scholarly journals A Note on Linear Trend Free Designs in Two Plots Per Block

2020 ◽  
Vol 34 (03) ◽  
Author(s):  
Rahul Kumar Gupta ◽  
Arpan Bhowmik ◽  
Seema Jaggi ◽  
Mohd. Harun ◽  
Cini Varghese ◽  
...  
Keyword(s):  
Linear Trend ◽  
Block Design ◽  
Sufficient Condition ◽  
Block Designs ◽  
Necessary And Sufficient Condition ◽  
Trend Component ◽  
Systematic Trend ◽  
Free Block ◽  
Necessary And Sufficient

In this article, we have discussed some aspects of block designs under systematic trend component. The necessary and sufficient condition for a block design to be trend free has been highlighted. A method of constructing linear trend free block designs in two plots per block have been discussed. The characterization properties of such designs have been investigated.

Another Proof of a Condition of Balancedness in a Connected Block Design

1987 ◽  
Vol 36 (1-2) ◽  
pp. 95-96
Author(s):  
Y. S. Sathe
Keyword(s):  
Spectral Decomposition ◽  
Block Design ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Characteristic Roots ◽  
Zero Characteristic ◽  
Necessary And Sufficient

The proof that a necessary and sufficient condition for a connected block design to be balanced is all the non-zero characteristic roots of the C-matrix of the design are equal requires spectral decomposition of C-matrix. Rao (1958). In this note another proof of the same result is obtained without using spectral decomposition.

A Generalization of Distinct Representatives and Its Applications

1989 ◽  
Vol 38 (1-2) ◽  
pp. 57-64 ◽  
Author(s):  
Ashish Das ◽  
A. Dey
Keyword(s):  
Sufficient Condition ◽  
Block Designs ◽  
Simple Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

A generalization of systems of distinct representatives is given. Based on this result, it is shown bow unequally replicated block designs, satisfying a simple condition, can be arranged in an array such that each row of the array contains a specified treatment the same number of times. Such arrays can be viewed as row-colum designs and have been called as Youden Type ( YT) designs. A necessary and sufficient condition for the existence of YT designs is given.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

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

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

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.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document