Class Of Derivatives Research Articles

The use patterns of novel psychedelics: experiential fingerprints of substituted phenethylamines, tryptamines and lysergamides

BackgroundNovel psychedelics (NPs) are an expanding set of compounds, presenting new challenges for drug policy and opportunities for clinical research. Unlike their classical derivatives, little is known regarding their use profiles or their subjective effects.AimsThe purpose of this study was to compile usage patterns and adverse event rates for individual NPs belonging to each of three main psychedelic structural families. Targeting the most widely used representatives for each class, we expanded on their phenomenological distinctions.MethodsA two-part survey was employed. We investigated the prevalence of novel phenethylamines, tryptamine and lysergamides in NP users (N = 1180), contrasting the type and incidence of adverse events (AEs) using a set of logistic regressions. Honing in on 2–4-Bromo-2,5-dimethoxyphenyl)ethanamine (2C-B) (48.6%), 1-propionyl-lysergic acid diethylamide (1P-LSD) (34.2%) and 4-Acetoxy-N,N-dimethyltryptamine (4-AcO-DMT) (23.1%), we examined their phenomenological separability using a gradient boosting (XGBoost) supervised classifier.ResultsNovel phenethylamines had the highest prevalence of use (61.5%) seconded by tryptamines (43.8%) and lysergamides (42.9%). Usage patterns were identified for 32 different compounds, demonstrating variable dosages, durations and a common oral route of administration. Compared to phenethylamines, the odds for tryptamines and lysergamides users were significantly less for overall physical AEs. No significant differences in overall psychological AEs were found. Overall model area under the curve (AUC) stood at 0.79 with sensitivity (50.0%) and specificity (60.0%) for 2C-B ranking lowest.ConclusionNP classes may hold distinct AE rates and phenomenology, the latter potentially clouded by the subjective nature of these experiences. Further targeted research is warranted.

Classical physics derivation of quantization of electron elliptical orbit in hydrogenlike atom

Classical physics derivation of quantization of electron elliptical orbit in hydrogenlike atom

Fractal fractional-order derivative for HIV/AIDS model with Mittag-Leffler kernel

In this paper, HIV/AIDS fractional-order model is studied. This epidemic phenomenon is analyzed using Caputo-Fabrizio and Fractal fractional derivative operator that includes an antiretroviral treatment compartment. The advanced approach is used for HIV/AIDS fractional-order model to get reliable outcomes with the help of sumudu transform. The fractional-order HIV/AIDS model is analyzed qualitatively as well as verify unique solutions. Numerical simulations are performed to explain the effects of changing the fractional-order and to support the theoretical results using proposed methods for a range of fractional orders. Also, the comparison has been made with classical order derivative to check the effectiveness of the proposed method for HIV/AIDS.

Classical physics derivation of quantization of electron elliptical orbit in hydrogenlike atom

Classical physics derivation of quantization of electron elliptical orbit in hydrogenlike atom

On the fractional order model for HPV and Syphilis using non–singular kernel

Most dynamical systems employ the classical integer-order derivatives which yield good results. However, recent trends have shown that the application of arbitrary order derivatives, popularly known as fractional order derivatives produces better and more realistic results to a given real life scenario because they are non-local operators. In this work, a fractional order co-infection model for human papilloma virus (HPV) and Syphilis is considered and studied using the non-singular kernel derivative. With the aid of Banach and Schauder’s fixed point theorems, the existence and uniqueness of the solution is proven. The conditions for the existence and uniqueness of the solution of the model are also established. The model’s disease free equilibrium (DFE) is shown to be locally asymptotically stable when the reproduction number is below one. The fractional order model is shown to be generalized Ulam Hyers–Rassias stable, under some conditions. The predictor–corrector method with convergence of min2,1+φ was used for the numerical simulations. Simulations of the model showed that the fractional derivative greatly influenced the dynamics of both diseases and their co-infection. Furthermore, it was observed that control strategy for single infection (syphilis only prevention strategy or HPV only prevention strategy) did not result in reduction of single infection cases, instead reduces the co-infection of new cases.

Certain New Models of the Multi-Space Fractal-Fractional Kuramoto-Sivashinsky and Korteweg-de Vries Equations

The main objective of this paper is to introduce and study the numerical solutions of the multi-space fractal-fractional Kuramoto-Sivashinsky equation (MSFFKS) and the multi-space fractal-fractional Korteweg-de Vries equation (MSFFKDV). These models are obtained by replacing the classical derivative by the fractal-fractional derivative based upon the generalized Mittag-Leffler kernel. In our investigation, we use the spectral collocation method (SCM) involving the shifted Legendre polynomials (SLPs) in order to reduce the new models to a system of algebraic equations. We then use one of the known numerical methods, the Newton-Raphson method (NRM), for solving the resulting system of the nonlinear algebraic equations. The efficiency and accuracy of the numerical results are validated by calculating the absolute error as well as the residual error. We also present several illustrative examples and graphical representations for the various results which we have derived in this paper.

Analytical model of inverse memelement with fractional order kinetic

AbstractIn this work, the analytical model of inverse memelement with fractional order kinetic has been proposed. The classical yet noncontroversial Caputo fractional derivative has been adopted for modeling such fractional order kinetic due to its simplicity yet accuracy. Based on the proposed model, the analysis of fractional order kinetic inverse memristor has been thoroughly performed where both nonperiodic and periodic excitations have been considered. Analytical formulations of the related parameters, for example, the rate of changes of inverse memristance, area of inverse memristance loop, and area of pinched hysteresis loop, and so on, have been performed. The extension of the proposed model to the fractional inverse memelement has been performed where the fractional inverse memristor has been analyzed. We have found that the inverse memristor still behaves in an opposite manner to the memristor even with the fractional order kinetic. All obtained results have been found to be intuitively applicable to any inverse memelement. The equivalent circuit models of both fractional inverse memristor and fractional inverse memelement have also been presented. This work provides a comprehensive understanding on both inverse memelement with fractional order kinetic and fractional inverse memelement. The realization of the emulator of such inverse memelement with fractional order kinetic and the fractional inverse memelement emulator has been found to be interesting opened research questions.

Analysis and dynamical behavior of a novel dengue model via fractional calculus

The infection of dengue is an intimidating vector-borne disease caused by a pathogenic agent that affects different temperature areas and brings many losses in human health and economy. Thus, it is valuable to identify the most influential parameters in the transmission process for the control of dengue to lessen these losses and to turn down the economic burden of dengue. In this research, we formulate the transmission phenomena of dengue infection with vaccination, treatment and reinfection via Atangana–Baleanu operator to thoroughly explore the intricate system of the disease. Furthermore, to come up with more realistic, dependable and valid results through fractional derivative rather than classical order derivative. The next-generation approach has been utilized to compute the basic reproduction number for the suggested fractional model, indicated by [Formula: see text]; moreover, we conducted sensitivity test of [Formula: see text] to recognize and point out the role of parameters on [Formula: see text]. Our numerical results predict that the reproduction number of the system of dengue infection can be controlled by controlling the index of memory. The uniqueness and existence result has been proved for the solution of the system. A novel numerical method is presented to highlight the time series of dengue system. Eventually, we get numerical results for different assumptions of [Formula: see text] with specifying factors to conceptualize the effect of [Formula: see text] on the dynamics. It has been noted that the fractional-order derivative offers realistic, clear-cut and valid information about the dynamics of dengue fever. Moreover, we note through our analysis that the input parameters’ index of memory, biting rate, transmission probability and recruitment rate of mosquitos can be used as control parameter to lower the level of infection.

The Prescribed Fixed Structure Intelligent Robust Control of an Electrohydraulic Servo System

The paper is focused to design a robust and a simple fixed structure H ∞ control synthesis for an Electrohydraulic Servo System (EHSS) and comparing its performance with the conventional H ∞ controller and the classical proportional integral derivative (PID) controller. The precise position tracking of the piston load of EHSS system using classical PID controller is a difficult task due to some non-linear properties of EHSS and the dynamic behaviour of its parameters. The conventional H ∞ controllers also have constraints on gain ( H ∞ norm) for typical design requirement such as the speed of response, higher order, complex structure, control bandwidth, and robust stability. To overcome the above limitations, the proposed synthesis is formulated in the MATLAB. The proposed synthesis has fixed order and fixed structure and is also a linear robust controller. The control parameters of proposed synthesis are tuned using Genetic Algorithm optimization in MATLAB. Another advantage of this design is to use higher order complex shaping fillers to shape the close loop sensitivity S s and complementary sensitivity T s for the desired robust performance, without effecting the structure fixed of proposed synthesis. The order of the proposed controller is not affected by using the higher order complex weights transfer functions W s s and W T s on sensitivity and complementary sensitivity, respectively, whereas the structure of the conventional H ∞ controller becomes more complex due to higher order shaping weights. Model of the Electrohydraulic Servo System is validated experimentally, and results of proposed robust synthesis are compared with conventional H ∞ controller and the classical PID.

Optimal control of hybrid variable-order fractional coronavirus (2019-nCov) mathematical model; numerical treatments

A novel coronavirus is a serious global issue and has a negative impact on the economy of Egypt. According to the publicly reported data, the first case of the novel corona virus in Egypt was reported on 14 February 2020. Total of 96753 cases were recorded in Egypt from the beginning of the pandemic until the eighteenth of August, where 96, 581 individuals were Egyptians and 172 were foreigners. Recently, many mathematical models have been considered to better understand coronavirus infection. Most of these models are based on classical integer-order derivatives which can not capture the fading memory and crossover behavior found in many biological phenomena. Therefore, we study the coronavirus disease in this paper by exploring the dynamics of COVID-19 infection using new variable-order fractional derivatives. This paper presents an optimal control problem of the hybrid variable-order fractional model of Coronavirus. The variable-order fractional operator is modified by an auxiliary parameter in order to satisfy the dimensional matching between the both sides of the resultant variable-order fractional equations. Existence, uniqueness, boundedness, positivity, local and global stability of the solutions are proved. Two control variables are considered to reduce the transmission of infection into healthy people. To approximate the new hybrid variable-order operator, Grünwald-Letnikov approximation is used. Finite difference method with a hybrid variable-order operator and generalized fourth order Runge-Kutta method are used to solve the optimality system. Numerical examples and comparative studies for testing the applicability of the utilized methods and to show the simplicity of these approximation approaches are presented. Moreover, by using the proposed methods we can concluded that, the model given in this paper describes well the confirmed real data given by WHO about Egypt.

High-resolution DTM-based estimation of geomorphometric parameters of selected putative martian scoria cones

Some previous studies have identified a number of features on Mars that are thought to be scoria cones. Since (terrestrial) scoria cones have special significance that they are monogenetic volcanoes, i.e. the volcanic edifice is created by a single eruptive event. The process usually produces fairly symmetrical cones, making them a target for morphometric research. In this study, we investigated features that were interpreted as scoria cones (or mud volcanoes), which are included in the HiRiSE database of stereopairs and thus, high-resolution DTMs can be generated for their area. We have computed DTMs using the tools of NASA Ames Stereo Pipeline and USGS ISIS system and calculated classic (cone width, cone height, crater width) and other volcano-geomorphometric indices and derivatives based on the elevation data. Polar Coordinate Transformation (PCT) images have been calculated in order to analyze the symmetry of the cones. Spatial Elliptical Fourier Descriptors (SEFD) have been computed to model the outer contours and the crater rims. The parameters (especially those of the fitted ellipses) are analyzed in order to visualize the orientation and extent of the properties of the cones. The classic relationship of the cone widths and cone heights can also be established for the Martian scoria cones. However, while for the terrestrial cases, a factor of 0.20–0.22 has been determined in the last decades, for the analyzed putative Martian scoria cones this factor is below 0.2, according to our calculations, they are in the range of 0.16–0.19. The analysis of the elevations of the cone contours reveals that in most of the cases the pre-eruptional surface could have been subhorizontal and flat. The fitted ellipses of SEFD method have a remarkably constant ratio of the lengths of the semimajor and semiminor axes, both for the outlines and for the crater rims. Although the contours and rims are slightly elliptical in most cases, our results show a high degree of symmetry in the selected cones. This symmetry is considered to be due to two main reasons: first, it is the result of a selection effect, as only those cone-shaped features are included in the study that are very probably scoria cones, and second, due to the different Martian conditions from those on Earth, in certain cases there is degradation on these cones, with e.g. at most minor mass movement traces modifying the high degree of symmetry.

Reliable auxiliary communication of UAV via relay cache optimization

With the continuous reduction of drone costs and the miniaturization of equipment, many new applications have emerged in the civil and commercial fields. The remote sensing technology of Unmanned Aerial Vehicle (UAV) is used to manage and partition farmland accurately. Compared with the traditional field grid sampling method, UAV remote sensing technology can break through operating conditions, continuously collect data at low altitudes, monitor the area more flexibly, and significantly reduce labor and safety costs. Since UAVs can only provide data transmission services to users through wireless backhaul links established with ground base stations, the need to access the network is easy to lead to the disclosure of user privacy. The capacity of wireless backhaul links is limited, limiting the transmission rate of drones and reducing the user’s quality of service. Therefore, we apply edge caching technology to the assisted relay communication network to study the impact of caching technology on the performance of mobile relay systems. In particular, we propose the horizontal position design method in the buffer auxiliary relay single-user system, and the 3D position design method in the buffer auxiliary relay multi-user system. Position system, which can be reached by the maximum system average and the optimal speed, is designed. Besides, with the help of objective function conversion and classic derivation analysis method, the semi-closed expression of the optimal position of the UAV is obtained, and the intersection of the mobile relay end velocity and the user end velocity is used as the initial value. Meanwhile, the solution formula is substituted after continuous iteration so that the best advantage of local velocity can be obtained. In addition, mobile relay system is deployed to establish a two-hop wireless link to achieve reliable communication between Base Station (BS) and users security trust. The simulation experiment proves that compared with other methods, the method proposed in this paper has considerable performance improvement in power convergence, speed, trajectory path loss, and energy cost, which can provide higher-quality communication services for users in the system and better support for the broad application of drones.

The topological ligament in shape optimization: a connection with thin tubular inhomogeneities

In this article, we propose a formal method for evaluating the asymptotic behavior of a shape functional when a thin tubular is added between two distant regions of the boundary of a domain. In the contexts of the conductivity equation and the linear elasticity system, we relate this issue to a perhaps more classical problem of thin tubular inhomogeneities: we analyze the solutions to versions of the physical partial differential equations which are posed inside a fixed background medium, and whose material coefficients are altered inside a tube with vanishing thickness. Our main contribution from the theoretical point of view is to propose a heuristic energy argument to calculate the limiting behavior of these solutions with a minimum amount of effort. We retrieve known formulas when they are available, and we manage to treat situations which are, to the best of our knowledge, not reported in the literature (including the setting of the 3d linear elasticity system). From the numerical point of view, we propose three different applications of the formal ligament approach derived from these expansions. At first, it is an original way to account for variations of a domain, and it thereby provides a new type of sensitivity for a shape functional, to be used concurrently with more classical shape and topological derivatives in optimal design frameworks. Besides, it suggests new, interesting algorithms for the design of the scaffold structure sustaining a shape during its fabrication by a 3d printing technique, and for the design of truss-like structures. Several numerical examples are presented in two and three space dimensions to appraise the efficiency of these methods.

Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis

This work devotes to solving a class of delay fractional partial differential equations that arises in physical, biological, medical, and climate models. For this, a numerical scheme is implemented that applies operational matrices to convert the main problem into a system of algebraic equations; then, solving the resultant system leads to an approximate solution. The two-variable Chebyshev polynomials of the sixth kind, as basis functions in the proposed method, are constructed by the one-variable ones, and their operational matrices are derived. Error bounds of approximate solutions and their fractional and classical derivatives are computed. With the aid of these bounds, a bound for the residual function is estimated. Three illustrative examples demonstrate the simplicity and efficiency of the proposed method.

Tempered fractional order compartment models and applications in biology

<p style='text-indent:20px;'>Compartment models with classical derivatives have diverse applications and attracted a lot of interest among scientists. To model the dynamical behavior of the particles that existed in the system for a long period of time with little chance to be removed, a power-law waiting time technique was introduced in the most recent work of Angstmann et al. [<xref ref-type="bibr" rid="b2">2</xref>]. The divergent first moment makes the power-law waiting time distribution less physical because of the finite lifespan of the particles. In this work, we take the tempered power-law function as the waiting time distribution, which has finite first moment while keeping the power-law properties. From the underlying physical stochastic process with the exponentially truncated power-law waiting time distribution, we build the tempered fractional compartment model. As an application, the tempered fractional SEIR epidemic model is proposed to simulate the real data of confirmed cases of pandemic AH1N1/09 influenza from Bogotá D.C. (Colombia). Some analysis and numerical simulations are carried out around the equilibrium behavior.</p>

A new local non-integer derivative and its application to optimal control problems

<abstract><p>Here, a new local non-integer derivative is defined and is shown that it coincides to classical derivative when the order of derivative be integer. We call this derivative, adaptive derivative and present some of its important properties. Also, we gain and state Rolle's theorem and mean-value theorem in the sense of this new derivative. Moreover, we define the optimal control problems governed by differential equations including adaptive derivative and apply the Legendre spectral collocation method to solve this type of problems. Finally, some numerical test problems are presented to clarify the applicability of new defined non-integer derivative with high accuracy. Through these examples, one can see the efficiency of this new non-integer derivative as a tool for modeling real phenomena in different branches of science and engineering that described by differential equations.</p></abstract>

Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity

We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex values fail. Based on previously obtained results for periodic problems in the single-valued cases, the existence of solutions is proven. It is also pointed out that the solution set is compact in the uniform convergence topology. In particular, the existence results are obtained for periodic impulsive differential inclusions (with multivalued impulsive maps and finite or possibly countable impulsive moments) without upper semicontinuity assumptions on the right-hand side, and also the existence of solutions is derived for dynamic inclusions on time scales with periodic boundary conditions.

Smooth Approximation of Lipschitz Maps and Their Subgradients

We derive new representations for the generalised Jacobian of a locally Lipschitz map between finite dimensional real Euclidean spaces as the lower limit (i.e., limit inferior) of the classical derivative of the map where it exists. The new representations lead to significantly shorter proofs for the basic properties of the subgradient and the generalised Jacobian including the chain rule. We establish that a sequence of locally Lipschitz maps between finite dimensional Euclidean spaces converges to a given locally Lipschitz map in the L-topology—that is, the weakest refinement of the sup norm topology on the space of locally Lipschitz maps that makes the generalised Jacobian a continuous functional—if and only if the limit superior of the sequence of directional derivatives of the maps in a given vector direction coincides with the generalised directional derivative of the given map in that direction, with the convergence to the limit superior being uniform for all unit vectors. We then prove our main result that the subspace of Lipschitz C ∞ maps between finite dimensional Euclidean spaces is dense in the space of Lipschitz maps equipped with the L-topology, and, for a given Lipschitz map, we explicitly construct a sequence of Lipschitz C ∞ maps converging to it in the L-topology, allowing global smooth approximation of a Lipschitz map and its differential properties. As an application, we obtain a short proof of the extension of Green’s theorem to interval-valued vector fields. For infinite dimensions, we show that the subgradient of a Lipschitz map on a Banach space is upper continuous, and, for a given real-valued Lipschitz map on a separable Banach space, we construct a sequence of Gateaux differentiable functions that converges to the map in the sup norm topology such that the limit superior of the directional derivatives in any direction coincides with the generalised directional derivative of the Lipschitz map in that direction.

Orthonormal shifted discrete Legendre polynomials for the variable-order fractional extended Fisher–Kolmogorov equation

This paper presents a numerical technique for solving the variable-order fractional extended Fisher–Kolmogorov equation. The method suggested to solve this problem is based on the orthonormal shifted discrete Legendre polynomials and the collocation method. First, we expand the unknown solution of the problem using the these polynomialss. Also, we approximate the second- and fourth-order classical derivatives, as well as the variable-order fractional derivatives by these basis functions. Then, we substitute these approximations in the equation. Next, we utilize the classical and fractional derivative matrices together with the collocation method to convert the main equation into a system containing nonlinear algebraic equations. We show the correctness of the proposed scheme by providing several numerical examples.

ANT-colony optimization-direct torque control for a doubly fed induction motor : An experimental validation

Direct Torque Control (DTC) presents an optimal solution to control the behaviors of the alternative motors, compared to other controls, because of several advantages offered by this technique, the speed overshoots, fluxes, and torque ripples remain the major factors which minimize the DTC robustness. The regulation speed in DTC is carried out by the classic Proportional Integrator Derivative (PID), which is known for its higher robustness in linear systems, except that in the case of non-linear systems, the PID controller gives poor reactions to variations in the system’s parameters. The best solutions adopted in this situation are often based on optimization algorithms that generate the controller’s gains in each period where there is an internal or external perturbation, adapting the behaviors of the PID against the system’s nonlinearity. For that reason, this work is focused on the theoretical studies and experimental validation on dSPACE Board DS1104 of the new proposed approach based on PID speed regulation, optimized by the Ant Colony Optimization algorithm (ACO) for DTC, applied to both sides of the Doubly Fed Induction Motor (DFIM), to overcome the previous drawbacks cited at the beginning. The new combined ACO-DTC strategy has been studied for optimizing the gains of the PID controller by using a cost function such as Integral Square Error (ISE). The proposed approach is implemented on Matlab/Simulink to validate the objectives adopted by this strategy. The simulation and experimental results extracted from Matlab and ControlDesk have proved the efficiency of the proposed ACO-DTC with the system’s nonlinearity, which attribute different enhancements in the global system performance.