Kinematic Geometry of Circular Surfaces With a Fixed Radius Based on Euclidean Invariants

A circular surface with a fixed radius can be swept out by moving a circle with its center following a curve, which acts as the spine curve. Based on a system of Euclidean invariants, the paper identifies those circular surfaces taking lines of curvature as generating circles and further explores the properties of the principal curvatures and Gaussian curvature of the tangent circular surfaces. The paper then applies the study to mechanism analysis by proving the necessary and sufficient condition for a circular surface to be generated by a serially connected C′R, HR, or RR mechanism, where C′ joint can be visualized as a special H joint with a variable pitch of one degree of freedom. Following the analysis, this paper reveals for the first time the relationship between the invariants of a circular surface and the commonly used D-H parameters of C′R, HR, and RR mechanisms.

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Interest rate option hedging portfolios without bank account

Studies in Economics and Finance ◽

10.1108/sef-02-2019-0058 ◽

2019 ◽

Vol 37 (1) ◽

pp. 134-142

Author(s):

Alberto Bueno-Guerrero

Keyword(s):

Design Methodology ◽

Contingent Claim ◽

Necessary And Sufficient Condition ◽

Barrier Option ◽

Bank Account ◽

Content Type ◽

Option Hedging ◽

Hedging Portfolio ◽

Necessary And Sufficient ◽

First Time

Purpose This paper aims to study the conditions for the hedging portfolio of any contingent claim on bonds to have no bank account part. Design/methodology/approach Hedging and Malliavin calculus techniques recently developed under a stochastic string framework are applied. Findings A necessary and sufficient condition for the hedging portfolio to have no bank account part is found. This condition is applied to a barrier option, and an example of a contingent claim whose hedging portfolio has a bank account part different from zero is provided. Originality/value To the best of the authors’ knowledge, this is the first time that this issue has been addressed in the literature.

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Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2011/164843 ◽

2011 ◽

Vol 2011 ◽

pp. 1-26 ◽

Cited By ~ 1

Author(s):

Roberto C. Raimondo

Keyword(s):

Bergman Space ◽

Toeplitz Operators ◽

Boundary Behavior ◽

Berezin Transform ◽

Planar Domain ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Planar Domains ◽

Necessary And Sufficient ◽

The Relationship

We study the problem of the boundedness and compactness of when and is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of

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On B- Covariant Derivative of First Order for Some Tensors in different Spaces

Journal of Mathematical Analysis and Modeling ◽

10.48185/jmam.v2i2.276 ◽

2021 ◽

Vol 2 (2) ◽

pp. 30-37

Author(s):

Alaa A. Abdallah ◽

A. A. Navlekar ◽

Kirtiwant P. Ghadle

Keyword(s):

Curvature Tensor ◽

Covariant Derivative ◽

Torsion Tensor ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

First Order ◽

Recurrence Property ◽

Necessary And Sufficient ◽

The Relationship

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

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A generalization of the practical numbers

International Journal of Number Theory ◽

10.1142/s1793042118500902 ◽

2018 ◽

Vol 14 (05) ◽

pp. 1487-1503

Author(s):

Nicholas Schwab ◽

Lola Thompson

Keyword(s):

Positive Integer ◽

Arithmetic Function ◽

Arithmetic Functions ◽

Asymptotic Density ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Necessary And Sufficient ◽

First Time

A positive integer [Formula: see text] is practical if every [Formula: see text] can be written as a sum of distinct divisors of [Formula: see text]. One can generalize the concept of practical numbers by applying an arithmetic function [Formula: see text] to each of the divisors of [Formula: see text] and asking whether all integers in a certain interval can be expressed as sums of [Formula: see text]’s, where the [Formula: see text]’s are distinct divisors of [Formula: see text]. We will refer to such [Formula: see text] as “[Formula: see text]-practical”. In this paper, we introduce the [Formula: see text]-practical numbers for the first time. We give criteria for when all [Formula: see text]-practical numbers can be constructed via a simple necessary-and-sufficient condition, demonstrate that it is possible to construct [Formula: see text]-practical sets with any asymptotic density, and prove a series of results related to the distribution of [Formula: see text]-practical numbers for many well-known arithmetic functions [Formula: see text].

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Generalized Bertrand Curves in Minkowski 3-Space

Mathematics ◽

10.3390/math8122199 ◽

2020 ◽

Vol 8 (12) ◽

pp. 2199

Author(s):

Chunxiao Zhang ◽

Donghe Pei

Keyword(s):

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Bertrand Curve ◽

Necessary And Sufficient ◽

The Relationship

We define a generalized lightlike Bertrand curve pair and a generalized non-lightlike Bertrand curve pair, discuss their properties and prove the necessary and sufficient condition of a curve which is a generalized lightlike or a generalized non-lightlike Bertrand curve. Moreover, we study the relationship between slant helices and generalized Bertrand curves.

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A study on timelike circular surfaces in Minkowski 3-space

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887820500747 ◽

2020 ◽

Vol 17 (06) ◽

pp. 2050074

Author(s):

Rashad A. Abdel-Baky ◽

Nadia Alluhaibi ◽

Akram Ali ◽

Fatemah Mofarreh

Keyword(s):

Geodesic Curvature ◽

Parameter Family ◽

Lines Of Curvature ◽

Constant Radius ◽

Spherical Indicatrix ◽

New Type ◽

Circular Surface ◽

Fixed Radius

This paper studies a smooth one-parameter family of standard Lorentzian circles with fixed radius. Such a surface is called a timelike circular surface with constant radius. We call each circle a generating circle. A new type of timelike circular surfaces was identified and coined as the timelike tangent circular surface. The new timelike tangent circular surface has the property of all generating circles being lines of curvature and its Gaussian and mean curvatures being independent of the geodesic curvature of the spherical indicatrix.

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A Euclidean Invariants Based Study of Circular Surfaces With Fixed Radius

Volume 8: 31st Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2007-34466 ◽

2007 ◽

Author(s):

Lei Cui ◽

Delun Wang

Keyword(s):

Complete System ◽

Distribution Parameter ◽

Moving Frame ◽

Necessary Condition ◽

Spherical Indicatrix ◽

Circular Surface ◽

Fixed Radius ◽

Curvature And Torsion ◽

The Relationship ◽

Sufficient And Necessary Condition

In this paper a complete system of Euclidean invariants is presented to study circular surfaces with fixed radius. The study of circular surfaces is simplified to the study of two curves: the spherical indicatrix of the unit normals of circle planes and the spine curve. After the geometric meanings of these Euclidean invariants are explained, the distribution parameter of a circular surface is defined. If the value of the distribution parameter of a circular surface is 0, the circular surface is a sphere. Then the relationship between the moving frame {E1, E2, E3} and the Frenet frame {t, n, b} of the spine curve is investigated, and the expressions of the curvature and torsion of the spine curve are obtained based on these Euclidean invariants. The fundamental theorem of circular surfaces is first proved. Next the first and second fundamental forms of circular surfaces are computed. The last part of this paper is devoted to constraint circular surfaces. The sufficient and necessary condition for a general circular surface to be one that can be generated by a series-connected C’R, HR, RR, or PR mechanism is proved.

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ON H-Sets and Open Filter Adherences(1)

Canadian Mathematical Bulletin ◽

10.4153/cmb-1988-006-8 ◽

1988 ◽

Vol 31 (1) ◽

pp. 37-44 ◽

Cited By ~ 2

Author(s):

Robert L. Krystock

Keyword(s):

Hausdorff Space ◽

Sufficient Conditions ◽

Definition of Derivative Function: Logical Error in Mathematics

Academic Journal of Applied Mathematical Sciences ◽

10.32861/ajams.58.124.129 ◽

2019 ◽

pp. 124-129

Author(s):

Temur Z. Kalanov

Keyword(s):

Differential Calculus ◽

Necessary And Sufficient Condition ◽

Derivative Function ◽

Essential Value ◽

Variable Quantity ◽

Starting Point ◽

Logical Error ◽

Definition Of ◽

Necessary And Sufficient ◽

The Relationship

The critical analysis of the foundations of the differential calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown that differential calculus is fictitious mathematical theory because the concept of the limiting process is the starting point for definition of the derivative function. The passage to the limit “zero” in the definition of the derivative function signifies that the variable quantity takes the only essential value “zero”. This fact leads to the following errors. (1) The definition of the derivative function is based on the violation of the necessary and sufficient condition for the validity of the relationship between the increment of the function argument and the increment of the function because the increment of the function is divided by the zero increment of the argument in the case of the limiting process. (2) The definition of the derivative function is based on the contradiction which is that the increment of the argument is both zero and not zero in the same relationship. This contradiction represents a violation of the formal-logical law of identity and of the formal-logical law of the lack of contradiction. (3) The definition of the differential of function is based on two contradictory (mutually exclusive) features: the differential of the argument is not zero while the increment of the argument in the definition of the derivative function is zero.

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On subprojectivity domains of g-semiartinian modules

Journal of Algebra and Its Applications ◽

10.1142/s021949882150119x ◽

2020 ◽

pp. 2150119

Author(s):

Yılmaz Durğun ◽

Ayşe Çobankaya

Keyword(s):

Homomorphic Image ◽

Proper Class ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Necessary And Sufficient ◽

The Relationship

The aim of this paper is to reveal the relationship between the proper class generated projectively by g-semiartinian modules and the subprojectivity domains of g-semiartinian modules. A module [Formula: see text] is called g-semiartinian if every nonzero homomorphic image of [Formula: see text] has a singular simple submodule. It is proven that every g-semiartinian right [Formula: see text]-module has an epic projective envelope if and only if [Formula: see text] is a right PS ring if and only if every subprojectivity domain of any g-semiartinian right [Formula: see text]-module is closed under submodules. A g-semiartinian module whose domain of subprojectivity as small as possible is called gsap-indigent. We investigated the structure of rings whose (simple, coatomic) g-semiartinian right modules are gsap-indigent or projective. Furthermore, over right PS rings, necessary and sufficient condition to be gsap-indigent module was determined.

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