scholarly journals Bounds for the Differences between Arithmetic and Geometric Means and Their Applications to Inequalities

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2398
Author(s):  
Shigeru Furuichi ◽  
Nicuşor Minculete
Keyword(s):  
Symmetric Functions ◽  
Geometric Mean ◽  
Concave Functions ◽  
Geometric Means ◽  
Weighted Arithmetic

Refining and reversing weighted arithmetic-geometric mean inequalities have been studied in many papers. In this paper, we provide some bounds for the differences between the weighted arithmetic and geometric means , using known inequalities. We improve the results given by Furuichi-Ghaemi-Gharakhanlu and Sababheh-Choi. We also give some bounds on entropies, applying the results in a different approach. In Section 4, we explore certain convex or concave functions, which are symmetric functions on the axis t=1/2.

scholarly journals Pharmacokinetic Interactions between the Hormonal Emergency Contraception, Levonorgestrel (Plan B), and Efavirenz

2012 ◽  
Vol 2012 ◽  
pp. 1-4 ◽  
Author(s):  
Monica L. Carten ◽  
Jennifer J. Kiser ◽  
Awewura Kwara ◽  
Samantha Mawhinney ◽  
Susan Cu-Uvin
Keyword(s):  
Geometric Mean ◽  
Liver Function Tests ◽  
Open Label ◽  
Time Curve ◽  
Geometric Means ◽  
Concentration Time ◽  
Plan B ◽  
Effective Contraception ◽  
Grade 3 ◽  
Hiv Negative

Objectives. Compare the Plan B levonorgestrel (LNG) area under the concentration- time curve (AUC12) prior to and with efavirenz (EFV).Design. Prospective, open-label, single-arm, equivalence study.Methods. Healthy HIV-negative subjects underwent 12 hr intensive pharmacokinetic (PK) sampling following single dose LNG alone and after 14 days of EFV. Geometric means, Geometric Mean Ratios, and 90% confidence intervals (CI) are reported for PK Parameters.T-tests were utilized. Clinical parameters and liver function tests (LFTs) were assessed.Results. 24 women enrolled and 21 completed the study. With EFV, LNG AUC12was reduced 56% (95% CI: 49%, 62%) from 42.9 to 17.8 ng*hr/mL, and maximum concentration (Cmax⁡) was reduced 41% (95% CI: 33%, 50%) from 8.4 to 4.6 ng/mL. LNG was well tolerated with no grade 3 or 4 treatment-related toxicities.Conclusions. EFV significantly reduced LNG exposures. Higher LNG doses may be required with EFV. These results reinforce the importance of effective contraception in women taking EFV.

On strengthened weighted Carleman's inequality

2003 ◽  
Vol 68 (3) ◽  
pp. 481-490 ◽  
Author(s):  
Aleksandra Čižmešija ◽  
Josip Pecarić ◽  
Lars–Erik Persson
Keyword(s):  
Geometric Mean ◽  
Weighted Arithmetic ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

In this paper we prove a new refinement of the weighted arithmetic-geometric mean inequality and apply this result in obtaining a sharpened version of the weighted Carleman's inequality.

scholarly journals The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 380 ◽  
Author(s):  
Yongtao Li ◽  
Xian-Ming Gu ◽  
Jianxing Zhao
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Hölder Inequality ◽  
Power Mean ◽  
Weighted Arithmetic ◽  
Mathematical Equivalence ◽  
Power Mean Inequality ◽  
Mathematical Relations

In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM–GM inequality, the weighted power-mean inequality and the Hölder inequality are fully achieved. The new results are more generalized than those of previous studies.

scholarly journals Analyzing Dependent Variables with Multiple Surrogates in Accounting Research

2018 ◽  
Author(s):  
Enyi Enyi
Keyword(s):  
Logistic Regression ◽  
Regression Analysis ◽  
Performance Studies ◽  
Geometric Mean ◽  
A Priori ◽  
Geometric Means ◽  
Canonical Correlations ◽  
Dependent Variables ◽  
Actual Outcome ◽  
Ethical Clearance

The paper contains details a research carried out to show that the use of geometric mean to unify multivariate dependent variables in financial performance studies gives better and more practical results than the multiple abstraction analysis provided using advanced econometric tools such as TLS, PLS, MCA, Canonical correlations etc.<div>The study used the logistic regression analysis to compare the a priori expectations of 30 Ph.D research theses with their actual outcomes using econometric tools and the actual outcome using geometric means. The study used Ph.D theses in accounting and finance sourced from the libraries of four universities in Nigeria.</div><div>The study was a desktop research using publicly available literary resources and as such requires no ethical clearance.</div>

scholarly journals Recognition of International Education in Japanese Teachers

2017 ◽  
Vol 5 (2) ◽  
pp. 53 ◽  
Author(s):  
Masami Yoshida
Keyword(s):  
International Education ◽  
School Environment ◽  
Geometric Mean ◽  
Intercultural Education ◽  
Multiple Comparison ◽  
Geometric Means ◽  
Suburban Areas ◽  
The Third ◽  
Questionnaire Method ◽  
Multiple Comparison Procedures

Education for international understanding in Japan was focused to develop its own national identity as well as to recognize its coexistence through intercultural education. Then, we have investigated the opinions of Japanese school teachers in terms of their recognition of the necessary content to introduce school instruction of intercultural education using a questionnaire method. In the questionnaire, 14 items of three principles were extracted from the criteria of UNESCO (United Nations Educational, Scientific, and Cultural Organization). For analyzing the collected data, the geometric mean was used. Subsequently, a one-way ANOVA test and multiple-comparison procedures were conducted. By including teachers in suburban areas in Japan, we obtained 123 valid responses. All items showed a necessary level of geometric means, and particularly items of the first principle “respect cultural identity” and items of the second principle “provide knowledge for participation” showed statistically significant positive necessity levels. However, an answer of “I have never thought” increased in the third principle “provide a chance to contribute” that was closely related to present world concern of global citizenship education and statistically was not significant. From the result of the multiple-comparison procedures of the second principle and the third principle, seven pairs of statistically different items were extracted. Then, we discussed the enhancement between Japan and UNESCO and influence of school environment in Japan.

Geospatial Suitability Indices Toolbox (GSI Toolbox)

2021 ◽  
Author(s):  
Christina Saltus ◽  
Todd Swannack ◽  
S. McKay
Keyword(s):  
Habitat Suitability ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Limiting Factor ◽  
Ecological Processes ◽  
Weighted Arithmetic ◽  
Suitability Index ◽  
Multiple Parameter ◽  
Spatially Distributed

Habitat suitability models are widely adopted in ecosystem management and restoration, where these index models are used to assess environmental impacts and benefits based on the quantity and quality of a given habitat. Many spatially distributed ecological processes require application of suitability models within a geographic information system (GIS). Here, we present a geospatial toolbox for assessing habitat suitability. The Geospatial Suitability Indices (GSI) toolbox was developed in ArcGIS Pro 2.7 using the Python® 3.7 programming language and is available for use on the local desktop in the Windows 10 environment. Two main tools comprise the GSI toolbox. First, the Suitability Index Calculator tool uses thematic or continuous geospatial raster layers to calculate parameter suitability indices based on user-specified habitat relationships. Second, the Overall Suitability Index Calculator combines multiple parameter suitability indices into one overarching index using one or more options, including: arithmetic mean, weighted arithmetic mean, geometric mean, and minimum limiting factor. The resultant output is a raster layer representing habitat suitability values from 0.0 to 1.0, where zero is unsuitable habitat and one is ideal suitability. This report documents the model purpose and development as well as provides a user’s guide for the GSI toolbox.

scholarly journals A Comparison of the Arithmetic and Geometric Means in Estimating Stump Diameter, Basal Area, and Volume in Appalachian Hardwoods

2007 ◽  
Vol 24 (1) ◽  
pp. 71-73 ◽  
Author(s):  
Harry V. Wiant ◽  
John R. Brooks
Keyword(s):  
Geometric Mean ◽  
Basal Area ◽  
Cross Sectional Area ◽  
Practical Significance ◽  
Sectional Area ◽  
Cross Sectional ◽  
Geometric Means ◽  
The Difference ◽  
Appalachian Hardwoods ◽  
Stump Diameter

Abstract The difference between the use of the arithmetic and geometric means for estimation of average stump diameter, stump cross-sectional area and estimated tree volume was investigated using measurements from 739 stumps from an Appalachian hardwood stand located in central West Virginia. Although average stump diameter, cross-sectional area, and tree volumes were statistically different between estimates based on the arithmetic and geometric mean diameter, these differences were of little practical significance. The difference in average stem diameter, cross-sectional area, tree cubic volume, and board foot volume were 0.05 in, 0.01 ft2, 0.45 ft3, and 2.41 bd ft, respectively.

scholarly journals Tobacco-Specific Nitrosamines (NNAL, NNN, NAT, and NAB) Exposures in the US Population Assessment of Tobacco and Health (PATH) Study Wave 1 (2013–2014)

2020 ◽  
Author(s):  
Baoyun Xia ◽  
Benjamin C Blount ◽  
Tonya Guillot ◽  
Christina Brosius ◽  
Yao Li ◽  
...  
Keyword(s):  
Solid Phase ◽  
Geometric Mean ◽  
Tobacco Product ◽  
Geometric Means ◽  
Population Assessment ◽  
Frequency Of Use ◽  
The Us ◽  
Liquid Chromatography Tandem Mass ◽  
Highly Correlated ◽  
Tobacco Specific Nitrosamines

Abstract Introduction The tobacco-specific nitrosamines (TSNAs) are an important group of carcinogens found in tobacco and tobacco smoke. To describe and characterize the levels of TSNAs in the Population Assessment of Tobacco and Health (PATH) Study Wave 1 (2013–2014), we present four biomarkers of TSNA exposure: N′-nitrosonornicotine, N′-nitrosoanabasine, N′-nitrosoanatabine, and 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanol (NNAL) which is the primary urinary metabolite of 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone. Methods We measured total TSNAs in 11 522 adults who provided urine using automated solid-phase extraction coupled to isotope dilution liquid chromatography–tandem mass spectrometry. After exclusions in this current analysis, we selected 11 004 NNAL results, 10 753 N′-nitrosonornicotine results, 10 919 N′-nitrosoanatabine results, and 10 996 N′-nitrosoanabasine results for data analysis. Geometric means and correlations were calculated using SAS and SUDAAN. Results TSNA concentrations were associated with choice of tobacco product and frequency of use. Among established, every day, exclusive tobacco product users, the geometric mean urinary NNAL concentration was highest for smokeless tobacco users (993.3; 95% confidence interval [CI: 839.2, 1147.3] ng/g creatinine), followed by all types of combustible tobacco product users (285.4; 95% CI: [267.9, 303.0] ng/g creatinine), poly tobacco users (278.6; 95% CI: [254.9, 302.2] ng/g creatinine), and e-cigarette product users (6.3; 95% CI: [4.7, 7.9] ng/g creatinine). TSNA concentrations were higher in every day users than in intermittent users for all the tobacco product groups. Among single product users, exposure to TSNAs differed by sex, age, race/ethnicity, and education. Urinary TSNAs and nicotine metabolite biomarkers were also highly correlated. Conclusions We have provided PATH Study estimates of TSNA exposure among US adult users of a variety of tobacco products. These data can inform future tobacco product and human exposure evaluations and related regulatory activities.

scholarly journals Retrospection of Anti–Blood Group Antibody Proficiency Testing Data Using the Geometric Mean and Standard Deviation

2019 ◽  
Vol 153 (4) ◽  
pp. 530-536 ◽  
Author(s):  
John Jeongseok Yang ◽  
Yousun Chung ◽  
Hyungsuk Kim ◽  
Dae-Hyun Ko ◽  
Sang-Hyun Hwang ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Blood Group ◽  
Proficiency Testing ◽  
Geometric Mean ◽  
Geometric Standard Deviation ◽  
Geometric Means ◽  
Consensus Criterion ◽  
Mode 2 ◽  
Testing Data ◽  
The Mean

Abstract Objectives We reanalyzed the data from proficiency testing (PT) to assess the effect of the geometric mean in the statistical analysis of immunohematologic data. Methods Using the five most recent anti–blood group antibody titer participant summary results, the geometric mean (GM) ±2 × geometric standard deviation (GSD) was used as the comparative consensus criterion to mode ±2 titers. Results Using the PT evaluation criterion of mode ±2 titers, the mean percentages of participants with acceptable results were 97.5% and 97.8% for anti-A and anti-D, respectively. When applying GM ±2 GSD, the mean percentages of acceptable results were 96.1% (anti-A) and 96.1% (anti-D). The percentages of responses included in each consensus criterion were lower using GM ±2 GSD, with a few exceptions. Conclusions Geometric means are more robust and precise in visualizing the central tendency. This method can improve the statistical robustness of PT evaluations.

The Use of Judgment Matrices in Subjective Workload Assessment: The Subjective Workload Dominance (SWORD) Technique

1989 ◽  
Vol 33 (20) ◽  
pp. 1406-1410 ◽  
Author(s):  
Michael A. Vidulich
Keyword(s):  
Analytic Hierarchy Process ◽  
Assessment Tool ◽  
Geometric Mean ◽  
Data Sets ◽  
Analytic Hierarchy ◽  
Geometric Means ◽  
Subjective Workload ◽  
Hierarchy Process

One objective of the project was to determine compare two analytic algorithms for converting judgment matrices into subjective workload ratings. The original eigenvector algorithm used in Saaty's Analytic Hierarchy Process (AHP) was compared an algorithm of calculating geometric means. Also, three methods of identifying excessively inconsistent matrices were compared. Data from nine previous experiments were re-examined in the present analysis. There were no differences between the AHP ratings and the geometric mean ratings in terms of their sensitivity to the experimental manipulations. However, two of the inconsistency measures were successfully used to cull the data-sets of inconsistent matrices and improved the statistical sensitivity of one set of ratings. These findings suggest that: (1) the computationally simpler geometric means algorithm can be used as an alternative to the eigenvector algorithm, and (2) culling inconsistent matrices can sometimes improve rating sensitivity. These findings, along with previous research, demonstrate that judgment matrices can be a very valuable workload assessment tool. The essential steps for the proper use of judgment matrices in workload assessment are reviewed. A user's guide and software are also being prepared to aid researchers and practitioners

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