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Two Inverse Problems Solution by Feedback Tracking Control -
Analytic Representation of Maxwell—Boltzmann and Tsallis Thermonuclear Functions with Depleted Tail -
Relaxation Limit of the Aggregation Equation with Pointy Potential -
A Fractional-in-Time Prey–Predator Model with Hunting Cooperation -
Singular Integral Neumann BC for Elliptic PDEs
Journal Description
Axioms
Axioms
is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published quarterly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT), International Fuzzy Systems Association (IFSA) and Union of Slovak Mathematicians and Physicists (JSMF) are affiliated with Axioms and their members receive discounts on the article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High visibility: indexed within Scopus, SCIE (Web of Science), dblp, and many other databases.
- Journal Rank: CiteScore - Q1 (Algebra and Number Theory)
- Rapid Publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 19.6 days after submission; acceptance to publication is undertaken in 3.8 days (median values for papers published in this journal in the first half of 2021).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Latest Articles
New Necessary Conditions for theWell-Posedness of Steady Bioconvective Flows and Their Small Perturbations
Axioms 2021, 10(3), 205; https://doi.org/10.3390/axioms10030205 - 29 Aug 2021
Abstract
We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the
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We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the application of the Galerkin method, and the system considered consists of three equations: the nonlinear Navier–Stokes equation, the incompressibility equation, and a parabolic conservation equation, where the unknowns are the fluid velocity, the hydrostatic pressure, and the concentration of microorganisms. The boundary conditions are homogeneous and of zero-flux-type, for the cases of fluid velocity and microorganism concentration, respectively.
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(This article belongs to the Special Issue Advances in Applied Mathematical Analysis)
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How Containment Can Effectively Suppress the Outbreak of COVID-19: A Mathematical Modeling
Axioms 2021, 10(3), 204; https://doi.org/10.3390/axioms10030204 - 28 Aug 2021
Abstract
In this paper, the aim is to capture the global pandemic of COVID-19 with parameters that consider the interactions among individuals by proposing a mathematical model. The introduction of a parsimonious model captures both the isolation of symptomatic infected individuals and population lockdown
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In this paper, the aim is to capture the global pandemic of COVID-19 with parameters that consider the interactions among individuals by proposing a mathematical model. The introduction of a parsimonious model captures both the isolation of symptomatic infected individuals and population lockdown practices in response to containment policies. Local stability and basic reproduction numbers are analyzed. Local sensitivity indices of the parameters of the proposed model are calculated, using the non-normalization, half-normalization, and full-normalization techniques. Numerical investigations show that the dynamics of the system depend on the model parameters. The infection transmission rate (as a function of the lockdown parameter) for both reported and unreported symptomatic infected peoples is a significant parameter in spreading the infection. A nationwide public lockdown decreases the number of infected cases and stops the pandemic’s peak from occurring. The results obtained from this study are beneficial worldwide for developing different COVID-19 management programs.
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(This article belongs to the Special Issue Mathematics of the COVID-19)
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The Soliton Solutions for Some Nonlinear Fractional Differential Equations with Beta-Derivative
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Axioms 2021, 10(3), 203; https://doi.org/10.3390/axioms10030203 - 26 Aug 2021
Abstract
Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, He’s semi-inverse variation method and the ansatz
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Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, He’s semi-inverse variation method and the ansatz method have been applied to find the soliton solutions for fractional Korteweg–de Vries equation, fractional equal width equation, and fractional modified equal width equation defined by Atangana’s conformable derivative (beta-derivative). These two methods are effective methods employed to get the soliton solutions of these nonlinear equations. All of the calculations in this work have been obtained using the Maple program and the solutions have been replaced in the equations and their accuracy has been confirmed. In addition, graphics of some of the solutions are also included. The found solutions in this study have the potential to be useful in mathematical physics and engineering.
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(This article belongs to the Special Issue Advances in Mathematics and Its Applications)
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Numerical Solution for Singular Boundary Value Problems Using a Pair of Hybrid Nyström Techniques
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Axioms 2021, 10(3), 202; https://doi.org/10.3390/axioms10030202 - 25 Aug 2021
Abstract
This manuscript presents an efficient pair of hybrid Nyström techniques to solve second-order Lane–Emden singular boundary value problems directly. One of the proposed strategies uses three off-step points. The obtained formulas are paired with an appropriate set of formulas implemented for the first
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This manuscript presents an efficient pair of hybrid Nyström techniques to solve second-order Lane–Emden singular boundary value problems directly. One of the proposed strategies uses three off-step points. The obtained formulas are paired with an appropriate set of formulas implemented for the first step to avoid singularity at the left end of the integration interval. The fundamental properties of the proposed scheme are analyzed. Some test problems, including chemical kinetics and physical model problems, are solved numerically to determine the efficiency and validity of the proposed approach.
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(This article belongs to the Special Issue Advances in Nonlinear Boundary Value Problems: Theory and Applications)
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On Self-Aggregations of Min-Subgroups
Axioms 2021, 10(3), 201; https://doi.org/10.3390/axioms10030201 - 24 Aug 2021
Abstract
Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has
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Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions . However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.
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(This article belongs to the Special Issue Advance in Topology and Functional Analysis——In Honour of María Jesús Chasco's 65th Birthday)
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Improved Block-Pulse Functions for Numerical Solution of Mixed Volterra-Fredholm Integral Equations
Axioms 2021, 10(3), 200; https://doi.org/10.3390/axioms10030200 - 24 Aug 2021
Abstract
The present paper employs a numerical method based on the improved block–pulse basis functions (IBPFs). This was mainly performed to resolve the Volterra–Fredholm integral equations of the second kind. Those equations are often simplified into a linear system of algebraic equations through the
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The present paper employs a numerical method based on the improved block–pulse basis functions (IBPFs). This was mainly performed to resolve the Volterra–Fredholm integral equations of the second kind. Those equations are often simplified into a linear system of algebraic equations through the use of IBPFs in addition to the operational matrix of integration. Typically, the classical alterations have enhanced the time taken by the computer program to solve the system of algebraic equations. The current modification works perfectly and has improved the efficiency over the regular block–pulse basis functions (BPF). Additionally, the paper handles the uniqueness plus the convergence theorems of the solution. Numerical examples have been presented to illustrate the efficiency as well as the accuracy of the method. Furthermore, tables and graphs are used to show and confirm how the method is highly efficient.
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(This article belongs to the Special Issue Dedicated to Professor Ji-Huan He on the Occasion of His 55th Birthday)
Open AccessArticle
Random Walk Analysis in a Reliability System under Constant Degradation and Random Shocks
Axioms 2021, 10(3), 199; https://doi.org/10.3390/axioms10030199 - 23 Aug 2021
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In this paper, we study a reliability system subject to occasional random shocks hitting an underlying device in accordance with a general marked point process with position dependent marking. In addition, the system ages according to a linear path that eventually fails even
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In this paper, we study a reliability system subject to occasional random shocks hitting an underlying device in accordance with a general marked point process with position dependent marking. In addition, the system ages according to a linear path that eventually fails even without any external shocks that accelerate the total failure. The approach for obtaining the distribution of the failure time falls into the area of random walk analysis. The results obtained are in closed form. A special case of a marked Poisson process with exponentially distributed marks is discussed that supports our claim of analytical tractability. The example is further confirmed by simulation. We also provide a classification of the literature pertaining to various reliability systems with degradation and shocks.
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Closure System and Its Semantics
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Axioms 2021, 10(3), 198; https://doi.org/10.3390/axioms10030198 - 23 Aug 2021
Abstract
It is well known that topological spaces are axiomatically characterized by the topological closure operator satisfying the Kuratowski Closure Axioms. Equivalently, they can be axiomatized by other set operators encoding primitive semantics of topology, such as interior operator, exterior operator, boundary operator, or
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It is well known that topological spaces are axiomatically characterized by the topological closure operator satisfying the Kuratowski Closure Axioms. Equivalently, they can be axiomatized by other set operators encoding primitive semantics of topology, such as interior operator, exterior operator, boundary operator, or derived-set operator (or dually, co-derived-set operator). It is also known that a topological closure operator (and dually, a topological interior operator) can be weakened into generalized closure (interior) systems. What about boundary operator, exterior operator, and derived-set (and co-derived-set) operator in the weakened systems? Our paper completely answers this question by showing that the above six set operators can all be weakened (from their topological counterparts) in an appropriate way such that their inter-relationships remain essentially the same as in topological systems. Moreover, we show that the semantics of an interior point, an exterior point, a boundary point, an accumulation point, a co-accumulation point, an isolated point, a repelling point, etc. with respect to a given set, can be extended to an arbitrary subset system simply by treating the subset system as a base of a generalized interior system (and hence its dual, a generalized closure system). This allows us to extend topological semantics, namely the characterization of points with respect to an arbitrary set, in terms of both its spatial relations (interior, exterior, or boundary) and its dynamic convergence of any sequence (accumulation, co-accumulation, and isolation), to much weakened systems and hence with wider applicability. Examples from the theory of matroid and of Knowledge/Learning Spaces are used as an illustration.
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Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem
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Axioms 2021, 10(3), 197; https://doi.org/10.3390/axioms10030197 - 23 Aug 2021
Abstract
In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms
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In this paper, we present some modified relaxed CQ algorithms with different kinds of step size and perturbation to solve the Multiple-sets Split Feasibility Problem (MSSFP). Under mild assumptions, we establish weak convergence and prove the bounded perturbation resilience of the proposed algorithms in Hilbert spaces. Treating appropriate inertial terms as bounded perturbations, we construct the inertial acceleration versions of the corresponding algorithms. Finally, for the LASSO problem and three experimental examples, numerical computations are given to demonstrate the efficiency of the proposed algorithms and the validity of the inertial perturbation.
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(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
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An Improved Tikhonov-Regularized Variable Projection Algorithm for Separable Nonlinear Least Squares
Axioms 2021, 10(3), 196; https://doi.org/10.3390/axioms10030196 - 22 Aug 2021
Abstract
In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using the variable projection method. Based on the truncated singular value decomposition method and the Tikhonov regularization method, we propose an improved Tikhonov regularization method, which neither
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In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using the variable projection method. Based on the truncated singular value decomposition method and the Tikhonov regularization method, we propose an improved Tikhonov regularization method, which neither discards small singular values, nor treats all singular value corrections. By fitting the Mackey–Glass time series in an exponential model, we compare the three regularization methods, and the numerically simulated results indicate that the improved regularization method is more effective at reducing the mean square error of the solution and increasing the accuracy of unknowns.
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(This article belongs to the Special Issue Dedicated to Professor Ji-Huan He on the Occasion of His 55th Birthday)
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Global Directed Dynamic Behaviors of a Lotka-Volterra Competition-Diffusion-Advection System
Axioms 2021, 10(3), 195; https://doi.org/10.3390/axioms10030195 - 20 Aug 2021
Abstract
This paper investigates the problem of the global directed dynamic behaviors of a Lotka-Volterra competition-diffusion-advection system between two organisms in heterogeneous environments. The two organisms not only compete for different basic resources, but also the advection and diffusion strategies follow the dispersal towards
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This paper investigates the problem of the global directed dynamic behaviors of a Lotka-Volterra competition-diffusion-advection system between two organisms in heterogeneous environments. The two organisms not only compete for different basic resources, but also the advection and diffusion strategies follow the dispersal towards a positive distribution. By virtue of the principal eigenvalue theory, the linear stability of the co-existing steady state is established. Furthermore, the classification of dynamical behaviors is shown by utilizing the monotone dynamical system theory. This work can be seen as a further development of a competition-diffusion system.
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(This article belongs to the Special Issue Nonlinear Dynamical Systems with Applications)
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Differential Evolution with Shadowed and General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal Design of Fuzzy Controllers
Axioms 2021, 10(3), 194; https://doi.org/10.3390/axioms10030194 - 19 Aug 2021
Abstract
This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems
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This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems in different types of benchmark problems and it has been found that the use of fuzzy logic in combination with the differential evolution algorithm gives good results. In some of the studies, it is clearly shown that, when compared to other algorithms, our methodology turns out to be statistically better. In this case, the mutation parameter is dynamically moved during the evolution process by using shadowed and general type-2 fuzzy systems. The main contribution of this work is the ability to determine, through experimentation in a benchmark control problem, which of the two kinds of the used fuzzy systems has better results when combined with the differential evolution algorithm. This is because there are no similar works to our proposal in which shadowed and general type 2 fuzzy systems are used and compared. Moreover, to validate the performance of both fuzzy systems, a noise level is used in the controller, which simulates the disturbances that may exist in the real world and is thus able to validate statistically if there are significant differences between shadowed and general type 2 fuzzy systems.
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(This article belongs to the Special Issue Fuzzy Control Systems: Theory and Applications)
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The Representation of D-Invariant Polynomial Subspaces Based on Symmetric Cartesian Tensors
Axioms 2021, 10(3), 193; https://doi.org/10.3390/axioms10030193 - 19 Aug 2021
Abstract
Multivariate polynomial interpolation plays a crucial role both in scientific computation and engineering application. Exploring the structure of the D-invariant (closed under differentiation) polynomial subspaces has significant meaning for multivariate Hermite-type interpolation (especially ideal interpolation). We analyze the structure of a D
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Multivariate polynomial interpolation plays a crucial role both in scientific computation and engineering application. Exploring the structure of the D-invariant (closed under differentiation) polynomial subspaces has significant meaning for multivariate Hermite-type interpolation (especially ideal interpolation). We analyze the structure of a D-invariant polynomial subspace in terms of Cartesian tensors, where is a subspace with a maximal total degree equal to . For an arbitrary homogeneous polynomial of total degree k in , can be rewritten as the inner products of a kth order symmetric Cartesian tensor and k column vectors of indeterminates. We show that can be determined by all polynomials of a total degree one in . Namely, if we treat all linear polynomials on the basis of as a column vector, then this vector can be written as a product of a coefficient matrix and a column vector of indeterminates; our main result shows that the kth order symmetric Cartesian tensor corresponds to is a product of some so-called relational matrices and .
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(This article belongs to the Special Issue Computing Methods in Mathematics and Engineering)
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Oscillation and Asymptotic Properties of Differential Equations of Third-Order
Axioms 2021, 10(3), 192; https://doi.org/10.3390/axioms10030192 - 18 Aug 2021
Abstract
The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator
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The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator where and . New oscillation results are established by using the generalized Riccati technique under the assumption of < . Our new results complement the related contributions to the subject. An example is given to prove the significance of new theorem.
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(This article belongs to the Special Issue Non-local Mathematical Models and Applications: A Theme Issue in Honor of Prof. Carlo Cattani)
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Periodic Property and Instability of a Rotating Pendulum System
Axioms 2021, 10(3), 191; https://doi.org/10.3390/axioms10030191 - 18 Aug 2021
Abstract
The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic
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The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.
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(This article belongs to the Special Issue Dedicated to Professor Ji-Huan He on the Occasion of His 55th Birthday)
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Advances in the Theory of Compact Groups and Pro-Lie Groups in the Last Quarter Century
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Axioms 2021, 10(3), 190; https://doi.org/10.3390/axioms10030190 - 17 Aug 2021
Abstract
This article surveys the development of the theory of compact groups and pro-Lie groups, contextualizing the major achievements over 125 years and focusing on some progress in the last quarter century. It begins with developments in the 18th and 19th centuries. Next is
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This article surveys the development of the theory of compact groups and pro-Lie groups, contextualizing the major achievements over 125 years and focusing on some progress in the last quarter century. It begins with developments in the 18th and 19th centuries. Next is from Hilbert’s Fifth Problem in 1900 to its solution in 1952 by Montgomery, Zippin, and Gleason and Yamabe’s important structure theorem on almost connected locally compact groups. This half century included profound contributions by Weyl and Peter, Haar, Pontryagin, van Kampen, Weil, and Iwasawa. The focus in the last quarter century has been structure theory, largely resulting from extending Lie Theory to compact groups and then to pro-Lie groups, which are projective limits of finite-dimensional Lie groups. The category of pro-Lie groups is the smallest complete category containing Lie groups and includes all compact groups, locally compact abelian groups, and connected locally compact groups. Amongst the structure theorems is that each almost connected pro-Lie group G is homeomorphic to for a suitable set I and some compact subgroup C. Finally, there is a perfect generalization to compact groups G of the age-old natural duality of the group algebra of a finite group G to its representation algebra , via the natural duality of the topological vector space to the vector space , for any set I, thus opening a new approach to the Hochschild-Tannaka duality of compact groups.
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(This article belongs to the Special Issue Advance in Topology and Functional Analysis——In Honour of María Jesús Chasco's 65th Birthday)
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Reinitializing Sea Surface Temperature in the Ensemble Intermediate Coupled Model for Improved Forecasts
Axioms 2021, 10(3), 189; https://doi.org/10.3390/axioms10030189 - 17 Aug 2021
Abstract
The Ensemble Intermediate Coupled Model (EICM) is a model used for studying the El Niño-Southern Oscillation (ENSO) phenomenon in the Pacific Ocean, which is anomalies in the Sea Surface Temperature (SST) are observed. This research aims to implement Cressman to improve SST forecasts.
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The Ensemble Intermediate Coupled Model (EICM) is a model used for studying the El Niño-Southern Oscillation (ENSO) phenomenon in the Pacific Ocean, which is anomalies in the Sea Surface Temperature (SST) are observed. This research aims to implement Cressman to improve SST forecasts. The simulation considers two cases in this work: the control case and the Cressman initialized case. These cases are simulations using different inputs where the two inputs differ in terms of their resolution and data source. The Cressman method is used to initialize the model with an analysis product based on satellite data and in situ data such as ships, buoys, and Argo floats, with a resolution of 0.25 × 0.25 degrees. The results of this inclusion are the Cressman Initialized Ensemble Intermediate Coupled Model (CIEICM). Forecasting of the sea surface temperature anomalies was conducted using both the EICM and the CIEICM. The results show that the calculation of SST field from the CIEICM was more accurate than that from the EICM. The forecast using the CIEICM initialization with the higher-resolution satellite-based analysis at a 6-month lead time improved the root mean square deviation to 0.794 from 0.808 and the correlation coefficient to 0.630 from 0.611, compared the control model that was directly initialized with the low-resolution in-situ-based analysis.
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(This article belongs to the Special Issue Modern Problems of Mathematical Physics and Their Applications)
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Analysis on Controllability Results for Wellposedness of Impulsive Functional Abstract Second-Order Differential Equation with State-Dependent Delay
Axioms 2021, 10(3), 188; https://doi.org/10.3390/axioms10030188 - 16 Aug 2021
Abstract
The functional abstract second order impulsive differential equation with state dependent delay is studied in this paper. First, we consider a second order system and use a control to determine the controllability result. Then, using Sadovskii’s fixed point theorem, we get sufficient conditions
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The functional abstract second order impulsive differential equation with state dependent delay is studied in this paper. First, we consider a second order system and use a control to determine the controllability result. Then, using Sadovskii’s fixed point theorem, we get sufficient conditions for the controllability of the proposed system in a Banach space. The major goal of this study is to demonstrate the controllability of an abstract second-order impulsive differential system with a state dependent delay mechanism. The wellposed condition is then defined. Next, we studied whether the defined problem is wellposed. Finally, we apply our results to examine the controllability of the second order state dependent delay impulsive equation.
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(This article belongs to the Section Mathematical Analysis)
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An Extension of Beta Function by Using Wiman’s Function
Axioms 2021, 10(3), 187; https://doi.org/10.3390/axioms10030187 - 16 Aug 2021
Abstract
The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman. In particular, we study some functional relations, integral representation, Mellin transform and derivative formulas for this
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The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman. In particular, we study some functional relations, integral representation, Mellin transform and derivative formulas for this extended beta function.
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(This article belongs to the Special Issue Special Functions Associated with Fractional Calculus)
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The Fourth Fundamental Form IV of Dini-Type Helicoidal Hypersurface in the Four Dimensional Euclidean Space
by
Axioms 2021, 10(3), 186; https://doi.org/10.3390/axioms10030186 - 16 Aug 2021
Abstract
We introduce the fourth fundamental form of a Dini-type helicoidal hypersurface in the four dimensional Euclidean space . We find the Gauss map of helicoidal hypersurface in . We obtain the characteristic polynomial of shape operator matrix. Then, we
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We introduce the fourth fundamental form of a Dini-type helicoidal hypersurface in the four dimensional Euclidean space . We find the Gauss map of helicoidal hypersurface in . We obtain the characteristic polynomial of shape operator matrix. Then, we compute the fourth fundamental form matrix IV of the Dini-type helicoidal hypersurface. Moreover, we obtain the Dini-type rotational hypersurface, and reveal its differential geometric objects.
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(This article belongs to the Special Issue Applications of Differential Geometry II)
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