Search

Despite the existence of a secure and reliable immunization, measles, also known as rubeola, continues to be a leading cause of fatalities globally, especially in underdeveloped nations. For investigation and observation of the dynamical transmission of the disease with the influence of vaccination, we proposed a novel fractional order measles model with a constant proportional (CP) Caputo operator. We analysed the proposed model's positivity, boundedness, well-posedness, and biological viability. Reproductive and strength numbers were also verified to examine how the illness dynamically behaves in society. For local and global stability analysis, we introduced the Lyapunov function with first and second derivatives. In order to evaluate the fractional integral operator, we used different techniques to invert the PC and CPC operators. We also used our suggested model's fractional differential equations to derive the eigenfunctions of the CPC operator. There is a detailed discussion of additional analysis on the CPC and Hilfer generalised proportional operators. Employing the Laplace with the Adomian decomposition technique, we simulated a system of fractional differential equations numerically. Finally, numerical results and simulations were derived with the proposed measles model. The intricate and vital study of systems with symmetry is one of the many applications of contemporary fractional mathematical control. A strong tool that makes it possible to create numerical answers to a given fractional differential equation methodically is symmetry analysis. It is discovered that the proposed fractional order model provides a more realistic way of understanding the dynamics of a measles epidemic. [ABSTRACT FROM AUTHOR]

The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a class of Liouville–Caputo difference equations of fractional-order with extremal conditions. Our monotonicity results use difference conditions Δ a LC μ f (a + J 0 + 1 − μ) ≥ (1 − μ) f (a + J 0) and Δ a LC μ f (a + J 0 + 1 − μ) ≤ (1 − μ) f (a + J 0) to derive the corresponding relative minimum and maximum, respectively. We find alternative conditions corresponding to the main conditions in the main monotonicity results, which are simpler and stronger than the existing ones. Two numerical examples are solved by achieving the main conditions to verify the obtained monotonicity results. [ABSTRACT FROM AUTHOR]

Throughout this article, generalizations of some Grónwall–Bellman integral inequalities for two real-valued unknown functions in n independent variables are introduced. We are looking at some novel explicit bounds of a particular class of Young and Pachpatte integral inequalities. The results in this paper can be utilized as a useful way to investigate the uniqueness, boundedness, continuousness, dependence and stability of nonlinear hyperbolic partial integro-differential equations. To highlight our research advantages, several implementations of these findings will be presented. Young's method, which depends on a Riemann method, will follow to prove the key results. Symmetry plays an essential role in determining the correct methods for solving dynamic inequalities. [ABSTRACT FROM AUTHOR]

We prove some new dynamic inequalities of the Gronwall–Bellman–Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations. [ABSTRACT FROM AUTHOR]

We established several novel inequalities of Gronwall–Pachpatte type on time scales. Our results can be used as handy tools to study the qualitative and quantitative properties of the solutions of the initial boundary value problem for a partial delay dynamic equation. The Leibniz integral rule on time scales has been used in the technique of our proof. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

In this article, with the help of Leibniz integral rule on time scales, we prove some new dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales. These inequalities can be used as handy tools to study the qualitative and quantitative properties of solutions of the initial boundary value problem for partial delay dynamic equation. [ABSTRACT FROM AUTHOR]

In this article, using a (γ ,a)-nabla conformable integral on time scales, we study several novel Hilbert-type dynamic inequalities via nabla time scales calculus. Our results generalize various inequalities on time scales, unifying and extending several discrete inequalities and their corresponding continuous analogues. We say that symmetry plays an essential role in determining the correct methods with which to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

The discrete fractional operators of Riemann–Liouville and Liouville–Caputo are omnipresent due to the singularity of the kernels. Therefore, convexity analysis of discrete fractional differences of these types plays a vital role in maintaining the safe operation of kernels and symmetry of discrete delta and nabla distribution. In their discrete version, the generalized or modified forms of various operators of fractional calculus are becoming increasingly important from the viewpoints of both pure and applied mathematical sciences. In this paper, we present the discrete version of the recently modified fractional calculus operator with the Mittag-Leffler-type kernel. Here, in this article, the expressions of both the discrete nabla derivative and its counterpart nabla integral are obtained. Some applications and illustrative examples are given to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, by using some algebraic inequalities, nabla Hölder inequalities, and nabla Jensen's inequalities on timescales, we proved some new nabla Hilbert-type dynamic inequalities on timescales. These inequalities extend some known dynamic inequalities on timescales and unify some continuous inequalities and their corresponding discrete analogues. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

Recent decades have witnessed the emergence of interesting models of fractional partial differential equations. In the current work, a class of parabolic equations with regularized Hyper-Bessel derivative and the exponential source is investigated. More specifically, we examine the existence and uniqueness of mild solutions in Hilbert scale-spaces which are constructed by a uniformly elliptic symmetry operator on a smooth bounded domain. Our main argument is based on the Banach principle argument. In order to achieve the necessary and sufficient requirements of this argument, we have smoothly combined the application of the Fourier series supportively represented by Mittag-Leffler functions, with Hilbert spaces and Sobolev embeddings. Because of the presence of the fractional operator, we face many challenges in handling proper integrals which appear in the representation of mild solutions. Besides, the source term of an exponential type also causes trouble for us when deriving the desired results. Therefore, powerful embeddings are used to limit the growth of nonlinearity. [ABSTRACT FROM AUTHOR]

In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using some algebraic inequalities, Hölder inequality, and Jensen's inequality on time scales. [ABSTRACT FROM AUTHOR]

In the present paper, we discuss a class of bi-univalent analytic functions by applying a principle of differential subordinations and convolutions. We also formulate a class of bi-univalent functions influenced by a definition of a fractional q-derivative operator in an open symmetric unit disc. Further, we provide an estimate for the function coefficients | a 2 | and | a 3 | of the new classes. Over and above, we study an interesting Fekete–Szego inequality for each function in the newly defined classes. [ABSTRACT FROM AUTHOR]

This investigation focuses on two novel Kadomtsev–Petviashvili (KP) equations with time-dependent variable coefficients that describe the nonlinear wave propagation of small-amplitude surface waves in narrow channels or large straits with slowly varying width and depth and non-vanishing vorticity. These two variable coefficients, Kadomtsev–Petviashvili (VCKP) equations in (2+1)-dimensions, are the main extensions of the KP equation. Applying the Lie symmetry technique, we carry out infinitesimal generators, potential vector fields, and various similarity reductions of the considered VCKP equations. These VCKP equations are converted into nonlinear ODEs via two similarity reductions. The closed-form analytic solutions are achieved, including in the shape of distinct complex wave structures of solitons, dark and bright soliton shapes, double W-shaped soliton shapes, multi-peakon shapes, curved-shaped multi-wave solitons, and novel solitary wave solitons. All the obtained solutions are verified and validated by using back substitution to the original equation through Wolfram Mathematica. We analyze the dynamical behaviors of these obtained solutions with some three-dimensional graphics via numerical simulation. The obtained variable coefficient solutions are more relevant and useful for understanding the dynamical structures of nonlinear KP equations and shallow water wave models. [ABSTRACT FROM AUTHOR]

A boundary value problem for Hadamard fractional differential equations of variable order is studied. Note the symmetry of a transformation of a system of differential equations is connected with the locally solvability which is the same as the existence of solutions. It leads to the necessity of obtaining existence criteria for a boundary value problem for Hadamard fractional differential equations of variable order. Also, the stability in the sense of Ulam–Hyers–Rassias is investigated. The results are obtained based on the Kuratowski measure of noncompactness. An example illustrates the validity of the observed results. [ABSTRACT FROM AUTHOR]

Color images have a wider range of applications than gray images. There are two ways to extend the traditional super-resolution reconstruction method to color images: Super resolution reconstructs each channel of the color image individually; Change the RGB color bands into YCrCb color bands, then super-resolution reconstructs the luminance component and interpolates the chrominance components.These algorithms cannot effectively utilize the property that the edges and textures are similar in the RGB channels, and the results of those methods may lead to color artifacts. Aiming to solve these problems, we propose a new super-resolution method based on cross channel prior. First, a cross channel prior is proposed to describe the similarity of gradient in RGB channels. Then, a new super-resolution method is proposed for color images via combination of the cross channel prior and the traditional super-resolution methods. Finally, the proposed method reconstructs the color channels alternately. The experimental results show that the proposed method could effectively suppress the generation of color artifacts and improve the quality of the reconstructed images. [ABSTRACT FROM AUTHOR]

In engineering disciplines, many important problems are to be formed as boundary value problems (BVPs) that have conditions that are specified at the extremes. To handle such problems, the conventional shooting method that transforms BVPs into initial value problems has been extensively used, but it does not always guarantee solving the problem due to the possible failure of finding a proper initial guess. This paper proposes a universal initial guess finder that is composed of Bézier functions. Various dimensional problems that include Lambert's problem for several orbits around the spherically symmetric Earth are studied to validate the efficacy of the proposed approach, and the results are compared. [ABSTRACT FROM AUTHOR]

This article presents a new method of image filtering based on a new kind of image processing transformation, particularly the wavelet-Ateb–Gabor transformation, that is a wider basis for Gabor functions. Ateb functions are symmetric functions. The developed type of filtering makes it possible to perform image transformation and to obtain better biometric image recognition results than traditional filters allow. These results are possible due to the construction of various forms and sizes of the curves of the developed functions. Further, the wavelet transformation of Gabor filtering is investigated, and the time spent by the system on the operation is substantiated. The filtration is based on the images taken from NIST Special Database 302, that is publicly available. The reliability of the proposed method of wavelet-Ateb–Gabor filtering is proved by calculating and comparing the values of peak signal-to-noise ratio (PSNR) and mean square error (MSE) between two biometric images, one of which is filtered by the developed filtration method, and the other by the Gabor filter. The time characteristics of this filtering process are studied as well. [ABSTRACT FROM AUTHOR]

The frame-compatible packing for 3D contents is the feasible approach to archive the compatibility with the existing monocular broadcasting system. To perceive better 3D quality, the packed 3D frames are expanded to the full size at the decoder. In this paper, an interpolation technique enhancing and comparing the quality of enlarged halt vertical left and right stereo video in the top–bottom frame-compatible packing is presented. To this end, the appropriate interpolation modes from fourteen available modes for each row segment, which exploit the correlation between left and right stereoscopic as well as current and adjacent frames of individual view, are estimated at the encoder. Based on the information received from the encoder, at the decoder, the interpolation scheme can select the most appropriate available original data to find the missing values of to-be-discarded row segments. The proposed method outperformed than the state-of-the-art interpolation methods in terms of subjective visualization and numerical PSNRs and SSMI about 11%, with an execution time of about 12% comparisons. [ABSTRACT FROM AUTHOR]

The emergence of computer-aided design (CAD) has propelled the evolution of the sheet metal engineering field. Sheet metal design software tools include parameters associated to the part's forming process during the pattern drawing calculation. Current methods avoid the calculation of a first pattern drawing of the flattened part's neutral surface, independent of the forming process, leading to several methodological limitations. The study evaluates the reliability of the Computer Extended Descriptive Geometry (CeDG) approach to surpass those limitations. Three study cases that cover a significative range of sheet metal systems are defined and the associated solid models and patterns' drawings are computed through Geogebra-based CeDG and two selected CAD tools (Solid Edge 2020, LogiTRACE v14), with the aim of comparing their reliability and accuracy. Our results pointed to several methodological lacks in LogiTRACE and Solid Edge that prevented to solve properly several study cases. In opposition, the novel CeDG approach for the computer parametric modeling of 3D geometric systems overcame those limitations so that all models could be built and flattened with accuracy and without methodological limitations. As additional conclusion, the success of CeDG suggests the necessity to recover the relevance of descriptive geometry as a key core in graphic engineering. [ABSTRACT FROM AUTHOR]

This note presents a fuzzy optimization of Gabor filter-based object and text detection. The derivation of a 2D Gabor filter and the guidelines for the fuzzification of the filter parameters are described. The fuzzy Gabor filter proved to be a robust text an object detection method in low-quality input images as extensively evaluated in the problem of license plate localization. The extended set of examples confirmed that the fuzzy optimized Gabor filter with adequately fuzzified parameters detected the desired license plate texture components and highly improved the object detection when compared to the classic Gabor filter. The robustness of the proposed approach was further demonstrated on other images of various origin containing text and different textures, captured using low-cost or modest quality acquisition procedures. The possibility to fine tune the fuzzification procedure to better suit certain applications offers the potential to further boost detection performance. [ABSTRACT FROM AUTHOR]

Diabetic Retinopathy (DR) refers to the damages endured by the retina as an effect of diabetes. DR has become a severe health concern worldwide, as the number of diabetes patients is soaring uncountably. Periodic eye examination allows doctors to detect DR in patients at an early stage to initiate proper treatments. Advancements in artificial intelligence and camera technology have allowed us to automate the diagnosis of DR, which can benefit millions of patients indeed. This paper inscribes a novel method for DR diagnosis based on the gray-level intensity and texture features extracted from fundus images using a decision tree-based ensemble learning technique. This study primarily works with the Asia Pacific Tele-Ophthalmology Society 2019 Blindness Detection (APTOS 2019 BD) dataset. We undertook several steps to curate its contents to make them more suitable for machine learning applications. Our approach incorporates several image processing techniques, two feature extraction techniques, and one feature selection technique, which results in a classification accuracy of 94.20% (margin of error: ±0.32%) and an F-measure of 93.51% (margin of error: ±0.5%). Several other parameters regarding the proposed method's performance have been presented to manifest its robustness and reliability. Details on each employed technique have been included to make the provided results reproducible. This method can be a valuable tool for mass retinal screening to detect DR, thus drastically reducing the rate of vision loss attributed to it. [ABSTRACT FROM AUTHOR]

In general dynamic scenes, blurring is the result of the motion of multiple objects, camera shaking or scene depth variations. As an inverse process, deblurring extracts a sharp video sequence from the information contained in one single blurry image—it is itself an ill-posed computer vision problem. To reconstruct these sharp frames, traditional methods aim to build several convolutional neural networks (CNN) to generate different frames, resulting in expensive computation. To vanquish this problem, an innovative framework which can generate several sharp frames based on one CNN model is proposed. The motion-based image is put into our framework and the spatio-temporal information is encoded via several convolutional and pooling layers, and the output of our model is several sharp frames. Moreover, a blurry image does not have one-to-one correspondence with any sharp video sequence, since different video sequences can create similar blurry images, so neither the traditional pixel2pixel nor perceptual loss is suitable for focusing on non-aligned data. To alleviate this problem and model the blurring process, a novel contiguous blurry loss function is proposed which focuses on measuring the loss of non-aligned data. Experimental results show that the proposed model combined with the contiguous blurry loss can generate sharp video sequences efficiently and perform better than state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Herein, we investigated the controllability of a semilinear multi-valued differential equation with non-instantaneous impulses of order α ∈ (1 , 2) , where the linear part is a strongly continuous cosine family without compactness. We did not assume any compactness conditions on either the semi-group, the multi-valued function, or the inverse of the controllability operator, which is different from the previous literature. [ABSTRACT FROM AUTHOR]

Symmetries and their associated conserved quantities are of great importance in the study of dynamic systems. In this paper, we describe nonconservative field theories on time scales—a model that brings together, in a single theory, discrete and continuous cases. After defining Hamilton's principle for nonconservative field theories on time scales, we obtain the associated Lagrange equations. Next, based on the Hamilton's action invariance for nonconservative field theories on time scales under the action of some infinitesimal transformations, we establish symmetric and quasi-symmetric Noether transformations, as well as generalized quasi-symmetric Noether transformations. Once the Noether symmetry selection criteria are defined, the conserved quantities for the nonconservative field theories on time scales are identified. We conclude with two examples to illustrate the applicability of the theory. [ABSTRACT FROM AUTHOR]

High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study spatial moduli of non-differentiability for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by space-time white noise. We use the underlying explicit kernels and spectral/harmonic analysis, yielding spatial moduli of non-differentiability for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. On the other hand, it builds on and complements Allouba and Xiao's earlier works on spatial uniform and local moduli of continuity of time fractional SPIDEs and their gradient. [ABSTRACT FROM AUTHOR]

Two distinct operational procedures are proposed for diagnosis and tracking of heart disease evolution (in particular atrial fibrillations). The first procedure, based on the application of non-linear dynamic methods (strange attractors, skewness, kurtosis, histograms, Lyapunov exponent, etc.) analyzes the electrical activity of the heart (electrocardiogram signals). The second procedure, based on multifractalization through Markovian and non-Markovian-type stochasticizations in the framework of the scale relativity theory, reconstructs any type of EKG signal by means of harmonic mappings from the usual space to the hyperbolic one. These mappings mime various scale transitions by differential geometries, in Riemann spaces with symmetries of S L (2 R) -type. Then, the two operational procedures are not mutually exclusive, but rather become complementary, through their finality, which is gaining valuable information concerning fibrillation crises. As such, the author's proposed method could be used for developing new models for medical diagnosis and evolution tracking of heart diseases (patterns dynamics, signal reconstruction, etc.). [ABSTRACT FROM AUTHOR]

Aerial images are large-scale and susceptible to light. Traditional image feature point matching algorithms cannot achieve satisfactory matching accuracy for aerial images. This paper proposes a recursive diffusion algorithm, which is scale-invariant and can be used to extract symmetrical areas of different images. This narrows the matching range of feature points by extracting high-density areas of the image and improving the matching accuracy through correlation analysis of high-density areas. Through experimental comparison, it can be found that the recursive diffusion algorithm has more advantages compared to the correlation coefficient method and the mean shift algorithm when matching accuracy of aerial images, especially when the light of aerial images changes greatly. [ABSTRACT FROM AUTHOR]

The assessment of immunogenicity of biopharmaceuticals is a crucial step in the process of their development. Immunogenicity is related to the activation of adaptive immunity. The complexity of the immune system manifests through numerous different mechanisms, which allows the use of different approaches for predicting the immunogenicity of biopharmaceuticals. The direct experimental approaches are sometimes expensive and time consuming, or their results need to be confirmed. In this case, computational methods for immunogenicity prediction appear as an appropriate complement in the process of drug design. In this review, we analyze the use of various In silico methods and approaches for immunogenicity prediction of biomolecules: sequence alignment algorithms, predicting subcellular localization, searching for major histocompatibility complex (MHC) binding motifs, predicting T and B cell epitopes based on machine learning algorithms, molecular docking, and molecular dynamics simulations. Computational tools for antigenicity and allergenicity prediction also are considered. [ABSTRACT FROM AUTHOR]

The paper proposes composite materials for the manufacturing of parts of the car body structure, namely a door. This work aims to analyze the possibility of replacing the metal door of a vehicle with a door made of composite materials. Specific issues related to this replacement are analyzed in the paper. Test specimens were made of composite materials of different sizes, using several types of constituents to determine which material might be most suitable to replace metal in the manufacturing of the door. The choice of materials for the car door was made starting from the characteristics of the analyzed composite materials, but also taking into account the manufacturing possibilities and other engineering limitations. The behavior of the automotive structure as analyzed, using the finite element method for determining the stresses in the structure. Experimental verifications were performed on an experimental stand which has been specially designed for this purpose, to validate the proposed model. [ABSTRACT FROM AUTHOR]

Geometric feature extraction of 3D point clouds plays an important role in many 3D computer vision applications such as region labeling, 3D reconstruction, object segmentation, and recognition. However, hand-designed features on point clouds lack semantic information, so cannot meet these requirements. In this paper, we propose local feature extraction network (LFE-Net) which focus on extracting local feature for point clouds analysis. Such geometric features learning from a relation of local points can be used in a variety of shape analysis problems such as classification, part segmentation, and point matching. LFE-Net consists of local geometric relation (LGR) module which aims to learn a high-dimensional local feature to express the relation between points and their neighbors. Benefiting from the additional singular values of local points and hierarchical neural networks, the learned local features are robust to permutation and rigid transformation so that they can be transformed into 3D descriptors. Moreover, we embed prior spatial information of the local points into the sub-features for combining features from multiple levels. LFE-Net achieves state-of-the-art performances on standard benchmarks including ModelNet40, ShapeNetPart. [ABSTRACT FROM AUTHOR]

Many man-made or natural objects are composed of symmetric parts and possess symmetric physical behavior. Although its shape can exactly follow a symmetry in the designing or modeling stage, its discretized mesh in the analysis stage may be asymmetric because generating a mesh exactly following the symmetry is usually costly. As a consequence, the expected symmetric physical behavior may not be faithfully reproduced due to the asymmetry of the mesh. To solve this problem, we propose to optimize the material parameters of the mesh for static and kinematic symmetry behavior. Specifically, under the situation of static equilibrium, Young's modulus is properly scaled so that a symmetric force field leads to symmetric displacement. For kinematics, the mass is optimized to reproduce symmetric acceleration under a symmetric force field. To efficiently measure the deviation from symmetry, we formulate a linear operator whose kernel contains all the symmetric vector fields, which helps to characterize the asymmetry error via a simple ℓ 2 norm. To make the resulting material suitable for the general situation, the symmetric training force fields are derived from modal analysis in the above kernel space. Results show that our optimized material significantly reduces the asymmetric error on an asymmetric mesh in both static and dynamic simulations. [ABSTRACT FROM AUTHOR]

The accuracy of novel lump solutions of the potential form of the three–dimensional potential Yu–Toda–Sasa–Fukuyama (3-Dp-YTSF) equation is investigated. These solutions are obtained by employing the extended simplest equation (ESE) and modified Kudryashov (MKud) schemes to explore its lump and breather wave solutions that characterizes the dynamics of solitons and nonlinear waves in weakly dispersive media, plasma physics, and fluid dynamics. The accuracy of the obtained analytical solutions is investigated through the perspective of numerical and semi-analytical strategies (septic B-spline (SBS) and variational iteration (VI) techniques). Additionally, matching the analytical and numerical solutions is represented along with some distinct types of sketches. The superiority of the MKud is showed as the fourth research paper in our series that has been beginning by Mostafa M. A. Khater and Carlo Cattani with the title "Accuracy of computational schemes". The functioning of employed schemes appears their effectual and ability to apply to different nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The time–fractional reaction–diffusion (TFRD) model has broad physical perspectives and theoretical interpretation, and its numerical techniques are of significant conceptual and applied importance. A numerical technique is constructed for the solution of the TFRD model with the non-singular kernel. The Caputo–Fabrizio operator is applied for the discretization of time levels while the extended cubic B-spline (ECBS) function is applied for the space direction. The ECBS function preserves geometrical invariability, convex hull and symmetry property. Unconditional stability and convergence analysis are also proved. The projected numerical method is tested on two numerical examples. The theoretical and numerical results demonstrate that the order of convergence of 2 in time and space directions. [ABSTRACT FROM AUTHOR]

This article aims to study numerically the rotating, steady, and three-dimensional (3D) flow of a hybrid nanofluid over an exponentially shrinking sheet with the suction effect. We considered water as base fluid and alumina ( A l 2 O 3 ), and copper ( C u ) as solid nanoparticles. The system of governing partial differential equations (PDEs) was transformed by an exponential similarity variable into the equivalent system of ordinary differential equations (ODEs). By applying a three-stage Labatto III-A method that is available in bvp4c solver in the Matlab software, the resultant system of ODEs was solved numerically. In the case of the hybrid nanofluid, the heat transfer rate improves relative to the viscous fluid and regular nanofluid. Two branches were obtained in certain ranges of the involved parameters. The results of the stability analysis revealed that the upper branch is stable. Moreover, the results also indicated that the equations of the hybrid nanofluid have a symmetrical solution for different values of the rotation parameter (Ω). [ABSTRACT FROM AUTHOR]

In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of S c ≤ S   and   M c ≤ M ( S c > S   and   M c > M ). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised. [ABSTRACT FROM AUTHOR]

This research article aims to investigate the consequences of binary chemical reaction, thermal radiation, and Soret–Dufour effects on a steady incompressible Darcy–Forchheimer flow of nanofluids. Stretching surface is assumed to drive the fluid along positive horizontal direction. Brownian motion, and the Thermophoresis are accounted in particular. The governing highly nonlinear system of problems which are advanced version of Navier–Stokes equations are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations invoking symmetric property of the independent variables. The numerical approach using RK45 in connection with shooting technique is adopted to solve the final equations. Graphical approach is used to interpret the results and the values of important physical quantities are given in tabular data form. Velocity field, temperature distribution and concentration distribution are graphically analyzed for variation in respective fluid parameters. Furthermore, density graphs and stream lines are sketched for the present model. The outputs indicate a rise of temperature field in connection with thermal radiation parameter. A clear decline is noticed in velocity field for elevated values of Forchheimer number and porosity factor. The Dufour effect anticipates a rising factor for temperature distribution and the same is noticed for concentration distribution in lieu of Soret effect. Thermal radiation and binary chemical reaction has strong impact on heat transport mechanism. The results for physical quantities such as skin friction, heat and mass flux rates are given in tabular data form in last section of this study. [ABSTRACT FROM AUTHOR]

In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces. [ABSTRACT FROM AUTHOR]

The telegraph model describes that the current and voltage waves can be reflected on a wire, that symmetrical wave patterns can form along a line. A numerical study of these voltage and current waves on a transferral line has been proposed via a modified extended cubic B-spline (MECBS) method. The B-spline functions have the flexibility and high order accuracy to approximate the solutions. These functions also preserve the symmetrical property. The MECBS and Crank Nicolson technique are employed to find out the solution of the non-linear time fractional telegraph equation. The time direction is discretized in the Caputo sense while the space dimension is discretized by the modified extended cubic B-spline. The non-linearity in the equation is linearized by Taylor's series. The proposed algorithm is unconditionally stable and convergent. The numerical examples are displayed to verify the authenticity and implementation of the method. [ABSTRACT FROM AUTHOR]

In this paper, a Bayesian analysis of finite mixture autoregressive (MAR) models based on the assumption of scale mixtures of skew-normal (SMSN) innovations (called SMSN–MAR) is considered. This model is not simultaneously sensitive to outliers, as the celebrated SMSN distributions, because the proposed MAR model covers the lightly/heavily-tailed symmetric and asymmetric innovations. This model allows us to have robust inferences on some non-linear time series with skewness and heavy tails. Classical inferences about the mixture models have some problematic issues that can be solved using Bayesian approaches. The stochastic representation of the SMSN family allows us to develop a Bayesian analysis considering the informative prior distributions in the proposed model. Some simulations and real data are also presented to illustrate the usefulness of the proposed models. [ABSTRACT FROM AUTHOR]

Recently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that the dynamics of the proposed fractional maps are sensitive to both initial conditions and fractional order. There are coexisting attractors which have been displayed in terms of bifurcation diagrams, phase portraits and a 0-1 test. Furthermore, control schemes are introduced to stabilize the chaotic trajectories of the two novel systems. [ABSTRACT FROM AUTHOR]

Our work is based on the multiple inequalities illustrated in 1967 by E. K. Godunova and V. I. Levin, in 1990 by Hwang and Yang and in 1993 by B. G. Pachpatte. With the help of the dynamic Jensen and Hölder inequality, we generalize a number of those inequalities to a general time scale. In addition to these generalizations, some integral and discrete inequalities will be obtained as special cases of our results. [ABSTRACT FROM AUTHOR]

Present communication aims to inspect the entropy optimization, heat and mass transport in Darcy-Forchheimer nanofluid flow surrounded by a non-linearly stretching surface. Navier-Stokes model based governing equations for non-Newtonian nanofluids having symmetric components in various terms are considered. Non-linear stretching is assumed to be the driving force whereas influence of thermal radiation, Brownian diffusion, dissipation and thermophoresis is considered. Importantly, entropy optimization is performed using second law of thermodynamics. Governing problems are converted into nonlinear ordinary problems (ODEs) using suitably adjusted transformations. RK-45 based built-in shooting mechanism is used to solve the problems. Final outcomes are plotted graphically. In addition to velocity, temperature, concentration and Bejan number, the stream lines, contour graphs and density graphs have been prepared. For their industrial and engineering importance, results for wall-drag force, heat flux (Nusselt) rate and mass flux (Sherwood) rate are also given in tabular data form. Outputs indicate that velocity reduces for Forchheimer number as well as for the porosity factor. However, a rise is noted in temperature distribution for elevated values of thermal radiation. Entropy optimization shows enhancement for larger values of temperature difference ratio. Skin-friction enhances for all relevant parameters involved in momentum equation. [ABSTRACT FROM AUTHOR]

Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a concrete role in the field of inequalities due to the behaviour of its definition. There is a strong relationship between convexity and symmetry. Which ever one we work on, we can apply to the other one due to the strong correlation produced between them especially in recent few years. In this article, we first introduced the notion of λ -incomplete gamma function. Using the new notation, we established a few inequalities of the Hermite–Hadamard (HH) type involved the tempered fractional integrals for the convex functions which cover the previously published result such as Riemann integrals, Riemann–Liouville fractional integrals. Finally, three example are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function. [ABSTRACT FROM AUTHOR]

Our work is based on the multiple inequalities illustrated in 2020 by Hamiaz and Abuelela. With the help of a Fenchel-Legendre transform, which is used in various problems involving symmetry, we generalize a number of those inequalities to a general time scale. Besides that, in order to get new results as special cases, we will extend our results to continuous and discrete calculus. [ABSTRACT FROM AUTHOR]

Numerical simulations are performed to examine the effect of size of control rods (d1) and spacing ratio (g) on flow around a square rod with upstream and downstream control rods aligned in-line using the lattice Boltzmann method (LBM). The Reynolds number (Re) is fixed at Re = 160, while the spacing between the main rod and control rods is taken in the range 1 ≤ g ≤ 5 and the size of the control rod is varied between 4 and 20. Seven different types of flow mods are observed in this study at different values of g and d1. Variation in force statistics, like mean drag coefficient (Cdmean), Strouhal number (St), root mean square values of drag (Cdrms) and lift coefficients (Clrms), and percentage reduction in mean drag coefficient is discussed in detail. It was examined that vortex shedding completely suppressed at (g, d1) = (1, 12), (2, 12), and (2, 16) where steady flow mode exists. Moreover, it was found that at large gap spacing, where g = 5, the effect of control rods on the main rod vanishes. Due to this strong vortex shedding produced and as a result, maximum value of Cdmean is found at (g, d1) = (5, 8). The negative values of mean drag force are also observed at some gap spacing and size of control rods are due to the effect of thrust. Furthermore, the maximum percentage reduction in Cdmean is 121%, found at (g, d1) = (2, 20). [ABSTRACT FROM AUTHOR]

By using the contemporary theory of inequalities, this study is devoted to proposing a number of refinements inequalities for the Hermite-Hadamard's type inequality and conclude explicit bounds for two new definitions of (p 1 p 2 , q 1 q 2) -differentiable function and (p 1 p 2 , q 1 q 2) -integral for two variables mappings over finite rectangles by using pre-invex set. We have derived a new auxiliary result for (p 1 p 2 , q 1 q 2) -integral. Meanwhile, by using the symmetry of an auxiliary result, it is shown that novel variants of the the Hermite-Hadamard type for (p 1 p 2 , q 1 q 2) -differentiable utilizing new definitions of generalized higher-order strongly pre-invex and quasi-pre-invex mappings. It is to be acknowledged that this research study would develop new possibilities in pre-invex theory, quantum mechanics and special relativity frameworks of varying nature for thorough investigation. [ABSTRACT FROM AUTHOR]

In this paper, the newly proposed concept of Raina's function and quantum calculus are utilized to anticipate the quantum behavior of two variable Ostrowski-type inequalities. This new technique is the convolution of special functions with hypergeometric and Mittag–Leffler functions, respectively. This new concept will have the option to reduce self-similitudes in the quantum attractors under investigation. We discuss the implications and other consequences of the quantum Ostrowski-type inequalities by deriving an auxiliary result for a q 1 q 2 -differentiable function by inserting Raina's functions. Meanwhile, we present a numerical scheme that can be used to derive variants for Ostrowski-type inequalities in the sense of coordinated generalized Φ -convex functions with the quantum approach. This new scheme of study for varying values of parameters with the involvement of Raina's function yields extremely intriguing outcomes with an illustrative example. It is supposed that this investigation will provide new directions for the capricious nature of quantum theory. [ABSTRACT FROM AUTHOR]

This paper studies a simple skewness measure to detect symmetry and asymmetry in samples. The statistic can be obviously applied with only three short central tendencies; i.e., the first and ninth deciles, and the median. The strength of the statistic to find symmetry and asymmetry is studied by employing numerous Monte Carlo simulations and is compared with some alternative measures by applying some simulation studies. The results show that the performance of this statistic is generally good in the simulation. [ABSTRACT FROM AUTHOR]

Similar to other fluids (Newtonian and non-Newtonian), micropolar fluid also exhibits symmetric flow and exact symmetric solution similar to the Navier–Stokes equation; however, it is not always realizable. In this article, the Buongiorno mathematical model of hydromagnetic micropolar nanofluid is considered. A joint phenomenon of heat and mass transfer is studied in this work. This model indeed incorporates two important effects, namely, the Brownian motion and the thermophoretic. In addition, the effects of magnetohydrodynamic (MHD) and chemical reaction are considered. The fluid is taken over a slanted, stretching surface making an inclination with the vertical one. Suitable similarity transformations are applied to develop a nonlinear transformed model in terms of ODEs (ordinary differential equations). For the numerical simulations, an efficient, stable, and reliable scheme of Keller-box is applied to the transformed model. More exactly, the governing system of equations is written in the first order system and then arranged in the forms of a matrix system using the block-tridiagonal factorization. These numerical simulations are then arranged in graphs for various parameters of interest. The physical quantities including skin friction, Nusselt number, and Sherwood number along with different effects involved in the governing equations are also justified through graphs. The consequences reveal that concentration profile increases by increasing chemical reaction parameters. In addition, the Nusselt number and Sherwood number decreases by decreasing the inclination. [ABSTRACT FROM AUTHOR]

In Hilbert space, we develop a novel framework to study for two new classes of convex function depending on arbitrary non-negative function, which is called a predominating ℏ-convex function and predominating quasiconvex function, with respect to η , are presented. To ensure the symmetry of data segmentation and with the discussion of special cases, it is shown that these classes capture other classes of η -convex functions, η -quasiconvex functions, strongly ℏ-convex functions of higher-order and strongly quasiconvex functions of a higher order, etc. Meanwhile, an auxiliary result is proved in the sense of κ -fractional integral operator to generate novel variants related to the Hermite–Hadamard type for p t h -order differentiability. It is hoped that this research study will open new doors for in-depth investigation in convexity theory frameworks of a varying nature. [ABSTRACT FROM AUTHOR]