scholarly journals Bounds of the Neuman-Sándor Mean Using Power and Identric Means

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yu-Ming Chu ◽  
Bo-Yong Long
Keyword(s):  
Power Mean ◽  
Sharp Bounds ◽  
Lower Power

In this paper we find the best possible lower power mean bounds for the Neuman-Sándor mean and present the sharp bounds for the ratio of the Neuman-Sándor and identric means.

scholarly journals Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Hongya Gao ◽  
Jianling Guo ◽  
Wanguo Yu
Keyword(s):  
Power Mean ◽  
Sharp Bounds ◽  
Power Means ◽  
Heronian Mean

For1<r<+∞, we find the least valueαand the greatest valueβsuch that the inequalityHα(a,b)<Ar(a,b)<Hβ(a,b)holds for alla,b>0witha≠b. Here,Hω(a,b)andAr(a,b)are the generalized Heronian and the power means of two positive numbersaandb, respectively.

scholarly journals The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Feng Xia ◽  
Yu-Ming Chu ◽  
Gen-Di Wang
Keyword(s):  
Convex Combination ◽  
Arithmetic Mean ◽  
Power Mean ◽  
Logarithmic Mean ◽  
Positive Real ◽  
Lower Power ◽  
Double Inequality ◽  
Logarithmic Means

Forp∈ℝ, the power meanMp(a,b)of orderp, logarithmic meanL(a,b), and arithmetic meanA(a,b)of two positive real valuesaandbare defined byMp(a,b)=((ap+bp)/2)1/p, forp≠0andMp(a,b)=ab, forp=0,L(a,b)=(b-a)/(log⁡b-log⁡a), fora≠bandL(a,b)=a, fora=bandA(a,b)=(a+b)/2, respectively. In this paper, we answer the question: forα∈(0,1), what are the greatest valuepand the least valueq, such that the double inequalityMp(a,b)≤αA(a,b)+(1-α)L(a,b)≤Mq(a,b)holds for alla,b>0?

scholarly journals Sharp bounds by the power mean for the generalized Heronian mean

2012 ◽  
Vol 2012 (1) ◽  
pp. 129 ◽  
Author(s):  
Yong-Min Li ◽  
Bo-Yong Long ◽  
Yu-Ming Chu
Keyword(s):  
Power Mean ◽  
Sharp Bounds ◽  
Heronian Mean

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.

Gaussian ϕ(ρz) curves: Comparison with other models

1990 ◽  
Vol 48 (2) ◽  
pp. 192-193
Author(s):  
Alberto Riveros ◽  
Gustavo Castellano
Keyword(s):  
Good Description ◽  
Bulk Sample ◽  
Incident Electron Energy ◽  
Power Mean ◽  
General Shape ◽  
Ionization Cross ◽  
X Ray ◽  
Mass Absorption ◽  
Absorption Correction ◽  
Image Position

X ray characteristic intensity Ii , emerging from element i in a bulk sample irradiated with an electron beam may be obtained throughwhere the function ϕi(ρz) is the distribution of ionizations for element i with the mass depth ρz, ψ is the take-off angle and μi the mass absorption coefficient to the radiation of element i.A number of models has been proposed for ϕ(ρz), involving several features concerning the interaction of electrons with matter, e.g. ionization cross section, stopping power, mean ionization potential, electron backscattering, mass absorption coefficients (MAC’s). Several expressions have been developed for these parameters, on which the accuracy of the correction procedures depends.A great number of experimental data and Monte Carlo simulations show that the general shape of ϕ(ρz) curves remains substantially the same when changing the incident electron energy or the sample material. These variables appear in the parameters involved in the expressions for ϕ(ρz). A good description of this function will produce an adequate combined atomic number and absorption correction.

scholarly journals Simulation of Self-Consumption Photovoltaic Installations: Profitability Thresholds

2021 ◽  
Vol 11 (14) ◽  
pp. 6517
Author(s):  
Marta Varo-Martínez ◽  
Luis Manuel Fernández-Ahumada ◽  
Rafael López-Luque ◽  
José Ramírez-Faz
Keyword(s):  
Systematic Study ◽  
Peak Power ◽  
Net Present Value ◽  
Energy Model ◽  
Present Value ◽  
Lower Power ◽  
Design Variables ◽  
Sunshine Hours ◽  
Optimal Value ◽  
Renewable Technology

PV self-consumption can contribute positively to the spread of PV and, therefore, to the progress of renewable energies as a key element in a decarbonized energy model. However, the policies of each country regarding the promotion of this type of renewable technology is fundamental for their growth. Despite the high number of sunshine hours registered in Spain, self-consumption in this country has not been authorized until recently. In this new context, this work presents a systematic study of the profitability limits of a self-consumption PV installation under different conditions of installed peak power, orientation and inclination of the PV panels and level of obstruction of the installation. It was proved that, for the case of study (Córdoba, Spain), the maximum profitability was achieved for PV panels oriented to the south and with an inclination of 15° whereas the most unfavourable conditions are those of PV panels with an orientation and inclination of 180° and 90°, respectively. Furthermore, when the level of obstruction increases the maximum of the Net Present Value of self-consumptions PV installations decreases and this optimal value is achieved for installations with lower power. Finally, empirical adjustment equations have been developed to estimate the profitability parameters of self-consumptions PV installations as a function of their design variables.

scholarly journals Sharp Bounds on Davenport-Schinzel Sequences of Every Order

2015 ◽  
Vol 62 (5) ◽  
pp. 1-40 ◽  
Author(s):  
Seth Pettie
Keyword(s):  
Sharp Bounds

scholarly journals A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenpeng Zhang ◽  
Xingxing Lv
Keyword(s):  
Exponential Sums ◽  
Exponential Sum ◽  
Gauss Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*

2020 ◽  
Vol 70 (4) ◽  
pp. 849-862
Author(s):  
Shagun Banga ◽  
S. Sivaprasad Kumar
Keyword(s):  
Triangle Inequality ◽  
Starlike Functions ◽  
Sharp Bound ◽  
The Novel ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Lemniscate Of Bernoulli ◽  
Carathéodory Functions ◽  
The Right

AbstractIn this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: $\begin{array}{} |a_3^2-a_5| \end{array}$ for the class 𝓢𝓛* is also estimated. Further, a couple of interesting results of 𝓢𝓛* are also discussed.

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