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This paper compares mortality transition in China and India in the period 1950-2021, highlighting similarities and differences. Mortality transition has been inconsistent in both countries, but differences remain. In China, the transition has been spread evenly across the age range, while in India, it has primarily been confined to younger ages, being markedly slow in ages 35-90. This difference in the older ages appears to explain the main difference between the respective mortality transition in the two countries. To address its ongoing mortality transition, the paper concludes, India needs to reinvigorate its health-care delivery system to meet the health care needs of the old people. The paper also emphasises using geometric mean of the age-specific probabilities of death as an appropriate measure to analyse mortality transition. [ABSTRACT FROM AUTHOR]

Traditional analysis of two-way contingency tables with explanatory and response variables focuses on the independence of two variables. However, if the variables do not show independence or a clear relationship, the analysis shifts to the degree of association. Various measures have been proposed to calculate the degree of association. One is the proportional reduction in variation (PRV) measure. This measure describes the PRV from the marginal distribution to the conditional distribution of the response variable. Although conventional PRV measures can assess the association of the entire contingency table, they cannot accurately assess the association for each explanatory variable. In this paper, we propose a geometric mean type of PRV (geoPRV) measure, which aims to sensitively capture the association of each explanatory variable to the response variable. Our approach uses a geometric mean, and enabling analysis without underestimating the values when the cells in the contingency table are partially biased. The geoPRV measure can be constructed using any function that satisfies specific conditions. This approach has practical advantages, and in special cases, conventional PRV measures can be expressed as geometric mean types. [ABSTRACT FROM AUTHOR]

An upper bound of the logarithmic mean is given by a convex combination of the arithmetic mean and the geometric mean. In addition, a lower bound of the logarithmic mean is given by a geometric bridge of the arithmetic mean and the geometric mean. In this paper, we study the bounds of the logarithmic mean. We give operator inequalities and norm inequalities for the fundamental inequalities on the logarithmic mean. We give monotonicity of the parameter for the unitarily invariant norm of the Heron mean, and give its optimality as the upper bound of the unitarily invariant norm of the logarithmic mean. We study the ordering of the unitarily invariant norms for the Heron mean, the Heinz mean, the binomial mean and the Lehmer mean. Finally, we give a new mean inequality chain as an application of the point--wise inequality. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some improvements and generalizations of Young's inequalities on the arithmetic, geometric, and harmonic mean. For example, In addition, we obtain some new results for Young's inequality for operators. [ABSTRACT FROM AUTHOR]

Copyright of Swiss Political Science Review is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The concept of Active citizenship is gaining importance. Ignoring the issues of selection of dimensions and items, the paper addresses methodological issues and aggregation of indicators of multidimensional active participation index (PI) by two methods. Policy makers and researchers can take advantages of the proposed methods of arithmetic aggregation (Method-1) with normally distributed transformed scores or multiplicative aggregation (Method-2) without scaling and choosing weights. Thus, the Method-2 avoids the problems of rank robustness specific to selection of weights. Multiplicative aggregation proposed in Method-2 can be converted to additive model by taking logarithms. Normal distributions of two or more groups by Method-1 are likely to give rise to lower value of Ginis coefficient indicating equality. Avoiding major limitations of ordinal scores, both methods satisfy desired properties, analysis under parametric set up for meaningful comparisons including testing of statistical hypothesis, identification of critical dimensions, ranking of the dimensions by elasticity, assessment of progress/decline of PI, etc. Method-2 offers more generalized approach satisfying time reversal test and formation of chain indices. However, test of normality is required for this method unlike the Method-1 which ensures normally distributed scores. [ABSTRACT FROM AUTHOR]

In this paper, we establish new generalizations of the Hermite-Hadamard-type inequalities. These inequalities are formulated in terms of modules of certain powers of proper functions. Generalizations for convex functions are also considered. As applications, some new inequalities for the digamma function in terms of the trigamma function and some inequalities involving special means of real numbers are given. The results also include estimates via arithmetic, geometric and logarithmic means. The examples are derived in order to demonstrate that some of our results in this paper are more exact than the existing ones and some improve several known results available in the literature. The constants in the derived inequalities are calculated; some of these constants are sharp. As a visual example, graphs of some technically important functions are included in the text. [ABSTRACT FROM AUTHOR]

This paper compares mortality transition in China and India in the period 1950–2021, highlighting similarities and differences. Mortality transition has been inconsistent in both countries, but differences remain. In China, the transition has been spread evenly across the age range, while in India, it has primarily been confined to younger ages, being markedly slow in ages 35–90. This difference in the older ages appears to explain the main difference between the respective mortality transition in the two countries. To address its ongoing mortality transition, the paper concludes, India needs to reinvigorate its health-care delivery system to meet the health care needs of the old people. The paper also emphasises using geometric mean of the age-specific probabilities of death as an appropriate measure to analyse mortality transition.

In this paper we introduce the generalized contraharmanic mean associated to a Kubo–Ando mean as where is the dual mean of and X, Y are positive definite matrices. We show that for a symmetric Kubo–Ando mean such as and for any positive definite matrices the inverse problem has a positive solution . [ABSTRACT FROM AUTHOR]

The main purpose of the paper is to strengthen the results of P. R. Mercer (2003) concerning the comparison of arithmetic, geometric, and harmonic weighted means. [ABSTRACT FROM AUTHOR]

Copyright of Cultura Educación y Sociedad is the property of Corporacion Universidad de la Costa, CUC and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Earthquake engineers have made a lot of efforts to derive a comprehensive set of closed form expressions for performance evaluation of frames, which are already presented in guidelines such as SAC/FEMA. These analytical expressions have been developed to estimate the annual probability of exceeding a limit state. In the process of such seismic assessments, some essential assumptions are adopted to simplify the process. One of these fundamental assumptions declares that drift demand at any seismic intensity level follows a lognormal distribution around its median. To investigate the validity of this assumption, this paper describes a case study of the types of errors that could be produced by using the sample median as the central tendency. Based on the Maximum Likelihood Estimation method as well as other statistical evidence, this paper proposes the use of the sample geometric mean instead of the sample median for the central tendency. Further, the results of seismic reliability evaluations of 4 sample frames are compared based on utilizing both the geometric mean and the sample median. In this process, both first and second order power law fits of the hazard curve are implemented to compare the effects of hazard estimation and the selection of the central tendency on the final results. It is observed in the application example that the sample geometric mean could lead to more accurate results. [ABSTRACT FROM AUTHOR]

It is well-known that using arithmetic averages of yearly return observations leads to downward biased discount rates estimations. Well-known corrections, however, lead to upward biased results under the presence of negative serial correlation. Using a simulation analysis, we first show that a specific variant of the Cooper estimator, labelled as C4 in this paper, leads to robust estimations even under the presence of both serial correlation and heteroscedasticity. We also show that among the simple estimators, i.e. the arithmetic (AM) or geometric mean (GM) or the mean of both (MoM), the first one tends to perform best unless there is a high degree of negative serial correlation. In that case using the so-called mean of means rule would be better. Secondly, using data from Jordà et al. (Q J Econ 134(3):1225–1298, 2019) we find negative serial correlation and heteroscedasticity in market risk premia to be a widely spread phenomenon. Finally, we use this data to derive presumably least biased market risk premia estimations based on the C4 estimator. For the majority of the countries we find that these estimations are somewhere between the arithmetic and geometric average. When comparing these simple estimators among each other based on the empirical data, we find the arithmetic mean and mean of means to perform almost equally well, while the geometric mean clearly underperforms. Moreover, we found some evidence that the MoM is slightly outperforming the AM under a local CAPM perspective, while the opposite tends to be true under a global CAPM perspective. This leads us the cautious conclusion that the mean of means rule used by practitioners has some empirical rationale when there is evidence for substantial negative serial correlation. [ABSTRACT FROM AUTHOR]

In a recent paper, Takacs and Bourrat (Biol Philos 37:12, 2022) examine the use of geometric mean reproductive output as a measure of biological fitness. We welcome Takacs and Bourrat's scrutiny of a fitness definition that some philosophers have adopted uncritically. We also welcome Takacs and Bourrat's attempt to marry the philosophical literature on fitness with the biological literature on mathematical measures of fitness. However, some of the main claims made by Takacs and Bourrat are not correct, while others are correct but not for the reasons they give. [ABSTRACT FROM AUTHOR]

This paper considers a cell-free massive multiple-input multiple-output network (cfm-MIMO) with a massive number of access points (APs) distributed across an area to deliver information to multiple users. Based on only local channel state information, conjugate beamforming is used under both proper and improper Gaussian signalings. To accomplish the mission of cfm-MIMO in providing fair service to all users, the problem of power allocation to maximize the geometric mean (GM) of users’ rates (GM-rate) is considered. A new scalable algorithm, which iterates linear-complex closed-form expressions and thus is practical regardless of the scale of the network, is developed for its solution. The problem of quality-of-service (QoS) aware network energy-efficiency is also addressed via maximizing the ratio of the GM-rate and the total power consumption, which is also addressed by iterating linear-complex closed-form expressions. Intensive simulations are provided to demonstrate the ability of the GM-rate based optimization to achieve multiple targets such as a uniform QoS, a good sum rate, and a fair power allocation to the APs. [ABSTRACT FROM AUTHOR]

Forest planning is a necessary requirement for long-term, economically efficient and environmentally responsible forest management and use. Iran has 12 million ha of forest cover, with 5 million ha in the mountainous Zagros area. Many of the improper uses in these forests, so far removed from the past, have resulted in significant degradation. The purpose of this paper is to check and compare the prepared methods, including the Iranian Ecological Model (with seven classes using Boolean logic), its revised method (with four classes using Boolean logic and four classes using geometric mean evaluation, as well) and a new model for ecological capability evaluation for better planning management for commercial and conservational forestry in Jahrom County located in Fars Province, Iran. In this study, we assessed the potential for conservational forestry in two ways: first, by adjusting the quantitative evaluation threshold of the model's primary topographic criterion, and then, by removing this criterion altogether. It is worth noting that the necessary information, including climatic, topographic, soil and other types, was compiled by national and local organisations in Iran for the research. The improved Boolean technique (with kappa = 0. 5 3) outperformed the Iranian Ecological Model (with kappa = 0. 0 6), while the revised method using geometric mean assessment and calibration (with kappa = 0. 6 5) outperformed the other methods tested. Furthermore, when all of the forestry capacity maps were compared, conservational forestry map demonstrated a higher capability after removing the topographic criterion in the region (with kappa = 0. 9 0 for calibration technique), indicating conservational forestry's potential in Jahrom County. Overall, because of its simplicity and excellent precision, this study may be utilised as a fundamental framework to evaluate ecological capability for other locations with similar conditions, and this model can help users and administrations undertake executive initiatives. [ABSTRACT FROM AUTHOR]

In many real-world domains, datasets with imbalanced class distributions occur frequently, which may confuse various machine learning tasks. Among all these tasks, learning classifiers from imbalanced datasets is an important topic. To perform this task well, it is crucial to train a distance metric which can accurately measure similarities between samples from imbalanced datasets. Unfortunately, existing distance metric methods, such as large margin nearest neighbor, information-theoretic metric learning, etc., care more about distances between samples and fail to take imbalanced class distributions into consideration. Traditional distance metrics have natural tendencies to favor the majority classes, which can more easily satisfy their objective function. Those important minority classes are always neglected during the construction process of distance metrics, which severely affects the decision system of most classifiers. Therefore, how to learn an appropriate distance metric which can deal with imbalanced datasets is of vital importance, but challenging. In order to solve this problem, this paper proposes a novel distance metric learning method named distance metric by balancing KL-divergence (DMBK). DMBK defines normalized divergences using KL-divergence to describe distinctions between different classes. Then it combines geometric mean with normalized divergences and separates samples from different classes simultaneously. This procedure separates all classes in a balanced way and avoids inaccurate similarities incurred by imbalanced class distributions. Various experiments on imbalanced datasets have verified the excellent performance of our novel method. [ABSTRACT FROM AUTHOR]

In this paper, we focus on two generalizations of the Lindley distribution and investigate, for each one separately, some special properties related to the geometric mean ( G M ) and the cumulative residual entropy ( C R E ), both of them being of great importance from the theoretical as well as from the practical point of view. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear matrix equation X p = A # t (M T (X − 1 + B) − 1 M) , where p ≥ 1 is a positive integer, t ∈ [ 0 , 1 ] , M is an n × n nonsingular matrix, A is a positive definite matrix and B is a positive semidefinite matrix, is considered. The notation A # t B is the t-weighted geometric mean of the positive definite matrices A and B. Based on the properties of the Thompson metric, we prove that the nonlinear matrix equation always has a unique positive definite solution and we compare it with the unique positive definite solution of the equation X p = A + M T (X − 1 + B) − 1 M , which has been studied in Jung et al. [On the solution of the nonlinear matrix equation X n = f (X). Linear Algebra Appl. 2009;430:2042–2052]; Meng and Kim [The positive definite solution of the nonlinear matrix equation X p = A + M (B + X − 1 ) − 1 M ∗ . J Comput Appl Math. 2017;322:139–147]. A fixed-point iteration method for obtaining the unique positive definite solution and an elegant estimate of the solution are given. Perturbation analysis of the unique positive definite solution is presented. [ABSTRACT FROM AUTHOR]

The numerous models in science and engineering, statistics and population dynamics are articulated in the terms of unidentified amounts and their derivatives. Movement of objects, flow of heat, materials twisting and cracking, vibrations and nuclear reaction, growth and decay of species etc., all these are modeled in terms of differential equations. Present paper is based on solving logistic model of population using the trio-geometric mean based three stage Runge-Kutta method to solve autonomous initial value problem. Convergence of the method is established and the method is compared with other competent methods in terms of accuracy and error analysis and it is found that proposed method is more compatible on logistic model with respect to several other existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we study nonlinear matrix equations X p = A + ∑ i = 1 m M i T (X # B) M i and X p = A + ∑ i = 1 j M i T (X # B) M i + ∑ i = j + 1 m M i T (X - 1 # B) M i , where p, m, j are positive integers, 1 ≤ j ≤ m , A, B are n × n positive definite matrices and M i (i = 1 , 2 , 3 , ... , m) are n × n nonsingular real matrices. Based on some fixed point theorems for monotone and mixed monotone operators in ordered Banach spaces and some properties of cone, we prove that these equations always have a unique positive definite solution. In addition, an iterative sequence can be given to approximate the unique positive definite solution by employing a multi-step stationary iterative method. [ABSTRACT FROM AUTHOR]

However, it is worth noting that the results are identical with the assumption of a constant HT ht ratio regardless of I j i (Hélias et al. [11]). With HT ht , the geometric mean of HT ht instead of HT ht , we have a normalization reference value that we only calculate with the LCI database, without having to deal with the final demand for the reference. Keywords: Consistency; Normalization; Multi-criteria; LCI database; Geometric mean EN Consistency Normalization Multi-criteria LCI database Geometric mean 1117 1122 6 06/23/21 20210601 NES 210601 Introduction Overview In this discussion paper, we focus on a topic that seems probably not sufficiently addressed in life cycle assessment (LCA): the normalization (Andreas et al. [1]). [Extracted from the article]

The Kubo–Ando theory deals with connections for positive bounded operators. On the other hand, in various analysis related to von Neumann algebras, it is impossible to avoid unbounded operators. In this paper, we try to extend a notion of connections to cover various classes of positive unbounded operators (or unbounded objects such as positive forms and weights) appearing naturally in the setting of von Neumann algebras, and we must keep all the expected properties maintained. This generalization is carried out for the following classes: (i) positive τ -measurable operators (affiliated with a semifinite von Neumann algebra equipped with a trace τ), (ii) positive elements in Haagerup's L p -spaces and (iii) semifinite normal weights on a von Neumann algebra. Investigation on these generalizations requires some analysis (such as certain upper semi-continuity) on decreasing sequences in various classes. Several results in this direction are proved, which may be of independent interest. Ando studied Lebesgue decomposition for positive bounded operators by making use of parallel sums. Here, such decomposition is obtained in the setting of noncommutative (Hilsum) L p -spaces. [ABSTRACT FROM AUTHOR]

Copyright of Soil Science Annual is the property of Polish Society of Soil Science and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Trapezoidal fuzzy reciprocal preference relation (TraFRPR), whose elements are trapezoidal fuzzy numbers, is a powerful tool to simulate the pairwise comparison judgments with imprecision and vagueness. How to define the consistency and derive the priority weights are two important research topics for decision making with TraFRPRs. This paper will focus on solving these two issues. The paper analyzes the existing definitions of consistent TraFRPRs and concludes that they are flawed by not being robust to permutations of the DM’s judgments. A new trapezoidal fuzzy arithmetic based consistency definition is proposed for TraFRPRs, and properties of consistent TraFRPRs in light of the new definition are studied in detail. An acceptably consistent TraFRPR is then defined. A geometric mean and uncertainty ratio based transformation formula is put forward to convert a normalized trapezoidal fuzzy multiplicative weight vector into a consistent TraFRPR. A logarithmic least square model is developed to derive a normalized trapezoidal fuzzy multiplicative weight vector from an acceptably consistent TraFRPR and to construct the fitted consistent TraFRPR. A numerical example is given to illustrate the validity and applicability of the proposed models. [ABSTRACT FROM AUTHOR]

In this paper, we study some important means of Jordan's totient function, especially, we obtain asymptotic formula for geometric mean and harmonic mean. We also study alternating sums of Jordan's totient function and Carleman's inequality for this function. [ABSTRACT FROM AUTHOR]

In this paper the geometric mean of partial positive definite matrices with missing entries is considered. The weighted geometric mean of two sets of positive matrices is defined, and we show whether such a geometric mean holds certain properties which the weighted geometric mean of two positive definite matrices satisfies. Additionally, counterexamples demonstrate that certain properties do not hold. A Loewner order on partial Hermitian matrices is also defined. The known results for the maximum determinant positive completion are developed with an integral representation, and the results are applied to the weighted geometric mean of two partial positive definite matrices with missing entries. Moreover, a relationship between two positive definite completions is established with respect to their determinants, showing relationship between their entropy for a zero-mean,multivariate Gaussian distribution. Computational results as well as one application are shown. [ABSTRACT FROM AUTHOR]

In this paper we study the monotonicity, in-betweenness and in-sphere properties of matrix means with respect to Bures–Wasserstein, Hellinger and log-determinant metrics. More precisely, we show that the matrix power means (Kubo–Ando and non-Kubo–Ando extensions) satisfy the in-betweenness property in the Hellinger metric. We also show that for two positive definite matrices A and B, the curve of weighted Heron means, the geodesic curve of the arithmetic and the geometric mean lie inside the sphere centered at the geometric mean with the radius equal to half of the log-determinant distance between A and B. [ABSTRACT FROM AUTHOR]

The paper revisits the two major concepts for average historical returns, i. e., the arithmetic mean and the geometric mean, in order to clarify which approach must be used for which application. Conducting a rigorous derivation with a geometric Brownian motion, we can explain that the appropriate discount rate refers to the mean discrete return and, therefore, to the arithmetic mean rather than the often wrongly applied geometric mean. Likewise, the prominent CAPM relationship between the expected asset return and the expected market return is only valid for the arithmetic mean rather than the geometric mean. Using historical data for the German stock index, we illustrate that an inconsistent application can cause severe deviations from the meaningful ex-ante expected performance of an asset, the true discount rate, the true CAPM risk-adjusted return, and the intended performance scenarios of packaged retail and insurance-based investment products (PRIIPs) within the key information documents (KIDs). [ABSTRACT FROM AUTHOR]

The first probabilistic definition of the geometric mean of a non negative random variable under certain assumptions was given in Feng et al. (2013). In this paper, we generalize the definition to a larger class of random variables. We also show the basic properties of the geometric mean and point out its discontinuity and instability. Some convergence properties are studied as well, for which we emphasize its link to the positive moments of the random variable. A discussion of potential applications of the new definition in biomedical research and open questions to complete the theory of geometric mean is highlighted. [ABSTRACT FROM PUBLISHER]

The main aim of this paper is to examine the performance of Half-Sweep Geometric Mean (HSGM) iterative method for solving large, dense, third order Newton-Cotes quadrature system associated with numerical solutions of second kind linear Fredholm integral equations. The formulation and implementation of the method are presented. Some numerical analysis are included to verify the efficiency of the method. [ABSTRACT FROM AUTHOR]

The most obvious characteristics of an excursion wafer is an elevated defect density, either confined within a signature or distributed across its surface. Quantifying the impact of such abnormal levels of defectivity is the focus of this paper. Three methods are described which provide increasingly precise predictions of Defect Limited Yield. The methods are also intended to accurately handle excursion wafers that include highly divergent signatures, as well as non-optimized defect inspection recipes which may contain elevated levels of nuisance defects. This is achieved by combining the defect distribution with the kill ratio, via a geometric progression. The conditions under which each method is ideally suited are presented. [ABSTRACT FROM AUTHOR]

In this paper, by the definition of Berezin number, we present some inequalities involving the operator geometric mean. For instance, it is shown that if X , Y , Z ∈ L (H) such that X and Y are positive operators, then ber r ((X ♯ Y) Z) ≤ ber ( (Z ⋆ Y Z) r q 2 q + X r p 2 p) − 1 p inf λ ∈ Ω ([ X ˜ (λ) ] r p 4 − [ (Z ⋆ Y Z) ˜ (λ) ] r q 4) 2 , in which X ♯ Y = X 1 2 (X − 1 2 Y X − 1 2 ) 1 2 X 1 2 , p ≥ q > 1 such that r ≥ 2 q and 1 p + 1 q = 1 . [ABSTRACT FROM AUTHOR]

The aggregation formula in the Human Development Index (HDI) was changed to a geometric mean in 2010. In this paper, we search for a theoretical justification for employing this new HDI formula. First, we find a maximal class of index functions, what we call quasi‐geometric means, that satisfy symmetry for the characteristics, normalization, and separability. Second, we show that power means are the only quasi‐geometric means satisfying homogeneity. Finally, the new HDI is the only power mean satisfying minimal lower boundedness, which is a local complementability axiom proposed by Herrero et al. (2010). [ABSTRACT FROM AUTHOR]

In this paper we consider Loos symmetric spaces on an open cone Ω in the Banach space setting and develop the foundations of a geometric theory based on the (modified) Loos axioms for such cones. In particular we establish exponential and log functions that exhibit many desirable features reminiscent of those of the exponential function from the space of self-adjoint elements to the cone of positive elements in a unital C ∗ -algebra. We also show that the Thompson metric arises as the distance function for a natural Finsler structure on Ω and its minimal geodesics agree with the geodesics of the spray arising from the Loos structure. We close by showing that some familiar operator inequalities can be derived in this very general setting using the differential and metric geometry of the cone. [ABSTRACT FROM AUTHOR]