The natural history of COVID-19 caused by SARS-CoV-2 is extremely variable, ranging from asymptomatic infection, to pneumonia, and to complications eventually fatal. We propose here the first model, explaining how the outcome of first, crucial 10-15 days after infection, hangs on the balance between the cumulative dose of viral exposure and the efficacy of the local innate immune response (natural IgA and IgM antibodies, MBL). If SARS-CoV-2 runs the blockade of this innate immunity and spreads from the upper airways to the alveoli in the early phases of the infections, it can replicate with no local resistance, causing pneumonia and releasing high amounts of antigens. The delayed and strong adaptive immune response (high affinity IgM and IgG antibodies) that follows, causes severe inflammation and triggers mediator cascades (complement, coagulation, and cytokine storm) leading to complications often requiring intensive therapy and being, in some patients, fatal. Strenuous exercise and high flow air in the incubation days and early stages of COVID-19, facilitates direct penetration of the virus to the lower airways and the alveoli, without impacting on the airway’s mucosae covered by neutralizing antibodies. This allows the virus to bypass the efficient immune barrier of the upper airways mucosa in young and healthy athletes. In conclusion, whether the virus or the adaptative immune response reach the lungs first, is a crucial factor deciding the fate of the patient. This “quantitative and time-sequence dependent” model has several implications for prevention, diagnosis, and therapy of COVID-19.

The evolution of integrable classical systems leads to conserved quantities and vanishing Poisson brackets. In contrast, such invariants do not exist in the dynamics of non-integrable systems, which include (but are not limited to) deterministic models with long-term chaotic behavior. The object of this review is to briefly survey the mathematical background of nonintegrability and its role in the physics unfolding well-above the Standard Model (SM) scale.

Build a special identical equation, use its calculation characters to prove and search for solution of any odd converging to 1 equation through (*3+1)/2^k operation, change the operation to (*3+2^m-1)/2^k, and get a solution for this equation, give a specific example to verify. Thus prove the Collatz Conjecture is true. Furthermore, analysis the sequences produced by iteration calculation during the procedure of searching for solution, build a weight function model, prove it decrease progressively to 0, build a complement weight function model, prove it increase to its convergence state. Build a (*3+2^m-1)/2^k odd tree, prove if odd in (*3+2^m-1)/2^k long huge odd sequence can not converge, the sequence must outstep the boundary of the tree after infinite steps of (*3+2^m-1)/2^k operation.

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.

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.

Recent discovery of triangular boron Nanotubes makes it a competitor of carbon in many respects. Closed forms of M-polynomial of nanotubes produce closed forms of many degree-based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M-polynomials of triangular boron nanotubes and recover many important topological degree-based indices of these nanotubes. We also plot surfaces associated to these nanotubes.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

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

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.

M-polynomial of different molecular structures helps to calculate many topological indices. A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR) quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of Octagonal network. From the M-polynomial we recover some degree-based topological indices for Octagonal network. Moreover, we give a graphical representation of our results.

The exact solutions in the wave form are derived for the time fractional KdV and the time fractional Burgers' equations in conformable fractional derivative sense. The fractional variable change using the fundamental properties of the conformable derivative reduces both equations to some nonlinear ODEs. The predicted solution is assumed to be a finite series form of a function satisfying a particular first-order ODE whose solution contains an exponential function in the denominator. The solutions are represented in the explicit forms and illustrated by some choices of the parameters for various fractional orders of the equations.

Exact solutions to conformable time fractional (3+1)- dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE. The resultant polynomial equation is solved by using algebraic operations. The method works for the Jimbo-Miwa, the Zakharov-Kuznetsov and the modified Zakharov-Kuznetsov equations in conformable time fractional forms. All the solutions are expressed in explicit forms.

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long Wave-Burgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker's parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational form of an exponential function is substituted to the ODE generated from the conformable time fractional PDE by using wave transformation. The coefficients used in the finite series are determined by solving the algebraic system derived from the coefficients of the powers of the predicted solution.

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.

Rifampicin is one of the most important chemotherapeutic agents used in the treatment of tuberculosis. M. tuberculosis clinical strains resistant to rifampicin harbor mainly mutation in an 81-base pair region of rpoB. These mutations mainly consist of single amino acid substitutions. However insertions also can be related with rifampicin resistance strains. Herein, we described an insertion of 12 nucleotides in clinical isolates of M. tuberculosis resistant to rifampicin, all obtained from inmates. To evaluate the importance this insertion in surviving and drug resistance, it were carried out fitness experimental assays as well as in silico studies of 3D structural models, molecular docking simulations and virtual screening. The medical records of the seven patients showed all were previously treated to tuberculosis. Growth curves shown that the insertion determines a biological cost when compared to wild type rpoB and katG; or the double mutated rpoB S531L and katG S315T. From docking and molecular dynamics simulations it can be inferred that the insertion does not affect the process of synthesis of RNA transcripts. On the other hand, in the mutant RNAP-RIF complex rifampicin confirmed a low affinity interaction for the mutant form. Interesting, virtual screening for potential inhibitors for wtRNAP and mRNAP using a library of 1446 compounds approved by the FDA showed that the best ligands were mainly compounds with antibiotic activity, although the targets involved in the pharmacological action are other than RNAP. In conclusion, seven strains of M. tuberculosis RIF resistant that present an insertion of four amino acids in RNA polymerase showed by growth curve assays, a biological cost. Further, bioinformatics tools had characterized the putative drug resistance dynamic as well as the maintenance of RNA polymerase activity.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES)(m)algorithm with Variable Restart Parameter (VRP-GMRES(m) algorithm) is proposed. By properly changing a variable restart parameter for the GMRES(m) algorithm, the iteration stagnation problem resulting from improper selection of the parameter is resolved efficiently. Based on the framework of the VRP-GMRES(m) algorithm and the relevant properties of generalized inverse matrix, the projection of the error vector r_m+1 on r_m is deduced. The result proves that the proposed algorithm is not only rapidly convergent but also highly accurate. Numerical experiments further show that the new algorithm can significantly improve the computational efficiency and accuracy. Its superiorities will be much more remarkable when it is used to solve larger scale problems. Therefore, it has extensive prospects in the FM-BEM field and other scientific and engineering computing.

Here we mathematically model black holes and the early universe following dynamics similar to RLC electrical models, focusing on their similarities at the singularity. We use this mathematically modelling to hypothesize the evolution of an expanding universe as the result of a black hole collapse followed by its evaporation. Or model consists of several steps defined by: (1) the formation of a black hole following general relativity equations; (2) growth of the black hole modelled as a resistance-capacitance-like electrical circuit; (3) expansion of space-time following the disintegration of the black hole, modelled by RLC-like dynamics. In updating this article, version 2, we will expand by presenting three additional examples related to the theory of the generalization Boltzmann's constant in curved space-time and the theory of general and especial relativity. We will calculate the critical mass to produce a black hole in the LHC, the existence of a high temperature Bose-Einstein condensate and finally we will demonstrate the existence of a tangential force to the repulsion force in the disintegration of subatomic particles. In the update of this article, version 3, we will expand to develop two examples. First, we will present the relationship between M-theory, extra dimensions with the theory of the generalization of Boltzmann's constant in curved space-time. Secondly, we will propose the idea of ​​updating the Lambda-CDM model, considering the primordial gravitational waves to correctly describe the evolution of the universe.

Suitable measures of grazing impacts on ground cover, that enable separation of the effects of climatic variations, are needed to inform land managers and policy makers across the arid rangelands of the Northern Territory of Australia. This work developed and tested a time-series, change-point detection method for application to time series of vegetation fractional cover derived from Landsat data to identify irregular and episodic ground-cover growth cycles. These cycles were classified to distinguish grazing impacts from that of climate variability. A measure of grazing impact was developed using a multivariate technique to quantify the rate and degree of ground cover change. The method was successful in detecting both long term (> 3 years) and short term (< 3 years) growth cycles. Growth cycle detection was assessed against rainfall surplus measures indicating a relationship with high rainfall periods. Ground cover change associated with grazing impacts was also assessed against field measurements of ground cover indicating a relationship between both field and remotely sensed ground cover. Cause and effects between grazing practices and ground cover resilience can now be explored in isolation to climatic drivers. This is important to the long term balance between ground cover utilisation and overall landscape function and resilience.

Here, applying the theory of the generalization of the Boltzmann constant in curved space-time, we will model the mechanism by which elementary particles are formed. We will determine the relationship between gravity and each of the elementary particles that form the standard model following analogies to that of stellar bodies. In order to achieve our goal, we will propose new models for photons, quarks and gluons; with this, we will demonstrate why there are stable and unstable elementary particles; why the first family of elementary particles forms hadrons and why the second and third families cannot form hadrons; why the fermions comply with the Pauli exclusion principle and why the bosons do not comply with the Pauli exclusion principle, etc. Finally, we will analyse the generalization of the ADS/CFT correspondence and propose a theory of everything (T.O.E.).

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.

Here we will electrically-quantum model the neutron and proton as a three-phase alternating current electric generator, for this, we will use the theory of three-phase electric generators and vector or phasor diagrams. We will use this model to hypothesize how the quarks that form neutrons and protons with a combined mass of 10 MeV/c², can generate, through quarks-antiquarks-gluon interactions, a mass of 939.56 MeV/c² for the neutron and a mass of 938.27 MeV/c² for the proton. Using quantum mechanics and the theory of the generalization of the Boltzmann constant in curved space-time we will calculate the number of quarks-antiquarks-gluons and gravitons inside a neutron. We will also analyse βˉ decay using vector diagrams, we will calculate the tension of the string T₀ and the length of the string ℓs between quarks-antiquark and finally, we will model a black hole using a neutron equivalent model. In version 2 of this article, we will update the vector diagrams of the βˉ decay and theoretically calculate the energy of the W⁻ boson, the Z⁰ boson, and the Θ angle, Θ = arc cos (W⁻/Z⁰). We will demonstrate, through vector diagrams, that quarks-antiquarks-gluon interactions are the cause of the origin of the W⁻ boson and the Z⁰ boson. We will also demonstrate how the fine structure constant α originates. It is important to make clear, in future updates, we will describe the relationship that exists between the theory described in this paper and the Isospin theory, flavour and colour theory

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

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.

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration ( ) falls close to the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

In clinical diagnostics and longitudinal studies, the reproducibility of MRI assessments is of high importance in order to detect pathological changes, but developments in MRI hard- and software often outrun extended periods of data acquisition and analysis. This could potentially introduce artefactual changes or mask pathological alterations. However, if and how changes of MRI hardware, scanning protocols or preprocessing software affect complex neuroimaging outcomes from e.g. diffusion weighted imaging (DWI) remains largely understudied. We therefore compared DWI outcomes and artefact severity of 121 healthy participants (age range 19-54 years) who underwent two matched DWI protocols (Siemens product and Center for Magnetic Resonance Research sequence) at two sites (Siemens 3T Magnetom Verio and Skyra^fit). After different preprocessing steps, fractional anisotropy (FA) and mean diffusivity (MD) maps,obtained by tensor fitting, were processed with tract-based spatial statistics (TBSS). Inter-scanner and inter-sequence variability of skeletonised FA values reached up to 5% and differed largely in magnitude and direction across the brain. Skeletonised MD values differed up to 14% between scanners. We here demonstrate that DTI outcome measures strongly depend on imaging site and software, and that these biases vary between brain regions. These regionally inhomogeneous biases may exceed and considerably confound physiological effects such as ageing, highlighting the need to harmonise data acquisition and analysis. Future studies thus need to implement novel strategies to augment neuroimaging data reliability and replicability.

This work is a top-level summary of several contributions published in the last three decades. It makes the case that complex dynamics of nonlinear systems lies at the heart of foundational physics.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

Visible Light Communication (VLC) uses an intensity-modulation and direct-detection (IM/DD) scheme to transmit data. The light source utilized in VLC structures is constantly switched on and off rapidly, resulting in flickering. Furthermore, most of illumination systems exclude dimming support to permit customers to dim the light source to the desired stage. Therefore, the modulation scheme for information transmission in VLC should consist of flicker mitigation and dimming manage abilities. Double inverse pulse position modulation (DIPPM), sub-carrier pulse position modulation (SC-L-PPM), and M-ary variable pulse position modulation (M-VPPM) are recommended for minimizing the flicker issues and supporting an excessive degree of dimming for VLC systems. In this paper, a comparison is introduced between DIPPM, SC-L-PPM, and M-VPPM according to error performance and bit rate. In addition, a simulation is carried out to measure the optical power distribution for a LED lamp in an indoor room topology for each modulation technique. The obtained results indicated that SC-L-PPM is the best choice regarding the bit error rate (BER) and optical power distribution compared to the other two schemes. A 10^-6 BER is achieved with a very low power requirement at L=8, while a remarkable power distribution of 1.5 to 6.5 dBm is observed from 3×5×5 m³ room corners to the center, respectively. According to the bit rate, it is noticed that, M-VPPM is the most efficient one compared to the two other schemes. It achieves 2.3×10⁷ bps at signal to noise ratio (SNR) of 22 dB and M=8.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

Acid proteins capable of nucleating Ca2+ and displaying aggregation capacity play key roles in the formation of calcium carbonate biominerals. EF-hands are among the largest Ca2+-binding motif in proteins. Gad m 1, an Atlantic cod β-parvalbumin isoform, is a monomeric EF-hand protein that acts as a Ca2+ buffer in fish muscle and is able to form amyloids under acidic conditions. Since nucleating Ca2+ protein have a propensity to form extended β-strand structures, we wondered whether amyloid assemblies of a protein containing refolded EF-hand motifs were able to influence the in vitro calcium carbonate crystallization. Here we have used the Gad m 1 chain as model to generate monomeric and amyloid assemblies and analyze their effect on in vitro calcite formation. We found that only amyloid assemblies alter calcite morphology.

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

The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave(RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters.

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.

The key objective of the present paper is to propose a numerical scheme based on the homotopy analysis transform technique to analyze the time-fractional nonlinear predator-prey population model. The population model is coupled fractional order nonlinear partial differential equations often employed to narrate the dynamics of biological systems in which two species interact, first is a predator and the second is a prey. The proposed scheme provides the series solution with great freedom and flexibility by choosing appropriate parameters. The convergence of results is free from small or large parameters. Three examples are discussed to demonstrate the correctness and efficiency of the used computational approach.

The CCAAT/enhancer-binding protein β (C/EBPβ) is a transcription factor that regulates cellular proliferation, differentiation, apoptosis and tumorigenesis. Although the pro-oncogenic roles of C/EBPβ have been implicated in various human cancers, how it contributes to tumorigenesis or tumor progression has not been determined. Immunohistochemistry with human non-small cell lung cancer (NSCLC) tissues revealed that higher levels of C/EBPβ protein are expressed compared to normal lung tissues. Knockdown of C/EBPβ by siRNA reduced the proliferative capacity of NSCLC cells by delaying G₂/M transition of the cell cycle. In C/EBPβ-knockdown cells, a prolonged increase in phosphorylation of cyclin dependent kinase 1 at tyrosine 15 (Y15-pCDK1) was displayed with increased Wee1 and decreased Cdc25B expression, simultaneously. ChIP analysis showed that C/EBPβ bound to distal promoter regions of WEE1 and repressed WEE1 transcription through the interaction with histone deacetylase 2. Treatment of C/EBPβ-knockdown cells with a Wee1 inhibitor induced a decrease in Y15-pCDK1 and recovered cells from G₂/M arrest. In the xenograft tumors, the depletion of C/EBPβ significantly reduced tumor growth. Taken together, these results indicate that Wee1 is a novel transcription target of C/EBPβ that is required for the G₂/M phase of cell cycle progression, ultimately regulating proliferation of NSCLC cells.

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.

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

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

In the present study, nonlinear vibration of a nanobeam resting on fractional order viscoelastic Winkler-Pasternak foundaion is studied using nonlocal elasticity theory. D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. Detailled parametric study is conducted, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations

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.

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.

Emulsion stabilisation of base layers surfaced with chip seals often proves problematic with chips punching into the base and early distress. This can be aggravated by the use of modified binders that restricts the evaporation of moisture from pavement layers. The introduction of New-age (Nano) Modified Emulsion (NME) stabilisation has the advantage that water is chemically repelled from the stabilised layer resulting in an accelerated development of strength. A need was identified to evaluate the early life performance of selected chip seals, together with identified binders. Three different chip seal surfacings with unconventional modified binders were constructed and evaluated using Accelerated Pavement Testing (APT) with the MMLS3. The objectives of the experimental design and testing were to evaluate binder performance, early loss of chips before chip orientation at low temperatures, punching of the chips into the NME stabilised base, deformation characteristics of a Cape seal and the effect of the use of a standard normal modified binder. This paper contains details of the NME base layer, the binder and seal selection and the test results. It is shown that a cost-effective thin chip seal in combination with a suitable binder can be used on a NME stabilised base with confidence.

The fractional telegraph partial differential equation with fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. Laplace method is used to find the exact solution of this equation. Stability inequalities are proved for the exact solution. Difference schemes for the implicit finite method are constructed. The implicit finite method is used to deal with modelling the fractional telegraph differential equation defined by Caputo fractional of Atangana-Baleanu (AB) derivative for different interval. Stability of difference schemes for this problem is proved by the matrix method. Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the proposed method.

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.

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

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

The space time fractional Korteweg-de Vries equation, modified Equal Width equation and Benney-Luke Equations are solved by using simple hyperbolic tangent Ansatz method. A simple compatible wave transformation in one dimension is employed to reduce the governing equations to integer ordered ODEs. Then, the ansatz approximation is used to derive exact solutions. Some illustrative examples are presented for some particular choices of parameters and derivative orders.

The epithelial-mesenchymal (E/M) hybrid state has emerged as an important mediator of elements of cancer progression, facilitated by epithelial mesenchymal plasticity (EMP). We review here evidence for the presence, prognostic significance, and therapeutic potential of the E/M hybrid state in carcinoma. We further assess modelling predictions and validation studies to demonstrate stabilised E/M hybrid states along the spectrum of EMP, as well as computational approaches for characterising and quantifying EMP phenotypes, with particular attention to the emerging realm of single-cell approaches through RNA sequencing and protein-based techniques.

The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function.

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.

In South Western Indian ocean (IO), Extended-Spectrum β-Lactamase producing Enterobacteriaceae (ESBL) are a main public health issue. In livestock, ESBL burden was unknown. The aim of this study was estimating the prevalence of ESBL on commercial farms in Reunion, Mayotte and Madagascar and genes involved. Secondly, risk factors of ESBL occurrence in broiler, beef cattle and pig farms were explored. In 2016-2017, commercial farms were sampled using boot swabs and samples stored at 4°C before microbiological analysis for phenotypical ESBL and gene characterization. A semi-directive questionnaire was performed. Prevalences observed in all production types and territories were elevated, except for beef cattle in Reunion which differed significantly. The most common ESBL gene was the CTX-M-1 subtype. Generalized linear models explaining ESBL occurrence varied between livestock production sectors and allowed identifying main protective (e.g., water quality control and detergent use for cleaning) and risk factors (e.g., recent antibiotic use, other farmers visiting the exploitation, pet presence). This study is the first to explore tools for antibiotic resistance management in IO farms. It provides interesting hypothesis to explore about antibiotic use in IO and ESBL transmission between pig, beef cattle and humans in Madagascar.

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

Formation of Fe- and Mg-rich smectite and zeolite under alkaline conditions is concerned as secondary minerals after alkaline alteration of bentonite in a repository of radioactive wastes. It might be crucial for safety assessment whether smectite will be formed or not as secondary minerals after alkaline alteration of bentonite. In present paper, Fe- and Mg-rich smectite which are currently interacting with hyperalkaline groundwater was found at Narra in Palawan, Philippines. Mineralogical and geochemical investigation was conducted to understand formation process of smectite and factors determined secondary mineral species. Our study revealed a certain amount of smectite may have been produced under hyperalkaline conditions, altered from amorphous or poorly crystalline material such as M-S-H and F-S-H. Key factor which decides smectite or zeolite as secondary minerals after alkaline alteration of bentonite might be whether nuclei of M-S-H and/or F-S-H will be formed or not. This might be decided by the presence of dissolved Mg2+ and Fe2+ in the system. Our suggested formation process of smectite under alkaline conditions is analogue with generally-accepted model of smectite formation that might have been occurred on early Mars.

Speckle noise corrupt the major part of ultrasound image, because of which the quality deteriorate and loss of valuable information leads to false diagnosis. A large community of images like synthetic aperture radar (SAR) image, Synthetic image, and simulated ultrasound image, require despeckling at pre-processing stage for better processing. Cleaning the speckle from image and preserving the edge details is a vital task. Nowadays not only despeckling is considered as an important process but also preserving information at boundary and edges of image is also important. As most of the algorithms able to remove speckle noise but fails to preserve the details of edges. This paper covers several recent methods for removal of speckle noise along with various metrics opted for comparisons. The distinctive part of this paper is, a mathematical and parametric review has been done. Also a table is also included which summarizes the entire paper.

Land Surface Temperature (LST) is a basic parameter in energy exchange between the land and atmosphere and is frequently used in many sciences such as climatology, hydrology, agriculture, ecology, etc. LST time series data have usually deficient, missing and unacceptable data caused by the presence of clouds in images, presence of dust in atmosphere and sensor failure. In this study, Singular Spectrum Analysis (SSA) algorithm was used to resolve the problem of missing and outlier data caused by cloud cover. The region studied in the present research included an image frame of MODIS with horizontal number 22 and vertical number 05 (h22v05). This image involved a large part of Iran and Turkmenistan and Caspian Sea. In this study, MODIS LST sensor (MOD11A1) was used during 2015 with 1×1 Km spatial resolution and day/night LST data (daily temporal resolution). The results of the data quality showed that cloud cover caused 36.37% of missing data in the studied time series with 730 day/night LST images. Further, the results of SSA algorithm in reconstruction of LST images indicated the Root Mean Square Error (RMSE) of 2.95 K between the original and reconstructed data in LST time series in the study region. In general, the findings showed that SSA algorithm using spatio-temporal interpolation in LST time series can be effectively used to resolve the problem of missing data caused by cloud cover.

Non-Orthogonal Multiple Access (NOMA) is the key technology promised to be applied in next-generation networks in the near future. In this study, we propose a multi-points cooperative relaying (MPCR) NOMA model instead of just using a relay as the previous studies. Based on the channel state information (CSI), the base station (BS) selects a closest user equipment (UE) and sends a superposed signal to this UE as a first relay node. We have assumed that there are N UEs in the network and Nth UE, which is farthest from BS, has the poorest quality signal transmitted from the BS compared other UEs. Nth UE received the forwarded signal from N-1 relaying nodes that are UEs with better signal quality. At the ith relaying node, it detect its own symbol by using successive interference cancellation (SIC) and will forward the composite signal to the next closest user, namely i+1th UE, and include an excess power which will use for energy harvesting (EH) intention at the next UE. By these, the farthest UE in network can be significantly improved. In addition, closed-form expressions of outage probability for users over both the Rayleigh and Nakagami-m fading channels are also presented. Analysis and simulation results performed by Matlab software which are presented accurately and clearly show that the effectiveness of our proposed model and this model consistents with the multi-access wireless network in future.

This paper uses the $\exp(-\Phi(\xi))$-Expansion method to investigate solitons to the M-fractional nonlinear Schrödingers equation with cubic nonlinearity. The results obtained are dark solitons, trigonometric function solutions, hyperbolic solutions and rational solutions. Thus, the constraint relations between the model coefficients and the traveling wave frequency coefficient for the existence of solitons solutions are also derived.

This research aims to estimate the micro-motion (m-m) of ships. The problem of motion and m-m detection of targets is usually solved using synthetic aperture radar (SAR) along-track interferometry (ATI) which is observed employing two radars spatially distanced by a baseline extended in the azimuth direction. This paper is proposing a new approach where the m-m estimation of ships, occupying thousands of pixels, is measured processing the information given by sub-pixel tracking generated during the coregistration process of several re-synthesized time-domain and overlapped sub-apertures. The SAR products are generated splitting the raw data, according to a small-temporal baseline strategy, observed by one single wide-band staring spotlight (ST) SAR image. The predominant vibrational modes of different ships are estimated and results are promising to extend this application in performing surveillance also of land-based industries activities. Experiments are performed processing one ST SAR image observed by the COSMO-SkyMed satellite system.

Graph theory plays a crucial role in modeling and designing of chemical structure or chemical network. Chemical Graph theory helps to understand the molecular structure of molecular graph. The molecular graph consists of atoms as vertices and bonds as edges. Topological indices capture symmetry of molecular structures and give it a mathematical language to predict properties such as boiling points, viscosity, the radius of gyrations etc. In this article, we study the chemical graph of carbon Crystal structure of graphite and cubic carbon and compute several degree-based topological indices. Firstly we compute M-Polynomials of these structures and then from these M-polynomials we recover nine degree-based topological indices.

During blooms, cyanobacteria produce diverse modified peptides. Among these are the microginins, which inhibit zinc-containing metalloproteases. Ten microginins, microginins KR767 (1), KR801(2), KR835 (3), KR785 (4), KR604 (5), KR638 (6), KR781 (7), KR815 (8), FR3 (9), and FR4 (10) were isolated from the extract of a bloom material of Microcystis sp. (IL-405) collected from the Kishon Reservoir, Israel in the fall of 2009. The structures of the pure compounds were elucidated using 1D and 2D NMR techniques and high-resolution mass spectrometry. The absolute configuration of the chiral centers of the amino acids were determined by Marfey’s and advance Marfey’s methods and by comparison of ¹H and ¹³C NMR chemical shifts of the Ahda derivatives with those of known microginins. These microginins differ in sequence and absolute configuration of the chiral centers of the Ahda moieties and by N-methylation of Ahda amine group and extent of chlorination of Ahda terminal methyl group. The compounds were evaluated for inhibition of the zinc metalloprotease aminopeptidase M and exhibited low- to sub-nanomolar IC₅₀ values.

C-type lectin CD209/DC-SIGN and CD209L/L-SIGN proteins are distinct cell adhesion and pathogen recognition receptors that mediate cellular interactions and recognize a wide range of pathogens including, viruses such as SARS, SARS-CoV-2, bacteria, fungi and parasites. Pathogens exploit CD209L family proteins to promote infection and evade the immune recognition system. CD209L and CD209 are widely expressed in SARS-CoV-2 target organs and can contribute to infection and pathogenesis. CD209L family receptors are highly susceptible to alternative splicing and genomic polymorphism, which may influence virus tropism and transmission in vivo. The carbohydrate-recognition domain (CRD) and the neck/repeat region represent the key features of CD209L family proteins that are also central to facilitating cellular ligand interactions and pathogen recognition. While, the neck/repeat region is involved in oligomeric dimerization, the CRD recognizes the mannose containing structures present on specific glycoproteins such as those found on the SARS-CoV-2 spike protein. Considering the role of CD209L and related proteins in diverse pathogen recognition, this review article discusses the recent advances in the cellular and biochemical characterization of CD209 and CD209L and their roles in viral uptake, which has important implications in understanding the host-pathogen interaction, the viral pathobiology and driving vaccine development of SARS-CoV-2.

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 paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalisedMittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes degree based topological indices of Bismuth Tri-Iodide chains and sheets with the help of M-polynomial.

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

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

This article is an effort to scrutinize the role of Information Technology development in the chronological transformation of Urban Planning domain using the exploratory research approach. In this research, it is argued that the theoretical and practical understanding of Urban Planning should absorb and integrate the bright outcome of the rise of Information and Technology to foster congruent future urban development. The article addresses the trends of transformation in the urban planning domain through the myopic lens of the expansion of information and communications technology era followed by investigating the key drivers shaping the interaction between modern-day urban planning and information technology considering both the dark and bright sides into account.

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.

ntroduction: Respiratory tract Infections are the greatest cause of death worldwide. Since its outbreak in 2019, the coronavirus pandemic (COVID-19) has been a challenge to humans in terms of treatment and prevention of this respiratory viral infection. The re-emergence of respiratory viral infections like influenza, pose a serious hazard to global public health because they occur seasonally. Creating broad-spectrum antiviral compounds for rapid action in the case of an outbreak crisis, as well as bioweapon defences, is critical. Human galectin-3 is found in high concentrations in activated T lymphocytes, epithelial and endothelial cells, and fibroblasts. ProLectin -I and ProLectin -M are both galectin antagonists. Blocking viral entry with a complex polysaccharide component "ProLectin-M" has downstream effects on viral reproduction enabling it to be used as a therapeutic tool and a safe alternative to conventional anti-viral medicines. Methods: In total, 3 cell based assays have been conducted to evaluate antiviral efficacy of ProLectin–I and ProLectin-M against SARS-CoV-2 virus, Influenza-A (H1N1), and human respiratory syncytial virus (hRSV) strain A2. ProLectin-M and ProLectin-I were evaluated for their anti-viral potency using SARS-CoV2 virus strain by viral RNA Extraction and qRT-PCR assays. The plaque assays were carried out to determine the antiviral activity of the test products (ProLectin-I and ProLectin-M) against ‘Influenza-A (H1N1)-A/PR/8/34 (TC adapted)’ and ‘Human respiratory syncytial virus (hRSV) strain A2’ in a cell based in vitro setting. As eference standard, "Oseltamivir Phosphate" and "Remdesivir" were used to determine antiviral activity of test products against H1N1 and hRSV strains respectively.Results: The IC_{50 of} ProLectin-M and ProLectin-I against SARS-CoV-2 virus was found to be 6248 ng/ml (6.2µg/ml) and 4207 ng/ml (4.2μg/ml) respectively. The CC₅₀ value was similar in both the test products i.e. >100 µg/ml. Against Influenza A (H1N1) strain, ProLectin-M exhibited 95 % reduction in the viral load at the test concentration of 21.8 µg/mL with an IC₅₀ value of 5.4 µg/mL whereas, ProLectin-I did not show any cytotoxicity till 250 µg/mL concentration. Against 'human respiratory syncytial virus (hRSV) strain A2, ProLectin-M exhibited 65 % reduction in the viral load at the test concentration of 43.75 µg/mL with an IC₅₀ value of 27.41 µg/mL whereas, ProLectin- I did not show any cytotoxicity till 250 µg/mL concentration. Conclusion: Both ProLectin-I and ProLectin-M have been reported to exhibit broad-spectrum antiviral activity in ‘in-vitro’ setting. ProLectin-M reducing influenza-A virus by 95% and hRSC strain A2 by 65%. To better understand broad spectrum antiviral activity of ProLectin-I and ProLectin-M, further pre-clinical research is warranted.

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.

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 study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp _a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

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

Since the electro-hydraulic servo shaking table exists many nonlinear elements, such as, dead zone, friction and blacklash, its acceleration response has higher harmonics which result in acceleration harmonic distortion, when the electro-hydraulic system is excited by sinusoidal signal. For suppressing the harmonic distortion and precisely identify harmonics, a combination of the adaptive linear neural network and least mean M-estimate (ADALINE-LMM), is proposed to identify the amplitude and phase of each harmonic component. Namely, the Hampel’s three-part M-estimator is applied to provide thresholds for detecting and suppressing the error signal. Harmonic generators are used by this harmonic identification scheme to create input vectors and the value of the identified acceleration signal is subtracted from the true value of the system acceleration response to construct the criterion function. The weight vector of the ADALINE is updated iteratively by the LMM algorithm, and the amplitude and phase of each harmonic, even the results of harmonic components, can be computed directly online. The simulation and experiment are performed to validate the performance of the proposed algorithm. According to the experiment result, the above method of harmonic identification possesses great real-time performance and it has not only good convergence performance but also high identification precision.

Complex modeling has received significant attention in recent years and is increasingly used to explain the statistical phenomenon with increasing and decreasing fluctuations such as the similarity or difference of spike protein charge patterns of coronaviruses. Different from the existing covariance or correlation coefficient methods in traditional integer dimension construction, this study proposes a simplified novel fractional dimension derivation with the exact Excel tool algorithm. It involves the fractional center moment extension to covariance, which ends up a complex covariance coefficient that is better than the Pearson correlation coefficient, in the sense that the nonlinearity relationship can be further depicted. The spike protein sequences of coronaviruses were obtained from the GenBank and GISAID database, including the coronaviruses from pangolin, bat, canine, swine (three variants), feline, tiger, SARS-CoV-1, MERS, and SARS-CoV-2 (including the strains of Wuhan, Beijing, New York, German, and UK variant B.1.1.7) were used as the representative examples in this study. By examining the values above and below the average/mean based on the positive and negative charge patterns of the amino acid residues of the spike proteins from coronaviruses, the proposed algorithm provides deep insights into the nonlinear evolving trends of spike proteins for understanding the viral evolution and identifying the protein characteristics associated with viral fatality. The calculation results demonstrate that the complex covariance coefficient analyzed by this algorithm is capable of distinguishing the subtle nonlinear differences in the spike protein charge patterns with reference to Wuhan strain SARS-CoV-2 for which the Pearson correlation coefficient may overlook. Our analysis reveals the unique convergent (positive correlative) to divergent (negative correlative) domain center positions of each virus. The convergent or conserved region may be critical to the viral stability or viability; while the divergent region is highly variable between coronaviruses suggesting high frequency of mutations in this region. The analyses show that the conserved center region of SARS-CoV-1 spike protein is located at amino acid residues 900, but shifted to the amino acid residues 700 in MERS spike protein, and then to amino acid residues 600 in SARS-COV-2 spike protein, indicating the evolvement of the coronaviruses. Interestingly, the conserved center region of the spike protein in SARS-COV-2 variant B.1.1.7 shifted back to amino acid residues 700, suggesting this variant is more virulent than the original SARS-COV-2 strain. Another important characteristic our study reveals is that the distance between the divergent mean and the maximal divergent point in each of the viruses (MERS>SARS-CoV-1>SARS-CoV-2) is proportional to viral fatality rate. This algorithm may help to understand and analyze the evolving trends and critical characteristics of SARS-COV-2 variants, other coronaviral proteins and viruses.

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

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of nonlocality and spatial heterogeneity of complex materials and systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such operators to complex-order counterparts. In this work, we introduce new definitions for the complex-order fractional Laplacian, fully consistent with the theory of averaging of smooth functions over fractal sets, and present tailored spectral methods for their numerical treatment. The proposed complex-order operators exhibit a dual particle-wave behaviour, with solutions manifesting wave-like features depending on the magnitude of the imaginary part of the fractional order. Reaction-diffusion systems driven by the complex-order fractional Laplacian exhibit unique spatio-temporal dynamics, such as equilibrium of diffusion in random materials by interference of scattered waves, conduction block and highly fractionated propagation, or the generation of completely novel Turing patterns. Taken together, our results support that the proposed complex-order operators hold unparalleled capabilities to advance the description of multiscale transport phenomena in physical and biological processes highly influenced by the heterogeneity of complex media.

To obtain drop-in fuel properties from non-feed biomass, we herein report the catalytic hydrotreatment of microalgae biocrude, produced from hydrothermal liquefaction (HTL) of Spirulina. Our contribution focuses on the effect of temperature, initial H2 pressure, and residence time on the removal of heteroatoms (O and N). In contrast to common hydrotreating experimental protocols at batch scale, we devised a set of two-level factorial experiments and studied the most influential parameters affecting the removal of heteroatoms. It was found that up to 350 °C, the degree of deoxygenation (de-O) is mainly driven by temperature, whereas the degree of denitrogenation (de-N) also relies on initial H2 pressure and temperature-pressure interaction.Based on this, complete deoxygenation was obtained at mild operating conditions (350 °C), reaching a concurrent 47 % denitrogenation. Moreover, three optimized experiments are reported with 100 % removal of oxygen. In addition, the analysis by GC-MS and Sim-Dis gives insight to the fuel quality. The distribution of heteroatom N in lower (<340 °C) and higher (>340 °C) fractional cuts is studied by a fractional distillation unit following ASTM D-1160. Final results show that 63-68 % of nitrogen is concentrated in higher fractional cuts.

This article aims to solve the problem of robust supervision of a reverse osmosis desalination system (RO-DS) with two models, external model and bond graph model. The structure of an industrial system from the point of view of the external model operates according to several modes of operation (degraded and normal). For this external model, we cannot locate the faults since we are talking about a global operation of the system. The possible solution for the development of research was to use the multidisciplinary model called bond graph. This model by its graphic nature and using a unified language makes it possible to model the industrial system element by element from where it helps the user not only to detect the faults but also to locate them when they appear in the system. The results suggest that the use of the bond graph model for alarm 02 is a reverse osmosis error (RO1); these phenomena are readable on the bond graph model and can be quantified by equations. The equation of the model of this reverse osmosis (RO1) is found in the residual equations (r5, r6 and r7), so that these residues will be sensitive to this rupture. The possible solution during research development was to use the bond graph model to supplement information with physical knowledge and to locate faults. This article also describes the operating safety (by minimizing false alarms and non-detections as well as delays in fault detection) of the desalination system by using the bond graph model described in Linear Fractional Transformation (LFT) form for enable it to manage the robust supervision of a desalination system. An approach based on (LFT-BG) is developed to monitor tank leakage (Cu) and reverse osmosis (RO1 and RO2) faults or valve level (V1 and V2) closures and membrane clogging reverse osmosis (Rm1 and Rm2) that can occur in the reverse osmosis desalination system (RO-DS).

A radical, albeit pragmatic protocol for experimental access to putative String/M-theoretic, Einstein Unified Field Mechanical (UFM) additional dimensionality (XD) of the brane-bouquet bulk is presented. If successful, results demonstrate the existence dimensionality beyond the metric of observed physical reality provided by the Standard Model (SM) of particle physics and Cosmology. Quantum Mechanics (QM), as well-known is incomplete and further, should no longer be considered the basement of reality; meaning, Locality and Unitarity – the fundaments of quantum theory are an insufficient basis for extending the representation of reality. A seminal model of Tight Bound States (TBS) below the lowest Bohr orbit in the hydrogen atom, proposed by Vigier, is extended to a Kaluza-Klein-like (KK) cyclical tier of XD hyperspherical cavities defined within a manifold of uncertainty (MOU) of finite radius up to the semi-quantum limit, predicting, within its domain, new spectral lines in Hydrogen. The proposed protocol for this process, with phase modifications, provides efficacy of large-scale additional dimensionality (LSXD) of the brane bulk; XD-LSXD incursion duality accesses nonlocal Einsteinian UFM phenomena, leading to myriad new classes of technological innovation.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

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.

Detection of PLA2R and THSD7A among primary membranous glomerulonephritis (MGN) patients transformed the diagnosis, treatment monitoring and prognosis. Anti-PLA2R can be detected in 70-90% of primary MGN patients while anti-THSD7A in 2-3% of anti-PLA2R negative primary MGN patients depending on the technique used. Serum and urine samples are less invasive and non-invasive respectively and can detect the presence of anti-PLA2R and anti-THSD7A with higher sensitivity and specificity, significant in patients’ monitoring and prognosis better than exposing patients to frequent biopsy which is an invasive procedure. Different techniques of detection of PLA2R and THSD7A in patients’ urine and sera were reviewed with the aim of providing newer and alternative techniques. We proposed the use of biomarkers (PLA2R and THSD7A) in making the diagnosis, treatment decision and follow up of patients with primary MGN. We also reviewed other prognostic renal biomarkers like retinol binding protein (RBP) and beta-2 microglobulin in order to detect progression of renal damage for early intervention.

This paper deals with the study of the existence and non existence of solutions of a three parameter's family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.

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.

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

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.

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

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.

In this study, we consider delta fractional Sturm--Liouville (DFSL) initial value problems in the sense of delta Caputo and delta Riemann-Liouville (R--L) operators. One of the properties of delta fractional difference operators which makes it different from nabla counterpart is to shift its domain. This feature makes it more complex than the nabla fractional operator. We obtain sum representation of solutions for DFSL initial value problems with the help of $\mathcal{Z}-$ transformation. Moreover, we get analytical solutions of homogeneous DFSL problem within Riemann-Liouville (R--L) and Caputo sense, discrete Sturm--Liouville (DSL) problem, continuous fractional Sturm--Liouville (FSL) problem in the sense of R--L and Caputo operators, and continuous Sturm--Liouville (SL) differential problem. From this point of view, we compare all the solutions with each other. Consequently, we show that all results for these four eigenvalue problems are compatible with each other and approach to each other while the orders tends to one, i.e. $\Delta^{\mu }\left( \Delta x\left( t-\mu \right) \right)\cong D_{0^{+}}^{\mu }\left( x^{\prime }\left( t\right) \right)\cong \Delta^2x(n-1) \cong x^{\prime \prime }\left( t\right) =\lambda x\left( t\right),\ \mu\rightarrow1 $ . We support our results comparatively by tables and simulations in detail.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

In the paper we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of differential equations of Cauchy-type in covariant derivatives. We have found the number of essential parameters which the solution of the system depends on. Similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

A variant of the von Neumann-Wigner Interpretation is proposed. It does not make use of the familiar language of wave functionsand observers. Instead it pictures the state of the physical world as a vector in a Fock space and, therefore not, literally, a functionof any spacetime coordinates. And, rather than segregating consciousness into individual points of view (each carrying with it asense of its proper time), this model proposes only unitary states of consciousness, Q(t), where t represents a fiducial time withrespect to which both the state of the physical world and the state of consciousness evolve. States in our world's Fock space areclassified as either 'admissible' (meaning they correspond to definite states of consciousness) or 'inadmissible' (meaning they donot). The evolution of the state vector of the world is such as to always keep it restricted to 'admissible' states. Consciousness istreated very much like what Chalmers calls an "M-Property." But we try to show that problems with the quantum Zeno effect do not arise from this model.

Here are given tight probabilistic inequalities that provide nearly best estimates for the Csiszar's f-divergence. These use the right and left psi -Hilfer fractional derivatives of the directing function f. Csiszar's f- divergence or the so called Csiszar's discrimination is used as a measure of dependence between two random variables which is a very essential aspect of stochastics, we apply our results there. The Csiszar's discrimination is the most important and general measure for the comparison between two probability measures. We give also other applications.

Cyclin dependent kinase 1 (CDK1) has been primarily identified as a key cell cycle regulator in both mitosis and meiosis. Recently, an extramitotic function of CDK1 emerged when evidence was found that CDK1 is involved in many cellular events that are essential for cell proliferation and survival. In this review we summarize the involvement of active CDK1 in the initiation and elongation steps of protein synthesis in eukaryotes. During its activation CDK1 influences the initiation of protein synthesis, promotes the activity of specific translational initiation factors and affects the functioning of a subset of elongation factors. Our review provides insights into gene expression regulation during the transcriptionally silent cell cycle/M-phase and describes quantitative and qualitative translational changes based on the extramitotic role of the cell cycle master regulator CDK1, to optimize temporal synthesis of proteins to sustain division-related processes: mitosis and cytokinesis.