New sufficient conditions for the unique solution of a square Sylvester-like absolute value equation

2020 ◽  
pp. 106966
Author(s):  
Cui-Xia Li ◽  
Li-Min Wang
Keyword(s):  
Unique Solution ◽  
Sufficient Conditions ◽  
Absolute Value Equation ◽  
Absolute Value

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

A Direct Rotatability Criterion for Spherical Four-Bar Linkages

1995 ◽  
Vol 117 (4) ◽  
pp. 597-600 ◽  
Author(s):  
K. C. Gupta ◽  
R. Ma
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Absolute Value ◽  
The Difference ◽  
Necessary And Sufficient ◽  
Four Bar Linkage

The necessary and sufficient conditions for the full input rotatability in a spherical four-bar linkage are proved. The direct criterion is: for all twist angles α in the range [0, π], the excess (deficit) of the sum of the frame and input twist angles over (from) π should, in absolute value, be greater than that for the coupler and follower twist angles; the difference between the follower and input twist angles, in absolute value, should be greater than that for the coupler and follower twist angles. Application of the direct criterion to full rotatability of other links are discussed and some variations in the form of the criterion are developed.

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