Three-terminal communication channels

1971 ◽  
Vol 3 (1) ◽  
pp. 120-154 ◽  
Author(s):  
Edward C. Van Der Meulen
Keyword(s):  
Mutual Information ◽  
Lower Bounds ◽  
Communication Channel ◽  
Communication Channels ◽  
Upper And Lower Bounds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Symmetric Structure ◽  
Necessary And Sufficient ◽  
Positive Capacity

The problem of transmitting information in a specified direction over a communication channel with three terminals is considered. Examples are given of the various ways of sending information. Basic inequalities for average mutual information rates are obtained. A coding theorem and weak converse are proved and a necessary and sufficient condition for a positive capacity is derived. Upper and lower bounds on the capacity are obtained, which coincide for channels with symmetric structure.

Three-terminal communication channels

1971 ◽  
Vol 3 (01) ◽  
pp. 120-154 ◽  
Author(s):  
Edward C. Van Der Meulen
Keyword(s):  
Mutual Information ◽  
Lower Bounds ◽  
Communication Channel ◽  
Communication Channels ◽  
Upper And Lower Bounds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Symmetric Structure ◽  
Necessary And Sufficient ◽  
Positive Capacity

The problem of transmitting information in a specified direction over a communication channel with three terminals is considered. Examples are given of the various ways of sending information. Basic inequalities for average mutual information rates are obtained. A coding theorem and weak converse are proved and a necessary and sufficient condition for a positive capacity is derived. Upper and lower bounds on the capacity are obtained, which coincide for channels with symmetric structure.

Capacity Estimates for Planar Cantor-Like Sets

1974 ◽  
Vol 26 (5) ◽  
pp. 1169-1172
Author(s):  
Carl David Minda
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Elementary Approach ◽  
Principal Tool ◽  
Linear Problems ◽  
Necessary And Sufficient ◽  
Positive Capacity ◽  
Capacity Estimates

Upper and lower bounds for the capacity of planar Cantor-like sets are presented. Chebichev polynomials are the principal tool employed in the derivation of these estimates. A necessary and sufficient condition for certain planar Cantor-like sets to have positive capacity is obtained. Related one-sided capacitary estimates for more general Cantor-like sets can be found in [3, pp. 106-109]. Techniques analogous to those used in this paper yield similar results for linear Cantor-like sets which are well-known [2, pp. 150-161]. The use of Chebichev polynomials to obtain these results provides an alternate, possibly more elementary, approach to these linear problems.

scholarly journals Monotonicity of the Ratio of the Power and Second Seiffert Means with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Zhen-Hang Yang ◽  
Ying-Qing Song ◽  
Yu-Ming Chu
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Power Mean ◽  
Seiffert Mean ◽  
Second Seiffert Mean ◽  
Necessary And Sufficient ◽  
The Second Seiffert Mean

We present the necessary and sufficient condition for the monotonicity of the ratio of the power and second Seiffert means. As applications, we get the sharp upper and lower bounds for the second Seiffert mean in terms of the power mean.

scholarly journals Prime n solutions of the Brocard’s Problem

2021 ◽  
Author(s):  
Devansh Singh
Keyword(s):  
Lower Bound ◽  
Laplace Transform ◽  
Lower Bounds ◽  
Polynomial Function ◽  
Necessary Conditions ◽  
Inverse Laplace Transform ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Quartic Equation ◽  
Necessary And Sufficient

Abstract In this paper on the [1]“Brocard’s Problem” , I have worked on case when n is prime and n divides m-1. Necessary conditions on m are given in Theorem and Corollaries.I used necessary and sufficient condition of primes. Assuming that n is prime and divides m-1, I applied Inverse Laplace Transform on the obtained equation and got a polynomial function which is easier to deal with. I worked with zero of the polynomial function and got lower bound of p which was not useful as p tends to infinity, but solving quartic equation which I have given at the end could give significant upper, lower bounds of p.What would happen to those upper, lower bounds if p tends to infinity?

scholarly journals Lower bounds of generalised normalised δ- Casorati curvature for real hypersurfaces in complex quadric endowed with semi-symmetric metric connection

2018 ◽  
Vol 50 (2) ◽  
pp. 187-198 ◽  
Author(s):  
Pooja Bansal ◽  
Mohammad Hasan Shahid
Keyword(s):  
Lower Bounds ◽  
Real Hypersurfaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complex Quadric ◽  
Metric Connection ◽  
Necessary And Sufficient ◽  
Casorati Curvature

The main intention of the present paper is to develop two extremal inequalities involving normalized δ-Casorati curvature and extrinsic generalised normalised δ-Casorati curvature for real hypersurfaces in complex quadric Qm admitting semi-symmetric metric connection. Further, we derive the necessary and sufficient condition for the equality in both cases

Almost sure convergence of measure-valued branching processes: a critical exponent

1994 ◽  
Vol 124 (4) ◽  
pp. 811-823
Author(s):  
Alison M. Etheridge
Keyword(s):  
Markov Process ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
Upper And Lower Bounds ◽  
Spatial Process ◽  
Sufficient Condition ◽  
Time Process ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Occupation Time Process

A large class of measure-valued critical branching processes can be classified in terms of a parameter ρ which arises as a measure of the recurrence of the underlying spatial Markov process. By establishing upper and lower bounds for the total weighted occupation time process, it is shown that if a measure-valued process is started from an invariant measure of its underlying spatial process, then a necessary and sufficient condition for (a.s.) local extinction is that ρ > 0.

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.

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