Primality of closed path polyominoes

New Class ◽

In this paper, we introduce a new class of polyominoes, called closed paths, and we study the primality of their associated ideal. Inspired by an existing conjecture that characterizes the primality of a polyomino ideal by nonexistence of zig-zag walks, we classify all closed paths which do not contain zig-zag walks, and we give opportune toric representations of the associated ideals. To support the conjecture, we prove that having no zig-zag walks is a necessary and sufficient condition for the primality of the associated ideal of a closed path. Finally, we present some classes of prime polyominoes viewed as generalizations of closed paths.

Semi Square Stable Graphs

Mathematics ◽

10.3390/math7070597 ◽

2019 ◽

Vol 7 (7) ◽

pp. 597

Author(s):

Mohammad Abudayah ◽

Omar Alomari

Keyword(s):

Independent Set ◽

Interval Graphs ◽

Maximum Independent Set ◽

Sufficient Condition ◽

New Class ◽

Dominating Number ◽

Independent Number ◽

The independent number of a graph G is the cardinality of the maximum independent set of G, denoted by α ( G ) . The independent dominating number is the cardinality of the smallest independent set that dominates all vertices of G. In this paper, we introduce a new class of graphs called semi-square stable for which α ( G 2 ) = i ( G ) . We give a necessary and sufficient condition for a graph to be semi-square stable, and we study when interval graphs are semi-square stable.

Integrability and L 1-Convergence of Modified Sine Sums

Georgian Mathematical Journal ◽

10.1515/gmj.2004.99 ◽

2004 ◽

Vol 11 (1) ◽

pp. 99-104

Author(s):

Kulwinder Kaur ◽

S. S. Bhatia ◽

Babu Ram

Keyword(s):

Sufficient Condition ◽

Cosine Series ◽

New Class ◽

Abstract New modified sine sums are introduced and a criterion for the L 1-convergence of these modified sine sums under a new class K is obtained. Also a necessary and sufficient condition for the L 1-convergence of the cosine series is deduced as a corollary.

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.