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This article investigates the impact of previous epidemics on rural development and convergence, and identifies the impact's mechanism based on convergence tests. Using a balanced panel of 31 provinces, the empirical results from 2002 to 2019 show that epidemics decelerated convergence in rural per capita income. The mechanism analysis shows that the accelerated divergence in wages and the decelerated convergence in business income were the major drivers, which also led to decelerated convergence in rural per capita consumption. Although epidemics have not threatened rural food consumption and the Engel coefficient of rural households, these two indicators of basic living needs have failed to achieve convergence across regions. The overall impact of an epidemic on convergence in rural-urban income disparity has also been insignificant, indicating that epidemics have affected rural and urban development simultaneously. Finally, COVID-19 is likely to decelerate convergence in rural income, rural consumption, and urban income.

The study assesses the per capita output (PCO) convergence hypothesis across 33 Indian states/Union‐Territories at the aggregate and sectoral level by using weak‐sigma and clustering‐algorithm convergence tests for the period of 2011–2012 to 2018–2019. Results from the weak‐sigma convergence test show mixed evidence. This suggests that Indian states are not converging to single steady‐state. Further, results revealed the existence of multiple club‐convergence at aggregate and sectoral level after applying the clustering‐algorithm test. Results also show that the service sector is converging faster than the industry and agriculture sectors. Our findings recommend that sector‐specific policies need to be adopted to boost the aggregate PCO at club level.

In this study, the method of fundamental solutions (MFS), which is a boundary-type meshfree method, is applied for solving two-dimensional stationary anisotropic thermoelastic problems. Because of the semi-analytic nature of the MFS, very accurate solutions can be obtained by this method. The solution of the problem is decomposed into homogeneous and particular solutions. The homogeneous solution is expressed in terms of the fundamental solutions of the anisotropic elastostatic problem. The particular solution corresponds to the effects of the temperature change in the domain of the problem. For cases with a quadratic distribution of the temperature change in the domain, the particular solution is derived in an explicit form. For cases with an arbitrary temperature change distribution, the thermal load is approximated by radial basis functions (RBFs), particular solutions of which are derived analytically. Three numerical examples in simply- and multiply-connected domains under plane stress and plane strain conditions are presented to verify the accuracy of the proposed method. The effects of some parameters, such as the number of source points and the magnitude of the location parameter of source points on the results are investigated. From the numerical results, it is observed that very accurate results can be obtained by the proposed MFS in problems with very complicated temperature change distribution. The numerical convergence tests performed in this study shows that the proposed MFS with a small number of source points can results in solutions that are comparable with the FEM solutions obtained using a large number of nodes.

We examine the relationship between fossil fuel (FF) endowments and economic convergence. Countries with plausibly exogenous FF endowments show patterns of convergence, as indicated by standard convergence tests. By contrast, we fi nd no evidence of convergence among countries without FF endowments. These patterns of convergence are consistent across measures of physical capital, human capital, and total factor productivity. We discuss the implications of this result for economic development and comment on its implications for global climate policy.

The Uzawa method is an iterative approach to find approximated solutions to the Stokes equations. This method solves velocity variables involving augmented Lagrangian operator and then updates pressure variable by Richardson update. In this paper, we construct a new version of the Uzawa method to find optimal numerical solutions of the Stokes equations including corner singularities. The proposed method is based on the dual singular function method which was developed for elliptic boundary value problems. We estimate the solvability of the proposed formulation and special orthogonality form for two singular functions. Numerical convergence tests are presented to verify our assertion.

The goal of this article is to answer two questions: Has world agricultural convergence occurred? If not, how can this goal be fulfilled? This article introduces a model averaging method to consider both a parametric and a semi-parametric SFA model to better estimate technical efficiency. Then, three types of convergence tests are employed to check if world agricultural catch-up occurs and to determine the degree of convergence across different groups of countries. The empirical results on a balanced panel of 126 countries from 1970-2014 show that world agricultural convergence has not occurred. This article then investigates the situations in different groups of countries and discusses how to use international trade, irrigation system, and structural transformation to improve agricultural efficiency and to diminish the efficiency gap among different countries in the future.

We recast a network generating partial differential equation system into a singular limit of a dissipative gradient flow model, which not only identifies the consistent physical boundary conditions but also generates networks. We then develop a set of structure-preserving numerical algorithms for the gradient flow model. Using the energy quadratization (EQ) method, we reformulate the gradient flow system into an equivalent one with a quadratic energy density by introducing auxiliary variables. Subsequently, we devise a series of fully discrete, linear, second order, energy-production-rate preserving, finite difference algorithms to solve the EQ-reformulated PDE system subject to various compatible boundary conditions. We show that the numerical schemes are energy-production-rate preserving for any time steps. Numerical convergence tests are given to validate the accuracy of the fully discrete schemes. Several 2D numerical examples are given to demonstrate the capability of the schemes in predicting network generating phenomena with the gradient flow PDE system, especially, the original network generating PDE model.

The present study aimed to identify the errors made by pre-service elementary mathematics teachers while investigating the convergence of infinite series. A qualitative exploratory case study design was used with a total of 43 undergraduate students. Data were obtained from a test administered in a paper-and-pencil form consisting of seven open-ended questions. The data analysis was done using descriptive and content analysis techniques. Findings were presented as follows: inappropriate test selections; failure to check convergence criteria; incorrect use of a comparison test; limit comparison test error; re-test convergence test results; considering ∑ as a multiplicative function; misunderstanding of special series; considering that series has no character when the convergence test is inconclusive; confusing sequences with series; misunderstanding of the nth-term test; misinterpretation of convergence test results. Findings showed that students with insufficient procedural knowledge had difficulty in solving the given problem even if they understood it, whereas those with insufficient conceptual knowledge could not literally understand what they did even if they solved the problem. Therefore, the establishment of a moderate balance between procedural and conceptual knowledge in the learning of the convergence of series is essential in reducing the errors or learning difficulties for developing deep mathematical understanding

Mathematical models of oceanology are equations of the Navier-Stokes type, the construction of stable effective algorithms for their solution is associated with certain difficulties due to the well-known problems of setting boundary conditions, the presence of integro-differential relations, etc. In practice, when solving problems of oceanology, finitedifference methods are widely used, but there are no works in the literature devoted to theoretical studies of the stability and convergence of the algorithms used. In most cases, stability and convergence tests are established through computational experiments. Therefore, we believe that the development and mathematical substantiation of converging methods for solving the system of oceanology equations are urgent problems of computational mathematics. The paper studies variants of the fictitious domain method for a nonlinear ocean model. An existence theorem for the convergence of solutions to approximate models obtained using the fictitious domain method is investigated. An unimprovable estimate of the rate of convergence of the solution of the fictitious domain method is derived.

Agricultural income support is to remain one of the main objectives of the European Union (EU)’s Common Agricultural Policy (CAP) after 2020. Subsidies contribute to increases in income, but the occurrence of income convergence between member states remains questionable. The aim of this article was to assess the phenomenon of convergence of agricultural income (labour factor remuneration) against a background of income in the broader economy. Eurostat data for the years 2001-2019 were used. Convergences were searched for using basic methods (beta and sigma convergence tests), as well as a stochastic framework (Pesaran unit root test) and the robust Phillips and Sul convergence test for comparison. These analyses indicate that there is convergence in the EU’s agricultural sector, specifically in terms of labour compensation, but also that this convergence is merely relative. This means that while countries’ income growth rates converge, their real income levels do not move to the same level. This conclusion may be an argument for the need to further equalise direct payment rates. The Phillips and Sul test results indicate that incomes in the overall economy are characterised by divergence, but it is possible to identify four convergence clubs.

This exploratory study extends the literature on the convergence of per capita carbon dioxide emissions in analyzing stochastic and club convergence within a panel framework for developing countries. The results from Pesaran (Journal of Applied Econometrics, 22(2), 265-312, 2007) and Bai and Carrion-i-Silvestre (Review of Economic Studies, 76(2), 471-501, 2009) panel unit root tests with allowance for cross-sectional dependence confirm stochastic convergence for low-income, lower middle-income, and combined country panels. Further analysis using the nonlinear time-varying factor model of Phillips and Sul (Econometrica, 75(6), 1771-1855, 2007; Journal of Applied Econometrics, 24(7), 1153-1185, 2009) to test for convergence reveals the emergence of multiple convergence clubs within each of the three country panels examined. We observe geographic proximity among many of the countries within the respective convergence clubs.

Parallel robots are usually required to perform real-time tracking control tasks in the presence of external disturbances in the complex environment. Conventional zeroing neural-dynamics (ZNDs) provide an alternative solution for the real-time tracking control of parallel robots due to its capacity of parallel processing and nonlinearity handling. However, it is still a challenge for the solution in a unified framework of the ZND to deal with the external disturbances, and simultaneously possess a finite-time convergence property. In this paper, a novel ZND model by exploring the super-twisting (ST) algorithm, named ST-ZND model, is proposed. The theoretical analyses on the global stability, finite-time convergence, as well as the robustness against the external disturbances are rigorously presented. Finally, the effectiveness and superiority of the ST-ZND model for the real-time tracking control of parallel robots are demonstrated by two illustrative examples, comparisons, and convergence tests.

This chapter introduces the fundamentals of weak convergence for real sequences. Definitions and examples are given. The Skorokhod representation theorem is proved and the chapter then considers the preservation of weak convergence under transformations. Next, the role of moments and characteristic functions is considered. In the leading case of random sums, the criteria for weak convergence and the concept of a stable distribution are studied.

This chapter concerns random sequences of functions on metric spaces. The main issue is the distinction between convergence at all points of the space (pointwise) and uniform convergence, where limit points are also taken into account. The role of the stochastic equicontinuity property is highlighted. Generic uniform convergence conditions are given and linked to the question of uniform laws of large numbers.

The analysis of convergence behavior with respect to emissions and measures of environmental quality can be categorized into four types of tests: absolute and conditional β-convergence, σ-convergence, club convergence, and stochastic convergence. In the context of emissions, absolute β-convergence occurs when countries with high initial levels of emissions have a lower emission growth rate than countries with low initial levels of emissions. Conditional β-convergence allows for possible differences among countries through the inclusion of exogenous variables to capture country-specific effects. Given that absolute and conditional β-convergence do not account for the dynamics of the growth process, which can potentially lead to dynamic panel data bias, σ-convergence evaluates the dynamics and intradistributional aspects of emissions to determine whether the cross-section variance of emissions decreases over time. The more recent club convergence approach tests the decline in the cross-sectional variation in emissions among countries over time and whether heterogeneous time-varying idiosyncratic components converge over time after controlling for a common growth component in emissions among countries. In essence, the club convergence approach evaluates both conditional σ- and β-convergence within a panel framework. Finally, stochastic convergence examines the time series behavior of a country’s emissions relative to another country or group of countries. Using univariate or panel unit root/stationarity tests, stochastic convergence is present if relative emissions, defined as the log of emissions for a particular country relative to another country or group of countries, is trend-stationary. The majority of the empirical literature analyzes carbon dioxide emissions and varies in terms of both the convergence tests deployed and the results. While the results supportive of emissions convergence for large global country coverage are limited, empirical studies that focus on country groupings defined by income classification, geographic region, or institutional structure (i.e., EU, OECD, etc.) are more likely to provide support for emissions convergence. The vast majority of studies have relied on tests of stochastic convergence with tests of σ-convergence and the distributional dynamics of emissions less so. With respect to tests of stochastic convergence, an alternative testing procedure accounts for structural breaks and cross-correlations simultaneously is presented. Using data for OECD countries, the results based on the inclusion of both structural breaks and cross-correlations through a factor structure provides less support for stochastic convergence when compared to unit root tests with the inclusion of just structural breaks. Future studies should increase focus on other air pollutants to include greenhouse gas emissions and their components, not to mention expanding the range of geographical regions analyzed and more robust analysis of the various types of convergence tests to render a more comprehensive view of convergence behavior. The examination of convergence through the use of eco-efficiency indicators that capture both the environmental and economic effects of production may be more fruitful in contributing to the debate on mitigation strategies and allocation mechanisms.

Obesity has become a serious public health problem in the last two decades and affects not only developed countries but also the developing world. To date, despite all attempts to stop its increase, obesity remains a serious social problem, and obesity-related diseases have a significant cost on the health system. In this paper, we investigate the convergence of obesity rates, overweight rates, and body mass index (BMI) across 35 OECD countries over the period 1975-2006. The empirical findings of the paper are expected to have important policy implications to better inform policymakers. In addition to the traditional convergence tests, this paper uses a newly developed LM based panel unit root test with endogenously determined structural breaks to test for the stochastic convergence. Given the shortcomings of traditional and stochastic convergence tests in light of the possibility of multiple equilibria associated with groups of countries following different convergence paths, the club convergence algorithm is also employed. Traditional cross-sectional tests show that both beta- and sigma-convergence of the variables of interest exist across sampled countries. Moreover, the univariate LM unit root test results provide support for convergence in the relative BMIs, obesity rates, and overweight rates for a majority of the OECD countries. The club convergence test results, however, suggest the rejection of full panel club convergence only in BMI variables and overweight rates for females and the presence of a certain number of clubs for these variables.

Complex reaction networks can be generated with automated network generators from initial reactants and reaction rules. Reaction rule specification is central to network generation. These reaction rules are, at present, user-defined based on (intuitive) expert knowledge of chemistry and are often transferred from gas-phase to surface processes. The catalyst active site geometry is usually left out but is often responsible for selectivity. We propose a first-principles-based reaction mechanism generation framework using density functional theory (DFT) data of published reaction mechanisms. The framework "learns the chemistry" from published mechanisms. It can generate reaction networks not studied before, "flag" reactions not seen before for further DFT convergence tests, and easily reconcile differences between catalysts and reactants that may introduce new pathways never seen before. As such, it can be a diagnostic tool for data (mechanism) quality assessment and novel pathway discovery to new molecules. A software, the Python Reaction Stencil (pReSt), was developed for this purpose to wrap around automatic mechanism generation software. Multiple catalytic chemistries are considered to show the efficacy of the proposed framework.

The aim of this study is to identify whether there is a common house price trend across provincial capitals in Poland. The log t regression is the main method of analysis. Additionally, traditional convergence tests based on the concepts of β- and σ-convergence are used. The obtained results indicate that the cities do not share a common price in the long-run. There are, however, convergence clubs on both primary and secondary markets. In each club, house prices across cities tend to converge to their own steady state. Moreover, research on the driving forces of convergence reports that factors affecting housing prices differ among the clubs. Therefore, policymakers should adjust housing policies in accordance with the characteristics of a given club. In turn, the σ-convergence model demonstrated a very interesting finding, namely, a U-shape pattern of convergence, both on the primary and secondary markets. This pattern is strictly correlated with the level of prices on the markets.

PurposeThe purpose of the study is to examine the long-run convergence properties of condominium prices based on the ripple effect for five major US metropolitan areas (Boston, Chicago, Los Angeles, New York and San Francisco). Specifically, we test for both overall convergence in condominium prices and the possibility of distinct convergence clubs to ascertain the interdependence of geographically dispersed metropolitan condominium markets.Design/methodology/approachOur analysis uses two approaches to identify the convergence properties of condominium prices: the Lee and Strazicich (2003) unit root test with endogenous structural breaks and the Phillips and Sul (2007, 2009) time-varying nonlinear club convergence tests.FindingsThe Lee and Strazicich (2003) unit root tests identify two structural breaks in 2006 and 2008 with the rejection of the null hypothesis of a unit root and long-run convergence in condominium prices in the cases of Boston and New York. The Phillips and Sul (2007, 2009) club convergence test reveals the absence of overall convergence in condominium prices across all metropolitan areas, but the emergence of two distinct convergence clubs with clear geographical segmentation: on the east coast with Boston and New York and the west coast with Los Angeles and San Francisco while Chicago exhibits a non-converging path.Research limitations/implicationsThe results highlight the distinct geographical segmentation of metropolitan condominium markets, which provides useful information to local policymakers, financial institutions, real estate developers and real estate portfolio managers. The limitations of the research are the identification of the underlying sources for the convergence clubs identified due to the availability of monthly data for a number of potential variables.Practical implicationsThe absence of overall convergence in condominium prices, but the emergence of distinct convergence clubs that reflects the geographical segmentation of metropolitan condominium markets raises the potential for portfolio diversification.Originality/valueUnlike previous studies that have focused on single-family housing, this is the first study to examine the convergence of metropolitan area condominium prices.

Crystal plasticity-finite element method (CP-FEM) is now widely used to understand the mechanical response of polycrystalline materials. However, quantitative mesh convergence tests and verification of the necessary size of polycrystalline representative volume elements (RVE) are often overlooked in CP-FEM simulations. Mesh convergence studies in CP-FEM models are more challenging compared to conventional finite element analysis (FEA) as they are not only computationally expensive but also require explicit discretization of individual grains using many finite elements. Resolving each grains within a polycrystalline domain complicates mesh convergence study since mesh convergence is strongly affected by the initial crystal orientations of grains and local loading conditions. In this work, large-scale CP-FEM simulations of single crystals and polycrystals are conducted to study mesh sensitivity in CP-FEM models. Various factors that may affect the mesh convergence in CP-FEM simulations, such as initial textures, hardening models and boundary conditions are investigated. In addition, the total number of grains required to obtain adequate RVE is investigated. This work provides a list of guidelines for mesh convergence and RVE generation in CP-FEM modeling.

Strazicich and List (Are CO 2 Emission Levels Converging among Industrial Countries? Environmental and Resource Economics 2003; 24: 263–271) examine whether CO 2 emissions converge among the twenty-one industrial countries from 1960 to 1997. This study replicates their main results and performs a similar analysis on a more recent dataset and a new econometric method. Their findings are confirmed to a large extent.

Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov Chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution, and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and have to be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles which are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.

This study examines the long-term inequality in body mass index (BMI) based on convergence tests applied to a database of 172 countries recently published by the NCD Risk Factor Collaboration. First, we find that countries converge in clubs, which indicates that country disparities in BMIs will persist over time. Second, there are three and six convergence clubs in BMIs for female and male individuals, respectively. That is, we would not observe a single convergence pattern in body weights as the nutrition transition theory and the dietary convergence hypothesis seem to suggest. Females have only one healthy club (18.5 ≤ BMI 25) and two overweight clubs (BMI ≥ 25). Males have three healthy clubs and three overweight clubs. Third, the analysis of club convergence indicates that BMI inequality has increased due to the BMI growth observed in club 1 (the one with the highest average BMI and led by the US) in each gender group. Finally, potential determinants of BMI such as globalization, human capital, income, and urbanization are relevant to understand differences across clubs. We interpret the club convergence as the result of a heterogeneous integration of countries into the global economy, which is probably related to strong domestic preferences, policies designed to manage the impacts of globalization, and shifts in productive structures.

The concept of relative convergence, which requires the ratio of two time series to converge to unity in the long run, explains convergent behavior when series share commonly divergent stochastic or deterministic trend components. Relative convergence of this type does not necessarily hold when series share common time decay patterns measured by evaporating rather than divergent trend behavior. To capture convergent behavior in panel data that do not involve stochastic or divergent deterministic trends, we introduce the notion of weak σ -convergence, whereby cross section variation in the panel decreases over time. The paper formalizes this concept and proposes a simple-to-implement linear trend regression test of the null of no σ -convergence. Asymptotic properties for the test are developed under general regularity conditions and various data generating processes. Simulations show that the test has good size control and discriminatory power. The method is applied to examine whether the idiosyncratic components of 46 disaggregate personal consumption expenditure (PCE) price inflation items σ -converge over time, finding strong evidence of weak σ -convergence in these data. In a second application, the method is used to test whether experimental data in ultimatum games converge over successive rounds, again finding evidence in favor of weak σ -convergence. A third application studies convergence and divergence in US States unemployment data over the period 2001–2016.

In this study, we present a novel numerical model for simulating detonation waves on unstructured grids. In contrast to the conventional finite volume method (FVM), two types of moment comprising the volume-integrated average (VIA) and the point value (PV) at the cell vertex are treated as the evolution variables for the reacting Euler equations. The VIA is computed based on a finite volume formulation of the flux form where the conventional Riemann problem is solved by the HLLC Riemann solver. The PV is updated in a point-wise manner by using the differential formulation where the Roe solver is used to compute the differential Riemann problems. In order to increase the accuracy around discontinuities, numerical oscillations and dissipations are reduced using the boundary variation diminishing algorithm. Convergence tests demonstrated that the proposed model could achieve third-order accuracy with unstructured grids for reacting Euler equations. The high resolution property of the proposed method was verified based on simulations of several detonation wave propagation problems in two and three dimensions. In particular, the current model could resolve the cellular structures with fewer degrees of freedom for the unstable oblique detonation wave problem. These fine structures may be smoothed out by the conventional FVM due to the excessive amount of numerical dissipation errors. Importantly, a simulation of stiff detonation waves showed that the proposed method could capture the correct position of the reaction front whereas the conventional FVMs produced spurious phenomena. Thus, the proposed model can obtain highly accurate solutions for detonation problems on unstructured grids, which is highly advantageous for real applications involving complex geometrical configurations.

We study criteria for the uniform convergence of trigonometric series with general monotone coefficients. We also obtain necessary and sufficient conditions for a given rate of convergence of partial Fourier sums of such series.

This paper deals with the presentation of a general, variational principle as theoretical support for the development of simple and efficient triangular elements having only one displacement and two rotations at the corner nodes to model thin to thick plates based on the first order Reissner- Mindlin plate theory. The functional is a modified Hellinger–Reissner mixed expression in terms of the kinematic variables (transverse displacement w and rotations βx and βy), and independent transverse shear strains (γx and γy). The approximations of the five independent variables of the mixed formulation take into account the accumulated knowledge on existing performing 2D Timoshenko beams and triangular elements such as T3γs, MITC3, DKT, DST, DKMT. The present mixed variational support is useful, not only to give a unique theoretical support to the above existing elements, usually based on assumed natural strain formulations, but it allows also to propose new simple and efficient elements, here called BAK1, BAK2 and BAK3. The paper includes a detailed presentation of results of patch tests for very thin and very thick plates, for convergence of displacements, bending moments and shear forces, for clamped circular and simply supported square plates and for s-norm convergence tests considering regular and irregular meshes. Shear force distribution is also considered for situations with boundary layer effects.

The transport sector is a crucial bottleneck in the decarbonization challenge. To study the sector’s decarbonization potential in the wider systems perspective, we couple a large-scale integrated assessment model, Regionalized Model of INvestments and Development (REMIND), to a detailed transport model, Energy Demand Generator-Transport (EDGE-T). This approach allows the analysis of mobility futures in the context of long-term and global energy sector transformations, at a high level of modal and technological granularity and internal consistency. The runtime of the coupled system increases by ~ 15–20% compared with a REMIND standalone application, and first convergence tests are promising. To illustrate the capabilities of our modeling approach, we focus on a reference pathway for Europe. Preliminary results indicate that transport service demands grow in the next decades for both passenger and freight transport. Transport system emissions are expected to decrease in the same time range, due to a shift towards electric drivetrains, advanced vehicles, more efficient modes as well as a slight increase in the share of biofuels.

This work was supported in part by grants from the National Natural Science Foundation of China (#71874023, #71725001, #71910107002, #71771037, #71971042), and European Regional Development Fund (FEDER), European Union funds in the project TIN2016-75850-R., In real-life group decision-making (GDM) problems, the preferences given by decision-makers(DMs) are often incomplete, because the complexity of decision-making problems and the limitation of knowledge of DM make it difficult for DMs to take a determined evaluation of alternatives. In addition, preference relations provided by DMs are often heterogeneous because they always have different decision habits and hobbies. However, the consensus method for GDM under incomplete heterogeneous preference relations is rarely studied. For four common preference relations: utility values, preference orderings, and (incomplete) multiplicative preference relations and (incomplete) fuzzy preference relations, this paper proposes a geometrical method for consensus building in GDM. Specifically, we integrate incomplete heterogeneous preference structures using a similarity-based optimization model and set a corresponding geometrical consensus measurement. Then, preference modification and weighting processes are proposed to improve consensus degree. Finally, we conduct a comparison analysis based on a qualitative analysis and algorithm complexity analysis of existing consensus reaching methods. Numerical analyses and convergence tests show that our method can promote the improvement of the consensus degree in GDM, and has less time complexity than the previous methods. The proposed geometrical method is a more explainable model due to operability and simplicity., National Natural Science Foundation of China (NSFC) 71874023 71725001 71910107002 71771037 71971042, European Regional Development Fund (FEDER), European Union TIN2016-75850-R

The aim of this paper is to test for overall and cluster convergence of housing rents across Polish provincial capitals and to identify drivers of convergence club formation. In order to achieve the goal of the study, several novel convergence tests were used, including the Kong et al. (J Econom 209:185–207, 2019. https://doi.org/10.1016/j.jeconom.2018.12.022) and Phillips and Sul (Econometrica 75:1771–1855, 2007. https://doi.org/10.1111/j.1468-0262.2007.00811.x) approaches. Moreover, club convergence analysis was carried out in four different configurations, varying in the technique of trend component extraction from the data. In particular, three well-known methods of time series decomposition were used, i.e. the Hodrick–Prescott, Butterworth and Christiano–Fitzgerald filters, as well as the most recent boosted Hodrick–Prescott filter. The results indicated that rental prices across the studied cities do not share a common path in the long run. It is possible, however, to identify convergence clubs where rents are moving towards a club-specific steady state. Detailed analysis of the structure of estimated clusters showed that data filtering using the boosted Hodrick–Prescott method leads to the most reliable allocation of cities to convergence clubs. Moreover, the estimation of logit models revealed that the likelihood of any two cities belonging to the same convergence club depends mainly on similar levels in terms of the unemployment rate, housing stock, city area, and the number of students. Finally, recommendations for local and national policy-makers concerning the development of the rental market have been formulated, particularly in the areas of urban land-use planning policy, housing legislation and public–private partnerships.

We present a very simple benchmark problem for the numerical methods of the Cahn–Hilliard (CH) equation. For the benchmark problem, we consider a cosine function as the initial condition. The periodic sinusoidal profile satisfies both the homogeneous and periodic boundary conditions. The strength of the proposed problem is that it is simpler than the previous works. For the benchmark numerical solution of the CH equation, we use a fourth-order Runge–Kutta method (RK4) for the temporal integration and a centered finite difference scheme for the spatial differential operator. Using the proposed benchmark problem solution, we perform the convergence tests for an unconditionally gradient stable scheme via linear convex splitting proposed by Eyre and the Crank–Nicolson scheme. We obtain the expected convergence rates in time for the numerical schemes for the one-, two-, and three-dimensional CH equations.

Measurements of the Ly$\alpha$ forest based on large numbers of quasar spectra from sky surveys such as SDSS/eBOSS accurately probe the distribution of matter on small scales and thus provide important constraints on several ingredients of the cosmological model. A main summary statistic derived from those measurements is the one-dimensional power spectrum, P1D, of the Ly$\alpha$ absorption. However, model predictions for P1D rely on expensive hydrodynamical simulations of the intergalactic medium, which was the limiting factor in previous analyses. Datasets from upcoming surveys such as DESI will push observational accuracy near the 1%-level and probe even smaller scales. This observational push mandate seven more accurate simulations as well as more careful exploration of parameter space. In this work we evaluate the robustness and accuracy of simulations and the statistical framework used to constrain cosmological parameters. We present a comparison between the grid-based simulation code Nyx and SPH-based code Gadget in the context ofP1D. In addition, we perform resolution and box-size convergence tests using Nyx code. We use a Gaussian process emulation scheme to reduce the number of simulations required for exploration of parameter space without sacrificing the model accuracy. We demonstrate the ability to produce unbiased parameter constraints in an end-to-end inference test using mock eBOSS- and DESI-like data, and we advocate for the usage of adaptive sampling schemes as opposed to using a fixed Latin hypercube design., Comment: 36 pages, 17 figures, accepted for publication in JCAP

International audience; This study compares GDP per capita levels and growth rates across 17 advanced economies over the period 1890–2013 using an accounting breakdown and runs Phillips and Sul (Econometrica 75(6):1771–1855, 2007) convergence tests. An overall convergence process has been at work among advanced economies, mainly after WWII, driven mostly by capital intensity and then TFP, while trends in hours worked and employment rates are disparate. However, this convergence process came to a halt during technology shocks, during the two world wars and since the 1990s, with the convergence of advanced economies stopping far from the level of US GDP per capita.

Algorithmic model tuning is a promising approach to yield the best possible performance of multiscale multi-phase atmospheric models once the model structure is fixed. We are curious about to what degree one can trust the algorithmic tuning process. We approach the problem by studying the convergence of this process in a semi-realistic case. Let us denote M(x0;θd) as the default model, where x0 and θd are the initial state and default model parameter vectors, respectively. A necessary condition for an algorithmic tuning process to converge in a fully-realistic case is that the default model is recovered if the tuning process is initialised with perturbed model parameters θ and the default model forecasts are used as pseudo-observations. In this paper we study the circumstances where this condition is valid by carrying out a large set of convergence tests using two different tuning methods and the OpenIFS model. These tests are interpreted as guidelines for algorithmic model tuning applications.The results of this study can be used as recipe for maximising efficiency of algorithmic tuning. In the convergence tests, maximised efficiency was reached with using ensemble initial conditions, cost function that covers entire model domain, short forecast length and medium-sized ensembles.

This research deals with the problem of agricultural land market efficiency using the spatial market integration concept as well as the present value (PV) model. Empirically, it aims to test the convergence of agricultural land prices across Polish provinces. In order to check the law of one price (LOP), good-quality, medium-quality and bad-quality land sales markets are examined separately. Furthermore, this study is complemented by an analysis of the drivers behind agricultural land price convergence. The main method of testing price convergence is the log t regression. The latter was performed in two configurations, i.e., based on trend components of time series extracted using the Hodrick&ndash, Prescott filter and the Hamilton filter. Additionally, traditional &beta, and &sigma, convergence tests were applied. The obtained results indicated that agricultural land prices tend to converge in relative terms, which means that the provinces share a common long-run growth path. This finding and estimates of traditional convergence tests prove the increasing integration in the agricultural land market in Poland. There is no evidence, however, to support the conclusion that the absolute version of the long-run LOP holds. Moreover, using dynamic fixed effects models, it was identified that for good-, medium- and bad-quality land prices almost the same drivers of convergence apply. The only differences concern the strength of the influence of independent variables on prices of farmland of various types. Additionally, bad-quality land prices are the only ones which are affected by livestock density. Furthermore, estimates of the present value model finally confirmed that the agricultural land sales market in Poland cannot be considered as efficient.

Measurement of diminishing or divergent cross section dispersion in a panel plays an important role in the assessment of convergence or divergence over time in key economic indicators. Econometric methods, known as weak σ-convergence tests, have recently been developed (Kong, Phillips, & Sul, 2019) to evaluate such trends in dispersion in panel data using simple linear trend regressions. To achieve generality in applications, these tests rely on heteroskedastic and autocorrelation consistent (HAC) variance estimates. The present chapter examines the behavior of these convergence tests when heteroskedastic and autocorrelation robust (HAR) variance estimates using fixed-b methods are employed instead of HAC estimates. Asymptotic theory for both HAC and HAR convergence tests is derived and numerical simulations are used to assess performance in null (no convergence) and alternative (convergence) cases. While the use of HAR statistics tends to reduce size distortion, as has been found in earlier analytic and numerical research, use of HAR estimates in nonparametric standardization leads to significant power differences asymptotically, which are reflected in finite sample performance in numerical exercises. The explanation is that weak σ-convergence tests rely on intentionally misspecified linear trend regression formulations of unknown trend decay functions that model convergence behavior rather than regressions with correctly specified trend decay functions. Some new results on the use of HAR inference with trending regressors are derived and an empirical application to assess diminishing variation in US State unemployment rates is included.

The predator-prey model is powerful mathematical tool to describe the dynamics of biological systems and promote research on biological populations. In this paper, we present a lumped mass finite element method for solving the predator-prey models on surfaces. The main purpose of the proposed method is to overcome the difficulty of the positivity preservation of the solutions. Based on positivity preservation results, we investigate the stabilities of semi-discrete and fully discrete approximations. Besides, numerical simulations are considered to illustrate the feasibility of the numerical method by convergence tests. Two classical phenomena of the predator-prey model are simulated on three different implicit surfaces.

This paper aims to examine the degree of dispersion in the loan pricing of commercial banks and its association with competitive conditions. To this end, an indexation mechanism processing a novel bank-level dataset is proposed to quantify the lending rate variability in general-purpose, vehicle, and housing loans for the period January 2007-April 2020. In panel convergence tests, we show that there exists heterogeneity in long-term co-movements in banks’ loan pricing, while periods following the tightening in financial conditions display short-term deviations from general tendencies demonstrated by dispersion indices. The methodological setting also entails the construction of competition indicators for total and segment-based credit market developments. The competitive conditions monitored by Herfindahl-Hirschman Indicator (HHI) present that housing and vehicle loan segments have been concentrated in recent years. Quantile regression results further validate that improvements in the competition are associated with a lower level of lending rate dispersion in housing and vehicle segments in a statistically significant manner, whereas this relation is not applicable for general-purpose loans.