We considered innovation as endogenous and determined by R&D through a process characterized by the role of the regional technological environment. Our analysis enabled us to propose an integrated model incorporating R&D, innovation and export, in a framework of simultaneous equations which consider their mutual correlations. To the best of our knowledge, this work is the first in recent years to empirically compute the relation between R&D and tangible investment at the micro level. Econometric results showed that product and process innovation are positively linked to the export intensity of European manufacturing firms. The results also showed complementarity effects between the two kinds of innovation. The av-erage effect on export intensity from carrying out process innovation is larger than that found for product innovation, except in cases where the product is new to the market. When both types of innovation have been carried out, a larger effect results than that found for product or process innovation alone. Furthermore, the average marginal effect on export intensity from innovations of any kind among those studied here is highly positive and significant.

In engineering practice, various types of information data are affected by many factors during the collection process. For example, information data measurement errors are caused by equipment performance and the working environment. During the transmission of detection information, the signal distortion caused by energy loss and signal interference causes unpredictable detection errors in the collected information data. Through the study of fractional calculus theory, it was found that it is suitable for studying nonlinear, non-causal, and non-stationary signals, and has the dual functions of improving detection information and enhancing signal strength. Therefore, under the influence of many factors, we applied the fractional difference algorithm to the field of information data processing. Multi-sensor detection data fusion algorithm based on the fractional partial differential equation was adopted to establish its online detection data. A multi-sensor detection data fusion algorithm based on a fractional partial differential equation is established, which effectively fuses the information data detection errors caused by various influencing factors and greatly improves the detection accuracy of information data. The effectiveness of this method is proved through its application in an experiment.

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon's theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

In this study we used a non-autonomous Chua’s Circuit, and the fractional Lorenz chaos system together with a detection method from Extension theory to analyze the voltage signals. The measured bearing signals by acceleration sensor were introduced into the master and slave systems through a Chua’s Circuit. In a chaotic system minor differences can cause significant changes that generate dynamic errors, and extension matter-element models can be used to judge the bearing conditions. Extension theory can be used to establish classical and sectional domains using the dynamic errors of the fault conditions. The results obtained were compared with those from Discrete Fourier Transform analysis, Wavelet analysis and an integer order chaos system. The diagnostic ratio showed the fractional order master and slave chaos system calculations. The results show that the method presented in this paper is very suitable for monitoring the operational state of ball bearing system to be superior to the other methods. The diagnosis ratio was better and there were other significant advantages such as low cost and few.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

In this paper, the concept of absolute airspace is further elaborated, and the time transform effect, the frequency transform relation of clock timing, and the principle of Doppler effect of special relativistic light are analyzed and demonstrated. Based on the concept of absolute airspace, a new and accurate Doppler effect relation of light (electromagnetic wave) is proposed. It is proved that there is a synchronous relationship between the time shift effect and the frequency change of the timing inside the clock. When the light (electromagnetic wave) source is in motion, the Doppler effect includes two physical mechanisms: the frequency change caused by time transformation effect and the frequency change caused by relative motion. When the light source is in motion, the Doppler effect of the light there are some differences in different directions due to the rotation of the earth. The relation of Doppler effect of special relativistic light is only a highly approximate relation, and its theoretical basis, special relativity, is flawed in principle.

Effects and interactions of incubation time and chick preplacement holding time on mortality at placement, utilization of yolk sac, crop filling rate, early feeding–drinking behavior and broiler live performance were investigated. Ross 308 broiler hatching eggs from a 39-week-old flock were set in two identical setters in a commercial hatchery,with setting time 12 hours earlier in one machine. At the end of incubation, chicks were removed from the hatchers at the same time. Thus, incubation times were either 504 h (normal incubation time (NIT) treatment) or 516 h (longer incubation time (LIT) treatment). After pull time, chicks from each incubation time group were subjected to either 6, 24, 48, 60 or 72 h preplacement holding times. At placement, chicks were given access to feed and water. In total, 19,200 chicks were randomly assigned to a total of 10 subtreatment groups (2 incubation times × 5 preplacement holding times). Therefore, a total of 1,920 chicks were used in each subtreatment group for the grow-out period in a commercial broiler house. An interaction was found between incubation time and preplacement holding time for residual yolk sac (RYS) weight (g, %) (p &lt; 0.001). RYS weight was greater at pull time and at 6 and 24 h of preplacement holding time in the NIT treatment compared to the LIT treatment, while differences were no longer evident at 48–72 h. The lowest percentage of chicks with full crops and eating activity was observed in the shortest preplacement holding time (6 h) group at 3 h after placement. As expected, the initial BW at placement clearly decreased with increasing duration after the pull time (p &lt; 0.05) with the highest and lowest weights were found in the 6 and 72 h holding time treatments respectively. This BW difference was still evident at 35 d after placement and chicks held for the longest period after the pull time (72 h) showed the lowest BW (p &lt; 0.001). However, there was no significant difference between the 6 and 60 h preplacement holding times. Mortality during the first 7 d after placement increased only when the preplacement holding time was extended to 72 h (p = 0.031). Similar to the 7 d results, chicks held for 72 h exhibited higher 0-35 day mortality compared to those held for 6 or 24 h (p = 0.028). Neither BW nor mortality was affected by incubation time treatment at 35 d after placement (p &gt; 0.05). It can be concluded that there were no significant differences in average BW and mortality, up to and including a 60-h holding time under thermal comfort conditions, but a 72-h preplacement holding time resulted in final BW and mortality being negatively affected. In addition, LIT tended to have a beneficial effect on BW and mortality compared to NIT when the preplacement holding time was shorter (6–24 h) but had a negative effect for extended holding times (48–72 h).

On the basis of the findings of this paper, the theories of quantum mechanics and general relativity can be expressed in a comprehensive theory. The events were surveyed length of the time, in the Euclidean six-dimensional space-time (R6=x1+x2+x3+t1+t2+t3). Previous studies have not studied the relationship between the origin of matter's inherent properties, fundamental constants, and quantum mechanics phenomenon with space-time geometry. This theory prediction the with certainty obtained probabilistic results of quantum mechanics. This prediction is on the basis of metric resulting from the Eccentricity of the Ellipse due to the object density, in the length of time. The cause and nature of dark matter and dark energy are the findings of this article.

Noise model selection criteria has a significant impact on identifying the stochastic noise proper-ties of any GNSS daily coordinate time series. The low-frequency random walk noise existing in these time series could lead to overestimation of the tectonic rate, so it is of great significance to accurately detect the random walk component. This study focuses on noise model estimation cri-terion (BIC_tp) derived from the AIC and the BIC by introducing 2π factors. It is more sensitive to abnormal steps (random jumps). Using observation data from 72 GNSS stations from 1992 to 2022 and simulated data, four combined noise models are used to explore the impacts of time se-ries lengths (ranging from2 to 24 years) and data loss (between 2% and 30%) on noise models and velocity estimation. The results show that as the time length increased, the selected optimal noise model, and the estimated uncertainty of the tectonic trend with different data gap, gradually con-verge. When the time length is short (less than 8 years), it could lead to the FNRWWN, FNWN, and PLWN models being mistakenly estimated as GGMWN models, thereby affecting the accura-cy of determining the station velocity parameters. When the time length is 12 years, the RW noise component is more probably detected, As the time length increases, the impact of RW on velocity uncertainty is weakened. Finally, we conclude that for a time series with a minimum time length of 12 years, both the selection of the optimal stochastic noise model and the estimation of the ve-locity parameters are reliable.

The gelation time tg necessary for a solution of functional (associating) molecules to reach its gel point after a temperature jump, or a sudden concentration change, is theoretically calculated as a function of the concentration and temperature for the molecules carrying the number f of functional groups. Quite generally, tg is given by the product of the relaxation time tR and a thermodynamic factor Q. For pairwise cross-linking, and cross-linking with a fixed multiplicity k, precise values of tg are derived. For cross-linking with variable multiplicity, kinetic equation of stepwise association is derived for the reactivity pk of the functional groups, on the basis of which tg and tR are estimated. The thermodynamic factor Q is shown to generate a singularity of logarithmic divergence as the temperature (concentration) approaches the equilibrium gel point, while the relaxation time tR changes continuously across it. The retardation effect on the gelation time due to the reversibility of the cross-linking is explicitly calculated for some specific models of cross-linking. For a micellar cross-linking covering a wide range of the multiplicity, as seen in hydrophobically-modified water-soluble polymers, tR is shown to obey a formula similar to the Aniansson-Wall law.

We are using the book “Towards Quantum Gravity with an article by Claus Kiefer as to a quantum gravity interpretation of the density matrix in the early universe. The density matrix we are using is a one loop approximation, with inflaton value and potential terms, like V(phi) using the Padmanabhan values one can expect if the scale factor is a ~ a(Initial) times t ^ gamma , from early times . In doing so, we isolate out presuming a very small initial time step candidates initial time values which are from a polynomial for time values due to the Kiefer Density value.

In this paper, we study the Parisian time of a reflected Brownian motion with drift on a finite collection of rays. We derive the Laplace transform of the Parisian time using a recursive method, and provide an exact simulation algorithm to sample from the distribution of the Parisian time. The paper is motivated by the settlement delay in the real-time gross settlement (RTGS) system. Both the central bank and the participating banks in the system are concerned about the liquidity risk, and are interested in the first time that the duration of settlement delay exceeds a predefined limit, we reduce this problem to the calculation of the Parisian time. The Parisian time is also crucial in the pricing of Parisian type options; to this end, we will compare our results with the existing literature.

Future cyber-physical systems may extend over broad geographical areas, like cities or regions, thus requiring the deployment of large real-time networks. A strategy to guarantee predictable communication over such networks is to synthesize an offline time-triggered communication schedule. However, this synthesis problem is computationally hard (NP-complete), and existing approaches do not scale satisfactorily to the required network sizes. This article presents a segmented offline synthesis method which substantially reduces this limitation, being able to generate time-triggered schedules for large hybrid (wired and wireless) networks. We also present a series of algorithms and optimizations that increase the performance and compactness of the obtained schedules while solving some of the problems inherent to segmented approaches. We evaluate our approach on a set of realistic large-size multi-hop networks, significantly larger than those considered in the existing literature. The results show that our segmentation reduces the synthesis time up to two orders of magnitude.

In Newtonian mechanics, time as well as space are perceived as absolute entities. In 2 Einstein’s special relativity, time is frame dependent. Time is also affected by gravitational field 3 and as the field varies in space, time also varies throughout space. In the present article, a 4 thermodynamic-based time is investigated. The entity is called "irreversibility", which is generated 5 when availability (also known as exergy) is destroyed. Since each thermodynamic system may 6 generate different amount of irreversibility, this quantity is system dependent. The time’s arrow is 7 automatically satisfied, since irreversibility generation always proceeds in one direction (toward 8 future). We have demonstrated that, like common time, irreversibility is frame dependent, and 9 affected by gravity in the similar manner as the common time. For this reason, we propose to 10 assign the entity irreversibility of the system as thermodynamic time. A possible application of the 11 thermodynamic time is an interpretation and managing of the aging of biological systems. The 12 metabolic efficiency is related to the irreversibility of the chemical processes and affect the aging of 13 the system. Our sensation of time-flow may be attributed to the flow of availability and destruction 14 of it through the living system. It is shown by other authors that entropy generation (equivalent to 15 irreversibility) is a parameter for the human life span. Since the thermodynamic time is based on a 16 concept of thermodynamics that is universal, further applications to other subjects, such as biological 17 clock, telomere, and cosmology are possible.

With the great development of intelligent transportation systems (ITS), travel time prediction has attracted the attentions of many researchers and a large number of prediction methods have been developed. However, as an unavoidable topic, the predictability of travel time series is the basic premise for travel time prediction has received less attention than the methodology. Based on the analysis of the complexity of travel time series, this paper defines travel time predictability to express the probability of correct travel time prediction and proposes an entropy-based method to measure the upper bound of travel time predictability. Multiscale entropy is employed to quantify the complexity of travel time series, and the relationships between entropy and the upper bound of travel time predictability are presented. Empirical studies are made with vehicle trajectory data in an express road section. The effectiveness of time scales, tolerance, and series length to entropy and travel time predictability are analysis, and some valuable suggestions about the accuracy of travel time predictability are discussed. Finally, the comparisons between travel time predictability and actual prediction results from two prediction models, ARIMA and BPNN, are conducted. Experimental results demonstrate the validity and reliability of the proposed travel time predictability.

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

The fractional diffusion equations with integrals play a significant role in describing anomalous diffusion phenomena. We first construct an appropriate resolvent family, and use the convolution theorem of Laplace transform, the probability density function, Cauchy integral formula and Fubini theorem to study its related equicontinuity, strongly continuity, compactness, etc. Then, a reasonable mild solution is defined. Finally, by combining some fixed point theorems, we obtain some conclusions on the existence and uniqueness of mild solutions.

The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials. The computing performance of the suggested methodology was demonstrated by using stable communication avoiding S-step – generalized minimal residual method (SCAS-GMRES) to solve discretized linear BEM systems. The benefits of SCAS-GMRES are investigated and compared to those of other iterative techniques. The numerical results are graphed to demonstrate the influence of fractional, piezoelectric, and length scale characteristics on total force-stresses. These findings also demonstrate that the BEM methodology is practical, feasible, effective, and has superiority over domain methods. The results of the present paper help to develop the industrial uses of smart nanomaterials.

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

The concepts of fractional calculus and the related techniques have been gaining momentum in circuit system fields, and an increasing body of evidence suggests that fractional-order characteristics are widely distributed in electronic components. In this paper, we consider the fractional characteristics of non-solid aluminum electrolytic capacitors and focus on the nonlinear dynamic characteristics of peak-current-mode controlled (PCMC) dc-dc boost converters with such components. In the work, we establish a piecewise smooth non-commensurate fractional-order model to describe the converter, in which the fractional-order equivalent impedance model of capacitors is adopted and the detailed control loop is considered. In order to analyze the converter, we use the fractional Adams-Bashforth-Moulton typed method (F-ABM) and stroboscopic map technique to obtain the time-domain solutions and the bifurcation diagram. The results of bifurcation diagrams indicate that, with the change of different parameters, the converter enters chaotic state through period doubling bifurcation. In order to provide empirical evidence for the nonlinear dynamic analysis, we consider both circuit-level simulation and experiments in the work, the results of which further confirm the results of theoretical analysis.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

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.

Complex diseases such as cancer are caused by changes in the Gene Regulatory Networks. Systems that model the complex dynamics of these networks along with adapting to real gene expression data are closer to reality and can help understand the creation and treatment of cancer. In this paper, for the first time, modelling of gene regulatory networks is performed using delayed nonlinear variable order fractional systems in the state space by a new tool called GENAVOS. This tool uses gene expression time series data to identify and optimize system parameters. This software has several tools for analyzing system dynamics. The results show that the nonlinear variable order fractional systems have very good flexibility in adapting to real data. We found that regulatory networks in cancer cells actually have a larger delay parameter than in normal cells. It is also possible to create chaos, periodic and quasi-periodic oscillations by changing the delay, degradation and synthesis rates. Our findings indicate a profound effect of time-varying order on these networks, which may be related to a type of cellular memory due to epigenetic and environmental factors. We showed that by changing the delay parameter and the variable order function for a normal cell system, its behavior changes and becomes quite similar to the behavior of a cancer cell. This work also confirms the effective role of the miR-17-92 cluster in the cancer cell cycle. GENAVOS is available at https://github.com/hanif-y/GENAVOS with its user guide and MATLAB codes.

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

A new method for short circuit fault location is proposed based on instantaneous signal measurement and its derivatives, and is based on the retardation phenomena. The difference between the times in which a signal is registered in two detectors is used to locate the fault. Although a description of faults in terms of a lumped circuit is useful for elucidating the methods for detecting the fault. This description will not suffice to describe the fault signal propagation hence a distributed models is needed which is given in terms of the telegraph equations. Those equations are used to derive a transmission line transfer function, and an exact analytical description of the short circuit signal propagating in the transmission line is obtained. The analytical solution was verified both by numerical simulations and experimentally.

How to build an optimal model where three terms “time, causality, and entropy” will be interrelated in a most correct way? This task has a semantic and physical aspect. We give in this article the solution that is based only on elementary perception. In physics, we experience time with our senses as the duration of material change running in space. This fact is the standpoint for our model where causality is only a principle, it is not a physical actuality and entropy runs only in space and not in time. Time is merely a duration of entropy increasing and is entering existence when measured by the observer.

Taking into account the growing interest in microalgae to be used as raw material for biodiesel production, this research is aimed at analyzing the rheological behaviour of microalgae suspensions (Chlorella sp) at different culture times under eight different conditions (temperature, salinity and CO₂, NO₃ and PO₄ levels) in order to estimate the energy demands of each step, with the purpose of optimizing a continuous feed tubular bioreactor construction. For each condition, it was calculated the biomass and oil yields, so as to correlate these results with rheological parameters. The suspension results indicated that the microalgae Chlorella sp is a non-Newtonian material with dilatant characteristics; the processing time hardly exerted an influence on the rheograms of the suspension of the microalgae Chlorella sp, except for the simultaneous conditions of low salinity and low CO₂ content; NO₃ and PO₄ contents and the amount of supplements influenced the rheological parameters of the suspension of the microalgae Chlorella sp, when in low concentration of CO₂ and low salinity levels.

An exposition is undertaken to reveal the significant impact of the time-dependent root parameter, on the stability of Pointwise Stationary Fluid Flow Approximation (PSFFA) model of the non-stationary queueing system. This opens new grounds to stability analysis of non-stationary queueing systems. Potential PSFFA applications of IoT are highlighted.

As urban populations continue to grow, efficient traffic management becomes paramount in reducing congestion, enhancing air quality, and improving overall quality of life. This study addresses the critical issue of intersection efficiency through the implementation of smart green time allocation strategies at a signalized intersection equipped with two LiDAR sensors. This research aims to investigate optimal green time allocations provided by two LiDAR sensors and analyze the LiDAR results by microsimulation in AIMSUN. The research first introduces the concept of LiDAR-equipped signalized intersections and their potential to enhance traffic control precision. Two LiDAR sensors are strategically placed at the intersection of Marlboro Pike and Brooks Dr. in Coral Hills, MD, USA to capture real-time data on vehicle and pedestrian movements. The data are then processed to generate accurate and dynamic traffic profiles, ensuring the responsiveness of the green time allocation system to varying traffic conditions.The heart of this study lies in the integration of AIMSUN microsimulation with LiDAR data. Through meticulous modeling and simulation, the research explores the optimal green allocation at morning, mid-day, and afternoon peak hours’ scenarios to comprehensively assess the impact of LiDAR-enabled dynamic signal control. The findings demonstrate that smart green time allocation, informed by real-time LiDAR data and implemented through AIMSUN microsimulation, significantly enhances intersection efficiency. By adapting signal timings to real-time traffic demands, congestion, travel times, and emissions are reduced. Furthermore, this research highlighted that the optimal green time allocation in morning, mid-day, and afternoon peak hour intervals can improve the delay time by 55.3%, 59.7%, and 55.6%, respectively.In conclusion, this paper sheds light on the potential of LiDAR technology to transform intersection management. Through a case study involving two LiDAR sensors and AIMSUN microsimulation, it reveals the tangible benefits of dynamic signal control in enhancing intersection efficiency and creating more sustainable urban environments. These findings are pivotal in advancing the discourse on modern urban traffic management and promoting data-driven solutions for the challenges of today's cities.

Traffic signal control plays a key role in managing urban traffic flow, enhancing safety, and minimizing congestion and conflicts. Effective green time allocation is a critical element of this control process. This research explores the utilization of LiDAR sensor technology in the optimization of green time allocation for one phase of a traffic signal at a signalized intersection. LiDAR sensors provide precise and real-time data on vehicle presence and traffic patterns, enabling a data-driven approach to traffic signal control. The study begins with an analysis of the limitations of traditional traffic signal control strategies, which often rely on fixed-time plans or rudimentary vehicle detection systems. These approaches can lead to suboptimal green time allocation, resulting in inefficient traffic management and increased vehicle delays.The integration of LiDAR sensors provides detailed information on vehicle queues, arrival rates, and vehicle types. The research presents a practical framework for green time allocation optimization, considering factors such as intersection geometry, traffic volumes, and signal coordination. An intelligent control algorithm was developed that uses LiDAR data to determine the optimal green time for a specific phase, thereby reducing unnecessary waiting times and enhancing intersection efficiency. The effectiveness of the proposed LiDAR-based green time allocation strategy is demonstrated through extensive field tests. The results indicate significant improvements in intersection throughput, reduced delays, and enhanced traffic safety. In conclusion, this research highlights the transformative potential of LiDAR sensor technology in traffic signal control, specifically in the context of optimizing green time allocation. The findings support the notion that adaptive and data-driven strategies, when integrated with LiDAR sensors, can contribute to more efficient, sustainable, and safe urban traffic management. This research aims to provide valuable insights for transportation engineers, policymakers, and researchers seeking innovative solutions for modern urban traffic control.

The alteration of natural land cover to impervious surfaces during development increases stormwater runoff. Stormwater Control Measures (SCMs) are used to manage water quantity and enhance water quality by restoring the hydrologic cycle altered by development. Often, SCMs have an outflow pipe to handle overflows or to manage the release of water detained when infiltration is not possible. Traditionally, these are static controls (e.g. a small orifice is used to restrict the volume of outflow), however, these systems can be improved by instituting real-time controls (RTC). RTC improve the functionality of SCMs by dynamically controlling outflows to adjust to environmental conditions. A major impediment to the widespread implementation of RTC is the high cost of installation and operation. This study utilized machine learning methods to develop a forecasting approach for the implementation of low-cost RTC that were implemented on a programmable gate of the outlet structure of a multi-stage basin in southeastern Pennsylvania. The goals were to decrease the peak flow exiting the basin during rain events, increase the volume of water detained, decrease the number of overtopping events, maintain healthy vegetation in the basin, and protect the downstream vegetation from erosion. Multiple popular data science algorithms were evaluated including multiple linear regression and long short-term memory. These algorithms were used with a dataset, which consisted of four years of historical sensor data, collected in 5-minute intervals, to train models to predict water levels to optimize operations. The accuracy of 30 models with three different methods of handling missing values were compared. A long short-term memory model configured with a 30-minute lead time produced the best results. Having an approximate same lag time of 30 minutes for the contributing drainage area of the SCM provided a sufficient RTC functioning period to improve the performance of the outlet structure.

Time series data are significant and are derived from temporal data, which involve real numbers representing values collected regularly over time. Time series have a great impact on many types of data. However, time series have anomalies. We introduce hybrid algorithm named novel matrix profile (NMP) to solve the all-pairs similarity search problem for time series data. The proposed NMP inherits the features from two state-of-the art algorithms: similarity time-series automatic multivariate prediction (STAMP), and short text online microblogging protocol (STOMP). The proposed algorithm caches the output in an easy-to-access fashion for single- and multidimensional data. The proposed NMP algorithm can be used on large data sets and generates approximate solutions of high quality in a reasonable time. The proposed NMP can also handle several data mining tasks. It is implemented on a Python platform. To determine its effectiveness, it is compared with the state-of-the-art matrix profile algorithms i.e., STAMP and STOMP. The results confirm that the proposed NMP provides higher accuracy than the compared algorithms.

The futures market plays a significant role in hedging and speculating by investors. Although various models and instruments are developed for real-time trading, it is difficult to realize profit by processing and trading a vast amount of real-time data. This study proposes a real-time index futures trading strategy that uses the pattern of KOSPI 200 index futures time series data. We construct a pattern matching trading system (PMTS) based on a dynamic time warping algorithm that recognizes patterns of market data movement in the morning and determines the afternoon's clearing strategy. We adopt 13 and 27 representative patterns and conduct simulations with various ranges of parameters to find optimal ones. Our experimental results show that the PMTS provides stable and effective trading strategies with relatively low trading frequencies. Investor communities that have sustained financial markets are able to make more efficient investments by using the PMTS. In this sense, the system developed in this paper is a sustainable investment technique and helps financial markets achieve efficient sustainability.

Markov chain Monte Carlo sampling propagators, including numerical integrators for stochastic dynamics, are central to the calculation of thermodynamic quantities and determination of structure for molecular systems. Efficiency is paramount, and to a great extent, this is determined by the integrated autocorrelation time (IAcT). This quantity varies depending on the observable that is being estimated. It is suggested that it is the maximum of the IAcT over all observables that is the relevant metric. Reviewed here is a method for estimating this quantity. For reversible propagators (which are those that satisfy detailed balance), the maximum IAcT is determined by the spectral gap in the forward transfer operator, but for irreversible propagators, the maximum IAcT can be far less than or greater than what might be inferred from the spectral gap. This is consistent with recent theoretical results (not to mention past practical experience) suggesting that irreversible propagators generally perform better if not much better than reversible ones. Typical irreversible propagators involve a parameter controlling the mix of ballistic and diffusive movement. To gain insight into the effect of the damping parameter for Langevin dynamics, its optimal value is obtained here for a multidimensional quadratic potential energy function.

The continuous flowing spacetime forms a spacetime group G, one of its fundamental groups is the Poincare group PO(1,3), and the matter and interaction fields are representations of its intrinsic spacetime group. As a kind of quantized space-time unit, space-time group elements generate both space-time manifolds and matter. Matter and fields are aggregates of the quantum space-time within them and determine their type: the Lorentz group SO(1,3) represents a rotating spacetime corresponding to visible matter and the translation group P^1,3 represents a translational spacetime corresponding to dark matter and dark energy. The aggregation mode of space-time degrees of freedom in matter reveals that charge conjugation symmetry is the inverse symmetry of internal time of charged particles, and the external parity breaking of neutrinos is also due to their internal spatial aggregation mode.

Our main goal is here to make a comparative analysis between the well-known MOND theory and a more recent model called κ-model. An additional connection, between the κ-model and two other novel MOND-type theories: Newtonian Fractional-Dimension Gravity (NFDG) and Refracted Gravity (RG), is likewise presented. All these models are built to overtake the DM paradigm, or at least to strongly reduce the dark matter content. Whereas they rely on different formalisms, however, all four seem to suggest that the universal parameter, a0, appearing in MOND theory could intrinsically be correlated to either the sole baryonic mean mass density (RG and κ-model) and/or to the dimension of the object under consideration (NFDG and κ-model). We could then confer to the parameter a0 a more flexible status of multiscale parameter, as required to explain the dynamics together in galaxies and in galaxy clusters. Eventually, the conformal gravity theory (CFT) also seems to have some remote link with the κ-model, even though the first one is an extension of general relativity, and the second one is Newtonian in essence. The κ-model has been tested on a small sample of spiral galaxies and in galaxy clusters. Now we test this model on a large sample of galaxies issued from the SPARC database.

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.