Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Hideto Nakashima
Keyword(s):  
Sufficient Conditions ◽  
Rational Functions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Symmetric Cones ◽  
The Real ◽  
Tube Domains ◽  
Homogeneous Cone ◽  
Necessary And Sufficient ◽  
Relative Invariants

AbstractIn this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].

scholarly journals Equipartitioning and balancing points of polygons

Pythagoras ◽  
2010 ◽  
Vol 0 (71) ◽  
Author(s):  
Shunmugam Pillay ◽  
Poobhalan Pillay
Keyword(s):  
General Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Sufficient Condition ◽  
Centre Of Mass ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The centre of mass G of a triangle has the property that the rays to the vertices from G sweep out triangles having equal areas. We show that such points, termed equipartitioning points in this paper, need not exist in other polygons. A necessary and sufficient condition for a quadrilateral to have an equipartitioning point is that one of its diagonals bisects the other. The general theorem, namely, necessary and sufficient conditions for equipartitioning points for arbitrary polygons to exist, is also stated and proved. When this happens, they are in general, distinct from the centre of mass. In parallelograms, and only in them, do the two points coincide.

Fair bets and inductive probabilities

1955 ◽  
Vol 20 (3) ◽  
pp. 263-273 ◽  
Author(s):  
John G. Kemeny
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Inductive Probability ◽  
Other Hand ◽  
Frequency Interpretation ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Degree Of Confirmation

The question of what constitutes fairness in betting quotients has been studied by Ramsey, deFinetti, and Shimony. Thanks to their combined efforts we now have a satisfactory definition of fairness.On the other hand, the explication of the concept of degree of confirmation (inductive probability) has progressed rapidly in recent years, thanks primarily to Carnap. This explication has usually proceeded by laying down the axioms for frequency-probabilities, and elaborating on these. While in the case where a frequency interpretation is intended these axioms are clearly justified, in our case they have been laid down without any justification. Carnap's presentation has been criticized for just this reason.The purpose of this paper is to show that the probability axioms are necessary and sufficient conditions to assure that the degrees of confirmation form a set of fair betting quotients. In addition it will be shown that one additional, highly controversial, axiom is precisely the condition needed to assure that not only deFinetti's weaker criterion but Shimony's criterion of fairness is also satisfied.

scholarly journals ON HYBRID SEQUENCES BUILT FROM NIEDERREITER–HALTON SEQUENCES AND KRONECKER SEQUENCES

2011 ◽  
Vol 84 (2) ◽  
pp. 238-254 ◽  
Author(s):  
ROSWITHA HOFER ◽  
PETER KRITZER
Keyword(s):  
Uniform Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Future Research ◽  
Short Summary ◽  
The One ◽  
Halton Sequences ◽  
Necessary And Sufficient

AbstractWe discuss the distribution properties of hybrid sequences whose components stem from Niederreiter–Halton sequences on the one hand, and Kronecker sequences on the other. In this paper, we give necessary and sufficient conditions on the uniform distribution of such sequences, and derive a result regarding their discrepancy. We conclude with a short summary and a discussion of topics for future research.

scholarly journals On a Periodic Solution of the 4-Body Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-3 ◽  
Author(s):  
Jian Chen ◽  
Bingyu Li
Keyword(s):  
Periodic Solution ◽  
Angular Velocity ◽  
Periodic Motion ◽  
Equilateral Triangle ◽  
Sufficient Conditions ◽  
Constant Angular Velocity ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
The Masses ◽  
Necessary And Sufficient

We study the necessary and sufficient conditions on the masses for the periodic solution of planar 4-body problems, where three particles locate at the vertices of an equilateral triangle and rotate with constant angular velocity about a resting particle. We prove that the above periodic motion is a solution of Newtonian 4-body problems if and only if the resting particle is at the origin and the masses of the other three particles are equal and their angular velocity satisfies a special condition.

A Subnormal Operator and its Dual

1996 ◽  
Vol 48 (2) ◽  
pp. 381-396
Author(s):  
Robert F. Olin ◽  
Liming Yang
Keyword(s):  
Unit Circle ◽  
Essential Spectrum ◽  
Real Axis ◽  
Additional Assumption ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Subnormal Operator ◽  
The Real ◽  
Necessary And Sufficient

AbstractIt is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.

Answerability

2018 ◽  
Author(s):  
Natalie Stoljar
Keyword(s):  
Moral Responsibility ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Alternative Approach ◽  
The One ◽  
Necessary And Sufficient

This chapter defends externalist or “constitutively relational” conceptions of autonomy through an examination of an alternative approach developed by Andrea Westlund. Westlund develops her approach in response to what has been called the “agency dilemma.” On the one hand, constraining external circumstances seem to undermine autonomy; on the other, the claim that people are nonautonomous because of their circumstances seems to erase their agency and disrespect their evaluative commitments. This chapter distinguishes the necessary and sufficient conditions of several interrelated aspects of agency: autonomy, authentic agential perspective, and moral responsibility. I argue that whereas answerability may be sufficient for moral responsibility, it is not sufficient for autonomy. Objections to externalist conceptions of autonomy, including the agency dilemma, wrongly assume that denying autonomy implies erasing agency. Once it is recognized that autonomy does not always overlap with authentic agential perspective or moral responsibility, the objections lose their force.

scholarly journals Maximal topologies

1973 ◽  
Vol 15 (3) ◽  
pp. 279-290 ◽  
Author(s):  
Asit Baran Raha
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Compact Spaces ◽  
Other Hand ◽  
Countably Compact ◽  
Countably Compact Spaces ◽  
Necessary And Sufficient

This article is devoted to studying maximal π spaces where π = Lindelöf, countably compact, connected, lightly compact or pseudocompact. Necessary and sufficient conditions for Lindelöf or countably compact spaces to be maximal Lindelöf or maximal countably compact have been obtained. On the other hand only necessary conditions for maximal π spaces have been deduced where π = connected, lightly compact or pseudocompact.

scholarly journals Normal and quasinormal weighted composition operators

1991 ◽  
Vol 33 (3) ◽  
pp. 275-279 ◽  
Author(s):  
James T. Campbell ◽  
Mary Embry-Wardrop ◽  
Richard J. Fleming ◽  
S. K. Narayan
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Necessary And Sufficient

In their paper [1], Campbell and Jamison attempted to give necessary and sufficient conditions for a weighted composition operator on an L2 space to be normal, and to be quasinormal. Those conditions, specifically Theorems I and II of that paper, are not valid (see [2] for precise comments on the other results in that paper). In this paper we present a counterexample to those theorems and state and prove characterizations of quasinormality (Theorem 1 below) and normality (Theorem 2 and Corollary 3 below). We also discuss additional examples and information concerning normal weighted composition operators which contribute to the further understanding of this class.

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