A Surface Family with a Common Asymptotic Null Curve in Minkowski 3-Space E 1 3

Developable Surfaces ◽

Null Curve ◽

This approach is on constructing a surface family with a common asymptotic null curve. It has provided the necessary and sufficient condition for the curve to be an asymptotic null curve and extended the study to ruled and developable surfaces. Subsequently, the study has examined the Bertrand offsets of a surface family with a common asymptotic null curve. Lastly, we support the results of this approach by some examples.

Sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-Space

WSEAS TRANSACTIONS ON MATHEMATICS ◽

10.37394/23206.2020.19.63 ◽

2020 ◽

Vol 19 ◽

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Sufficient Condition ◽

Developable Surface ◽

Parametric Curves ◽

Developable Surfaces ◽

Lines Of Curvature ◽

Tangent Surface ◽

In this paper, we introduce the notion of sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-space E3 . We also show that the parametric curves on these surfaces are lines of curvature. Then, we derive the necessary and sufficient condition for the sweeping surface to become a developable ruled surface. In particular, we analyze the necessary and sufficient conditions when the resulting developable surface is a cylinder, cone or tangent surface. Finally, some representative curves are chosen to construct the corresponding developable surfaces which possessing these curves as lines of curvature.

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

The existence of cosmic time functions

10.1098/rspa.1969.0018 ◽

1969 ◽

Vol 308 (1494) ◽

pp. 433-435 ◽

Cited By ~ 54

Keyword(s):

Cosmic Time ◽

Space Time ◽

Time Function ◽

Sufficient Condition ◽

Null Curve ◽

Null Curves ◽

Stable Causality ◽

It is shown that stable causality is the necessary and sufficient condition that there should exist a cosmic time function which increases along every future directed timelike or null curve. Stable causality means that there are no closed timelike or null curves in any Lorentz metric that is sufficiently close to the space-time metric.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

A Necessary and Sufficient Condition of Supply and Threshold Voltages in CMOS Circuits for Minimum Energy Point Operation

10.1587/transfun.e100.a.2764 ◽

2017 ◽

Vol E100.A (12) ◽

pp. 2764-2775 ◽

Cited By ~ 1

Author(s):

Jun SHIOMI ◽

Tohru ISHIHARA ◽

Hidetoshi ONODERA

Keyword(s):

Minimum Energy ◽

Cmos Circuits ◽

Sufficient Condition ◽

Energy Point ◽

Threshold Voltages ◽

Necessary And Sufficient ◽

Minimum Energy Point

A Necessary and Sufficient Condition for a Local Commutative Algebra to be a Moduli Algebra: Weighted Homogeneous Case

Complex Analytic Singularities ◽

10.2969/aspm/00810687 ◽

2018 ◽

Author(s):

Stephen S.-T. Yau

Keyword(s):

Commutative Algebra ◽

Sufficient Condition ◽

Homogeneous Case ◽

Moduli Algebra ◽

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

Accounting Horizons ◽

10.2308/acch.2003.17.3.257 ◽

2003 ◽

Vol 17 (3) ◽

pp. 257-266 ◽

Cited By ~ 31

Author(s):

Mark H. Taylor ◽

F. Todd DeZoort ◽

Edward Munn ◽

Martha Wetterhall Thomas

Keyword(s):

Public Interest ◽

Auditor Independence ◽

Public Confidence ◽

Sufficient Condition ◽

Accounting Profession ◽

The Public ◽

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

10.1093/oso/9780198813972.003.0002 ◽

2018 ◽

Author(s):

Thomas Sinclair

Keyword(s):

Detailed Analysis ◽

Political Authority ◽

The State ◽

Sufficient Condition ◽

State Institutions ◽

State Of Nature ◽

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science - SIGMETRICS '16 ◽

A Necessary and Sufficient Condition for Throughput Scalability of Fork and Join Networks with Blocking

10.1145/2896377.2901470 ◽

2016 ◽

Cited By ~ 4

Author(s):

Yun Zeng ◽

Augustin Chaintreau ◽

Don Towsley ◽

Cathy H. Xia

Keyword(s):

Sufficient Condition ◽

Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽

10.3390/physics3020024 ◽

2021 ◽

Vol 3 (2) ◽

pp. 352-366

Author(s):

Thomas Berry ◽

Matt Visser

Keyword(s):

Point Of View ◽

Sufficient Condition ◽

Use Of Self ◽

Wigner Rotation ◽

Inertial Frames ◽

Explicit Formulae ◽

Specific Implementation ◽

Necessary And Sufficient ◽

Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.