1,231 results
Search Results
2. Multivariate Tail Moments for Log-Elliptical Dependence Structures as Measures of Risks
- Author
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Tomer Shushi and Zinoviy Landsman
- Subjects
Multivariate statistics ,tail conditional expectation ,Physics and Astronomy (miscellaneous) ,log-skew-elliptical distributions ,General Mathematics ,Short paper ,Structure (category theory) ,Conditional expectation ,01 natural sciences ,Measure (mathematics) ,010104 statistics & probability ,log-elliptical distributions ,0502 economics and business ,Computer Science (miscellaneous) ,Econometrics ,multivariate tail covariance ,0101 mathematics ,Mathematics ,050208 finance ,lcsh:Mathematics ,05 social sciences ,Covariance ,lcsh:QA1-939 ,Chemistry (miscellaneous) ,Portfolio ,multivariate tail conditional expectation - Abstract
The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.
- Published
- 2021
3. Approximation of Endpoints for α—Reich–Suzuki Nonexpansive Mappings in Hyperbolic Metric Spaces
- Author
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Afrah An Abdou, Izhar Uddin, and Sajan Aggarwal
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,endpoint ,MathematicsofComputing_GENERAL ,Fixed-point theorem ,Fixed point ,01 natural sciences ,fixed point theorems ,010101 applied mathematics ,Metric space ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,α—Riech–Suzuki nonexpansive mapping ,Convergence (routing) ,Computer Science (miscellaneous) ,QA1-939 ,Computer Science::Programming Languages ,hyperbolic metric space ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics - Abstract
The concept of an endpoint is a relatively new concept compared to the concept of a fixed point. The aim of this paper is to perform a convergence analysis of M—iteration involving α—Reich–Suzuki nonexpansive mappings. In this paper, we prove strong and Δ—convergence theorems in a hyperbolic metric space. Thus, our results generalize and improve many existing results.
- Published
- 2021
4. Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings
- Author
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Mohammed Said Souid, Mohammed K. A. Kaabar, Zailan Siri, Shahram Rezapour, Francisco Martínez, Sina Etemad, and Ahmed Refice
- Subjects
Ulam–Hyers–Rassias stability ,Mathematics::Functional Analysis ,General Mathematics ,010102 general mathematics ,Fixed-point theorem ,variable-order operators ,implicit problem ,01 natural sciences ,Stability (probability) ,fixed point theorems ,010101 applied mathematics ,Nonlinear fractional differential equations ,piecewise constant functions ,Nonlinear system ,Computer Science (miscellaneous) ,QA1-939 ,Applied mathematics ,Order (group theory) ,Boundary value problem ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,Variable (mathematics) - Abstract
In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings.
- Published
- 2021
5. Altruistic Preference Models of Low-Carbon E-Commerce Supply Chain
- Author
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Liguo Zhou, Yuyan Wang, and Jianfeng Liu
- Subjects
General Mathematics ,media_common.quotation_subject ,Supply chain ,0211 other engineering and technologies ,02 engineering and technology ,Commission ,E-commerce ,010501 environmental sciences ,e-commerce platform ,altruistic preference ,01 natural sciences ,Altruism ,Profit (economics) ,Microeconomics ,low-carbon e-commerce supply chain ,Computer Science (miscellaneous) ,Economics ,QA1-939 ,Elasticity coefficient ,Engineering (miscellaneous) ,0105 earth and related environmental sciences ,media_common ,021103 operations research ,business.industry ,Preference ,Service level ,business ,Mathematics - Abstract
With the gradual popularity of online sales and the enhancement of consumers’ low-carbon awareness, the low-carbon e-commerce supply chain (LCECSC) has developed rapidly. However, most of the current research on LCECSC assumes that the decision-making body is rational, and there is less research on the irrational behavior of the e-platform altruistic preference. Therefore, aiming at the LCECSC composed of a single e-platform and a single manufacturer, this paper establishes two basic models with or without altruistic preference. Additionally, this paper combines the characteristics of online sales and assumes that altruistic preference is a proportional function of commission, then establishes a commission-based extended model with altruistic preference to further explore the influence of commission on its altruistic preference. The current literature does not consider this point, nor does it analyze the influence of other parameters on the degree of altruism preference. By comparing the optimal decisions and numerical analysis among the models, the following conclusions can be drawn that: (1) different from the traditional offline supply chain, the profit of the dominator e-platform is lower than the profit of the follower manufacturer, (2) when the consumers’ carbon emission reduction elasticity coefficient increases, service level, sales price, carbon emission reduction, sales, supply chain members profits, and system profit increase, ultimately improving economic and environmental performances, (3) the altruistic preference behavior of the e-platform is a behavior of ‘profit transferring’. The moderate altruistic preference is conducive to the stable operation and long-term development of LCECSC.
- Published
- 2021
6. Estimation of Electricity Generation by an Electro-Technical Complex with Photoelectric Panels Using Statistical Methods
- Author
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Anna Turysheva, Irina Voytyuk, and Daniel Guerra
- Subjects
Physics and Astronomy (miscellaneous) ,020209 energy ,General Mathematics ,solar power ,02 engineering and technology ,solar systems ,photovoltaic panel ,mathematical modeling ,statistics ,correlation ,skewness ,symmetry ,random variable distribution ,01 natural sciences ,010104 statistics & probability ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,QA1-939 ,Statistical physics ,0101 mathematics ,Solar power ,Mathematics ,business.industry ,Photovoltaic system ,Statistical model ,Symmetry (physics) ,Electricity generation ,Chemistry (miscellaneous) ,Skewness ,Probability distribution ,business ,Random variable - Abstract
This paper presents a computational tool for estimating energy generated by low-power photovoltaic systems based on the specific conditions of the study region since the characteristic energy equation can be obtained considering the main climatological factors affecting these systems in terms of the symmetry or skewness of the random distribution of the generated energy. Furthermore, this paper is aimed at determining any correlation that exists between meteorological variables with respect to the energy generated by 5-kW solar systems in the specific climatic conditions of the Republic of Cuba. The paper also presents the results of the influence of each climate factor on the distribution symmetry of the generated energy of the solar system. Studying symmetry in statistical models is important because they allow us to establish the degree of symmetry (or skewness), which is the probability distribution of a random variable, without having to make a graphical representation of it. Statistical skewness reports the degree to which observations are distributed evenly and proportionally above and below the center (highest) point of the distribution. In the case when the mentioned distribution is balanced, it is called symmetric.
- Published
- 2021
7. On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros
- Author
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Petko D. Proinov and Milena Petkova
- Subjects
Polynomial ,iteration functions ,Iterative method ,General Mathematics ,010103 numerical & computational mathematics ,Construct (python library) ,multi-point iterative methods ,Type (model theory) ,01 natural sciences ,Local convergence ,010101 applied mathematics ,error estimates ,Convergence (routing) ,semilocal convergence ,Computer Science (miscellaneous) ,QA1-939 ,Applied mathematics ,local convergence ,0101 mathematics ,polynomial zeros ,Engineering (miscellaneous) ,Multi point ,Mathematics - Abstract
In this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a uni-variate polynomial simultaneously. The first member of this family is the two-point Ehrlich-type iterative method introduced and studied by Trićković and Petković in 1999. The main purpose of the paper is to provide local and semilocal convergence analysis of the multi-point Ehrlich-type methods. Our local convergence theorem is obtained by an approach that was introduced by the authors in 2020. Two numerical examples are presented to show the applicability of our semilocal convergence theorem.
- Published
- 2021
8. Canonical Correlations and Nonlinear Dependencies
- Author
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Nicola Loperfido
- Subjects
Multivariate statistics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,canonical correlations ,02 engineering and technology ,01 natural sciences ,010104 statistics & probability ,sign symmetry ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,QA1-939 ,Statistical physics ,0101 mathematics ,skew-symmetric distribution ,Independence (probability theory) ,Mathematics ,central symmetry ,Probabilistic logic ,Conditional probability distribution ,Semiparametric model ,Nonlinear system ,Distribution (mathematics) ,Chemistry (miscellaneous) ,020201 artificial intelligence & image processing ,Canonical correlation - Abstract
Canonical correlation analysis (CCA) is the default method for investigating the linear dependence structure between two random vectors, but it might not detect nonlinear dependencies. This paper models the nonlinear dependencies between two random vectors by the perturbed independence distribution, a multivariate semiparametric model where CCA provides an insight into their nonlinear dependence structure. The paper also investigates some of its probabilistic and inferential properties, including marginal and conditional distributions, nonlinear transformations, maximum likelihood estimation and independence testing. Perturbed independence distributions are closely related to skew-symmetric ones.
- Published
- 2021
9. A New Class of Plane Curves with Arc Length Parametrization and Its Application to Linear Analysis of Curved Beams
- Author
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Snježana Maksimović and Aleksandar Borković
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Basis (linear algebra) ,Plane curve ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Static analysis ,Space (mathematics) ,01 natural sciences ,Computer Science::Digital Libraries ,010101 applied mathematics ,analytical solution ,Bernoulli–Euler beam ,special functions ,Special functions ,Computer Science (miscellaneous) ,QA1-939 ,arc-length parametrization ,Development (differential geometry) ,0101 mathematics ,Sturm–Liouville differential equation ,Engineering (miscellaneous) ,Arc length ,Parametrization ,Mathematics - Abstract
The objective of this paper is to define one class of plane curves with arc-length parametrization. To accomplish this, we constructed a novel class of special polynomials and special functions. These functions form a basis of L2(R) space and some of their interesting properties are discussed. The developed curves are used for the linear static analysis of curved Bernoulli–Euler beam. Due to the parametrization with arc length, the exact analytical solution can be obtained. These closed-form solutions serve as the benchmark results for the development of numerical procedures. One such example is provided in this paper.
- Published
- 2021
10. Hermite–Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus
- Author
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Jessada Tariboon, Sotiris K. Ntouyas, Hüseyin Budak, Muhammad Ali, and [Belirlenecek]
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Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Quantum calculus ,co-ordinated convexity ,quantum calculus ,01 natural sciences ,Interval valued ,Hadamard transform ,(p ,Hermite–Hadamard inequality ,Hermite–Hadamard inclusion ,Computer Science (miscellaneous) ,QA1-939 ,0101 mathematics ,interval-valued functions ,Mathematics ,Hermite polynomials ,010102 general mathematics ,Regular polygon ,(p, q)-integral ,Convex ,010101 applied mathematics ,Hermite-Hadamard inequality ,Chemistry (miscellaneous) ,Hermite-Hadamard inclusion ,q)-integral ,Midpoint Type Inequalities ,Symmetry (geometry) - Abstract
In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described integrals are then used to prove some new Hermite-Hadamard inclusions for co-ordinated convex interval-valued functions. Many of the findings in this paper are important extensions of previous findings in the literature. Finally, we present a few examples of our new findings. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. WOS:000677046700001 2-s2.0-85110868353
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- 2021
11. Second-Order PDE Constrained Controlled Optimization Problems with Application in Mechanics
- Author
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Savin Treanţă
- Subjects
0209 industrial biotechnology ,Class (computer programming) ,Mathematical optimization ,Optimization problem ,multi-time controlled second-order Lagrangian ,multiple integral functional ,Computer science ,General Mathematics ,Multiple integral ,010102 general mathematics ,02 engineering and technology ,Euler–Lagrange equations ,01 natural sciences ,020901 industrial engineering & automation ,second-order PDE constraints ,Computer Science (miscellaneous) ,QA1-939 ,Order (group theory) ,Partial derivative ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics - Abstract
The present paper deals with a class of second-order PDE constrained controlled optimization problems with application in Lagrange–Hamilton dynamics. Concretely, we formulate and prove necessary conditions of optimality for the considered class of control problems driven by multiple integral cost functionals involving second-order partial derivatives. Moreover, an illustrative example is provided to highlight the effectiveness of the results derived in the paper. In the final part of the paper, we present an algorithm to summarize the steps for solving a control problem such as the one investigated here.
- Published
- 2021
12. Symmetric and Asymmetric Data in Solution Models
- Author
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Jurgita Antucheviciene, Zenonas Turskis, and Edmundas Kazimieras Zavadskas
- Subjects
Physics and Astronomy (miscellaneous) ,Computer science ,General Mathematics ,media_common.quotation_subject ,Fuzzy set ,02 engineering and technology ,symmetric data ,01 natural sciences ,Asymmetry ,Data type ,neutrosophic sets ,asymmetric data ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,QA1-939 ,MCDM ,media_common ,Balance (metaphysics) ,Uncertain data ,010308 nuclear & particles physics ,Management science ,solution models ,Multiple-criteria decision analysis ,Symmetry (physics) ,fuzzy sets ,Chemistry (miscellaneous) ,020201 artificial intelligence & image processing ,Mathematics ,Economic problem - Abstract
This Special Issue covers symmetric and asymmetric data that occur in real-life problems. We invited authors to submit their theoretical or experimental research to present engineering and economic problem solution models that deal with symmetry or asymmetry of different data types. The Special Issue gained interest in the research community and received many submissions. After rigorous scientific evaluation by editors and reviewers, seventeen papers were accepted and published. The authors proposed different solution models, mainly covering uncertain data in multi-criteria decision-making problems as complex tools to balance the symmetry between goals, risks, and constraints to cope with the complicated problems in engineering or management. Therefore, we invite researchers interested in the topics to read the papers provided in the Special Issue.
- Published
- 2021
13. Gottlieb Polynomials and Their q-Extensions
- Author
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Esra ErkuŞ-Duman and Junesang Choi
- Subjects
Power series ,General Mathematics ,q-Jacobi polynomials ,q-Meixner polynomials ,q-exponential functions ,q-binomial theorem ,02 engineering and technology ,q-Gottlieb polynomials in several variables ,01 natural sciences ,generating functions ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,QA1-939 ,q-calculus ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,generalized and generalized basic (or -q) hypergeometric function ,Discrete orthogonal polynomials ,Multivariable calculus ,010102 general mathematics ,Representation (systemics) ,020206 networking & telecommunications ,Function of several real variables ,Lauricella’s multiple hypergeometric series in several variables ,Algebra ,Gottlieb polynomials in several variables - Abstract
Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles. In this paper, we aimed to investigate the q-extensions of these polynomials to provide certain q-generating functions for three sequences associated with a finite power series whose coefficients are products of the known q-extended multivariable and multiparameter Gottlieb polynomials and another non-vanishing multivariable function. Furthermore, numerous possible particular cases of our main identities are considered. Finally, we return to Khan and Asif’s q-Gottlieb polynomials to highlight certain connections with several other known q-polynomials, and provide its q-integral representation. Furthermore, we conclude this paper by disclosing our future investigation plan.
- Published
- 2021
14. Error Estimations for Total Variation Type Regularization
- Author
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Chun Huang, Ziyang Yuan, and Kuan Li
- Subjects
Series (mathematics) ,General Mathematics ,Stability (learning theory) ,010103 numerical & computational mathematics ,Inverse problem ,Type (model theory) ,01 natural sciences ,Regularization (mathematics) ,010101 applied mathematics ,regularization ,total variation ,Rate of convergence ,Consistency (statistics) ,Computer Science (miscellaneous) ,QA1-939 ,Applied mathematics ,A priori and a posteriori ,inverse problem ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics - Abstract
This paper provides several error estimations for total variation (TV) type regularization, which arises in a series of areas, for instance, signal and imaging processing, machine learning, etc. In this paper, some basic properties of the minimizer for the TV regularization problem such as stability, consistency and convergence rate are fully investigated. Both a priori and a posteriori rules are considered in this paper. Furthermore, an improved convergence rate is given based on the sparsity assumption. The problem under the condition of non-sparsity, which is common in practice, is also discussed, the results of the corresponding convergence rate are also presented under certain mild conditions.
- Published
- 2021
15. On New Classes of Stancu-Kantorovich-Type Operators
- Author
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Cristina Maria Păcurar, Bianca Ioana Vasian, and Ștefan Lucian Garoiu
- Subjects
Discrete mathematics ,Class (set theory) ,Generalization ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,Type (model theory) ,01 natural sciences ,Stancu–Kantorovich operators ,Convergence (routing) ,approximation by positive linear operators ,Computer Science (miscellaneous) ,QA1-939 ,Kantorovich operators ,0101 mathematics ,Engineering (miscellaneous) ,Stancu operators ,King-type operators ,Mathematics - Abstract
The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.
- Published
- 2021
16. A Real Time Bolometer Tomographic Reconstruction Algorithm in Nuclear Fusion Reactors
- Author
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Alessandra Fanni, Augusto Montisci, Giuliana Sias, Sara Carcangiu, and Barbara Cannas
- Subjects
Tokamak ,Computer science ,General Mathematics ,01 natural sciences ,010305 fluids & plasmas ,law.invention ,bolometer ,law ,0103 physical sciences ,Computer Science (miscellaneous) ,Emissivity ,QA1-939 ,Projection (set theory) ,Engineering (miscellaneous) ,Condition number ,nuclear fusion ,010302 applied physics ,plasma tomography ,Tomographic reconstruction ,Bolometer ,Constrained optimization ,mathematical modeling ,numerical techniques ,Tomography ,tokamaks ,Algorithm ,Mathematics - Abstract
In tokamak nuclear fusion reactors, one of the main issues is to know the total emission of radiation, which is mandatory to understand the plasma physics and is very useful to monitor and control the plasma evolution. This radiation can be measured by means of a bolometer system that consists in a certain number of elements sensitive to the integral of the radiation along straight lines crossing the plasma. By placing the sensors in such a way to have families of crossing lines, sophisticated tomographic inversion algorithms allow to reconstruct the radiation tomography in the 2D poloidal cross-section of the plasma. In tokamaks, the number of projection cameras is often quite limited resulting in an inversion mathematic problem very ill conditioned so that, usually, it is solved by means of a grid-based, iterative constrained optimization procedure, whose convergence time is not suitable for the real time requirements. In this paper, to illustrate the method, an assumption not valid in general is made on the correlation among the grid elements, based on the statistical distribution of the radiation emissivity over a set of tomographic reconstructions, performed off-line. Then, a regularization procedure is carried out, which merge highly correlated grid elements providing a squared coefficients matrix with an enough low condition number. This matrix, which is inverted offline once for all, can be multiplied by the actual bolometer measures returning the tomographic reconstruction, with calculations suitable for real time application. The proposed algorithm is applied, in this paper, to a synthetic case study.
- Published
- 2021
17. Minimax Estimation in Regression under Sample Conformity Constraints
- Author
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Andrey Borisov
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Optimization problem ,General Mathematics ,02 engineering and technology ,minimax techniques ,Conditional expectation ,01 natural sciences ,Multi-objective optimization ,regression analysis ,010104 statistics & probability ,020901 industrial engineering & automation ,Saddle point ,Computer Science (miscellaneous) ,QA1-939 ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,estimation ,mathematical modeling ,Estimator ,statistical uncertainty ,Regression analysis ,Minimax ,pareto optimization ,Probability distribution - Abstract
The paper is devoted to the guaranteeing estimation of parameters in the uncertain stochastic nonlinear regression. The loss function is the conditional mean square of the estimation error given the available observations. The distribution of regression parameters is partially unknown, and the uncertainty is described by a subset of probability distributions with a known compact domain. The essential feature is the usage of some additional constraints describing the conformity of the uncertain distribution to the realized observation sample. The paper contains various examples of the conformity indices. The estimation task is formulated as the minimax optimization problem, which, in turn, is solved in terms of saddle points. The paper presents the characterization of both the optimal estimator and the set of least favorable distributions. The saddle points are found via the solution to a dual finite-dimensional optimization problem, which is simpler than the initial minimax problem. The paper proposes a numerical mesh procedure of the solution to the dual optimization problem. The interconnection between the least favorable distributions under the conformity constraint, and their Pareto efficiency in the sense of a vector criterion is also indicated. The influence of various conformity constraints on the estimation performance is demonstrated by the illustrative numerical examples.
- Published
- 2021
18. Integral Equations of Non-Integer Orders and Discrete Maps with Memory
- Author
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Vasily E. Tarasov
- Subjects
General Mathematics ,fractional calculus ,01 natural sciences ,010305 fluids & plasmas ,Quantum nonlocality ,Integer ,Hadamard transform ,0103 physical sciences ,Computer Science (miscellaneous) ,QA1-939 ,Applied mathematics ,010301 acoustics ,Engineering (miscellaneous) ,Mathematics ,processes with memory ,Dirac (video compression format) ,Periodic sequence ,fractional integral equation ,Integral equation ,Fractional calculus ,Fractional dynamics ,discrete map with memory ,fractional dynamics ,Hadamard type fractional integral ,Riemann–Liouville fractional integral - Abstract
In this paper, we use integral equations of non-integer orders to derive discrete maps with memory. Note that discrete maps with memory were not previously derived from fractional integral equations of non-integer orders. Such a derivation of discrete maps with memory is proposed for the first time in this work. In this paper, we derived discrete maps with nonlocality in time and memory from exact solutions of fractional integral equations with the Riemann–Liouville and Hadamard type fractional integrals of non-integer orders and periodic sequence of kicks that are described by Dirac delta-functions. The suggested discrete maps with nonlocality in time are derived from these fractional integral equations without any approximation and can be considered as exact discrete analogs of these equations. The discrete maps with memory, which are derived from integral equations with the Hadamard type fractional integrals, do not depend on the period of kicks.
- Published
- 2021
19. On Certain Differential Subordination of Harmonic Mean Related to a Linear Function
- Author
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Anna Dobosz, Piotr Jastrzębski, and Adam Lecko
- Subjects
Subordination (linguistics) ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,Generalization ,General Mathematics ,Harmonic mean ,harmonic mean ,01 natural sciences ,arithmetic mean ,Mathematics::Probability ,Computer Science (miscellaneous) ,QA1-939 ,0101 mathematics ,Mathematics ,convex function ,Linear function (calculus) ,010102 general mathematics ,010101 applied mathematics ,geometric mean ,Chemistry (miscellaneous) ,Geometric mean ,Convex function ,differential subordination ,Differential (mathematics) ,Arithmetic mean - Abstract
In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordinations of the harmonic mean in which the dominant was any convex function, one can study such differential subordinations for the selected convex function. In this case, a reasonable and difficult issue is to look for the best dominant or one that is close to it. This paper is devoted to this issue, in which the dominant is a linear function, and the differential subordination of the harmonic mean is a generalization of the Briot–Bouquet differential subordination.
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- 2021
20. Smooth kNN Local Linear Estimation of the Conditional Distribution Function
- Author
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Ali Laksaci, Zouaoui Chikr Elmezouar, Ibrahim M. Almanjahie, and Mustapha Rachdi
- Subjects
General Mathematics ,01 natural sciences ,conditional predictive region ,010104 statistics & probability ,Mixing (mathematics) ,Computer Science (miscellaneous) ,QA1-939 ,Applied mathematics ,0101 mathematics ,distribution function ,Engineering (miscellaneous) ,Mathematics ,Variable (mathematics) ,Sequence ,Series (mathematics) ,kernel weighting ,k nearest neighbors smoothing (kNN) ,functional mixing data ,Estimator ,Linearity ,Function (mathematics) ,Conditional probability distribution ,complete convergence (a.co.) ,010101 applied mathematics ,Local Linear Fitting (LLM) - Abstract
Previous works were dedicated to the functional k-Nearest Neighbors (kNN) and the local linearity method estimations of a regression operator. In this paper, a sequence pair of (Xi,Yi)i=1,…,n of functional mixing observations are considered. We treat the local linear estimation of the cumulative function of Yi given functional input variable Xi. Precisely, we combine the kNN method with the local linear algorithm to construct a new and fast efficiency estimator of the conditional distribution function. The main purpose of this paper is to prove the strong convergence of the constructed estimator under mixing conditions. An application to the functional times series prediction is used to compare our proposed estimator with the existing competitive estimators, and show its efficiency and superiority.
- Published
- 2021
21. On the Generalized Laplace Transform
- Author
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Paul Bosch, Héctor José Carmenate García, José M. Rodríguez, José M. Sigarreta, Comunidad de Madrid, and Ministerio de Ciencia, Innovación y Universidades (España)
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Work (thermodynamics) ,Physics and Astronomy (miscellaneous) ,Matemáticas ,General Mathematics ,Inverse ,010103 numerical & computational mathematics ,01 natural sciences ,Convolution ,Computer Science (miscellaneous) ,Applied mathematics ,convolution ,0101 mathematics ,Harmonic oscillator ,Mathematics ,Laplace transform ,lcsh:Mathematics ,010102 general mathematics ,Order (ring theory) ,fractional derivative ,Fractional derivative ,lcsh:QA1-939 ,Generalized Laplace transform ,Fractional calculus ,generalized Laplace transform ,Chemistry (miscellaneous) ,Fractional differential - Abstract
This article belongs to the Special Issue Discrete and Fractional Mathematics: Symmetry and Applications. In this paper we introduce a generalized Laplace transform in order to work with a very general fractional derivative, and we obtain the properties of this new transform. We also include the corresponding convolution and inverse formula. In particular, the definition of convolution for this generalized Laplace transform improves previous results. Additionally, we deal with the generalized harmonic oscillator equation, showing that this transform and its properties allow one to solve fractional differential equations. We would like to thank the referees for their comments, which have improved the paper. The research of José M. Rodríguez and José M. Sigarreta was supported by a grant from Agencia Estatal de Investigación (PID2019-106433GB-I00/AEI/10.13039/501100011033), Spain. The research of José M. Rodríguez is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).
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- 2021
22. An Intuitive Introduction to Fractional and Rough Volatilities
- Author
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Jorge Leon and Elisa Alòs
- Subjects
Statistics::Theory ,Skorohod integral ,General Mathematics ,Structure (category theory) ,rough volatility ,fractional Brownian motion ,Itô’s formula ,Implied volatility ,Type (model theory) ,Malliavin calculus ,01 natural sciences ,010104 statistics & probability ,Mathematics::Probability ,derivative operator in the Malliavin calculus sense ,0502 economics and business ,Computer Science (miscellaneous) ,Filtration (mathematics) ,QA1-939 ,Applied mathematics ,0101 mathematics ,Engineering (miscellaneous) ,stochastic volatility models ,future average volatility ,Mathematics ,Hull and White formula ,050208 finance ,Fractional Brownian motion ,05 social sciences ,skews and smiles ,Semimartingale ,Volatility (finance) ,implied volatility - Abstract
Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.
- Published
- 2021
23. On the Reciprocal Sums of Products of Balancing and Lucas-Balancing Numbers
- Author
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Younseok Choo
- Subjects
Fibonacci number ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,reciprocal ,Fibonacci numbers ,floor function ,lcsh:QA1-939 ,01 natural sciences ,Lucas-balancing numbers ,010101 applied mathematics ,Combinatorics ,Computer Science (miscellaneous) ,balancing numbers ,0101 mathematics ,Engineering (miscellaneous) ,Reciprocal ,Mathematics - Abstract
Recently Panda et al. obtained some identities for the reciprocal sums of balancing and Lucas-balancing numbers. In this paper, we derive general identities related to reciprocal sums of products of two balancing numbers, products of two Lucas-balancing numbers and products of balancing and Lucas-balancing numbers. The method of this paper can also be applied to even-indexed and odd-indexed Fibonacci, Lucas, Pell and Pell–Lucas numbers.
- Published
- 2021
24. Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (p,q)-Calculus
- Author
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Julalak Prabseang, Sotiris Ntouyas, Jessada Tariboon, and Kamsing Nonlaopon
- Subjects
Pure mathematics ,convex functions ,General Mathematics ,Mathematics::Classical Analysis and ODEs ,MathematicsofComputing_GENERAL ,(p,q)-derivative ,01 natural sciences ,Computer Science::Digital Libraries ,Hadamard transform ,Hermite–Hadamard inequality ,Computer Science (miscellaneous) ,medicine ,0101 mathematics ,Engineering (miscellaneous) ,Calculus (medicine) ,Mathematics ,Hermite polynomials ,Multiple integral ,lcsh:Mathematics ,010102 general mathematics ,(p,q)-integral ,medicine.disease ,lcsh:QA1-939 ,010101 applied mathematics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Computer Science::Programming Languages ,Convex function - Abstract
In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using (p,q)-calculus. Moreover, we study some new (p,q)-Hermite–Hadamard inequalities for multiple integrals. Many results given in this paper provide extensions of others given in previous research.
- Published
- 2021
25. Differential Subordination and Superordination Results Using Fractional Integral of Confluent Hypergeometric Function
- Author
-
Alina Alb Lupaş and Georgia Irina Oros
- Subjects
Subordination (linguistics) ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,subordinant ,02 engineering and technology ,univalent function ,01 natural sciences ,analytic function ,best subordinant ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,dominant ,Mathematics ,best dominant ,Confluent hypergeometric function ,lcsh:Mathematics ,010102 general mathematics ,differential superordination ,Differential operator ,lcsh:QA1-939 ,Dual (category theory) ,Chemistry (miscellaneous) ,differential operator ,020201 artificial intelligence & image processing ,differential subordination ,Differential (mathematics) ,Analytic function ,Univalent function - Abstract
Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories.
- Published
- 2021
26. Applications of Inequalities in the Complex Plane Associated with Confluent Hypergeometric Function
- Author
-
Georgia Irina Oros
- Subjects
Subordination (linguistics) ,Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,subordinant ,02 engineering and technology ,univalent function ,01 natural sciences ,analytic function ,best subordinant ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,Hypergeometric function ,Mathematics ,convex function ,Conjecture ,Confluent hypergeometric function ,lcsh:Mathematics ,010102 general mathematics ,differential superordination ,lcsh:QA1-939 ,confluent hypergeometric function ,Chemistry (miscellaneous) ,020201 artificial intelligence & image processing ,Complex plane ,Differential (mathematics) ,Analytic function ,Univalent function - Abstract
The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach’s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied.
- Published
- 2021
27. Stability Analysis and Cauchy Matrix of a Mathematical Model of Hepatitis B Virus with Control on Immune System near Neighborhood of Equilibrium Free Point
- Author
-
Salvo Danilo Lombardo, Irina Volinsky, and Paz Cheredman
- Subjects
Physics and Astronomy (miscellaneous) ,exponential stability ,General Mathematics ,medicine.disease_cause ,integro-differential systems ,01 natural sciences ,Stability (probability) ,03 medical and health sciences ,0302 clinical medicine ,Exponential stability ,Computer Science (miscellaneous) ,medicine ,Applied mathematics ,0101 mathematics ,Mathematics ,Hepatitis B virus ,Mathematical model ,lcsh:Mathematics ,010102 general mathematics ,Cauchy distribution ,Hepatitis B ,medicine.disease ,lcsh:QA1-939 ,Cauchy matrix ,feedback control ,immune system ,CTL ,functional differential equations ,Chemistry (miscellaneous) ,030211 gastroenterology & hepatology ,hepatitis B - Abstract
Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices C(t,s), which allow us to construct and analyze the stability of corresponding integro-differential systems.
- Published
- 2021
28. Amended criteria of oscillation for nonlinear functional dynamic equations of second-order
- Author
-
Amir Abdel Menaem, Taher S. Hassan, and Rami Ahmad El-Nabulsi
- Subjects
TIME SCALES ,Scale (ratio) ,General Mathematics ,second-order ,01 natural sciences ,Computer Science (miscellaneous) ,QA1-939 ,OSCILLATION BEHAVIOR ,Applied mathematics ,Order (group theory) ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,NONLINEAR ,Oscillation ,time scales ,010102 general mathematics ,FUNCTIONAL DYNAMIC EQUATION ,oscillation behavior ,SECOND-ORDER ,010101 applied mathematics ,Nonlinear system ,Transformation (function) ,functional dynamic equation ,nonlinear ,Dynamic equation - Abstract
In this paper, the sharp Hille-type oscillation criteria are proposed for a class of secondorder nonlinear functional dynamic equations on an arbitrary time scale, by using the technique of Riccati transformation and integral averaging method. The obtained results demonstrate an improvement in Hille-type compared with the results reported in the literature. Some examples are provided to illustrate the significance of the obtained results. © 2021 by the authors. Licensee MDPI, Basel, Switzerland. The authors would like to thank anonymous referees for their careful reading of the entire manuscript, which helped significantly improve this paper’s quality. This work was supported by Research Deanship of Hail University under grant No. 0150396.
- Published
- 2021
29. Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions
- Author
-
Daliang Zhao and Juan Mao
- Subjects
Physics and Astronomy (miscellaneous) ,General Mathematics ,Banach space ,Fixed-point theorem ,fixed point theorem ,01 natural sciences ,Computer Science::Digital Libraries ,Singularity ,Computer Science (miscellaneous) ,Boundary value problem ,0101 mathematics ,Mathematics ,Variable (mathematics) ,lcsh:Mathematics ,010102 general mathematics ,Mathematical analysis ,Riemann–Stieltjes integral ,fractional differential equations ,cone ,lcsh:QA1-939 ,singularity ,010101 applied mathematics ,Nonlinear system ,Cone (topology) ,Chemistry (miscellaneous) ,Computer Science::Programming Languages ,coupled integral boundary value conditions - Abstract
In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann&ndash, Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann&ndash, Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green&rsquo, s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.
- Published
- 2021
30. On Coding by (2,q)-Distance Fibonacci Numbers
- Author
-
Pavel Trojovský and Ivana Matoušová
- Subjects
Fibonacci coding ,Fibonacci number ,General Mathematics ,02 engineering and technology ,Data_CODINGANDINFORMATIONTHEORY ,01 natural sciences ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,Discrete mathematics ,lcsh:Mathematics ,010102 general mathematics ,Characteristic equation ,characteristic equation ,Coding theory ,lcsh:QA1-939 ,fibonacci numbers ,generalizd fibonacci numbers ,020201 artificial intelligence & image processing ,coding theory ,Decoding methods ,Coding (social sciences) ,MathematicsofComputing_DISCRETEMATHEMATICS - Abstract
In 2006, A. Stakhov introduced a new coding/decoding process based on generating matrices of the Fibonacci p-numbers, which he called the Fibonacci coding/decoding method. Stakhov&rsquo, s papers have motivated many other scientists to seek certain generalizations by introducing new additional coefficients into recurrence of Fibonacci p-numbers. In 2013, I. Włoch et al. studied (2,q)-distance Fibonacci numbers F2(q,n) and found some of their combinatorial properties. In this paper, we state a new coding theory based on the sequence (Tq(n))n=&minus, &infin, which is an extension of Włoch&rsquo, s sequence (F2(q,n))n=0&infin
- Published
- 2020
31. The Consistency of the CUSUM-Type Estimator of the Change-Point and Its Application
- Author
-
Xiang Dong, Xiaoqin Li, Saisai Ding, and Wenzhi Yang
- Subjects
General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Estimator ,financial time series ,CUSUM ,negatively associated sequences ,lcsh:QA1-939 ,01 natural sciences ,010104 statistics & probability ,Negatively associated ,CUSUM estimator ,Statistics ,Computer Science (miscellaneous) ,0101 mathematics ,change-point ,Engineering (miscellaneous) ,Mathematics - Abstract
In this paper, we investigate the CUSUM-type estimator of mean change-point models based on m-asymptotically almost negatively associated (m-AANA) sequences. The family of m-AANA sequences contains AANA, NA, m-NA, and independent sequences as special cases. Under some weak conditions, some convergence rates are obtained such as OP(n1/p&minus, 1), OP(n1/p&minus, 1log1/pn) and OP(n&alpha, &minus, 1), where 0&le, &alpha, <, 1 and 1<, p&le, 2. Our rates are better than the ones obtained by Kokoszka and Leipus (Stat. Probab. Lett., 1998, 40, 385&ndash, 393). In order to illustrate our results, we do perform simulations based on m-AANA sequences. As important applications, we use the CUSUM-type estimator to do the change-point analysis based on three real data such as Quebec temperature, Nile flow, and stock returns for Tesla. Some potential applications to change-point models in finance and economics are also discussed in this paper.
- Published
- 2020
32. Estimates of Coefficient Functionals for Functions Convex in the Imaginary-Axis Direction
- Author
-
Paweł Zaprawa and Katarzyna Tra̧bka-Wiȩcław
- Subjects
Pure mathematics ,Class (set theory) ,convexity in imaginary-axis direction ,coefficient problems ,Physics and Astronomy (miscellaneous) ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Regular polygon ,close-to-convex functions ,typically real functions ,lcsh:QA1-939 ,01 natural sciences ,Unit disk ,010101 applied mathematics ,Chemistry (miscellaneous) ,Computer Science (miscellaneous) ,successive coefficients ,0101 mathematics ,Mathematics - Abstract
Let C0(h) be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula ()(1&minus, z2)f&prime, (z)}>, 0. In this paper, some coefficient problems for C0(h) are considered. Some properties and bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates of the difference and of sum of successive coefficients, bounds of the sum of the first n coefficients and bounds of the n-th coefficient. The obtained results are used to determine coefficient estimates for both functions convex in the imaginary-axis direction with real coefficients and typically real functions. Moreover, the sum of the first initial coefficients for functions with a positive real part and with a fixed second coefficient is estimated.
- Published
- 2020
33. D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations
- Author
-
Michal Fečkan, Natalia Dilna, and Mykola Solovyov
- Subjects
Cauchy problem ,Physics and Astronomy (miscellaneous) ,Differential equation ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Mathematical analysis ,Scalar (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Symmetric property ,Chemistry (miscellaneous) ,symmetric solution ,Computer Science (miscellaneous) ,Symmetric solution ,Initial value problem ,unique solution ,0101 mathematics ,D stability ,D-stability ,Mathematics - Abstract
This paper presents a method of establishing the D-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties.
- Published
- 2020
34. On Singular Distributions With Statistical Structure
- Author
-
Sergey Stepanov, Vladimir Rovenski, and Paul Popescu
- Subjects
Lie algebroid ,Pure mathematics ,General Mathematics ,Type (model theory) ,Curvature ,01 natural sciences ,Operator (computer programming) ,statistical structure ,Computer Science (miscellaneous) ,harmonic differential form ,0101 mathematics ,Engineering (miscellaneous) ,almost Lie algebroid ,Mathematics ,Riemannian manifold ,singular distribution ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,010101 applied mathematics ,Singular distribution ,Mathematics::Differential Geometry ,Laplace operator ,Weitzenböck curvature operator ,Distribution (differential geometry) - Abstract
In this paper, we extend our previous study regarding a Riemannian manifold endowed with a singular (or regular) distribution, generalizing Bochner&rsquo, s technique and a statistical structure. Following the construction of an almost Lie algebroid, we define the central concept of the paper: The Weitzenbö, ck type curvature operator on tensors, prove the Bochner&ndash, Weitzenbö, ck type formula and obtain some vanishing results about the null space of the Hodge type Laplacian on a distribution.
- Published
- 2020
35. Interpolative Reich-Rus-Ciric and Hardy-Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results
- Author
-
Pragati Gautam, Swapnil Verma, Luis Manuel Sánchez Ruiz, and Vishnu Narayan Mishra
- Subjects
Pure mathematics ,Quasi-partial b-metric space ,General Mathematics ,Fixed point ,01 natural sciences ,Common fixed point ,Complete metric space ,Computer Science (miscellaneous) ,0101 mathematics ,Engineering (miscellaneous) ,Contraction (operator theory) ,Hardy-Rogers contraction ,Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Reich–Rus–Ćirić contraction ,lcsh:QA1-939 ,Hardy–Rogers contraction ,Interpolation ,010101 applied mathematics ,Metric space ,Reich-Rus-Ciric contraction ,04.- Garantizar una educación de calidad inclusiva y equitativa, y promover las oportunidades de aprendizaje permanente para todos ,MATEMATICA APLICADA ,Common fixed point theorem - Abstract
The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich&ndash, Rus&ndash, Ćirić type contraction and Hardy&ndash, Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.
- Published
- 2020
36. Fixed Point Sets of k-Continuous Self-Maps of m-Iterated Digital Wedges
- Author
-
Sang-Eon Han
- Subjects
digital topology ,General Mathematics ,digital k-curve ,Fixed-point theorem ,Natural number ,02 engineering and technology ,Fixed point ,01 natural sciences ,Digital image ,digital image ,Simple (abstract algebra) ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,Engineering (miscellaneous) ,Digital topology ,Mathematics ,Discrete mathematics ,k-contractibility ,lcsh:Mathematics ,010102 general mathematics ,alignment ,lcsh:QA1-939 ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Iterated function ,020201 artificial intelligence & image processing ,digital wedge ,perfect ,fixed point set - Abstract
Let Ckn,l be a simple closed k-curves with l elements in Zn and W:=Ckn,l&or, ⋯&or, Ckn,l︷m-times be an m-iterated digital wedges of Ckn,l, and F(Conk(W)) be an alignment of fixed point sets of W. Then, the aim of the paper is devoted to investigating various properties of F(Conk(W)). Furthermore, when proceeding with this work, this paper addresses several unsolved problems. To be specific, we firstly formulate an alignment of fixed point sets of Ckn,l, denoted by F(Conk(Ckn,l)), where l(&ge, 7) is an odd natural number and k&ne, 2n. Secondly, given a digital image (X,k) with X♯=n, we find a certain condition that supports n&minus, 1,n&minus, 2&isin, F(Conk(X)). Thirdly, after finding some features of F(Conk(W)), we develop a method of making F(Conk(W)) perfect according to the (even or odd) number l of Ckn,l. Finally, we prove that the perfectness of F(Conk(W)) is equivalent to that of F(Conk(Ckn,l)). This can play an important role in studying fixed point theory and digital curve theory. This paper only deals with k-connected digital images (X,k) such that X♯&ge, 2.
- Published
- 2020
37. A Survey on Sharp Oscillation Conditions of Differential Equations with Several Delays
- Author
-
Mahmoud Abdel-Aty, Nour Zidan, Ioannis P. Stavroulakis, and Musa E. Kavgaci
- Subjects
Oscillation ,Differential equation ,General Mathematics ,media_common.quotation_subject ,lcsh:Mathematics ,010102 general mathematics ,Mathematical analysis ,differential equations ,oscillation ,Infinity ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Computer Science (miscellaneous) ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,media_common ,delay arguments - Abstract
This paper deals with the oscillation of the first-order differential equation with several delay arguments x′t+∑i=1mpitxτit=0,t≥t0, where the functions pi,τi∈Ct0,∞,R+, for every i=1,2,…,m,τit≤t for t≥t0 and limt→∞τit=∞. In this paper, the state-of-the-art on the sharp oscillation conditions are presented. In particular, several sufficient oscillation conditions are presented and it is shown that, under additional hypotheses dealing with slowly varying at infinity functions, some of the “liminf” oscillation conditions can be essentially improved replacing “liminf” by “limsup”. The importance of the slowly varying hypothesis and the essential improvement of the sufficient oscillation conditions are illustrated by examples.
- Published
- 2020
38. Strong Tolerance and Strong Universality of Interval Eigenvectors in a Max-ukasiewicz Algebra
- Author
-
Martin Gavalec, Zuzana Němcová, and Ján Plavka
- Subjects
General Mathematics ,max-Łukasiewicz algebra ,interval matrix ,interval eigenvector ,strong interval eigenvector ,Fuzzy set ,02 engineering and technology ,01 natural sciences ,0202 electrical engineering, electronic engineering, information engineering ,Computer Science (miscellaneous) ,0101 mathematics ,Linear combination ,Engineering (miscellaneous) ,Eigenvalues and eigenvectors ,Mathematics ,Real systems ,max-ukasiewicz algebra ,lcsh:Mathematics ,010102 general mathematics ,Stochastic matrix ,lcsh:QA1-939 ,Universality (dynamical systems) ,Algebra ,Binary operation ,Interval matrix ,020201 artificial intelligence & image processing ,Hardware_LOGICDESIGN - Abstract
The Łukasiewicz conjunction (sometimes also considered to be a logic of absolute comparison), which is used in multivalued logic and in fuzzy set theory, is one of the most important t-norms. In combination with the binary operation ‘maximum’, the Łukasiewicz t-norm forms the basis for the so-called max-Łuk algebra, with applications to the investigation of systems working in discrete steps (discrete events systems; DES, in short). Similar algebras describing the work of DES’s are based on other pairs of operations, such as max-min algebra, max-plus algebra, or max-T algebra (with a given t-norm, T). The investigation of the steady states in a DES leads to the study of the eigenvectors of the transition matrix in the corresponding max-algebra. In real systems, the input values are usually taken to be in some interval. Various types of interval eigenvectors of interval matrices in max-min and max-plus algebras have been described. This paper is oriented to the investigation of strong, strongly tolerable, and strongly universal interval eigenvectors in a max-Łuk algebra. The main method used in this paper is based on max-Ł linear combinations of matrices and vectors. Necessary and sufficient conditions for the recognition of strong, strongly tolerable, and strongly universal eigenvectors have been found. The theoretical results are illustrated by numerical examples.
- Published
- 2020
39. Coefficient Related Studies for New Classes of Bi-Univalent Functions
- Author
-
Ágnes Orsolya Páll-Szabó and Georgia Irina Oros
- Subjects
General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,coefficient bounds ,lcsh:QA1-939 ,01 natural sciences ,bi-univalent functions ,010101 applied mathematics ,Algebra ,Sălăgean integral and differential operator ,Operator (computer programming) ,Fekete–Szego problem ,Computer Science (miscellaneous) ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics - Abstract
Using the recently introduced Sălăgean integro-differential operator, three new classes of bi-univalent functions are introduced in this paper. In the study of bi-univalent functions, estimates on the first two Taylor&ndash, Maclaurin coefficients are usually given. We go further in the present paper and bounds of the first three coefficients a 2 , a 3 and a 4 of the functions in the newly defined classes are given. Obtaining Fekete&ndash, Szego inequalities for different classes of functions is a topic of interest at this time as it will be shown later by citing recent papers. So, continuing the study on the coefficients of those classes, the well-known Fekete&ndash, Szego functional is obtained for each of the three classes.
- Published
- 2020
40. Localized Boundary Knot Method for Solving Two-Dimensional Laplace and Bi-harmonic Equations
- Author
-
Yan-Cheng Liu, Jingang Xiong, and Jiancong Wen
- Subjects
sparse matrix ,multiply connected domain ,General Mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,Boundary (topology) ,Harmonic (mathematics) ,boundary knot method ,02 engineering and technology ,01 natural sciences ,0203 mechanical engineering ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Computer Science (miscellaneous) ,Method of fundamental solutions ,Boundary value problem ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,Laplace's equation ,lcsh:Mathematics ,Mathematical analysis ,localized meshless method ,Laplace equation ,Boundary knot method ,lcsh:QA1-939 ,Mathematics::Geometric Topology ,Numerical integration ,010101 applied mathematics ,Algebraic equation ,020303 mechanical engineering & transports ,bi-harmonic equation - Abstract
In this paper, a localized boundary knot method is proposed, based on the local concept in the localized method of fundamental solutions. The localized boundary knot method is formed by combining the classical boundary knot method and the localization approach. The localized boundary knot method is truly free from mesh and numerical quadrature, so it has great potential for solving complicated engineering applications, such as multiply connected problems. In the proposed localized boundary knot method, both of the boundary nodes and interior nodes are required, and the algebraic equations at each node represent the satisfaction of the boundary condition or governing equation, which can be derived by using the boundary knot method at every subdomain. A sparse system of linear algebraic equations can be yielded using the proposed localized boundary knot method, which can greatly reduce the computer time and memory required in computer calculations. In this paper, several cases of simply connected domains and multi-connected domains of the Laplace equation and bi-harmonic equation are demonstrated to evidently verify the accuracy, convergence and stability of this proposed meshless method.
- Published
- 2020
41. Detection of Near-Nulticollinearity through Centered and Noncentered Regression
- Author
-
José García Pérez, Román Salmerón Gómez, and Catalina Beatriz García García
- Subjects
centered model ,General Mathematics ,media_common.quotation_subject ,noncentered model ,01 natural sciences ,010104 statistics & probability ,Rest (finance) ,0502 economics and business ,Linear regression ,Statistics ,Computer Science (miscellaneous) ,nonessential multicollinearity ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics ,media_common ,Variance inflation factor ,Intercept ,Variables ,lcsh:Mathematics ,05 social sciences ,Nonessential multicollinearity ,Centered model ,lcsh:QA1-939 ,Noncentered model ,Regression ,Expression (mathematics) ,Econometric model ,Multicollinearity ,essential multicollinearity ,Essential multicollinearity ,050211 marketing ,essential multicollinearit ,intercept - Abstract
This paper analyzes the diagnostic of near-multicollinearity in a multiple linear regression from auxiliary centered (with intercept) and noncentered (without intercept) regressions. From these auxiliary regressions, the centered and noncentered variance inflation factors (VIFs) are calculated. An expression is also presented that relates both of them. In addition, this paper analyzes why the VIF is not able to detect the relation between the intercept and the rest of the independent variables of an econometric model. At the same time, an analysis is also provided to determine how the auxiliary regression applied to calculate the VIF can be useful to detect this kind of multicollinearity., University of Almeria
- Published
- 2020
42. Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms
- Author
-
Velu Muthulakshmi, Jehad Alzabut, James Viji, and Weerawat Sudsutad
- Subjects
Forcing (recursion theory) ,damping and forcing terms ,Oscillation ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,generalized proportional fractional operator ,nonoscillatory behavior ,Computer Science (miscellaneous) ,Applied mathematics ,oscillation criteria ,0101 mathematics ,Fractional differential ,Engineering (miscellaneous) ,Mathematics - Abstract
In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior.
- Published
- 2020
43. Multiparametric Contractions and Related Hardy-Roger Type Fixed Point Theorems
- Author
-
Antonio Francisco Roldán López de Hierro, Andreea Fulga, and Erdal Karapınar
- Subjects
Pure mathematics ,Contractivity condition ,b-metric space ,multiparametric contraction ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Multiparametric contraction ,Fixed-point theorem ,Fixed point ,Type (model theory) ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,contractivity condition ,Similarity (network science) ,fixed point ,Computer Science (miscellaneous) ,Hardy-Rogers contractivity condition ,Computer Science::Programming Languages ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics - Abstract
The authors acknowledge with thanks DSR for financial support. A.F. Roldán López de Hierro is grateful to Junta de Andalucía by project FQM-365 of the Andalusian CICYE and Project TIN2017-89517-P of the Ministerio de Economía, Industria y Competitividad., In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b-metric spaces because they allow to consider some families of functions endowed with b-metrics deriving from similarity measures that are more general than norms. Taking into account that the contractivity condition we will employ is very general (of Hardy-Rogers type), we will discuss the validation and usage of this novel condition. After that, we introduce the main results of this paper and, finally, we deduce some consequences of them which illustrates the wide applicability of the main results., Junta de Andalucia FQM-365, Ministerio de Economia, Industria y Competitividad TIN2017-89517-P, DSR
- Published
- 2020
44. The Four-Parameters Wright Function of the Second kind and its Applications in FC
- Author
-
Yuri Luchko
- Subjects
Subordination (linguistics) ,Diffusion equation ,subordination formula ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Spectrum (functional analysis) ,scale-invariant solutions ,Wright Omega function ,left- and right-hand sided Erdélyi-Kober fractional derivatives ,lcsh:QA1-939 ,01 natural sciences ,Fractional calculus ,010101 applied mathematics ,one-dimensional time-fractional diffusion-wave equation ,Operational calculus ,Kernel (statistics) ,Computer Science (miscellaneous) ,Applied mathematics ,0101 mathematics ,Special case ,Engineering (miscellaneous) ,Mathematics ,four-parameters Wright function of the second kind ,multi-dimensional space-time-fractional diffusion equation - Abstract
In this survey paper, we present both some basic properties of the four-parameters Wright function and its applications in Fractional Calculus. For applications in Fractional Calculus, the four-parameters Wright function of the second kind is especially important. In the paper, three case studies illustrating a wide spectrum of its applications are presented. The first case study deals with the scale-invariant solutions to a one-dimensional time-fractional diffusion-wave equation that can be represented in terms of the Wright function of the second kind and the four-parameters Wright function of the second kind. In the second case study, we consider a subordination formula for the solutions to a multi-dimensional space-time-fractional diffusion equation with different orders of the fractional derivatives. The kernel of the subordination integral is a special case of the four-parameters Wright function of the second kind. Finally, in the third case study, we shortly present an application of an operational calculus for a composed Erdélyi-Kober fractional operator for solving some initial-value problems for the fractional differential equations with the left- and right-hand sided Erdélyi-Kober fractional derivatives. In particular, we present an example with an explicit solution in terms of the four-parameters Wright function of the second kind.
- Published
- 2020
45. Analysis of Homotopy Decomposition Varieties in Quotient Topological Spaces
- Author
-
Susmit Bagchi and Gyeongsang National University
- Subjects
Pure mathematics ,Connected space ,Fundamental group ,Physics and Astronomy (miscellaneous) ,General Mathematics ,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] ,Topological space ,01 natural sciences ,Mathematics::Algebraic Topology ,Separable space ,0103 physical sciences ,Computer Science (miscellaneous) ,[MATH]Mathematics [math] ,0101 mathematics ,010306 general physics ,Quotient ,Mathematics ,fundamental groups ,Homotopy ,lcsh:Mathematics ,010102 general mathematics ,homotopy ,Quotient space (topology) ,lcsh:QA1-939 ,topological spaces ,Sierpiński space ,Chemistry (miscellaneous) ,[MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT] ,quotient topology ,embeddings - Abstract
The fundamental groups and homotopy decompositions of algebraic topology have applications in systems involving symmetry breaking with topological excitations. The main aim of this paper is to analyze the properties of homotopy decompositions in quotient topological spaces depending on the connectedness of the space and the fundamental groups. This paper presents constructions and analysis of two varieties of homotopy decompositions depending on the variations in topological connectedness of decomposed subspaces. The proposed homotopy decomposition considers connected fundamental groups, where the homotopy equivalences are relaxed and the homeomorphisms between the fundamental groups are maintained. It is considered that one fundamental group is strictly homotopy equivalent to a set of 1-spheres on a plane and as a result it is homotopy rigid. The other fundamental group is topologically homeomorphic to the first one within the connected space and it is not homotopy rigid. The homotopy decompositions are analyzed in quotient topological spaces, where the base space and the quotient space are separable topological spaces. In specific cases, the decomposed quotient space symmetrically extends Sierpinski space with respect to origin. The connectedness of fundamental groups in the topological space is maintained by open curve embeddings without enforcing the conditions of homotopy classes on it. The extended decomposed quotient topological space preserves the trivial group structure of Sierpinski space.
- Published
- 2020
46. Fixed Point Problems on Generalized Metric Spaces in Perov’s Sense
- Author
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Liliana Guran, Asim Naseem, and Monica-Felicia Bota
- Subjects
Pure mathematics ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Data dependence ,Stability (learning theory) ,Type (model theory) ,Fixed point ,Ulam–Hyers stability ,01 natural sciences ,coupled fixed points ,well-posedness ,Computer Science (miscellaneous) ,0101 mathematics ,Mathematics ,lcsh:Mathematics ,data dependence ,010102 general mathematics ,Perov space ,Sense (electronics) ,generalized w-distance ,lcsh:QA1-939 ,010101 applied mathematics ,Metric space ,fixed point ,Chemistry (miscellaneous) ,Metric (mathematics) ,Symmetry (geometry) - Abstract
The aim of this paper is to give some fixed point results in generalized metric spaces in Perov&rsquo, s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy&ndash, Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam&ndash, Hyers stability of the fixed point problem. An example is also given to sustain the presented results.
- Published
- 2020
47. On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks
- Author
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Marco Menale, Carlo Bianca, Bruno Carbonaro, Bianca, Carlo, Carbonaro, Bruno, and Menale, Marco
- Subjects
State variable ,Physics and Astronomy (miscellaneous) ,integro-differential equation ,General Mathematics ,Complex system ,010103 numerical & computational mathematics ,complexity ,kinetic theory ,Cauchy problem ,nonlinearity ,Mathematical models, Boltzmann equation, Vlasov equation, Kinetic Theory for Active Particles, well-posedness problems ,01 natural sciences ,Quadratic equation ,Computer Science (miscellaneous) ,Applied mathematics ,Initial value problem ,Uniqueness ,0101 mathematics ,Mathematics ,Variable (mathematics) ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,Nonlinear system ,Chemistry (miscellaneous) - Abstract
This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Specifically, the paper is divided in two parts. In the first part the thermostatted framework with a continuous vectorial variable is proposed and analyzed. The framework consists of a system of partial integro-differential equations with quadratic type nonlinearities. In the second part the thermostatted framework with a discrete vectorial variable is investigated. Real world applications, such as social systems and crowd dynamics, and future research directions are outlined in the paper.
- Published
- 2020
48. Certain Hadamard Proportional Fractional Integral Inequalities
- Author
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Kottakkaran Sooppy Nisar, Thabet Abdeljawad, and Gauhar Rahman
- Subjects
Pure mathematics ,hadamard proportional fractional integrals ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,fractional integrals ,lcsh:QA1-939 ,01 natural sciences ,Computer Science::Digital Libraries ,fractional integral inequalities ,Exponential function ,010101 applied mathematics ,Operator (computer programming) ,Hadamard transform ,Computer Science (miscellaneous) ,Computer Science::Programming Languages ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics - Abstract
In this present paper we study the non-local Hadmard proportional integrals recently proposed by Rahman et al. (Advances in Difference Equations, (2019) 2019:454) which containing exponential functions in their kernels. Then we establish certain new weighted fractional integral inequalities involving a family of n ( n &isin, N ) positive functions by utilizing Hadamard proportional fractional integral operator. The inequalities presented in this paper are more general than the inequalities existing in the literature.
- Published
- 2020
49. CARS Algorithm-Based Detection of Wheat Moisture Content before Harvest
- Author
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Chong Dongfeng, Wanzhang Wang, Zhang Boyang, and Hong Ji
- Subjects
panicle moisture content (pmc) ,Physics and Astronomy (miscellaneous) ,Logarithm ,Correlation coefficient ,Mean squared error ,wheat moisture content (wmc) ,cars algorithm ,General Mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Approximation error ,wheat ,Partial least squares regression ,Computer Science (miscellaneous) ,Range (statistics) ,0101 mathematics ,Mathematics ,lcsh:Mathematics ,spectral detection ,0402 animal and dairy science ,Univariate ,Regression analysis ,04 agricultural and veterinary sciences ,lcsh:QA1-939 ,040201 dairy & animal science ,Chemistry (miscellaneous) ,Algorithm - Abstract
To rapidly detect the wheat moisture content (WMC) without harm to the wheat and before harvest, this paper measured wheat and panicle moisture content (PMC) and the corresponding spectral reflectance of panicle before harvest at the Beijing Tongzhou experimental station of China Agricultural University. Firstly, we used correlation analysis to determine the optimal regression model of WMC and PMC. Secondly, we derived the spectral sensitive band of PMC before filtering the redundant variables competitive adaptive reweighted sampling (CARS) to select the variable subset with the least error. Finally, partial least squares regression (PLSR) was used to build and analyze the prediction model of PMC. At the early stage of wheat harvest, a high correlation existed between WMC and PMC. Among all regression models such as exponential, univariate linear, polynomial models, and the power function regression model, the logarithm regression model was the best. The determination coefficients of the modeling sample were: R2 = 0.9284, the significance F = 362.957, the determination coefficient of calibration sample R2v = 0.987, the root mean square error RMSEv = 3.859, and the relative error REv = 7.532. Within the range of 350&ndash, 2500 nm, bands of 728&ndash, 907 nm, 1407&ndash, 1809 nm, and 1940&ndash, 2459 nm had a correlation coefficient of PMC and wavelength reflectivity higher than 0.6. This paper used the CARS algorithm to optimize the variables and obtained the best variable subset, which included 30 wavelength variables. The PLSR model was established based on 30 variables optimized by the CARS algorithm. Compared with the all-sensitive band, which had 1103 variables, the PLSR model not only reduced the number of variables by 1073, but also had a higher accuracy in terms of prediction. The results showed that: RMSEC = 0.9301, R2c = 0.995, RMSEP = 2.676, R2p = 0.945, and RPD = 3.362, indicating that the CARS algorithm could effectively remove the variables of spectral redundant information. The CARS algorithm provided a new way of thinking for the non-destructive and rapid detection of WMC before harvest.
- Published
- 2020
50. Optimal Trajectory Synthesis for Spacecraft Asteroid Rendezvous
- Author
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Ranjan Vepa and M. Hasan Shaheed
- Subjects
asteroids ,Physics and Astronomy (miscellaneous) ,General Mathematics ,02 engineering and technology ,01 natural sciences ,optimal trajectory synthesis ,0203 mechanical engineering ,0103 physical sciences ,QA1-939 ,Computer Science (miscellaneous) ,State space ,Aerospace engineering ,010303 astronomy & astrophysics ,Physics ,020301 aerospace & aeronautics ,Spacecraft ,State-space representation ,business.industry ,Rendezvous ,dynamic modelling of satellite relative motion ,simulation ,optimal control of relative motion ,Orbit ,Chemistry (miscellaneous) ,Asteroid ,Physics::Space Physics ,Trajectory ,Satellite ,Astrophysics::Earth and Planetary Astrophysics ,business ,Mathematics - Abstract
Several researchers are considering the plausibility of being able to rapidly launch a mission to an asteroid, which would fly in close proximity of the asteroid to deliver an impulse in a particular direction so as to deflect the asteroid from its current orbit. Planetary motion, in general, and the motion of asteroids, in particular, are subject to planetary influences that are characterised by a kind of natural symmetry, which results in an asteroid orbiting in a stable and periodic or almost periodic orbit exhibiting a number of natural orbital symmetries. Tracking and following an asteroid, in close proximity, is the subject of this paper. In this paper, the problem of synthesizing an optimal trajectory to a NEO such as an asteroid is considered. A particular strategy involving the optimization of a co-planar trajectory segment that permits the satellite to approach and fly alongside the asteroid is chosen. Two different state space representations of the Hill–Clohessy–Wiltshire (HCW) linearized equations of relative motion are used to obtain optimal trajectories for a spacecraft approaching an asteroid. It is shown that by using a state space representation of HCW equations where the secular states are explicitly represented, the optimal trajectories are not only synthesized rapidly but also result in lower magnitudes of control inputs which must be applied continuously over extended periods of time. Thus, the solutions obtained are particularly suitable for low thrust control of the satellites orbit which can be realized by electric thrusters.
- Published
- 2021
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