scholarly journals Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Wei-Mao Qian ◽  
Zhong-Hua Shen
Keyword(s):  
Power Means ◽  
Logarithmic Means

We prove thatαH(a,b)+(1−α)L(a,b)>M(1−4α)/3(a,b)forα∈(0,1)and alla,b>0witha≠bif and only ifα∈[1/4,1)andαH(a,b)+(1−α)L(a,b)<M(1−4α)/3(a,b)if and only ifα∈(0,3345/80−11/16), and the parameter(1−4α)/3is the best possible in either case. Here,H(a,b)=2ab/(a+b),L(a,b)=(a−b)/(log a−log b), andMp(a,b)=((ap+bp)/2)1/p(p≠0)andM0(a,b)=abare the harmonic, logarithmic, andpth power means ofaandb, respectively.

scholarly journals Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Yu-Ming Chu ◽  
Shan-Shan Wang ◽  
Cheng Zong
Keyword(s):  
Convex Combination ◽  
Power Mean ◽  
Lower Power ◽  
Power Means ◽  
Logarithmic Means

We find the least valueλ∈(0,1)and the greatest valuep=p(α)such thatαH(a,b)+(1−α)L(a,b)>Mp(a,b)forα∈[λ,1)and alla,b>0witha≠b, whereH(a,b),L(a,b), andMp(a,b)are the harmonic, logarithmic, andp-th power means of two positive numbersaandb, respectively.

scholarly journals Generalized power means and interpolating inequalities

1999 ◽  
Vol 127 (1) ◽  
pp. 145-154 ◽  
Author(s):  
Hsu-Tung Ku ◽  
Mei-Chin Ku ◽  
Xin-Min Zhang
Keyword(s):  
Power Means

The Study on Preventing Users Electic Larceny

2014 ◽  
Vol 602-605 ◽  
pp. 2939-2942
Author(s):  
Ying Ying Yang ◽  
Yi Shan ◽  
Zhi Tong Liu ◽  
Jian Feng Li ◽  
Jing Jin ◽  
...  
Keyword(s):  
Electric Power ◽  
Power Supply ◽  
Economic Loss ◽  
The Road ◽  
Energy Meter ◽  
Power Means ◽  
Long Time

For a long time,users electic larceny has been a headache topic of the electric power department.The users long-term electic larceny has brought great economic loss to the power supply department.In recent years,the stealing power means are emerging in an endless stream,and they have been broght mant difficulties to prevent electic larceny.But the road is high one feet evil spirite is high one a unit of lengh, according to the study on electic energy meter,we will understand the electic larceny means at the sours.Therefore, further study of stealing power means is also our current priority,only the better anti-stealing electic power means, can be completely blocked leak.

The reverse Hölder inequality for power means

2012 ◽  
Vol 183 (6) ◽  
pp. 762-771
Author(s):  
Viktor D. Didenko ◽  
Anatolii A. Korenovskyi
Keyword(s):  
Hölder Inequality ◽  
Reverse Hölder Inequality ◽  
Power Means ◽  
Reverse Hölder

scholarly journals Interval-type theorems concerning means

2018 ◽  
Vol 17 (1) ◽  
pp. 37-43
Author(s):  
Paweł Pasteczka
Keyword(s):  
Partial Order ◽  
Natural Isomorphism ◽  
Natural Partial Order ◽  
Real Numbers ◽  
Power Means ◽  
Interval Type ◽  
Type Sets

Abstract Each family ℳ of means has a natural, partial order (point-wise order), that is M ≤ N iff M(x) ≤ N(x) for all admissible x. In this setting we can introduce the notion of interval-type set (a subset ℐ ⊂ℳ such that whenever M ≤ P ≤ N for some M, N ∈ℐ and P ∈ℳ then P ∈ℐ). For example, in the case of power means there exists a natural isomorphism between interval-type sets and intervals contained in real numbers. Nevertheless there appear a number of interesting objects for a families which cannot be linearly ordered. In the present paper we consider this property for Gini means and Hardy means. Moreover, some results concerning L∞ metric among (abstract) means will be obtained.

The Expected Utility of Insurance

2019 ◽  
pp. 8-47
Author(s):  
Brad Epperly
Keyword(s):  
Expected Utility ◽  
Judicial Independence ◽  
Utility Model ◽  
Personal Security ◽  
Power Means ◽  
Democratic Regimes ◽  
The Future ◽  
Autocratic Regimes ◽  
Expected Utility Model

This chapter offers a new version of popular “insurance” models of judicial independence, in which the competitiveness of the electoral arena induces leaders to prefer more independent courts, as a means of offering policy and personal security if they lose power. That is, paying the “premium” of increased constraints on behavior imposed by independent courts now for the insurance of protection in the future if out of office. The crux of the argument is that the risks associated with losing power in autocratic regimes are greater than in democracies, and therefore competition should be more salient in dictatorships than democracies. The stakes are higher because autocratic power means access to wealth and state resources in a way rarely equaled in democratic regimes, and more importantly the likelihood of being punished after leaving office is greater for former autocrats. Judiciaries exercising greater independence, however, can minimize the risks of being a former leader, and the chapter leverages this finding to develop an expected utility model, the empirical implication of which is higher salience of competition—when present—in autocracies. Unlike previous theories of how competition affects independence, this model integrates both the likelihood of losing office and the risks associated with such an outcome, and thus allows us to examine the phenomena across the democracy/dictatorship divide.

scholarly journals On the monotonicity of weighted power means for matrices

2017 ◽  
Vol 527 ◽  
pp. 128-140 ◽  
Author(s):  
Trung Hoa Dinh ◽  
Raluca Dumitru ◽  
Jose A. Franco
Keyword(s):  
Power Means
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