scholarly journals Quadratic curvature gravity with second order trace and massive gravity models in three dimensions

2012 ◽  
Vol 44 (8) ◽  
pp. 1993-2017 ◽  
Author(s):  
Ahmet Baykal
Keyword(s):  
Massive Gravity ◽  
Second Order ◽  
Three Dimensions ◽  
Gravity Models

scholarly journals MASTER ACTIONS FOR LINEARIZED MASSIVE GRAVITY MODELS IN 3D

2012 ◽  
Vol 27 (03n04) ◽  
pp. 1250015 ◽  
Author(s):  
PIO J. ARIAS ◽  
ADEL KHOUDEIR ◽  
J. STEPHANY
Keyword(s):  
Fourth Order ◽  
General Model ◽  
Massive Gravity ◽  
Second Order ◽  
The Self ◽  
Gravity Models ◽  
Order Model ◽  
Duality Transformation ◽  
First Order ◽  
Chern Simons

We present a unified analysis of the self-dual, second order, topologically massive and the recently introduced fourth-order models of massive gravity in 3D. We show that there is a family of first-order actions which interpolate between these different single excitation models. We show how the master actions are related by duality transformation. We construct by the same method the master action which relates the fourth-order new massive model with two excitations and the usual second-order model with Fierz–Pauli mass. We show that the more general model obtained by adding a Chern–Simons term to the new massive model is equivalent off-shell to the second-order spontaneously broken linearized massive gravity.

scholarly journals The holographic c-theorem and infinite-dimensional Lie algebras

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Eric A. Bergshoeff ◽  
Mehmet Ozkan ◽  
Mustafa Salih Zöğ
Keyword(s):  
Lie Algebra ◽  
Massive Gravity ◽  
Dynamical Theory ◽  
Three Dimensions ◽  
Gravity Models ◽  
Algebra Structure ◽  
Infinite Dimensional ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Infinite Dimensional Lie Algebra

Abstract We discuss a non-dynamical theory of gravity in three dimensions which is based on an infinite-dimensional Lie algebra that is closely related to an infinite-dimensional extended AdS algebra. We find an intriguing connection between on the one hand higher-derivative gravity theories that are consistent with the holographic c-theorem and on the other hand truncations of this infinite-dimensional Lie algebra that violate the Lie algebra structure. We show that in three dimensions different truncations reproduce, up to terms that do not contribute to the c-theorem, Chern-Simons-like gravity models describing extended 3D massive gravity theories. Performing the same procedure with similar truncations in dimensions larger than or equal to four reproduces higher derivative gravity models that are known in the literature to be consistent with the c-theorem but do not have an obvious connection to massive gravity like in three dimensions.

scholarly journals Can We Compare Solidarity Across Europe? What, Why, When, and How to Assess Exact and Approximate Equivalence of First- and Second-Order Factor Models

2021 ◽  
Vol 3 ◽  
Author(s):  
Vera Lomazzi
Keyword(s):  
Factor Model ◽  
Second Order ◽  
Three Dimensions ◽  
Alignment Method ◽  
Cross Sectional ◽  
Political Values ◽  
First Order ◽  
Measurement Models ◽  
European Values ◽  
Order Factor

Although measurement invariance is widely considered a precondition for meaningful cross-sectional comparisons, substantive studies have often neglected evaluating this assumption, thereby risking drawing conclusions and making theoretical generalizations based on misleading results. This study offers a theoretical overview of the key issues concerning the measurement and the comparison of socio-political values and aims to answer the questions of what must be evaluated, why, when, and how to assess measurement equivalence. This paper discusses the implications of formative and reflective approaches to the measurement of socio-political values and introduces challenges in their comparison across different countries. From this perspective, exact and approximate approaches to equivalence are described as well as their empirical translation in statistical techniques, such as the multigroup confirmatory factor analysis (MGCFA) and the frequentist alignment method. To illustrate the application of these methods, the study investigates the construct of solidarity as measured by European Values Study (EVS) and using data collected in 34 countries in the last wave of the EVS (2017–2020). The concept is captured through a battery of nine items reflecting three dimensions of solidarity: social, local, and global. Two measurement models are hypothesized: a first-order factor model, in which the three independent dimensions of solidarity are correlated, and a second-order factor model, in which solidarity is conceived according to a hierarchical principle, and the construct of solidarity is reflected in the three sub-factors. In testing the equivalence of the first-order factor model, the results of the MGCFA indicated that metric invariance was achieved. The alignment method supported approximate equivalence only when the model was reduced to two factors, excluding global solidarity. The second-order factor model fit the data of only seven countries, in which this model could be used to study solidarity as a second-order concept. However, the comparison across countries resulted not appropriate at any level of invariance. Finally, the implications of these results for further substantive research are discussed.

Relating renormalizability of D-dimensional higher-order electromagnetic and gravitational models to the classical potential at the origin

2017 ◽  
Vol 32 (08) ◽  
pp. 1750048 ◽  
Author(s):  
Antonio Accioly ◽  
Gilson Correia ◽  
Gustavo P. de Brito ◽  
José de Almeida ◽  
Wallace Herdy
Keyword(s):  
Fourth Order ◽  
Massive Gravity ◽  
Higher Order ◽  
Sixth Order ◽  
Gravity Models ◽  
Local Models ◽  
Order Model ◽  
Functional Generator ◽  
Classical Potential ◽  
Real Poles

Simple prescriptions for computing the D-dimensional classical potential related to electromagnetic and gravitational models, based on the functional generator, are built out. These recipes are employed afterward as a support for probing the premise that renormalizable higher-order systems have a finite classical potential at the origin. It is also shown that the opposite of the conjecture above is not true. In other words, if a higher-order model is renormalizable, it is necessarily endowed with a finite classical potential at the origin, but the reverse of this statement is untrue. The systems used to check the conjecture were D-dimensional fourth-order Lee–Wick electrodynamics, and the D-dimensional fourth- and sixth-order gravity models. A special attention is devoted to New Massive Gravity (NMG) since it was the analysis of this model that inspired our surmise. In particular, we made use of our premise to resolve trivially the issue of the renormalizability of NMG, which was initially considered to be renormalizable, but it was shown some years later to be non-renormalizable. We remark that our analysis is restricted to local models in which the propagator has simple and real poles.

scholarly journals Modified Gravity Models Admitting Second Order Equations of Motion

Entropy ◽  
2015 ◽  
Vol 17 (12) ◽  
pp. 6643-6662 ◽  
Author(s):  
Aimeric Colléaux ◽  
Sergio Zerbini
Keyword(s):  
Modified Gravity ◽  
Equations Of Motion ◽  
Second Order ◽  
Gravity Models ◽  
Second Order Equations ◽  
Modified Gravity Models

scholarly journals Massive gravity with mass term in three dimensions

2009 ◽  
Vol 79 (10) ◽  
Author(s):  
Masashi Nakasone ◽  
Ichiro Oda
Keyword(s):  
Mass Term ◽  
Massive Gravity ◽  
Three Dimensions

scholarly journals Modeling of rose coco beans using twenty four points optimum second order rotatable design

2017 ◽  
Vol 5 (2) ◽  
pp. 96
Author(s):  
Isaac Tum ◽  
John Mutiso ◽  
Joseph Koske
Keyword(s):  
Response Surface ◽  
Maximum Yield ◽  
Second Order ◽  
Three Dimensions ◽  
Coefficient Of Determination ◽  
Yield Response ◽  
Efficient Production ◽  
Phosphorus And Potassium ◽  
Nitrogen Phosphorus ◽  
Rotatable Design

The response surface methodology (RSM) is a collection of mathematical and statistical techniques useful for the modeling and analysis of problems in which a response of interest is influenced by several variables, and the objective is to optimize the response. The objective of the study was to model the rose coco beans (Phaseolus vulgaris) through an existing A-optimum and D-efficient second order rotatable design of twenty four points in three dimensions in a greenhouse setting using three inorganic fertilizers, namely, nitrogen, phosphorus and potassium. Thus, the objective of the study was accomplished using the calculus optimum value of the free/letter parameter f=1.1072569. This was done by estimating the parameters via least square's techniques, by making available for the yield response of rose coco beans at calculus optimum value design for the first time. The results showed that, the three factors: nitrogen, phosphorus, and potassium contributed significantly on the yield of rose coco beans (p<0.05). In GP3G, the second-order model was adequate for 1% level of significance with p value of 0.0034. The analysis of variance (ANOVA) of response surface for rose coco yield showed that this design was adequate due to satisfactory level of a coefficient of determination, R2, 0.8066 and coefficient variation, CV was 10.30. This study demonstrated the importance of statistical methods in the optimal and efficient production of rose coco beans. We do recommend a randomize screening of all the fertilizer components with which it has influence on rose coco beans be done to ascertain the right initial amount of each fertilizer that could achieve maximum yield than this study realized.

scholarly journals Development of the high-order decoupled direct method in three dimensions for particulate matter: enabling advanced sensitivity analysis in air quality models

2012 ◽  
Vol 5 (2) ◽  
pp. 355-368 ◽  
Author(s):  
W. Zhang ◽  
S. L. Capps ◽  
Y. Hu ◽  
A. Nenes ◽  
S. L. Napelenok ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Particulate Matter ◽  
Air Quality ◽  
Direct Method ◽  
Statistical Significance ◽  
Second Order ◽  
High Order ◽  
Three Dimensions ◽  
So2 Emissions ◽  
Aerosol Module

Abstract. The high-order decoupled direct method in three dimensions for particulate matter (HDDM-3D/PM) has been implemented in the Community Multiscale Air Quality (CMAQ) model to enable advanced sensitivity analysis. The major effort of this work is to develop high-order DDM sensitivity analysis of ISORROPIA, the inorganic aerosol module of CMAQ. A case-specific approach has been applied, and the sensitivities of activity coefficients and water content are explicitly computed. Stand-alone tests are performed for ISORROPIA by comparing the sensitivities (first- and second-order) computed by HDDM and the brute force (BF) approximations. Similar comparison has also been carried out for CMAQ sensitivities simulated using a week-long winter episode for a continental US domain. Second-order sensitivities of aerosol species (e.g., sulfate, nitrate, and ammonium) with respect to domain-wide SO2, NOx, and NH3 emissions show agreement with BF results, yet exhibit less noise in locations where BF results are demonstrably inaccurate. Second-order sensitivity analysis elucidates poorly understood nonlinear responses of secondary inorganic aerosols to their precursors and competing species. Adding second-order sensitivity terms to the Taylor series projection of the nitrate concentrations with a 50% reduction in domain-wide NOx or SO2 emissions rates improves the prediction with statistical significance.

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