5,094 results on '"Regular polygon"'
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2. Regular Polygon Central Configuration of the Restricted 1 + N -Body Problem.
- Author
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Chen, Jian, Bi, Peng, and Yang, Mingfang
- Subjects
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POLYGONS , *CELESTIAL mechanics - Abstract
We consider the central configurations of the 1 + N -body problem, where N bodies are infinitesimal and the remaining one body is dominant. For regular polygon central configurations, we prove that the masses of all the infinitesimal bodies are equal when N is odd and the masses of the alternate infinitesimal bodies must be equal when N is even. Moreover, in the case of N being even, we present the relationship of the mass parameters between two consecutive infinitesimal bodies. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. Solving geometry problems by alternative methods in mathematics education.
- Author
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Aliyev, Samed J., Heydarova, Maftun N., and Aghazade, Shahin M.
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MATHEMATICS education , *PROBLEM solving , *CIRCLE , *GEOMETRY - Abstract
Solving geometry problems is both difficult and interesting. Difficult because there is no general algorithm to solve more or less non-trivial problems as every single problem requires individual and creative approach. At the same time, this is a very interesting activity, because for almost every problem there are plenty of ways to solve it. In this work, we present the method of auxiliary circle divided into equal parts. This method allows finding solution algorithm for some geometry problems which are hard to solve by the method of additional constructions. [ABSTRACT FROM AUTHOR]
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- 2023
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4. TWO NON-CONGRUENT REGULAR POLYGONS HAVING VERTICES AT THE SAME DISTANCES FROM THE POINT.
- Author
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Meskhishvili, Mamuka
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GEOMETRICAL constructions - Abstract
For the given regular plane polygon and an arbitrary point in the plane of the polygon, the distances from the point to the vertices of the polygon are defined. We proved that there is one more non-congruent regular polygon having the vertices at the same distances from the point. The sizes of both regular polygons are uniquely determined by these distances. In general case, geometrical construction of the second regular polygon is given. It is proved that there are two points in the plane, which separately have the same set of the distances to the vertices of two non-congruent regular polygons with a shared vertex. [ABSTRACT FROM AUTHOR]
- Published
- 2023
5. Synthesis of 1-DOF mechanisms for exact regular polygonal path generation based on non-circular gear transmissions.
- Author
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Castillo, Carlos, López-Martínez, Javier, García-Vallejo, Daniel, and Blanco-Claraco, José Luis
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ACCELERATION (Mechanics) , *GEARING machinery , *KINEMATICS , *POLYGONS , *VELOCITY , *ANGLES - Abstract
Design of one-degree-of-freedom (1-DOF) mechanisms is of paramount interest. This work deals with the generation of exact regular polygonal paths by using two particular 1-DOF mechanisms. The design of two-bar and three-bar mechanisms including non-circular gears is presented and evaluated. Differences in the kinematics of both mechanisms are discussed. The three-bar mechanism allows derivable velocity and acceleration curves during the whole trajectory, including the polygon vertices, a feature that cannot be achieved with the simpler two-bar mechanism. Hence, the three-bar mechanism makes it possible to generate perfect vertices using non-circular gears. To the best of the authors' knowledge, this mechanism is the first 1-DOF mechanism with articulated links and a non-circular gear transmission that can generate exact regular polygonal paths. The proposed mechanisms can also be applied to generate two straight lines with a given angle, which is another novel contribution of this work. A prototype of the three-bar mechanism has been developed for experimental validation. • A 1-DOF mechanism that can generate exact regular polygonal paths is presented. • Solutions with two- and three-bar mechanisms are analyzed. • The mechanism can also generate two exact straight lines with a given angle. • Non-circular gears are used to generate the required non-linear transmission. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
6. Regular Polygon Central Configuration of the Restricted 1 + N-Body Problem
- Author
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Jian Chen, Peng Bi, and Mingfang Yang
- Subjects
celestial mechanics ,central configuration ,restricted 1 + N-body problem ,regular polygon ,Elementary particle physics ,QC793-793.5 - Abstract
We consider the central configurations of the 1+N-body problem, where N bodies are infinitesimal and the remaining one body is dominant. For regular polygon central configurations, we prove that the masses of all the infinitesimal bodies are equal when N is odd and the masses of the alternate infinitesimal bodies must be equal when N is even. Moreover, in the case of N being even, we present the relationship of the mass parameters between two consecutive infinitesimal bodies.
- Published
- 2023
- Full Text
- View/download PDF
7. Constructive geometric generating of concave pyramids of fourth sort
- Author
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Mišić Slobodan Ž. and Backović Marija V.
- Subjects
concave pyramids ,polyhedral ,equilateral triangle ,regular polygon ,Engineering (General). Civil engineering (General) ,TA1-2040 ,Mechanics of engineering. Applied mechanics ,TA349-359 - Abstract
The paper presents the results of the study of the new set of polihedra, the Concave pyramids of the fourth sort, the construction procedures for generating them and their possible application. Correspondingly to the method of generating the Concave cupolae of fourth sort, the Concave pyramids of fourth sort have the similar logic of origination, and their counterpart in regular faced convex pyramids. They are characterised by the polygonal base, deltahedral surface net, obtained by folding the planar net of unilateral triangles, the polar distribution of the unit space cells with common apex - the top of the Concave pyramid. Polihedral surface of the planar net of Concave pyramids is produced by polar distribution of unit cells, consisting of a spatial sexagon and spatial pentagon - six, or five, unilateral triangles grouped around the common vertex. In the deltahedral surface, the two neighbouring unit cells are joined by means of a unilateral triangle in the zone of the polygonal base and a spatial quadrangle with which they share common sides. The criterion of face regularity is respected, as well as the criterion of multiple axial symmetry. The sort of the Concave pyramids is determined by the number of equilateral triangle rows in thus obtained polyhedron's net. The parameters of the solids were determined constructively by geometric methods.
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- 2021
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8. Free vibration and buckling of heavy column with regular polygon cross-section.
- Author
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Lee, Joon Kyu and Lee, Byoung Koo
- Abstract
This paper deals with the free vibration and buckling of heavy column, considering its own self-weight. The column has a regular polygonal cross-section with a constant area. The column is applied to an external axial load as well as the self-weight. The five end conditions of the column are considered. Based on equilibrium equations of the column element, differential equations governing the vibrational and buckled mode shapes of column are derived. In solution methods, differential equations are numerically integrated by the direct integration method and eigenvalues of the natural frequency, buckling load and self-weight buckling length are calculated by the determinant search method. The numerical results of this study were in good agreement with those of the reference. Parametric study of the end condition, side number and self-weight on the natural frequency and buckling load was carried out. [ABSTRACT FROM AUTHOR]
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- 2022
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9. Buckling optimization of axially functionally graded columns having constant volume.
- Author
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Lee, Joon Kyu and Lee, Byoung Koo
- Subjects
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EULER-Bernoulli beam theory , *YOUNG'S modulus , *FINITE element method , *MODE shapes , *SEARCH algorithms - Abstract
In this article, the buckling optimization of axially functionally graded (AFG) columns to maximize the buckling capacity is studied. Consideration is given to an AFG column having a tapered regular polygon cross section and variable material properties. The governing differential equation is derived based on Euler–Bernoulli beam theory with the relevant boundary conditions and is solved using the direct integration method combined with a determinant search algorithm. The computed buckling loads are compared with those presented in the literature and obtained from finite element analysis. Numerical examples for buckling load and buckled mode shape are given to highlight the effect of parameters related to the Young's modulus, cross-sectional shape, tapering and column volume. In particular, the geometry and material parameters that provide buckling optimization at constant volume of the column are analysed. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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10. Y-equivalence and rhombic realization of projective-planar quadrangulations.
- Author
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Nakamoto, Atsuhiro and Omizo, Yuta
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POLYGONS , *QUADRILATERALS , *EDGES (Geometry) - Abstract
Let G be a quadrangulation on the projective plane P , i.e., a map of a simple graph on P such that each face is quadrilateral. For a vertex v ∈ V (G) of degree 3 with neighbors v 1 , v 3 , v 5 , a Y-rotation is to delete three edges v v 1 , v v 3 , v v 5 and add v v 2 , v v 4 , v v 6 , where the union of three faces incident to v is surrounded by a closed walk v 1 v 2 v 3 v 4 v 5 v 6 . We say that G is k -minimal if its shortest noncontractible cycle is of length k and if any face contraction yields a noncontractible cycle of length less than k. It was proved that for any k ≥ 3 , any two k -minimal quadrangulations on P are Y -equivalent , i.e., can be transformed into each other by Y-rotations (Nakamoto and Suzuki, 2012). In this paper, we find wider Y-equivalence classes of quadrangulations on P , extending a result on a geometric realization of quadrangulations on P as a rhombus tiling in an even-sided regular polygon (Hamanaka et al., 2020). [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
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11. Mean value theorems for polynomial solutions of linear elliptic equations with constant coefficients in the complex plane.
- Author
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Trofymenko, Olga D.
- Subjects
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ELLIPTIC equations , *LINEAR equations , *POLYNOMIALS , *MEAN value theorems , *POLYGONS - Abstract
We characterize solutions of the mean value linear elliptic equation with constant coefficients in the complex plane in the case of regular polygon. [ABSTRACT FROM AUTHOR]
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- 2021
- Full Text
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12. On inverse construction of isoptics and isochordal-viewed curves.
- Author
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Rochera, David and Bartoň, Michael
- Subjects
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INVERSE problems , *POLYGONS , *LOCUS (Mathematics) - Abstract
Given a regular closed curve α in the plane, a ϕ -isoptic of α is a locus of points from which pairs of tangent lines to α span a fixed angle ϕ. If, in addition, the chord that connects the two points delimiting the visibility angle is of constant length ℓ , then α is said to be (ϕ , ℓ) -isochordal viewed. Some properties of these curves have been studied, yet their full classification is not known. We approach the problem in an inverse manner, namely that we consider a ϕ -isoptic curve c as an input and construct a curve whose ϕ -isoptic is c. We provide thus a sufficient condition that constitutes a partial solution to the inverse isoptic problem. In the process, we also study a relation of isoptics to multihedgehogs. Moreover, we formulate conditions on the behavior of the visibility lines so as their envelope is a (ϕ , ℓ) -isochordal-viewed curve with a prescribed ϕ -isoptic c. Our results are constructive and offer a tool to easily generate this type of curves. In particular, we show examples of (ϕ , ℓ) -isochordal-viewed curves whose ϕ -isoptic is not circular. Finally, we prove that these curves allow the motion of a regular polygon whose vertices lie along the (ϕ , ℓ) -isochordal-viewed curve. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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13. CYCLIC AVERAGES OF REGULAR POLYGONAL DISTANCES.
- Author
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Meskhishvili, Mamuka
- Subjects
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POWER (Social sciences) , *DISTANCES , *POLYGONS - Abstract
We consider a regular plane polygon with n vertices and an arbitrary point in the plane. Let R be the circumscribed radius of the polygon and L a distance from the point to the centroid of the polygon. Then the averages of the (2m)-th powers of distances from the point to the polygon vertices satisfy the relations Sn(2) = R² + L²; Sn(2m) = (R²> + L²)m + bm 2 ∑ k=1 (m 2k) (2k k) (R² + L²)m-2k (RL)2k, where m = 2,..., n - 1. [ABSTRACT FROM AUTHOR]
- Published
- 2021
14. REGULAR POLYGONS IN 2D OBJECTS SHAPE DESCRIPTION.
- Author
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Kwinta, Andrzej and Bac-Bronowicz, Joanna
- Subjects
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GEOMETRIC shapes , *CENTROID , *THREE-dimensional imaging , *POLYGONS , *GEOMETRY , *DATA analysis - Abstract
Many real 3D objects have complex geometric shapes in various types of analyses. Image of these objects is recorded in the form of a 2D map. In the analysis, a simplification of this image to basic 2D figures with defined geometry is often needed. The paper presents an analysis of the geometry of a flat image (an image of a 3D object) using regular polygons. Geometry properties (F form, C centroid, S size) were determined to describe the object. Various criteria of selection of the 'best ' regular n-sided polygon for a given 2D object (solved theoretically) were put forward. In the paper, criteria for describing a 2D object by regular n-sided polygons were defined on the basis of determining the measure of object shape elongation (e). In the 'blind ' theoretical example, it was tested whether the individual shape measures listed in the paper allow for correct identification of the shapes of given 2D objects. The practical application of measures is illustrated by two actual examples. While in the first example the shape of the Canary Islands is analysed, the second example describes the shape of Poland 's borders. Actual examples deliver different results for different measures. In effect, there is no clear objective criterion for selecting a polygon shape. The simplifications of the shape of an object presented in the paper should not be equated with the object 's generalization. Such simplifications are used in GIS to visualize geographic analyses based on the data available in the primary database, because the object will retain the character of the shape in the simplest possible geometry and neighborhood, and does not lose any of the scope and accuracy of the attributes assigned to a given object in the database. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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15. Rhombus Tilings of an Even-Sided Polygon and Quadrangulations on the Projective Plane.
- Author
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Hamanaka, Hiroaki, Nakamoto, Atsuhiro, and Suzuki, Yusuke
- Subjects
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POLYGONS , *PROJECTIVE planes , *MINIMAL surfaces , *TILES - Abstract
A quadrangulation on a closed surface is k-minimal if its shortest noncontractible cycle is of length k and if any face contraction yields a noncontractible cycle of length less than k. We prove that the rhombus tilings of a regular 2k-gon bijectively correspond to the pairs of a k-minimal quadrangulations on the projective plane and its specified noncontractible k-cycle. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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16. EQUIVALENCE CONDITIONS OF TWO SYSTEMS OF VECTORS IN THE TAXICAB PLANE AND ITS APPLICATIONS TO TAXICAB POLYGONS.
- Author
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ÖREN, IDRIS and ÇOBAN, HÜSNÜ ANIL
- Subjects
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MATHEMATICAL equivalence , *POLYGONS , *INVARIANTS (Mathematics) - Abstract
This study presents the conditions of MT (2)-equivalence for two systems of vectors fx1; x2; x3g and {x1, x2, x3} in R2T, where MT (2) is the group of all isometries of the 2-dimensional taxicab space RT². Firstly a minimal complete system of MT (2)-invariants of {x1, x2, x3} is obtained. Then, using the conditions of MT (2)-equivalence, an answer is given to the open prob- lem posed in [10, p.428]. Furthermore, an algorithm is given for constructing taxicab regular polygons in terms of MT (2)-invariants. This algorithm is gen- eral and useful to construct the taxicab regular 2n-gons and gives a tool to solve special cases of the open problem posed in [2, p.32]. Besides, both the conditions of the taxicab regularity of Euclidean regular polygons and Euclidean regularity of taxicab regular polygons are given in terms of MT (2)-invariants. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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17. ALTERNATING COLOURINGS OF THE VERTICES OF A REGULAR POLYGON.
- Author
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SINGH, SHIVANI and ZELENYUK, YULIYA
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COLOR , *MATHEMATICAL equivalence , *ROTATIONAL motion - Abstract
Let $n,r,k\in \mathbb{N}$. An $r$ -colouring of the vertices of a regular $n$ -gon is any mapping $\unicode[STIX]{x1D712}:\mathbb{Z}_{n}\rightarrow \{1,2,\ldots ,r\}$. Two colourings are equivalent if one of them can be obtained from another by a rotation of the polygon. An $r$ -ary necklace of length $n$ is an equivalence class of $r$ -colourings of $\mathbb{Z}_{n}$. We say that a colouring is $k$ -alternating if all $k$ consecutive vertices have pairwise distinct colours. We compute the smallest number $r$ for which there exists a $k$ -alternating $r$ -colouring of $\mathbb{Z}_{n}$ and we count, for any $r$ , 2-alternating $r$ -colourings of $\mathbb{Z}_{n}$ and 2-alternating $r$ -ary necklaces of length $n$. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
18. Catching all geodesics of a manifold with moving balls and application to controllability of the wave equation
- Author
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Cyril Letrouit, Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université (SU), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Universités, Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Sorbonne Université, and École normale supérieure - Paris (ENS Paris)
- Subjects
Geodesic ,[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] ,Regular polygon ,Dynamical Systems (math.DS) ,Riemannian manifold ,Absolute continuity ,Wave equation ,Domain (mathematical analysis) ,Manifold ,Theoretical Computer Science ,Combinatorics ,Mathematics - Analysis of PDEs ,Mathematics (miscellaneous) ,Optimization and Control (math.OC) ,FOS: Mathematics ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Ball (mathematics) ,Mathematics::Differential Geometry ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Mathematics - Dynamical Systems ,Mathematics - Optimization and Control ,Analysis of PDEs (math.AP) ,Mathematics - Abstract
We address the problem of catching all speed $1$ geodesics of a Riemannian manifold with a moving ball: given a compact Riemannian manifold $(M,g)$ and small parameters $\varepsilon>0$ and $v>0$, is it possible to find $T>0$ and an absolutely continuous map $x:[0,T]\rightarrow M, t\mapsto x(t)$ satisfying $\|\dot{x}\|_{\infty}\leq v$ and such that any geodesic of $(M,g)$ traveled at speed $1$ meets the open ball $B_g(x(t),\varepsilon)\subset M$ within time $T$? Our main motivation comes from the control of the wave equation: our results show that the controllability of the wave equation can sometimes be improved by allowing the domain of control to move adequately, even very slowly. We first prove that, in any Riemannian manifold $(M,g)$ satisfying a geodesic recurrence condition (GRC), our problem has a positive answer for any $\varepsilon>0$ and $v>0$, and we give examples of Riemannian manifolds $(M,g)$ for which (GRC) is satisfied. Then, we build an explicit example of a domain $X\subset\mathbb{R}^2$ (with flat metric) containing convex obstacles, not satisfying (GRC), for which our problem has a negative answer if $��$ and $v$ are small enough, i.e., no sufficiently small ball moving sufficiently slowly can catch all geodesics of $X$., Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore In press
- Published
- 2023
19. An improved upper bound on dilation of regular polygons.
- Author
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Sattari, Sattar and Izadi, Mohammad
- Subjects
- *
POLYGONS , *POINT set theory , *MATHEMATICAL proofs , *TRIANGULATION - Abstract
Dilation of a set of points on the plane is the lowest possible dilation of a plane spanner on the point set. We show that dilation of vertices of any regular polygon is less than 1.4482. We introduce a method for constructing a triangulation of a regular polygon and prove this bound on its dilation. The upper bound on dilation is shown using mathematical proofs and experimental results. The new upper bound improves the previously known bound of 1.48454. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
20. Generalized Second Moment of Areas of Regular Polygons for Ludwick Type Material and its Application to Cantilever Column Buckling.
- Author
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Lee, Joon Kyu and Lee, Byoung Koo
- Subjects
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POLYGONS , *CANTILEVERS , *MATERIALS , *MECHANICAL buckling , *HEXAGONS , *TRIANGLES - Abstract
This study deals with the generalized second moment of area (GSMA) of regular polygon cross-sections for the Ludwick type material and its application to cantilever column buckling. In the literature, the GSMA for the Ludwick type material has only been considered for rectangular, elliptical and superellipsoidal cross-sections. This study calculates the GSMAs of regular polygon cross-sections other than those mentioned above. The GSMAs calculated by varying the mechanical constant of the Ludwick type material for the equilateral triangle, square, regular pentagon, regular hexagon and circular cross-sections are reported in tables and figures. The GSMAs obtained from this study are applied to cantilever column buckling, with results shown in tables and figures. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
21. Near-optimal asset allocation in financial markets with trading constraints
- Author
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Antoon Pelsser, Thijs Kamma, QE Econometrics, RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory, RS: GSBE Theme Human Decisions and Policy Design, RS: FSE DACS Mathematics Centre Maastricht, and RS: GSBE UM-BIC
- Subjects
Mathematical optimization ,Information Systems and Management ,General Computer Science ,Utility maximisation ,Investment strategy ,Computer science ,0211 other engineering and technologies ,Asset allocation ,02 engineering and technology ,Management Science and Operations Research ,Industrial and Manufacturing Engineering ,RANDOM ENDOWMENT ,DUALITY ,Bellman equation ,Incomplete markets ,0502 economics and business ,OPTIMAL CONSUMPTION ,Projection (set theory) ,TIGHT BOUNDS ,Stochastic control ,UTILITY ,050210 logistics & transportation ,021103 operations research ,Convex duality ,05 social sciences ,Financial market ,Regular polygon ,MONTE-CARLO METHOD ,HABIT FORMATION ,OPTIMAL INVESTMENT ,Stochastic optimal control ,PORTFOLIO CHOICE ,Modeling and Simulation ,Finance - Abstract
We develop a dual-control method for approximating investment strategies in multidimensional financial markets with convex trading constraints. The method relies on a projection of the optimal solution to an (unconstrained) auxiliary problem to obtain a feasible and near-optimal solution to the original problem. We obtain lower and upper bounds on the optimal value function using convex duality methods. The gap between the bounds indicates the precision of the near-optimal solution. We illustrate the effectiveness of our method in a market with different trading constraints such as borrowing, short-sale constraints and non-traded assets. We also show that our method works well for state-dependent utility functions.
- Published
- 2022
22. Hahn-Banach type theorems and the separation of convex sets for fuzzy quasi-normed spaces
- Author
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Ruini Li and Jianrong Wu
- Subjects
Pure mathematics ,General Mathematics ,Separation (statistics) ,Regular polygon ,Hahn–Banach theorem ,Type (model theory) ,Fuzzy logic ,separation theorem ,fuzzy quasi-normed space ,hahn-banach extension theorem ,QA1-939 ,continuous linear functional ,Mathematics - Abstract
In this paper, we first study continuous linear functionals on a fuzzy quasi-normed space, obtain a characterization of continuous linear functionals, and point out that the set of all continuous linear functionals forms a convex cone and can be equipped with a weak fuzzy quasi-norm. Next, we prove a theorem of Hahn-Banach type and two separation theorems for convex subsets of fuzzy quasinormed spaces.
- Published
- 2022
23. Some integral inequalities for coordinated log-h-convex interval-valued functions
- Author
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Guoju Ye, Fangfang Shi, Wei Liu, and Dafang Zhao
- Subjects
Inequality ,General Mathematics ,media_common.quotation_subject ,Regular polygon ,jensen type inequalities ,hermite-hadamard type inequalities ,Interval valued ,Combinatorics ,QA1-939 ,interval-valued functions ,Mathematics ,media_common ,coordinated log-h-convex - Abstract
We introduce and investigate the coordinated log-$ h $-convexity for interval-valued functions. Also, we prove some new Jensen type inequalities and Hermite-Hadamard type inequalities, which generalize some known results in the literature. Moreover, some examples are given to illustrate our results.
- Published
- 2022
24. Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals
- Author
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Hari M. Srivastava, Taghreed M. Jawa, Pshtiwan Othman Mohammed, Muhammad Bilal Khan, and Dumitru Baleanu
- Subjects
Discrete mathematics ,hermite-hadamard inequality ,jense's type inequality ,General Mathematics ,p-convex fuzzy-interval-valued function ,Regular polygon ,Fuzzy logic ,schur's type inequality ,Interval valued ,hermite-hadamard-fejér inequality ,Riemann hypothesis ,symbols.namesake ,symbols ,QA1-939 ,Interval (graph theory) ,fuzzy riemann integral ,Mathematics - Abstract
The objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as $ p $-convex fuzzy-interval-valued functions ($ p $-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of $ p $-convex FIVFs, we have presented some Hermite-Hadamard type inequalities ($ H-H $ type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejér type inequality ($ H-H $ Fejér type inequality) for $ p $-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense's type inequality and Schur's type inequality for $ p $-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.
- Published
- 2022
25. Some fuzzy-interval integral inequalities for harmonically convex fuzzy-interval-valued functions
- Author
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Bahaaeldin Abdalla, Muhammad Aslam Noor, Muhammad Bilal Khan, Ali Althobaiti, and Thabet Abdeljawad
- Subjects
Pure mathematics ,Relation (database) ,Mathematics::General Mathematics ,hermite-hadamard inequality ,General Mathematics ,harmonically convex fuzzy interval-valued function ,fuzzy-interval integrals ,Regular polygon ,Interval (mathematics) ,Space (mathematics) ,Fuzzy logic ,Riemann hypothesis ,symbols.namesake ,Hermite–Hadamard inequality ,symbols ,QA1-939 ,Order (group theory) ,hermite-hadamard fejér inequality ,Mathematics - Abstract
It is well-known fact that fuzzy interval-valued functions (F-I-V-Fs) are generalizations of interval-valued functions (I-V-Fs), and inclusion relation and fuzzy order relation on interval space and fuzzy space are two different concepts. Therefore, by using fuzzy order relation (FOR), we derive inequalities of Hermite-Hadamard (H·H) and Hermite-Hadamard Fejér (H·H Fejér) like for harmonically convex fuzzy interval-valued functions by applying fuzzy Riemann integrals. Moreover, we establish the relation between fuzzy integral inequalities and fuzzy products of harmonically convex fuzzy interval-valued functions. The outcomes of this study are generalizations of many known results which can be viewed as an application of a defined new version of inequalities.
- Published
- 2022
26. On stochastic accelerated gradient with non-strongly convexity
- Author
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Xingxing Zha, Yongquan Zhang, Dongyin Wang, and Yiyuan Cheng
- Subjects
least-square regression ,General Mathematics ,Carry (arithmetic) ,logistic regression ,Supervised learning ,Regular polygon ,Lipschitz continuity ,Stochastic approximation ,accelerated stochastic approximation ,Convexity ,Stochastic programming ,convergence rate ,Rate of convergence ,QA1-939 ,Applied mathematics ,Mathematics - Abstract
In this paper, we consider stochastic approximation algorithms for least-square and logistic regression with no strong-convexity assumption on the convex loss functions. We develop two algorithms with varied step-size motivated by the accelerated gradient algorithm which is initiated for convex stochastic programming. We analyse the developed algorithms that achieve a rate of $ O(1/n^{2}) $ where $ n $ is the number of samples, which is tighter than the best convergence rate $ O(1/n) $ achieved so far on non-strongly-convex stochastic approximation with constant-step-size, for classic supervised learning problems. Our analysis is based on a non-asymptotic analysis of the empirical risk (in expectation) with less assumptions that existing analysis results. It does not require the finite-dimensionality assumption and the Lipschitz condition. We carry out controlled experiments on synthetic and some standard machine learning data sets. Empirical results justify our theoretical analysis and show a faster convergence rate than existing other methods.
- Published
- 2022
27. Algorithmic Aspects of Secure Connected Domination in Graphs
- Author
-
P. Venkata Subba Reddy and Jakkepalli Pavan Kumar
- Subjects
FOS: Computer and information sciences ,Discrete Mathematics (cs.DM) ,Computational Complexity (cs.CC) ,Star (graph theory) ,68q25 ,Connected dominating set ,Combinatorics ,tree-width ,Integer ,Chordal graph ,QA1-939 ,Discrete Mathematics and Combinatorics ,Connectivity ,Mathematics ,05C69, 68Q25 ,Applied Mathematics ,Regular polygon ,Approximation algorithm ,chordal graphs ,complexity classes ,Computer Science - Computational Complexity ,05c69 ,Bipartite graph ,secure domination ,Computer Science - Discrete Mathematics - Abstract
Let $G = (V,E)$ be a simple, undirected and connected graph. A connected dominating set $S \subseteq V$ is a secure connected dominating set of $G$, if for each $ u \in V\setminus S$, there exists $v\in S$ such that $(u,v) \in E$ and the set $(S \setminus \{ v \}) \cup \{ u \} $ is a connected dominating set of $G$. The minimum size of a secure connected dominating set of $G$ denoted by $ \gamma_{sc} (G)$, is called the secure connected domination number of $G$. Given a graph $ G$ and a positive integer $ k,$ the Secure Connected Domination (SCDM) problem is to check whether $ G $ has a secure connected dominating set of size at most $ k.$ In this paper, we prove that the SCDM problem is NP-complete for doubly chordal graphs, a subclass of chordal graphs. We investigate the complexity of this problem for some subclasses of bipartite graphs namely, star convex bipartite, comb convex bipartite, chordal bipartite and chain graphs. The Minimum Secure Connected Dominating Set (MSCDS) problem is to find a secure connected dominating set of minimum size in the input graph. We propose a $ (\Delta(G)+1) $ - approximation algorithm for MSCDS, where $ \Delta(G) $ is the maximum degree of the input graph $ G $ and prove that MSCDS cannot be approximated within $ (1 -\epsilon) ln(| V |)$ for any $ \epsilon > 0 $ unless $ NP \subseteq DTIME(| V |^{O(log log | V |)})$ even for bipartite graphs. Finally, we show that the MSCDS is APX-complete for graphs with $\Delta(G)=4$.
- Published
- 2021
28. Kinematic calculation of convex cam profile using MATHCAD program
- Author
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V. V. Ryndin, L. Yu. Volkova, Yu. P. Makushev, Siberian State Automobile, and T. A. Polyakova
- Subjects
graphs ,Mathematical analysis ,Regular polygon ,Kinematics ,convex cam ,Engineering (General). Civil engineering (General) ,engine mechanisms ,Computer Science::Robotics ,derivation of formulas ,TA1-2040 ,mathcad program ,calculation of pusher kinematics ,Mathematics ,ComputingMethodologies_COMPUTERGRAPHICS - Abstract
The article shows the features of the construction of cams with a convex profile, the method of kinematic calculation of the pusher when it moves along a convex and rounded surface is given. A technique is proposed to determine the coordinate center of the radius of the convex surface of the cam. Calculations of the stroke, speed and acceleration of the pusher depending on the angle of rotation of the cam shaft are performed using the Mathcad system. Using the Mathcad program for cams with a convex profile, graphs of the pusher lift, changes in its speed and acceleration are constructed. The proposed method of calculating the cams of a convex profile of various sizes with the determination of the lifting height, speed, acceleration of the pusher and the construction of their graphs in the Mathcad system will allow designing cams and copiers necessary for processing cam shafts.
- Published
- 2021
29. Almost sure convergence of randomised‐difference descent algorithm for stochastic convex optimisation
- Author
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Wenxiao Zhao, Gao Huang, and Xiaoxue Geng
- Subjects
Human-Computer Interaction ,Control and Optimization ,Convergence of random variables ,Control engineering systems. Automatic machinery (General) ,Control and Systems Engineering ,Computer science ,Control theory ,TJ212-225 ,Regular polygon ,Applied mathematics ,Electrical and Electronic Engineering ,Descent algorithm ,Computer Science Applications - Abstract
Stochastic gradient descent algorithm is a classical and useful method for stochastic optimisation. While stochastic gradient descent has been theoretically investigated for decades and successfully applied in machine learning such as training of deep neural networks, it essentially relies on obtaining the unbiased estimates of gradients/subgradients of the objective functions. In this paper, by constructing the randomised differences of the objective function, a gradient‐free algorithm, named the stochastic randomised‐difference descent algorithm, is proposed for stochastic convex optimisation. Under the strongly convex assumption of the objective function, it is proved that the estimates generated from stochastic randomised‐difference descent converge to the optimal value with probability one, and the convergence rates of both the mean square error of estimates and the regret functions are established. Finally, some numerical examples are prsented.
- Published
- 2021
30. Maximization of a PSD quadratic form and factorization
- Author
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David Hartman, Milan Hladík, Moslem Zamani, and Econometrics and Operations Research
- Subjects
021103 operations research ,Control and Optimization ,Duality gap ,0211 other engineering and technologies ,Regular polygon ,Duality (optimization) ,Computational intelligence ,Preconditioning ,010103 numerical & computational mathematics ,02 engineering and technology ,Maximization ,01 natural sciences ,Upper and lower bounds ,Maximum norm ,Factorization ,Concave programming ,Convex quadratic form ,Euclidean geometry ,NP-hardness ,Applied mathematics ,0101 mathematics ,Upper bound ,Mathematics - Abstract
We consider the problem of maximization of a convex quadratic form on a convex polyhedral set, which is known to be NP-hard. In particular, we focus on upper bounds on the maximum value. We investigate utilization of different vector norms (estimating the Euclidean one) and different objective matrix factorizations. We arrive at some kind of duality with positive duality gap in general, but with possibly tight bounds. We discuss theoretical properties of these bounds and also extensions to generally preconditioned factors. We employ mainly the maximum vector norm since it yields efficiently computable bounds, however, we study other norms, too. Eventually, we leave many challenging open problems that arose during the research.
- Published
- 2021
31. New version of fractional Simpson type inequalities for twice differentiable functions
- Author
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Fatih Hezenci, Hüseyin Budak, Hasan Kara, and [Belirlenecek]
- Subjects
Pure mathematics ,Convex-Functions ,Algebra and Number Theory ,Applied Mathematics ,Fractional integrals ,Regular polygon ,Mathematics::Classical Analysis and ODEs ,Absolute value (algebra) ,Type (model theory) ,Integral-Inequalities ,Identity (mathematics) ,Mathematics::Algebraic Geometry ,Convex function ,Ordinary differential equation ,QA1-939 ,Differentiable function ,Analysis ,Simpson type inequalities ,Mathematics ,Second derivative - Abstract
Simpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. Simpson type inequalities for twice differentiable functions are also investigated. More precisely, Budak et al. established the first result on fractional Simpson inequality for twice differentiable functions. In the present article, we prove a new identity for twice differentiable functions. In addition to this, we establish several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. This paper is a new version of fractional Simpson type inequalities for twice differentiable functions.
- Published
- 2021
32. Existence and nonexistence of entire k-convex radial solutions to Hessian type system
- Author
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Jixian Cui
- Subjects
Hessian matrix ,Algebra and Number Theory ,Partial differential equation ,Monotone iterative method ,Functional analysis ,Applied Mathematics ,Regular polygon ,MathematicsofComputing_NUMERICALANALYSIS ,Existence ,Type (model theory) ,Fixed point ,Nonexistence ,symbols.namesake ,Ordinary differential equation ,symbols ,QA1-939 ,Applied mathematics ,Analysis ,k-convex radial solution ,Hessian type system ,Mathematics - Abstract
In this paper, a Hessian type system is studied. After converting the existence of an entire solution to the existence of a fixed point of a continuous mapping, the existence of entirek-convex radial solutions is established by the monotone iterative method. Moreover, a nonexistence result is also obtained.
- Published
- 2021
33. Necessary and sufficient conditions on the Schur convexity of a bivariate mean
- Author
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Bai-Ni Guo, Hong-Ping Yin, Xi-Min Liu, and Jing-Yu Wang
- Subjects
Mathematics::Combinatorics ,inequality ,General Mathematics ,lcsh:Mathematics ,Regular polygon ,Bivariate analysis ,lcsh:QA1-939 ,Convexity ,Combinatorics ,schur harmonically convex function ,schur convex function ,majorization ,Majorization ,Mathematics::Representation Theory ,bivariate mean ,Mathematics ,Schur-convex function ,necessary and sufficient condition - Abstract
In the paper, the authors find and apply necessary and sufficient conditions for a bivariate mean of two positive numbers with three parameters to be Schur convex or Schur harmonically convex respectively.
- Published
- 2021
34. Computational Modeling Methods for Deployable Structure Based on Alternatively Asymmetric Triangulation
- Author
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Qingwen Zhang, Danmin Yu, Xinye Li, and Feng Fan
- Subjects
deployable structure ,regular polygon ,alternatively asymmetric triangulation ,parametric modeling ,rigid-foldable origami ,Mathematics ,QA1-939 - Abstract
Asymmetric triangulation is an interesting method combined with concentric pleating to obtain a 3D shape without stretching or tearing. There exists some geometric properties in the process of folding to help realize extension and contraction, which can be used in parametric modeling of different regular polygons. To facilitate design and modeling, adequate computational modeling methods are indispensable. This paper proposes a new mathematical idea and presents a feasible way to build the parameterized models in the digital environment of Rhinoceros, utilizing the Kangaroo plugin in Grasshopper. Designers can directly observe the models’ kinematic deployment and calculate the folding efficiency. It is concluded that the tendencies of folding efficiency in different regular polygons are not the same. To realize rigid folding, each polygon has a limited folding angle.
- Published
- 2019
- Full Text
- View/download PDF
35. Convergence of a Three-step Iteration Scheme to the Common Fixed Points of Mixed-Type Total Asymtotically Nonexpansive Mappings in Uniformly Convex Banach Spaces
- Author
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Donatus Ikechi Igbokwe, Nathenial C. Ukeje, and Imo Kalu Agwu
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,uniformly convex banach space ,QA299.6-433 ,T57-57.97 ,Applied mathematics. Quantitative methods ,Weak convergence ,Banach space ,Regular polygon ,Mixed type ,common fixed point ,Fixed point ,asymtotically nonexpansive mapping ,hybrid mixed type iteration scheme ,Scheme (mathematics) ,Convergence (routing) ,Common fixed point ,weak convergence ,total asymptotically nonexpansive nonself mapping ,Analysis ,Mathematics - Abstract
We propose a three-step iteration scheme of hybrid mixed-type for three total asymptotically nonexpansive self mappings and three total asymptotically nonexpansive nonself mappings. In addition, we establish some weak convergence theorems of the scheme to the common fixed point of the mappings in uniformly convex Banach spaces. Our results extend and generalize numerous results currently in literature.
- Published
- 2021
36. A class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$
- Author
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Zijian Wu and Haibo Chen
- Subjects
Pure mathematics ,Class (set theory) ,multiple solutions ,fourth-order elliptic equation ,Applied Mathematics ,Regular polygon ,Multiplicity (mathematics) ,nehari manifold ,Fourth order ,Variational principle ,ekeland variational principle ,QA1-939 ,Nehari manifold ,Ground state ,Mathematics - Abstract
In this article, we study the multiplicity of solutions for a class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$. Under the appropriate assumption, we prove that there are at least two solutions for the equation by Nehari manifold and Ekeland variational principle, one of which is the ground state solution.
- Published
- 2021
37. On a Bernoulli-type overdetermined free boundary problem
- Author
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Mariana Smit Vega Garcia, Murat Akman, and Agnid Banerjee
- Subjects
Physics ,Regular polygon ,Function (mathematics) ,Articles ,Type (model theory) ,35R35, 35A01, 35J92, 35J25, 35J70 ,Omega ,Combinatorics ,Overdetermined system ,Mathematics - Analysis of PDEs ,free boundary problems ,Bernoulli-type free boundary problems ,Free boundary problem ,FOS: Mathematics ,degenerate elliptic equations ,Nabla symbol ,Constant (mathematics) ,Analysis of PDEs (math.AP) ,Quasilinear elliptic equations and p-Laplacian - Abstract
In this article we study a Bernoulli-type free boundary problem and generalize a work of Henrot and Shahgholian in [25] to \(\mathcal{A}\)-harmonic PDEs. These are quasi-linear elliptic PDEs whose structure is modelled on the \(p\)-Laplace equation for a fixed \(10\) is a given constant, then there exists a unique convex domain \(\Omega\) with \(K\subset \Omega\) and a function \(u\) which is \(\mathcal{A}\)-harmonic in \(\Omega\setminus K\), has continuous boundary values 1 on \(\partial K\) and 0 on \(\partial\Omega\), such that \(|\nabla u|=c\) on \(\partial \Omega\). Moreover, \(\partial\Omega\) is \(C^{1,\gamma}\) for some \(\gamma>0\), and it is smooth provided \(\mathcal{A}\) is smooth in \(\mathbf{R}^n \setminus \{0\}\). We also show that the super level sets \(\{u>t\}\) are convex for \(t\in (0,1)\).
- Published
- 2021
38. Refinements of some fractional integral inequalities for refined ( α , h − m ) $(\alpha ,h-m)$ -convex function
- Author
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Hafsa Yasmeen, Yu-Pei Lv, Ghulam Farid, Josip Pečarić, and Chahn Yong Jung
- Subjects
Pure mathematics ,Algebra and Number Theory ,Partial differential equation ,Functional analysis ,Applied Mathematics ,Regular polygon ,Substitution (algebra) ,Hermite–Hadamard inequality ,Alpha (programming language) ,Refined ( α , h − m ) $(\alpha ,h-m)$ -convex function ,Ordinary differential equation ,Riemann–Liouville fractional integrals ,QA1-939 ,Convex function ,Analysis ,Refined ( h − m ) $(h-m)$ -convex function ,Mathematics - Abstract
This article investigates new inequalities for generalized Riemann–Liouville fractional integrals via the refined $(\alpha ,h-m)$ ( α , h − m ) -convex function. The established results give refinements of fractional integral inequalities for $(h-m)$ ( h − m ) -convex, $(\alpha ,m)$ ( α , m ) -convex, $(s,m)$ ( s , m ) -convex, and related functions. Also, the k-fractional versions of given inequalities by using a parameter substitution are provided.
- Published
- 2021
39. Riemann-Liouville Fractional integral operators with respect to increasing functions and strongly (α,m)-convex functions
- Author
-
Ghulam Farid, Hijaz Ahmad, Hafsa Yasmeen, and Chahn Yong Jung
- Subjects
m)-convex function ,Pure mathematics ,General Mathematics ,Regular polygon ,Type (model theory) ,Hadamard inequality ,Riemann liouville ,hadamard inequality ,Alpha (programming language) ,strongly (α ,Hadamard transform ,riemann-liouville fractional integrals ,(α ,QA1-939 ,Convex function ,Mathematics - Abstract
In this paper Hadamard type inequalities for strongly $ (\alpha, m) $-convex functions via generalized Riemann-Liouville fractional integrals are studied. These inequalities provide generalizations as well as refinements of several well known inequalities. The established results are further connected with fractional integral inequalities for Riemann-Liouville fractional integrals of convex, strongly convex and strongly $ m $-convex functions. By using two fractional integral identities some more Hadamard type inequalities are proved.
- Published
- 2021
40. On some new midpoint inequalities for the functions of two variables via quantum calculus
- Author
-
Yu-Ming Chu, Samet Erden, Hüseyin Budak, Muhammad Ali, Xuexiao You, and [Belirlenecek]
- Subjects
Pure mathematics ,Quantum calculus ,Type (model theory) ,Midpoint ,Identity (mathematics) ,QA1-939 ,Discrete Mathematics and Combinatorics ,q(1)q(2)-derivatives ,Differentiable function ,Rectangle ,Quantum ,Mathematics ,q 1 q 2 $q_{1}q_{2}$ -derivatives ,Hadamard Inequality ,Convex-Functions ,Applied Mathematics ,q 1 q 2 $q_{1}q_{2}$ -integrals ,Regular polygon ,Extension (predicate logic) ,Hermite–Hadamard inequality ,Hermite-Hadamard inequality ,Co-ordinated convexity ,q(1)q(2)-integrals ,Analysis - Abstract
In this paper, first we obtain a new identity for quantum integrals, the result is then used to prove midpoint type inequalities for differentiable coordinated convex mappings. The outcomes provided in this article are an extension of the comparable consequences in the literature on the midpoint inequalities for differentiable coordinated convex mappings. Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [61673169, 11301127, 11701176, 11626101, 11601485, 11971241] The work was supported by the Natural Science Foundation of China (Grant Nos. 61673169, 11301127, 11701176, 11626101, 11601485, 11971241). WOS:000687145200001 2-s2.0-85113245658
- Published
- 2021
41. Some new Hermite-Hadamard type inequalities for generalized harmonically convex functions involving local fractional integrals
- Author
-
Wenbing Sun and Rui Xu
- Subjects
Pure mathematics ,local fractional integral ,Hermite polynomials ,General Mathematics ,generalized harmonically convex function ,010102 general mathematics ,Regular polygon ,Monotonic function ,Function (mathematics) ,Type (model theory) ,hermite-hadamard type inequality ,01 natural sciences ,010305 fluids & plasmas ,Identity (mathematics) ,Hadamard transform ,yang's fractal sets ,0103 physical sciences ,QA1-939 ,0101 mathematics ,Convex function ,Mathematics - Abstract
In this paper, we establish a new integral identity involving local fractional integral on Yang's fractal sets. Using this integral identity, some new generalized Hermite-Hadamard type inequalities whose function is monotonically increasing and generalized harmonically convex are obtained. Finally, we construct some generalized special means to explain the applications of these inequalities.
- Published
- 2021
42. Non-convex proximal pair and relatively nonexpansive maps with respect to orbits
- Author
-
Yumnam Rohen and Laishram Shanjit
- Subjects
Best proximity point ,0211 other engineering and technologies ,Structure (category theory) ,Banach space ,02 engineering and technology ,Fixed point ,01 natural sciences ,Combinatorics ,Set (abstract data type) ,symbols.namesake ,Cyclic T-regular set ,Proximal parallel pair ,Convergence (routing) ,QA1-939 ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Iteration process ,Mathematics ,021103 operations research ,Applied Mathematics ,Regular polygon ,Hilbert space ,010101 applied mathematics ,symbols ,Analysis ,Kranoselskii’s iteration - Abstract
Every non-convex pair $(C, D)$ ( C , D ) may not have proximal normal structure even in a Hilbert space. In this article, we use cyclic relatively nonexpansive maps with respect to orbits to show the presence of best proximity points in $C\cup D$ C ∪ D , where $C\cup D$ C ∪ D is a cyclic T-regular set and $(C, D)$ ( C , D ) is a non-empty, non-convex proximal pair in a real Hilbert space. Moreover, we show the presence of best proximity points and fixed points for non-cyclic relatively nonexpansive maps with respect to orbits defined on $C\cup D$ C ∪ D , where C and D are T-regular sets in a uniformly convex Banach space satisfying $T(C)\subseteq C$ T ( C ) ⊆ C , $T(D)\subseteq D$ T ( D ) ⊆ D wherein the convergence of Kranoselskii’s iteration process is also discussed.
- Published
- 2021
43. New fuzzy-interval inequalities in fuzzy-interval fractional calculus by means of fuzzy order relation
- Author
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Pshtiwan Othman Mohammed, Muhammad Aslam Noor, Muhammad Bilal Khan, Khalida Inayat Noor, and Abdullah M. Alsharif
- Subjects
Pure mathematics ,hermite-hadamard inequality ,General Mathematics ,h-convex fuzzy-interval-valued function ,010102 general mathematics ,Regular polygon ,Field (mathematics) ,02 engineering and technology ,Interval (mathematics) ,01 natural sciences ,Fuzzy logic ,Interval arithmetic ,Fractional calculus ,Operator (computer programming) ,Hermite–Hadamard inequality ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,020201 artificial intelligence & image processing ,0101 mathematics ,hermite-hadamard fejér inequality ,Mathematics ,fuzzy-interval riemann liouville fractional integral operator - Abstract
It is well-known that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis and fuzzy-interval analysis, the inclusion relation (⊆) and fuzzy order relation $\left(\preccurlyeq \right)$ both are two different concepts, respectively. In this article, with the help of fuzzy order relation, we introduce fractional Hermite-Hadamard inequality (HH-inequality) for h-convex fuzzy-interval-valued functions (h-convex-IVFs). Moreover, we also establish a strong relationship between h-convex fuzzy-IVFs and Hermite-Hadamard Fejér inequality (HH-Fejér inequality) via fuzzy Riemann Liouville fractional integral operator. It is also shown that our results include a wide class of new and known inequalities for h-convex fuzz-IVFs and their variant forms as special cases. Nontrivial examples are presented to illustrate the validity of the concept suggested in this review. This paper's techniques and approaches may serve as a springboard for further research in this field.
- Published
- 2021
44. Convex Risk Measures for the Aggregation of Multiple Information Sources and Applications in Insurance
- Author
-
A. N. Yannacopoulos and G. I. Papayiannis
- Subjects
Statistics and Probability ,Economics and Econometrics ,Mathematical optimization ,Computer science ,media_common.quotation_subject ,01 natural sciences ,Robust decision-making ,FOS: Economics and business ,010104 statistics & probability ,Robustness (computer science) ,Order (exchange) ,Prior probability ,0101 mathematics ,Robustness (economics) ,Set (psychology) ,media_common ,Class (computer programming) ,Regular polygon ,Ambiguity ,Model aggregation ,010101 applied mathematics ,Fréchet mean ,Risk Management (q-fin.RM) ,A priori and a posteriori ,Statistics, Probability and Uncertainty ,Quantitative Finance - Risk Management - Abstract
We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk measures robustly characterize the exposure of the firm, by filtering out appropriately the partial information available in individual sources into an aggregate model for the risk factors of interest. Importantly, the proposed risks can be expressed in closed analytic forms allowing for interesting qualitative interpretations as well as comparative statics and thus facilitate their use in the everyday risk management process of the insurance firms. The potential use of the proposed risk measures in insurance is illustrated by two concrete applications, capital risk allocation and premia calculation under uncertainty., Comment: 32 pages
- Published
- 2022
45. Set characterizations and convex extensions for geometric convex-hull proofs
- Author
-
Andreas Bärmann, Oskar Schneider, and Publica
- Subjects
Convex hull ,General Mathematics ,Regular polygon ,Extension (predicate logic) ,Mathematical proof ,Algebra ,Set (abstract data type) ,Polyhedron ,90C57, 52B05, 90C10, 90C27, 90C25 ,Optimization and Control (math.OC) ,Completeness (order theory) ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,FOS: Mathematics ,Algebraic number ,ddc:510 ,Mathematics - Optimization and Control ,Software ,Mathematics - Abstract
In the present work, we consider Zuckerberg's method for geometric convex-hull proofs introduced in [Geometric proofs for convex hull defining formulations, Operations Research Letters 44(5), 625-629 (2016)]. It has only been scarcely adopted in the literature so far, despite the great flexibility in designing algorithmic proofs for the completeness of polyhedral descriptions that it offers. We suspect that this is partly due to the rather heavy algebraic framework its original statement entails. This is why we present a much more lightweight and accessible approach to Zuckerberg's proof technique, building on ideas from [Extended formulations for convex hulls of some bilinear functions, Discrete Optimization 36, 100569 (2020)]. We introduce the concept of set characterizations to replace the set-theoretic expressions needed in the original version and to facilitate the construction of algorithmic proof schemes. Along with this, we develop several different strategies to conduct Zuckerberg-type convex-hull proofs. Very importantly, we also show that our concept allows for a significant extension of Zuckerberg's proof technique. While the original method was only applicable to 0/1-polytopes, our extended framework allows to treat arbitrary polyhedra and even general convex sets. We demonstrate this increase in expressive power by characterizing the convex hull of Boolean and bilinear functions over polytopal domains. All results are illustrated with indicative examples to underline the practical usefulness and wide applicability of our framework.
- Published
- 2022
46. Accurate coupled lines fitting in an errors-in-variables framework.
- Author
-
Zhou, Yongjun, Gong, Jinghai, and Fang, Xing
- Subjects
- *
LIDAR , *REVERSE engineering , *METROLOGY , *GEOMETRY , *ALGORITHMS - Abstract
For the purpose of accurate measurement of regular polygons, the boundary lines with parallel, perpendicular or given angles are defined as coupled lines. Provided that the noisy data points are measured from each line without outliers, an accurate and numerical reliable weighted total least squares (WTLS) method is proposed for two dimensional coupled lines fitting task. The underlying problem is modelled within an errors-in-variables framework by assuming all the coordinates are subject to random errors. In order to overcome the possible ill-posedness, the lines are parameterised as constrained Hessian normal form instead of the intercept and slope one. A generic WTLS algorithm is derived in case of the random columns are corrupted by fully correlated errors. Special case that the data are corrupted by homocedastic errors are considered and solved with less computational expenses. A single line fitting and a simulated regular hexagon fitting examples are performed with comparisons and discussions. The proposed methods can be used for accurate regular polygon measurement in vision metrology or reverse engineering. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
47. Solutions of regular polygon with an inner particle for Newtonian N + 1-body problem.
- Author
-
Chen, Jian and Luo, Jianbo
- Subjects
- *
POLYGONS , *GEOMETRIC vertices , *CIRCULANT matrices , *DIFFERENTIAL equations , *MATHEMATICAL analysis - Abstract
In this paper, we prove that if the solution of the planar N + 1 -body problem has N bodies rotating at the vertices of a regular N -gon then the N bodies have equal mass and the remaining body must be at the center. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
48. The Clockwork Universe : 1583 ce–1819 ce
- Author
-
Ben-Menahem, Ari and Ben-Menahem, Ari
- Published
- 2009
- Full Text
- View/download PDF
49. Creating and Testing Textbooks for Secondary Schools : An Example: Programming in LOGO
- Author
-
Freiermuth, Karin, Hromkovič, Juraj, Steffen, Björn, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Mittermeir, Roland T., editor, and Sysło, Maciej M., editor
- Published
- 2008
- Full Text
- View/download PDF
50. Generalization of some fractional versions of Hadamard inequalities via exponentially (α,h−m)-convex functions
- Author
-
Ghulam Farid, Waqas Nazeer, Hafsa Yasmeen, Yu-Pei Lv, and Chahn Yong Jung
- Subjects
Generalization ,General Mathematics ,Regular polygon ,Function (mathematics) ,Hadamard inequality ,h−m)-convex function ,hadamard inequality ,exponentionally (α ,Combinatorics ,Alpha (programming language) ,Exponential growth ,Hadamard transform ,riemann-liouville fractional integrals ,(α ,QA1-939 ,Convex function ,Mathematics - Abstract
In this paper we give Hadamard inequalities for exponentially $ (\alpha, h-m) $-convex functions using Riemann-Liouville fractional integrals for strictly increasing function. Results for Riemann-Liouville fractional integrals of convex, $ m $-convex, $ s $-convex, $ (\alpha, m) $-convex, $ (s, m) $-convex, $ (h-m) $-convex, $ (\alpha, h-m) $-convex, exponentially convex, exponentially $ m $-convex, exponentially $ s $-convex, exponentially $ (s, m) $-convex, exponentially $ (h-m) $-convex, exponentially $ (\alpha, h-m) $-convex functions are particular cases of the results of this paper. The error estimations of these inequalities by using two fractional integral identities are also given.
- Published
- 2021
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