scholarly journals A Note on the Signature Representations of the Symmetric Groups

2021 ◽  
Vol 28 (03) ◽  
pp. 469-478
Author(s):  
Kay Jin Lim ◽  
Jialin Wang
Keyword(s):  
Symmetric Groups ◽  
Partial Sums ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Composition Formula ◽  
Kostka Numbers ◽  
Necessary And Sufficient

For a partition [Formula: see text] and a prime [Formula: see text], we prove a necessary and sufficient condition for there to exist a composition [Formula: see text] such that [Formula: see text] can be obtained from [Formula: see text] after rearrangement and no partial sums of [Formula: see text] are divisible by [Formula: see text]. To demonstrate why we are interested in the question, we compute some signed [Formula: see text]-Kostka numbers.

THE VARIANCE OF AN INTEGRATED PROCESS NEED NOT DIVERGE TO INFINITY, AND RELATED RESULTS ON PARTIAL SUMS OF STATIONARY PROCESSES

2001 ◽  
Vol 17 (4) ◽  
pp. 671-685 ◽  
Author(s):  
Hannes Leeb ◽  
Benedikt M. Pötscher
Keyword(s):  
Sufficient Conditions ◽  
Partial Sums ◽  
Stationary Processes ◽  
Sufficient Condition ◽  
Integrated Process ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

For a process with stationary first differences a necessary and sufficient condition for the variance of the process to be unbounded is given. An example shows that the variance of an integrated process—although unbounded—need not diverge to infinity. Sufficient conditions for the variance of an integrated process to diverge to infinity are provided.

scholarly journals Applications of Mittag-Leffer Type Poisson Distribution to a Subclass of Analytic Functions Involving Conic-Type Regions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Nazar Khan ◽  
Wali Khan Mashwani ◽  
Sama Arjika ◽  
...  
Keyword(s):  
Poisson Distribution ◽  
Analytic Functions ◽  
Convex Combination ◽  
Partial Sums ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Properties ◽  
Distortion Bounds ◽  
Janowski Functions ◽  
Necessary And Sufficient

In this article, we introduce a new subclass of analytic functions utilizing the idea of Mittag-Leffler type Poisson distribution associated with the Janowski functions. Further, we discuss some important geometric properties like necessary and sufficient condition, convex combination, growth and distortion bounds, Fekete-Szegö inequality, and partial sums for this newly defined class.

scholarly journals Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1676
Author(s):  
Saeed Islam ◽  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Muhammad Arif ◽  
Ronnason Chinram
Keyword(s):  
Extreme Point ◽  
Point Theorem ◽  
Starlike Functions ◽  
Partial Sums ◽  
Sufficient Condition ◽  
Sine Function ◽  
Necessary And Sufficient Condition ◽  
Closure Theorem ◽  
Necessary And Sufficient ◽  
Distortion Bound

The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and sufficient condition, the growth and distortion bound, closure theorem, convolution results, radii of starlikeness, extreme point theorem and the problem with partial sums for this class.

scholarly journals Invariance principle via orthomartingale approximation

2018 ◽  
Vol 18 (06) ◽  
pp. 1850043 ◽  
Author(s):  
Davide Giraudo
Keyword(s):  
Invariance Principle ◽  
Random Fields ◽  
Partial Sums ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Stationary Random Fields ◽  
Necessary And Sufficient

We obtain a necessary and sufficient condition for the orthomartingale-coboundary decomposition. We establish a sufficient condition for the approximation of the partial sums of a strictly stationary random fields by those of stationary orthomartingale differences. This condition can be checked under multidimensional analogues of the Hannan condition and the Maxwell–Woodroofe condition.

scholarly journals Limits of Characters of Wreath Products 𝔖n(T) of a Compact Group T With the Symmetric Groups and Characters of 𝔖∞(T), I

2009 ◽  
Vol 193 ◽  
pp. 1-93
Author(s):  
Takeshi Hirai ◽  
Etsuko Hirai ◽  
Akihito Hora
Keyword(s):  
Compact Group ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Continuous Limit ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Irreducible Characters ◽  
Induced Representations ◽  
Irreducible Components ◽  
Necessary And Sufficient

AbstractIn the first half of this paper, all the limits of irreducible characters of Gn = 𝔖n(T) as n → ∞ are calculated. The set of all continuous limit functions on G = 𝔖 ∞(T) is exactly equal to the set of all characters of G determined in [HH6]. We give a necessary and sufficient condition for a series of irreducible characters of Gn to have a continuous limit and also such a condition to have a discontinuous limit. In the second half, we study the limits of characters of certain induced representations of Gn which are usually reducible. The limits turn out to be characters of G, and we analyse which of irreducible components are responsible to these limits.

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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