Let g be a strictly increasing function on $\left(a,b\right),$ having a continuous derivative g′ on $\left(a,b\right).$ For the Lebesgue integrable function $f:\left(a,b\right)\to \mathbb{C}$ , we define the k-g-left-sided fractional integral of f by $S_{k,g,a+}f\left(x\right)={\int }_a^{x}k\left(g\left(x\right)-g\left(t\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in \left(a,b\right]$ and the k-g-right-sided fractional integral of f by $S_{k,g,b-}f\left(x\right)={\int }_x^{b}k\left(g\left(t\right)-g\left(x\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in [a,b),$ where the kernel k is defined either on $\left(0,\infty \right)$ or on $\left[0,\infty \right)$ with complex values and integrable on any finite subinterval. In this paper we establish some Ostrowski and trapezoid type inequalities for the k-g-fractional integrals of functions of bounded variation. Applications for mid-point and trapezoid inequalities are provided as well. Some examples for a general exponential fractional integral are also given.

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

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

This paper deals with the analysis of trends in road accidents on major highways in Brazil. Using updated time series techniques, our results indicate that a low degree of long memory was detected in the series with shocks having transitory effects over time. We further find that the number of accidents taking place in Brazil has been reducing over time, though in the presence of negative shocks, the recovery is not going to be immediate due to the long memory nature of the data. Despite the absence of relevant investment relating to infrastructure expansion, it is worth mentioning the consolidation of a nationwide tolled road system in Brazil involving concessions to private administrators, alongside more severe traffic laws that can impose limitations on driving licences.

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

Integrating nanomaterials like carbon nanotubes (CNTs) and iron oxide (Fe₃O₄) into epoxy composites has significant interest due to their potential to enhance mechanical properties. This study evaluates the impact of dispersion quality on the mechanical performance of CNT/Fe₃O₄/Epoxy composites, comparing stirring and sonication methods at three different loadings: 0.1, 0.3, and 0.5 wt.%. Tensile testing revealed that sonicated composites consistently outperformed stirred composites, with a significant increase in elastic modulus and ultimate tensile strength (UTS). However, fracture strain decreased in both composite types compared to pure epoxy, with sonicated composites experiencing a more significant reduction than stirred composites. These results underscore the importance of high-quality dispersion for optimizing mechanical properties.

Refractive index measurements have been an important task for a long time because that index plays an essential role in describing the optical properties of a material. Many methods have been developed to perform that task. Some of them use interferometry to achieve high precision, however these configurations are complicated. Some measure the critical angle using simple structures, but the accuracy is not satisfactory because it is difficult to judge the exact critical angle with intensity variations. Here we propose several new schemes based on measuring the polarization change in the total internal reflection. The proposed method has the merits of simple structure and easy incident angle determination that gives the maximum phase change. Additionally, it is possible to find the material dispersion by measuring the wavelength dependence of the polarization ellipticity. Some useful formulas relating the refractive index with the maximum phase change are obtained. This work can provide valuable alternatives for index measurement.

This paper aims to search for lump waves in a spatial symmetric (2+1)-dimensional dispersive wave model. Through an ansatz on positive quadratic functions, we conduct symbolic computations with Maple to generate lump waves for the proposed nonlinear model. A line of critical points of the lump waves is computed, whose two spatial coordinates travel at constant speeds. The corresponding maximum and minimum values are evaluated in terms of the wave numbers, and interestingly, all those extreme values do not change with time, either. The last section is the conclusion.

Guided ultrasonic waves are suitable for use in the context of structural health monitoring of thin-walled, plate-like structures. Hence, observing the wave propagation in the plates can provide an indication of whether damage has occurred in the structure. In this work, the wave propagation in fiber metal laminate consisting of thin steel foils and layers of carbon fiber-reinforced polymer is studied, focusing on the main propagation characteristics like dispersion diagrams and displacement fields. For this purpose, the dispersion diagrams derived from the analytical framework and numerical simulations are first determined and compared to each other. Next, the displacement fields are computed using the global matrix method for two excitation frequencies. The results derived from the analytical framework is used to validate numerically determined displacement fields based on a 2D and a 3D modeling approach. For both investigations the results of the analytical treatment and the numerical simulation show good agreement. Furthermore, the displacement field reveals the typical and well-known characteristics of the propagation of guided waves in thin-walled structures. Since the use of full 3D models involves a very high computational cost, this work also successfully investigates the possibility for model order reduction to decrease the computational time and costs of the simulation without the loss of accuracy.

A brief review of the history of the problem is intended to trace the progress in the development of scientific views on the structure of water. The discoveries in this area made in the first half of the last century are considered in comparison with modern data. It is shown that due to the de facto ban on the study of the structure of water in 1971, work in this direction was frozen for a long time. The paradox is that many forgotten truths have been independently "rediscovered" in our time, which speaks of their authenticity. On the basis of scientific literature and their own research, the authors come to the conclusion that water under room conditions is a microdispersed system, one phase of which is represented by continuous water, and the other - by polywater, discovered in the 70s of the last century.

Long-term continuous time series of SO2 emissions are considered critical elements of both volcano monitoring and basic research into processes within magmatic systems. One highly successful framework for computing these fluxes involves reconstructing a representative time-averaged SO2 plume from which to estimate the SO2 source flux. Previous methods within this framework have used ancillary wind datasets from reanalysis or numerical weather prediction (NWP) to construct the mean plume and then again as a constrained parameter in the fitting. Additionally, traditional SO2 datasets from ultraviolet (UV) sensors lack altitude information which must be assumed to correctly calibrate the SO2 data and to capture the appropriate NWP wind level which can be a significant source of error. We have made novel modifications to this framework which do not rely on prior knowledge of the winds and therefore do not inherit errors associated with NWP winds. To perform the plume rotation, we modify a rudimentary computer vision algorithm designed for object detection in medical imaging to detect plume-like objects in gridded SO2 data. We then fit a solution to the general time-averaged dispersion of SO2 from a point source. We demonstrate these techniques using SO2 data generated by a newly developed probabilistic layer height and column loading algorithm designed for the Cross-track Infrared Sounder (CrIS), a hyperspectral infrared sensor aboard the Joint Polar Satellite System’s Suomi-NPP and NOAA-20 satellites. This SO2 data source is best suited to flux estimates at high-latitude volcanoes and at low-latitude, but high-altitude volcanoes. Of particular importance, IR SO2 data can fill an important data gap in the UV-based record: estimating SO2 emissions from high-latitude volcanoes through the polar winters when there is insufficient solar backscatter for UV sensors to be used.

Scattering of elastic waves in heterogeneous media has become one of the most important problems in the field of wave propagation due to its broad applications in seismology, natural resource exploration, ultrasonic nondestructive evaluation and biomedical ultrasound. Nevertheless, it is one of the most challenging problems because of the complicated medium inhomogeneity and the complexity of the elastodynamic equations. A widely accepted model for the propagation and scattering of elastic waves, which properly incorporates the multiple scattering phenomenon and the statistical information of the inhomogeneities is still missing. In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation under the first-order smoothing approximation. The model establishes an accurate quantitative relation between the microstructural properties and the coherent wave propagation parameters and can be used for characterization or inversion of microstructures. Starting from the elastodynamic differential equations, a system of integral equation for the Green functions of the heterogeneous medium was developed by using Green’s functions of a homogeneous reference medium. After properly eliminating the singularity of the Green tensor and introducing a new set of renormalized field variables, the original integral equation is reformulated into a system of renormalized integral equations. Dyson’s equation and its first-order smoothing approximation, describing the ensemble averaged response of the heterogeneous system, are then derived with the aid of Feynman’s diagram technique. The dispersion equations for the longitudinal and transverse coherent waves are then obtained by applying Fourier transform to the Dyson equation. The exact solution to the dispersion equations are obtained numerically. To validate the new model, the results for weak-property-fluctuation materials are compared to the predictions given by an improved weak-fluctuation multiple scattering theory. It is shown that the new model is capable of giving a more robust and accurate prediction of the dispersion behavior of weak-property-fluctuation materials. Numerical results further show that the new model is still able to provide accurate results for strong-property-fluctuation materials while the weak-fluctuation model is completely failed. As applications of the new model, dispersion and attenuation curves for coherent waves in the Earth’s lithosphere, the porous and two-phase alloys, and human cortical bone are calculated. Detailed analysis shows the model can capture the major dispersion and attenuation characteristics, such as the longitudinal and transverse wave Q-factors and their ratios, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and even the disappearance of coherent waves. Additionally, it helps gain new insights into a series of longstanding problems, such as the dominant mechanism of seismic attenuation and the existence of the Mohorovičić discontinuity. This work provides a general and accurate theoretical framework for quantitative characterization of microstructures in a broad spectrum of heterogeneous materials and it is anticipated to have vital applications in seismology, ultrasonic nondestructive evaluation and biomedical ultrasound.

Abstract: The air pollution dispersion modelling via spatial analyses (Land Use Regression – LUR) is an alternative approach to the air quality assessment to the standard air pollution dispersion modelling techniques. Its advantages are mainly much simpler mathematical apparatus, quicker and simpler calculations and a possibility to incorporate other factors affecting pollutant’s concentration. The goal of the study was to model the PM10 particles dispersion modelling via spatial analyses v in Czech-Polish border area of Upper Silesian industrial agglomeration and compare results with results of the standard Gaussian dispersion model SYMOS’97. Results show that standard Gaussian model with the same data as the LUR model gives better results (determination coefficient 71% for Gaussian model to 48% for LUR model). When factors of the land cover and were included into the LUR model, the LUR model results were significantly improved (65% determination coefficient) to the level comparable with Gaussian model. The hybrid approach combining the Gaussian model with the LUR gives superior quality of results (65% determination coefficient).

It is currently difficult to obtain accurate fine dust information in residential areas due to the insufficient number of air quality monitoring systems and spatial imbalances. Therefore, a detailed particulate matter dispersion model including factors such as land use and meteorological information was developed in this study and used to create fine dust concentration distribution maps. The fine dust concentration distribution maps currently available to citizens were compared with those obtained by dispersion modeling, and population distribution data were employed to compare the populations exposed to fine dust according to the two methods. The results of the existing method and the developed particulate matter dispersion model differed significantly. For instance, the PM2.5 concentrations in Daejeon, South Korea, on February 17, 2018, were 56% “Good” and 44% “Moderate,” according to the existing method, while they were 31% “Good,” 26% “Moderate,” 28% “Unhealthy,” and 15% “Very Unhealthy,” according to the dispersion model. Furthermore, the existing method indicated that no portion of the population was exposed to poor fine dust concentrations, while the proposed model revealed that over 170 thousand people were exposed to such concentrations. These results on fine dust distributions will contribute to sustainable urban and environmental planning.

Since fine powders tend strongly to adhesion and agglomeration, their processing with conventional methods is difficult or impossible. Typically, in order to enable the handling of fine powders, chemicals are added to increase the flowability and reduce adhesion. This contribution shows that instead of additives also vibrations can be used to increase the flowability, to reduce adhesion and cohesion, and thus to enable or improve processes such as precision dosing, mixing, and transport of very fine powders. The methods for manipulating powder properties are described in detail and prototypes for experimental studies are presented. It is shown that the handling of fine powders can be improved by using low-frequency, high-frequency or a combination of low- and high-frequency vibration.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

New exact solutions to conformable time fractional EW and modified EW equations are constructed by using Sine-Gordon expansion approach. The fractional traveling wave transform and homogeneous balance have significant roles in the solution procedure. The predicted solution is of the form of some finite series of multiplication of powers of cos and sin functions. The relation among trigonometric and hyperbolic functions in sense of Sine-Gordon expansion gives opportunity to construct the solutions in terms of hyperbolic functions.

Spray technology is widely used in various industries, including medicine, food production, mechanical engineering, and nanopowder manufacturing. Achieving high dispersion and a narrow particle size distribution is crucial for many applications. Ultrasonic spraying is commonly used to achieve this. On other hand, hydraulic nozzles provide high atomization performance. Combining these two technologies promises to offer significant benefits, but the complex processes that occur simultaneously in such a device require careful study. This work proposes a fundamental design for an acoustic-hydraulic nozzle and investigates the physical processes when a liquid is sprayed using this nozzle, both theoretically and experimentally. The study identifies the critical modes of spraying and confirms that the simultaneous use of ultrasound and hydraulic pressure can produce a fine spray (droplet size less than 50 μm) with high productivity (5-10 ml/s). This approach has significant potential for modern industries and technologies.

In natural, laboratory and industrial conditions, the density of a fluid or gas, depending on temperature, pressure, concentration of dissolved substances or suspended particles, changes under the influence of a large number of physical factors. We assume that undisturbed liquid is stratified. The analysis is based on a system of fundamental equations for the transfer of energy, momentum and matter in periodic flows of a viscous compressible fluid. The propagation of periodic flows in viscous uniformly stratified fluids is considered. Taking into account the compatibility condition, dispersion relations are constructed for two-dimensional internal, acoustic and surface linear disturbances with a positive definite frequency and complex wave number in a compressible viscous fluid exponentially stratified by density. The temperature conductivity and diffusion effects are neglected. The obtained regularly perturbed solutions to the equations describe weakly damped waves. Singular solutions characterize the thin ligaments that accompany each type of wave. In limiting cases, the constructed solutions transform into known expressions for a viscous homogeneous and ideal fluid or degenerate.

Background. COVID-19 efforts were often ineffective in controlling the spread of the pandemic. Identifying ineffective controls during a pandemic is thus vital. Method. Utilizing publicly available data on COVID deaths in the counties of US states, we create an index to capture and interpret ineffectiveness in the efforts to reduce the spread of the pandemic in US counties. This index is based on the Intervened Poisson Distribution (IPD) introduced originally by Shanmugam. Motivation for the research idea occurred while we noticed the data dispersion of the COVID deaths is smaller than the average only in some counties. Under-dispersed data is common in statistical modeling. A novel approach we adapted in this article includes the estimation of an intervention parameter estimated through iterative non-linear optimization. Results. Twenty-five counties in California, Idaho, Minnesota, Mississippi, Montana, Nebraska, North Carolina, North Dakota, Texas, and Utah were found to be ineffective in controlling for fatalities based on the expected probability distribution. A review of the policies enacted in these areas would provide insight into ineffective prevention efforts, and some of these issues are documented in current literature. Conclusion. The IPD index an innovate way to document efficacy of interventions during pandemics. The IPD may identify ineffective efforts prior to statistical models intended to evaluate efficacy of efforts.

The density functional theory was used to explore the structural, electronic, dynamical, and thermoelectric properties of a VIrSi Half-Heulser (HH) alloy. The minimum lattice constant of 5.69 ( ̊A) was obtained for VIrSi alloy. Besides, the band structure and the projected density of states for this HH alloy were calculated, and the gap between the valence and conduction bands was noted to be 0.2 eV. Also, the quasi-harmonic approximation was used to predict the dynamical stability of the VIrSi HH alloy. At 300 K, the Seebeck Coefficient of 370 and -270 μV.K−1., respectively, was achieved for the p and n-type doping. From the power factor result, the highest peak of 18 X 1011W/cm.K2 is obtained in the n-type doping. The Figure of Merit (ZT) result revealed that VIrSi alloy possesses a high ZT at room temperature, which would make VIrSi alloy applicable for thermoelectric performance.

Melt mixing is a convenient method to prepare polymer nanocomposites, but the extent of the dispersion of the solid filler reached is often limited, and may compromise the anticipated performance of these materials during service. Since the efficiency of extensional flows on dispersion is now well recognized, several mixers were designed with the aim of inducing both shear and extensional flow components. This work combines experimental and numerical data to better understand the kinetics of the dispersion of graphite nanoplates in a polypropylene melt, using a mixing device that consists of a series of stacked rings with equal outer diameter and alternating larger and smaller inner diameters, thus creating a series of converging/diverging flows. Numerical simulation of the flow using the opensource OpenFOAM software assuming both inelastic and viscoelastic responses predicted the velocity, streamlines, flow type and shear and normal stress fields for the mixer. Experimental and computed data were combined to determine the trade-off between the local degree of dispersion of the PP/GnP nanocomposite, measured as Area ratio, and the absolute average value of the hydrodynamic stresses multiplied by the local cumulative residence time. From considerations based on a theoretical approach to dispersion, the cohesive strength of the GnP agglomerates studied was estimated to be in the range 3 - 10kPa.

The wave packet consisting of two harmonic plane waves with the same frequencies, but with different wave vectors is considered. The dispersion relation of a packet is structurally similar to the dispersion relation of a relativistic particle with a nonzero rest mass. The possibility of controlling the group velocity of a quasi-monochromatic wave packet by varying the angle between the wave vectors of its constituent waves is discussed.

Pharmaceuticals contain biologically active components that can pollute water courses as a result of the excretions from individuals and/or uncontrolled release of residues from chemical plants, and they can pose a hazard to health. Pharmaceutical residues can persist at low concentrations in the environment, and thus may be potentially harmful to aquatic animals and to humans. Controlling and monitoring such residues are therefore a prime interest, for example, a solid-phase extraction uses solid sorbents to purify and preconcentrate the residues prior to their chemical analysis. In the present study, poly (acrylonitrile-co-divinylbenzene-80) sorbents are synthesised by varying the comonomer feed ratios under precipitation polymerisation conditions to deliver a family of porous polymer microspheres. Acrylonitrile confers polar characters onto the sorbents, and the acrylonitrile-derived nitrile groups can be chemically transformed via polymer-analogous reactions into thioamide and sulfonated residues which make the sorbents even more suitable for the capture of polar analytes, including selected pharmaceuticals. The utility of the porous thioamide-sulfonated containing sorbents is demonstrated via the dispersion-solid phase extraction of mefenamic acid from aqueous media; mefenamic acid is an anthranilic acid derivative which is a potent, non-steroidal anti-inflammatory drug which is found in environmental waters at low concentrations.

Extraction of high-resolution surface waves is essential in surface-wave survey. Because reflections usually interfere with surface waves on X component in a multicomponent seismic exploration, it is difficult to extract dispersion curves of surface waves. The situation goes more serious when the frequencies and velocities of higher-mode surface waves are close to those of PS-waves. A method for surface-wave extraction is proposed based on the morphological differences between reflections and surface waves. Frequency-domain high-resolution linear Radon transform (LRT) and time-domain high-resolution hyperbolic Radon transform (HRT) are used to represent surface waves and reflections respectively. Then, the sparse representation problem based on the morphological component analysis (MCA) is built and optimally solved to obtain high-fidelity surface waves. An advantage of our method is its ability to extract surface waves when their frequencies and velocities are close to those of reflections. Furthermore, results of synthetic and field examples confirm that the proposed method can attenuate the distortion of surface-wave dispersive energy caused by reflections, which contributes to extracting accurate dispersion curves.

The sustainability of irrigated agriculture depends on the quality of irrigation water used. The electrolyte concentration (EC) of irrigation water may lead to the accumulation of salts in the root zone layers and affect the physiological functions of the crop by osmotic and ion toxicity effects. Further, the cationic and anionic composition of the water may alter the exchangeable cation composition of the soil and as well as its pH. Because of the dominance of sodium salts in many sources of irrigation water, parameters related to sodium such as exchangeable sodium percentage (ESP) of soils and sodium adsorption ratio (SAR) of soil solutions have been commonly used to study the effects of sodium in irrigation water on soil structural stability. Quirk and Schofield concept of ‘threshold electrolyte concentration’ (TEC) has shown the importance of electrolytes in preventing the effects of sodium on soil structure. Based on this concept, several models have been proposed to relate ESP or SAR with EC to predict the possible impacts of irrigation water on soil structural stability. However, many research reports indicate that this relationship varies with soils and a given model is not suitable for all types of soils. Further, the effects of potassium and magnesium in the processes leading to clay dispersion are disregarded in these models. This essay analyses all the factors involved in the structural failure of soils with different cationic composition, identify the defects in these TEC models and re-defines TEC on the basis of new insights on dispersive and flocculating charges of soils. This review does not deal with EC effects on crops and also the role of contaminant ions not involved with soil structural stability.

The precise prediction of air contaminant dispersion is essential to the air quality monitoring and the emergency management of the contaminant gases leakage incidents in the chemical industry park. The conventional atmospheric dispersion models can seldom give precise prediction due to inaccurate input parameters. In order to improve the prediction accuracy of dispersion model, two data assimilation methods (i.e. one is merely based on the typical particle filter while the other is a combination of particle filter and expectation-maximization algorithm) are proposed to assimilate the UAV observations into the atmospheric dispersion model. Two emission cases are taken into consideration, the difference between which is the different dimensions of state variables. To test the performances of the proposed methods, experiments corresponding to the two emission cases are designed and implemented. The results show that the particle filter can effectively estimate the model parameters and improve the accuracy of model prediction when the dimension of state variables is low. In contrast, when the dimension of state variables becomes higher, the method of particle filter combining expectation-maximization algorithm performs better in the parameter estimation accuracy and warm-up time. Therefore, the data assimilation methods are able to effectively support the air quality monitoring and emergency management in chemical industry parks.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

Objective: This study aimed to demonstrate the availability of portable devices for nasal FeNO measurement, which could replace exhaled NO measurement based on the continuous aspiration of multiple flow measurement systems. Methods: A descriptive cross-sectional study. The healthy subjects without rhinosinusis disorders (control group) and those with diagnosed allergic rhinitis (AR group) were enrolled in the study. They underwent nasal and bronchial FeNO measurements by both fixed flow NObreath® connected to nasal mask and multiple flows HypAir FeNO®. Results: A total of 153 people were recruited including 63 healthy subjects and 90 subjects with AR. There were no statistically significant differences in anthropometric characteristics between the two groups (P > 0.05). There were a significant increase in FeNO values in the AR group compared to the control group; concentrations of nasal and bronchial FeNO mearsured by NObreath® were 76.0 ± 50.7 ppb (vs 36.0 ± 28.1 ppb, P < 0.01) and 32.3 ± 15.4 ppb (vs 9.2 ± 5.6 ppb, P < 0.001), and those mearsured by NObreath® Hypair FeNO® were 1796.9 ± 523.3 ppb (vs 400.2 ± 123.1 ppb, P < 0.001) and 37.3 ± 23.0 ppb (vs 17.4 ± 18.3 ppb, P < 0.01). A weak correlation between the values measured by NObreath® and Hypair FeNO® devices was observed (r = 0.023 and r = 0.089, respectively; p < 0.05). Conclusions: The handheld NObreath® device is effective in measuring FeNO concentrations in both normal subjects and AR patients. The advantages in price and size, creating a compact, low-cost device that is convenient for use and research.

Micro and small wood-processing enterprises represent the heart of the European forest-based industries, being among the key drivers of economic growth in rural, mountainous, and poor regions. Their economic efficiency is of fundamental importance for their existence and the pro-vision of income for the local population in rural areas. Data Envelopment Analysis (DEA) is nonparametric, linear-programming-based approach, commonly used to analyse the efficiency of organizational units. This method allows estimating the economic efficiency of a certain eco-nomic system without assumptions about the functional form between resources and products. Furthermore, DEA determines the efficiency frontier and gives results of whether an enterprise, i.e., a Decision Making Unit (DMU) is efficient or not. The main objective of this study was to investigate and evaluate the economic efficiency of micro and small wood-processing enterpris-es in the EU countries and reveal the hidden inputs that facilitate efficiency generation. The eco-nomic efficiency evaluation was carried out on the basis of the official statistical data for the mi-cro and small wood-processing companies in the EU member states for the period 2015-2020 by performing a two-stage DEA analysis. The data used were standardized by value per employee. In addition to the first stage of DEA, fractional regression probit and logit models with four contextual variables were used to reveal the influence of the hidden inputs in the model. The results showed that the micro and small wood-processing enterprises can be regarded as more scale-efficient than technically-efficient entities. The only contextual variable affecting the eco-nomic efficiency was Investments per Person Employed, improving the efficiency by 2% per 1% increase of the investments.

This article introduces a new fractional approach to the concept of information dimension of complex networks, based on a (q,q′)-entropy proposed in the literature. The q parameter measures how far is the number of subsystems (for a given size ε) from the mean number of overall sizes. The q′ (interaction index) measures when the interactions between subsystems are greater (q′&gt;1), lesser (q′&lt;1) or equal to the interactions into these subsystems. The computations of the proposed information dimension are carried out on several real-world and synthetic complex networks. The results from the proposed information dimension are compared with those from the information dimension based on the Shannon entropy.

COVID-19 outbreak started in the Chinese city of Wuhan and spread around the globe in months due to its high contagious level. Hence, this disease posed a great challenge to researchers and mathematicians. Numerous mathematical models have been suggested to visualize the spreading speed and trends of this pandemic. In this paper, a comparison of a widely established and accepted method, the Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP) model with a newly-proposed fractional-order SEIQRDP is studied. Densely populated Countries of Asia (Pakistan, India, and Bangladesh) have been chosen as data sets and both algorithms have been applied to their data. The same comparison technique has also been used on the data of two polar countries, New Zealand and Russia, that validated our findings. Error comparison of both algorithms has been recorded in a tabulated form which shows multi-fold erroneous trends over WHO data of selected countries.

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalization and deaths have been observed, and thousands of cases daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to understand the transmission of the disease better. Nonlocality involved in the model has made fractional differential equations appropriate for modeling the behavior. However, solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate (from exposed quarantine and recovered to susceptible and infected quarantined individuals), quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium analysis, and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam-Bashforth-Moulton method developed for the fractional order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19, especially quarantining exposed and infected individuals and the effective contact rate. Based on the results with different fractional order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is what is happening right now in many countries.

Complex models have received significant interest in recent years and are being increasingly used to explain the stochastic phenomenon with upward and downward fluctuation such as the stock market. Different from existing semi-variance methods in traditional integer dimension construction for two variables, this paper proposes a simplified multi-factorized fractional dimension derivation with the exact Excel tool algorithm involving the fractional center moment extension to covariance, which is a complex parameter average that is a multi-factorized extension to Pearson covariance. By examining the peaks and troughs of gold price averages, the proposed algorithm provides more insight into revealing underlying stock market trends to see who is the financial market leader during good economic times. The calculation results demonstrate that the complex covariance is able to distinguish subtle differences among stock market performances and gold prices for the same field that the two variable covariance may overlook. We take the London, Tokyo, Shanghai, Toronto and Nasdaq as the representative examples.

We investigated preschool-aged children’s understanding of early fractional tasks and how that performance correlates with fine motor skills and use of gestures while counting. Participants were 33 preschoolers aged 4 to 5 in two Southeastern public elementary schools. Children were tested individually in an interview-like setting. Mathematics tasks were presented in a paper and pencil format and the Grooved Pegboard test assessed fine motor skills. Finally, utilization of gestures was evaluated by taking a behavioral rating of the child’s hand morphology, accuracy of gestures, and synchrony of gestures and spoken word while performing a counting task. Results indicate performance on fractional reasoning tasks significantly predicts both fine motor ability and accuracy of gestures.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

The use of salt rock for underground radioactive waste disposal facilities requires a comprehensive analysis of creep-damage process in salt rock. A computer-controlled creep setup is employed to carry out a creep test of salt rock lasted as long as 359 days under a constant uniaxial stress. The AE space-time evolution and energy releasing characteristics during creep test are studied in the meantime. A new creep-damage model is proposed on the basis of fractional derivative by combining the AE statistical regularity. It indicates that the AE data in non-decay creep process of salt rock can be divided into three stages. Furthermore, the parameters of new creep-damage model are determined by Quasi-Newton method. The fitting analysis suggests that the creep-damage model based on fractional derivative in this paper provides a precise description of full creep regions in salt rock.

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

An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equation in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions.

The three dimensional conformable time fractional Kadomtsev-Petviashvili and the conformable time fractional modified Kawahara equations are solved by implementing the Kudryashov's procedure. The corresponding wave transformation reduces both equations to some ODEs. Balancing the nonlinear and the highest order derivative terms gives the structure of the solutions in the finite series form. The useful symbolic tools are used to solve the resultant algebraic systems. The solutions are expressed in explicit forms.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

The removal of chromium(VI) from acidic (HCl) medium through non-dispersive extraction with strip dispersion (NDXSD) was investigated using a microporous PVDF membrane support in a permeation cell. The ionic liquid Cyphos IL102 (phosphonium salt) in Solvesso 100 was used as organic phase. In NDXSD the stripping phase (NaOH) is dispersed in the organic phase in the cell side with an impeller stirrer adequate to form a strip dispersion. This pseudo-emulsion phase (organic + strip solutions) provides a constant supply of the Cyphos IL102/Solvesso 100 to the membrane phase. Various hydrodynamic and chemical parameters, such as variation in the feed and pseudo-emulsion stirring speeds, HCl and Cr(VI) concentrations in the feed phase, and carrier concentration, were investigated. From the experimental data, several mass transfer coefficients were estimated, as well as it was investigated the performance of the present system against other ionic liquids and the presence of base metals in the feed phase.

Theoretical studies on the generation of nondiffracting and nondispersive light pulses and their experimental implementation are one of the renowned problems within electromagnetics. Current technologies enable creation of short-duration pulses of a few cycles with high power and fluency. An application of these techniques to the field of nondiffracting and nondispersive pulses requires a proper mathematical description of highly focused vector pulses. In this work, we study vector optical bullets in a dielectric medium with different polarization structures: linear, azimuthal, and radial. We report the differences caused by the vector model compared to the scalar model. We analyze effects caused by superluminal, subluminal, or even negative group velocity on properties of vector optical bullets inside a dielectric material.

The jet-slit milk homogenizer is one of the most energy-efficient among all types of homogenizers in the dairy industry. The principle of its operation is based on the creation of a maximum speed difference between the fat globules of cream and the flow of skimmed milk. Reducing the specific energy consumption and finding the optimal parameters of the homogenizer were based on the results of both theoretical and experimental studies. The optimization criteria (decreasing specific energy consumption while maintaining high homogenization quality) were chosen to achieve a dispersion of 0.8 μm with minimal energy consumption. The parameters of the width of the ring gap, the fat content and the speed of the cream have been optimized. It is possible to reduce the specific energy intensity of the process to values of 0.88–0.92 kWh/t when using cream with a fat content of 33–43%, which should be fed through an annular gap with a width of 0.6–0.8 mm. Optimum values of the cream feed speed had been found, which should be equal to 7–11 m/s. The research results are of high practical value for the further development of the energy-efficient industrial model of a jet-slit homogenizer.

Mechanochemical technology is developing rapidly, judging by the scientific information in both basic and applied studies. However, many issues and points of view remain to be discussed. This review presents some new key issues for the optimization of mechanochemical processes in theoretical and practical aspects. Emphasis is placed on powder technology aspects, which are not always discussed compared to functional or microscopic viewpoints. The transfer of chemical species across the interparticle interface between organic and inorganic species during the mechanosynthesis of nanocomposite oxides offers many new possibilities, which are discussed here in detail. Since all material transport is preceded by charge transfer, its driving force has been searched for using terminology beyond the well-established electrochemical ones. The role of organic compounds during the whole process is emphasized, regardless of their survival in the final product. The similarity with the pharmaceutical phenomena is pointed out, although its mentality is very different from that of the synthesis of nanocomposites. Not only for the rational amorphization of the active pharmaceutical ingredient, but also for the stabilization of molecular dispersion states with the participation of excipients are discussed. The effects of liquids, either added or formed by mechanochemical auto-liquefaction, are presented with reference to the comparison between wet and dry grinding. Finally, mechanisms of apparent stabilization of mechanically activated states of products are elucidated to investigate the practical applicability of mechanochemically synthesized products

We evaluated the change in water dispersibility of lactic acid bacteria (LAB, Enterococcus faecalis KH2) upon powderization and its influence on their efficacy. When cultured LAB are washed, heat-killed, and powdered, adhesion between LAB occurs and they form aggregation (non-treated LAB, n-LAB). However, a dispersed LAB (d-LAB) powder with less aggregates can be prepared by treating them with a high-pressure homogenizer and adding an excipient during powdering. n-LAB or d-LAB was administered to mice and the Peyer's patches in the small intestine were observed. n-LAB administration showed a high amount of aggregated LAB drifting in the intestinal mucosa, whereas d-LAB reached the Peyer's patches and was taken up into the Peyer's patches. Evaluation in a mouse influenza virus infection model showed that d-LAB was more effective than n-LAB in influenza yield of bronchoalveolar lavage fluids (BALFs) on day 3 post-infection, neutralizing antibody titers of sera and influenza virus-specific IgA in the feces on day 14 post-infection. Thus, the physical properties of LAB affect their efficacy; controlling their water dispersibility can improve their effectiveness.

This article reveals a best possible design for hybrid dispersion compensating fiber (HyDCF) with high birefringence established on modified broadband compensating structure through S, C and L telecommunication bands. The simulation outcome exhibits relatively higher birefringence of 3.76×10-2 at wavelength of 1550 nm. The suggested fiber also has dispersion compensation characteristics in an inclusive series of wavelengths which covers 1400-1625 nm. The reported design can achieve dispersion quantity of – 606 ps/ (nm.km) at 1550 nm effective wavelength. The reported fiber design matches the relative dispersion slope (RDS) 0.003694 nm-1 similar to single mode fiber at 1550 nm operating wavelength. This fiber demonstrates negatively flattened effective dispersion of – 2.703 ± 0.734 ps/ (nm.km) within 180 nm flat band ranging from 1460-1640 nm wavelength. It is also convenient to optical high bit rate communication systems. The low confinement loss is found 3.756×10-10 dB/m at the operating wavelength. This design also achieves highly nonlinear coefficient of 50.34 W-1km-1. In some cases, it can also be used in sensing applications.

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

In the paper the new, fractional order, state space model of a heat transfer in a one- 1 dimensional metallic rod is addressed. The fractional orders of derivative along space and time 2 are not exactly known and they are described by intervals. The proposed model is the interval 3 expanding of the state space fractional model of the one dimensional heat transfer. It is expected to 4 better describe the reality because interval order of each real process is hard to estimate. Elementary 5 properties of the proposed model are analysed. Theoretical results are experimentally validated using 6 data from real experimental laboratory system.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

Natural vegetation restoration can take decades to achieve and requires information on species composition and trend to inform management strategies. Here we demonstrate the potential and portability of drone, dove and Sentinel-2 imagery for species level classification and trajectory monitoring using three study sites with different revegetation histories. Drone imagery (4 cm) was classified using random forests. Dove (3 m) and Sentinel-2 (10 m) images were acquired close to the anniversary of the drone flights and converted into fractional cover maps showing the proportion of exotics, natives and other land covers using ordinary least squares (OLS) and geographically weighted regression (GWR). The time series of fractional cover maps were converted into positive and negative slope and second-order curvature and summarised as one RGB composite to illustrate trend and observe exotic expansion. Drone classification accuracies ranged from 73%-76% when applied to the full plant species list and between 93% and 97% when grouped into natives, exotics, and other land covers. GWR outperformed OLS for all fractional cover mapping and GWR with dove imagery was more accurate than with Sentinel imagery. The combination of very high-resolution drone acquired imagery with the versatility of dove acquired imagery arms land managers with highly accurate species composition and their spatio-temporal dynamics to promote timely intervention.

We investigate the influence of a self-propelling, out-of-equilibrium active particle on generalized elastic systems, including flexible and semiflexible polymers, fluid membranes, and fluctuating interfaces, while accounting for long-ranged hydrodynamic effects. We derive the fractional Langevin equation governing the dynamics of the active particle, as well as that of any other passive particle (or probe) bound to the elastic system. Our study explores the diffusional behavior emerging for both the active particle and a distant probe.

Recently, Li et al [1] investigated the nonlinear Langevin equations existence including two fractional orders with infinite-point boundary conditions. It has shown that the outcomes given it does count on the solution form for which it has boundary values. It means that their solution needs more to be in the final step. In current work, we will have discussion about the existence and uniqueness for the same boundary conditions by investigating the closely explicit solution form that has no boundary values. Numerical example is supported to have more vision to compare the between new and previous results. It turns out that our results are superior.

We study the existence of positive solutions for a system of Hadamard fractional differential equations on an infinite interval with nonnegative nonlinearities, subject to coupled nonlocal boundary conditions which contain Hadamard fractional derivatives and Riemann-Stieltjes integrals. In the proof of the main results, we use the Guo-Krasnosel'skii fixed point theorem and the Leggett-Williams fixed point theorem.

Covid-19 is a lung disease caused by a Coronavirus family virus. Due to its extraordinary prevalence and death rates, it has spread quickly to every country in the world. Thus, achieving peaks and outlines and curing different types of relapses is extremely important. Given the worldwide prevalence of Coronavirus and the participation of physicians in all countries, Information has been gathered regarding the properties of the virus, its diverse types, and the means of analyzing it. Numerous approaches have been used to identify this evolving virus. It is generally considered the most accurate and acceptable method of examining the patient's lungs and chest through a CT scan. As part of the feature extraction process, a method known as fractional Fourier transform (FrFT) has been applied as one of the time-frequency domain transformations. The proposed method was applied to a database consisting of 2481 CT images. Following the transformation of all images into equal sizes and the removal of non-lung areas, multiple combination windows are used to reduce the number of features extracted from the images. In this paper, the results obtained for KNN and SVM classification have been obtained with accuracy values of 99.84% and 99.90%, respectively.

In this article we investigate the generalized Kawahara-KdV system. A new topological approach is applied to prove the existence of at least one classical solution and at least two nonnegative classical solutions. The arguments are based upon recent theoretical results.

The operation status of manufacturing equipment is directly related to the reliability of the operation of manufacturing equipment and the continuity of operation of the production system. Based on the analysis of the operation status of manufacturing equipment and its characteristics, it is proposed that the concept of assessing the operation status of manufacturing equipment can be realized by applying real-time acquisition of accurate inspection data of important parts of weak motion units and comparing them with their motion status evaluation criteria. Through the study of the application characteristics of fractional-order calculus theory, a differential data fusion model based on the fractional-order differential operator is established. The advantages of Internet of Things (IoT）technology and fractional order differential fusion algorithm are integrated to obtain real-time high-precision data of the operating parameters of manufacturing equipment, and the research objective of operating condition assessment of manufacturing equipment is realized. The feasibility and effectiveness of the method are verified by the application of the method in machining center operation status assessment.

The role of fractional calculus in circuit systems has received increased attention in recent years. In order to evaluate the effectiveness of time-domain calculation methods in the analysis of fractional-order piecewise smooth circuit systems, an experimental prototype is developed and the effects of three typical calculation methods in different test scenarios are compared and studied in this paper. It is proved that Oustaloup’s rational approximation method usually overestimates the peak-to-peak current and brings in pulse-voltage phenomenon in piecewise smooth test scenarios, while the results of two iterative recurrence-form numerical methods are in good agreement with the experimental results. The study results are dedicated to provide a reference for efficiently deploying calculation methods in fractional-order piecewise smooth circuit systems. Some quantitative analysis results are concluded in this paper.

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.

This study employs the FLACS code to analyze hydrogen leakage, vapor dispersion, and subsequent explosions. Utilizing pseudo-source models, a liquid pool model, and a hybrid model combining both, we investigate dispersion processes for varying leak mass flow rates (0.225 kg/s and 0.73 kg/s) in a large open space. We also evaluate explosion hazards based on overpressure and impulse effects on humans. The computational results, compared with experimental data, demonstrated reasonable hydrogen vapor cloud concentration predictions, especially aligned with the wind direction. For higher mass flow rate of 0.73 kg/s, the pseudo-source model and hybrid model proved appropriate, while the liquid pool model was more suitable for lower mass flow rate of 0.225 kg/s. Regarding explosion analyses using overpressure-impulse diagram, higher mass flow rates leaded to potentially fatal overpressure and impulse effects on humans. However, lower mass flow rates may cause severe eardrum damage at the maximum overpressure point.

In tire tread applications, achieving enhanced abrasion resistance, wet grip, and rolling resistance is crucial for optimizing overall performance. To realize improvements in these attributes for silica-filled tire tread compound, it becomes imperative to improve dispersity of silica filler with investigating the effect of each component in tire tread compound. In this work, we study the effect of styrene content within solution styrene butadiene rubber (SSBR) on the properties of tire tread compounds. A higher styrene segment within SSBR contributes to increased silica dispersion and crosslink density. Thus, tire tread compounds featuring SSBR with increased styrene content not only improve physical and mechanical properties but also enhance major characteristics tailored for tire tread applications. These findings provide valuable insights into advancing the reinforced performance of tire tread compounds through the strategic utilization of SSBR enriched in styrene content.

We consider the propagation of electromagnetic waves in the Friedman – Lemaître – Robertson – Walker metric. The exact solutions for plane and spherical wave are written down. The corresponding redshift, amplitude change, and dispersion are discussed. We also speculate about the connection of the electromagnetic wave equation to the Klein–Gordon equation.

This study aimed to develop chitosan-based apigenin spray dried solid dispersion using 1:1,1:1.5,1:2 w/w ratios. The results of process yield and drug assay were found to be (87.5%, 94.2%, and 95.86%), (95.2 ±1.34%), (99.5 ±0.85%), and (97.6 ±2.42%), respectively, for AC1, AC2, and AC3. Flow properties indicate the free flow of powders. FTIR revealed compatibility among chitosan and apigenin, and DSC and XRD showed prepared solid dispersion was on a molecular level and available in amorphous. In contrast, SEM images reflect irregular block and near-spherical shape elongated particles in the selected AC2. The antimicrobial examination reflects that AC2 was more effective against Gram-positive, negative, and fungal strains. AC2 SDSDs has more anti-oxidant property compared to pure flavonoid (AGN). Anti-proliferative activity against A549 lung cancer cell lines showed better anti-cancer activity by AC2 SDSDs. The selected AC2 SDSD filled in a 3D shell pill and further characterized for 3D shell pill for dissolution profiles and stability studies. The product has sustained release and similar release profiles after three months of storage. The findings suggest that the AC2 SDSDs may be a promising candidate for further development as a 3D printed drug delivery system for treating multiple disease conditions using model flavonoid- apigenin.

Seismic travel time tomography using surface waves is an effective tool for three-dimensional crustal imaging. Historically, these surface waves are the result of active seismic sources or earthquakes. More recently, however, also surface waves retrieved through the application of seismic interferometry are exploited. Conventionally, two-step inversion algorithms are employed to solve the tomographic inverse problem. That is, a first inversion results in frequency-dependent, two-dimensional maps of phase velocity, which then serve as input for a series of independent, one-dimensional frequency-to-depth inversions. As such, a two-dimensional grid of localized depth-dependent velocity profiles are obtained. Stitching these separate profiles together subsequently yields a three-dimensional velocity model. Relatively recently, a one-step three-dimensional non-linear tomographic algorithm has been proposed. The algorithm is rooted in a Bayesian framework using Markov chains with reversible jumps, and is referred to as transdimensional tomography. Specifically, the three-dimensional velocity field is parameterized by means of a polyhedral Voronoi tessellation. In this study, we investigate the potential of this algorithm for the purpose of recovering the three-dimensional surface-wave-velocity structure from ambient noise recorded on and around the Reykjanes Peninsula, southwest Iceland. To that end, we design a number of synthetic tests that take into account the station configuration of the Reykjanes seismic network. We find that the algorithm is able to recover the 3D velocity structure at various scales in areas where station density is high. In addition, we find that the standard deviation on the recovered velocities is low in those regions. At the same time, the velocity structure is less well recovered in parts of the peninsula sampled by fewer stations. This implies that the algorithm successfully adapts model resolution to the density of rays. Also, it adapts model resolution to the amount of noise on the travel times. Because the algorithm is computationally demanding, we modify the algorithm such that computational costs are reduced while sufficiently preserving non-linearity. We conclude that the algorithm can now be applied adequately to travel times extracted from (time-averaged) station-station cross correlations by the Reykjanes seismic network.

Is it possible to measure the dispersion of ex-ante chances (i.e. chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex-ante chances in various areas with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk to become ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk like the overwhelming majority of the population but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.

In this paper, design of optical spectral filters based on mode coupling of optical fibers is presented. The finite difference method is applied to find the dispersion characteristics of optical fiber coupler constructing from two fibers as a composite multi-dielectric waveguide with different cores but the same cladding. Also, the field distribution for both fibers as a separate and as a composite waveguide. The spectral characteristics of the filters are investigated depending on the coupling of two linear polarized modes LP01 and LP11. The dependence of the transmission coefficient on operating wavelengths is illustrated. Finally, the spectral bandwidth of filter as a function of the distance between the two cores is addressed.

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 &gt;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.

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.

Abstract: Composite sintered bodies comprising silicon dioxide (SiO2) nanoparticles dispersed in β-tricalcium phosphate (β-TCP) were prepared. The addition of nano-sized colloidal SiO2 to the β-TCP produced well-dispersed secondary phase nanoparticles that promoted densification by suppressing grain growth and increasing volume shrinkage of the sintered bodies. The SiO2 was found not to react with the β-TCP at 1120 °C and the substitution of silicon for phosphorous to produce a solid solution did not occur. This lack of a reaction is ascribed to the absence of avail-able calcium ions to compensate for the increase in charge associated with this substitution. The SiO2 nanoparticles were found to be present near the intersections of grain boundaries in the β-TCP. A β-TCP composite sintered body containing 4.0 wt% SiO2 exhibited a bending strength comparable to that of cortical bone and hence could potentially be used as a bone filling material.

Location-and-scale transformation of a random variable underpins normal distribution, but it is however fundamentally incorrect for scale estimation such as relative dispersion. In this paper, a parametrized alternative to a normal distribution, called scaloc-normal distribution, is proposed that efficiently works and is fundamentally correct with absolute and relative dispersion estimators. The Monte Carlos simulation experiment was used to generate a total of 600,000 artificial datasets in 600 different simulation scenarios from loc-normal (normal) and scaloc-normal distributions. The absolute and relative dispersion were estimated and compared from the two distributions. The results show that scaloc-normal distribution is a good parametrized alternative to loc-normal distribution, fundamentally correct and efficient with both standard deviation and coefficient of variation. The key statistical advancement from loc-normal to scaloc-normal distribution is its fundamental correctness (i.e., scale-invariant property) with an efficient relative estimator of dispersion (i.e., coefficient of variation). Parametrically, the loc-normal and scaloc-normal distributions are very different, but both have linear transformations.

Reactive transport (RT) couples bio-geo-chemical reactions and transport. RT is important to understand numerous scientific questions and solve some engineering problems. RT is highly multidisciplinary, which hinders the development of a body of knowledge shared by RT modelers and developers. The goal of this paper is to review the basic conceptual issues shared by all RT problems, so as to facilitate advance along the current frontier: biochemical reactions. To this end, we review the basic equations to point that chemical systems are controlled by the set of equilibrium reactions, which are easy to model, but whose rate is controlled by mixing. Since mixing is not properly represented by the standard advection-dispersion equation (ADE), we conclude that this equation is poor for RT. This leads us to review alternative transport formulations, and the methods to solve RT problems using both the ADE and alternative equations. Since equilibrium is easy, difficulties arise for kinetic reactions, which is especially true for biochemistry, where numerous frontiers are open (how to represent microbial communities, impact of genomics, effect of biofilms on flow and transport, etc.). We conclude with the basic 10 issues that we consider fundamental for any conceptually sound RT effort.

Intermetallic alloys like e.g. Iron-Aluminides, Titanium-Aluminides or Molybdenum- Silizides are prospective materials for high-temperature applications. For additive manufacturing (AM) intermetallic structural materials are particularly challenging due to their high melting points, oxygen susceptibility and low temperature brittleness. The feasibility of manufacturing intermetallic Mo-Si-B alloys with the laser additive manufacturing process of direct energy deposition (DED) is demonstrated and recent results in characterizing rapidly solidified material with respect to correlations between process, composition and microstructures are presented. The possibility to dope the material with Yttrium oxide (Y2O3) for dispersion is successfully demonstrated. Current challenges, e.g. homogenous distribution of alloying elements and applicability are addressed.

Downwind odor characteristics can be very different depending upon the size of the upwind point-source, interim topography, and wind conditions. At one extreme, the downwind odor plume from a relatively large, confined animal feeding operation (CAFO), located on a flat open plain and under stable, near-straight-line wind conditions can be rather broad, sustained and predictable relative to a fixed receptor site downwind. In contrast, the plume from a small point-source (e.g., a roof vent stack) located on irregular topography and under rapidly shifting wind conditions can be intermittent and fleeting. These transient odor events can be surprisingly intense and offensive, in spite of their fleeting occurrence and perception. This work reports on efforts to optimize an environmental odor sampling strategy, which is optimized for the challenges of (1) sampling of such transient odor 'spikes' and (2) the prioritization of odors/odorants from multiple, closely co-located point-sources, under such transient event conditions. Protocol refinement has emerged by way of 2 environmental odor assessment projects which have been undertaken on behalf of the Missouri Department of Natural Resources. The challenge of transient odor events has been mitigated utilizing rapid, odor cued whole-air grab capture sampling into metalized-FEP gas sampling bags, followed by immediate adsorption transfer onto SPME fibers or sorbent tubes for stabilization during the shipment and storage interval between collection and final analysis. Initial results demonstrated approximately 11 fold increases in target odorant yields for 900 mL sorbent tube transfers from 2-3 second 'burst' odor event bag-captures, as compared to equivalent direct collections at the same downwind receptor location but during perceived (stable) odor 'lull' periods. Results-to-date targeting refinement and field trials of this integrated environmental odor assessment strategy are presented. Preliminary application targeting general odor sampling and point-source differentiation utilizing tracer gases is also presented.

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

Snow cover products are primarily derived from the Moderate-resolution Imaging Spectrometer (MODIS) and Advanced Very High-Resolution Radiometer (AVHRR) datasets. MODIS achieves both snow/non-snow discrimination and snow cover fractional retrieval, while early AVHRR-based snow cover products only focused on snow/non-snow discrimination. The AVHRR Climate Data Record (AVHRR -CDR) provides a nearly 40-year global dataset that has a potential to fill a gap in long term snow cover fractional monitoring. Our study selects the Qinghai-Tibet Plateau as the experimental area, utilizing AVHRR-CDR surface reflectance data (AVH09C1) and calibrating with MODIS snow product MOD10A1. The snow cover percentage retrieval from the AVHRR dataset is performed using Surface reflectance at 0.64μm (SR1) and Surface reflectance at 0.86μm (SR2), along with a simulated Normalized Difference Snow Index (NDSI) model. Also, in order to detect the effects of land cover type and topography on snow inversion, we tested the accuracy of the algorithm with and without these influences, respectively (vanilla algorithm & improved algorithm). The accuracy of the AVHRR snow cover percentage data product is evaluated using MOD10A1、 ground snow-depth measurements and ERA5. Results indicate that the logic model based on NDSI has the best fitting effect, with R-square and RMSE values of 0.83 and 0.10, respectively. Meanwhile, the accuracy was improved after taking into account the effects of land cover type and topography. The model is validated using MOD10A1 snow-covered areas, showing snow cover area differences of less than 4% across 6 temporal phases. Improved algorithm results in better consistency with MOD10A1 than vanilla algorithm. Moreover, the RMSE reaches greater levels when the elevation is below 2,000 meters or above 6,000 meters, and is lower when the slope is between 16° and 20°. Using ground snow-depth measurements as ground truth, the multi-year recall rates are mostly above 0.7, with an average recall rate of 0.81. Results also show a high degree of consistency with ERA5. The validation results demonstrate that the AVHRR snow cover percentage remote sensing product proposed in this study exhibits high accuracy in the Tibetan Plateau region, also demonstrating that land cover type and topographic factors are important to the algorithm. Our study lays the foundation for the global snow cover percentage product based on AVHRR-CDR，furthermore lays a basic work for generating a long-term AVHRR-MODIS fractional snow cover dataset.