Concluding Remarks on the Negative Natural Rate of Interest

The Great Divergence: The period of production T is not rising anymore. The “waiting period” Z is rising over time with the rising standard of living and rising life expectancy, and this is the case worldwide. In the interest of full employment, the public debt periodD has to compensate for this divergence: T = Z − D. Using an extrapolation procedure that we have developed and the available empirical data, we calculate total private wealth in the OECD plus China region. Net public debt already accounts for nearly half of private wealth today. COVID-19 increases the optimal steady-statepublic debt period. Both our theory and our empirical findings are increasingly confirmed by the work of other economists: for example, by Lawrence Summers’secular stagnation thesis and by the study of Jordà, Schularick and others on the secular evolution of private wealth.

A Privacy-Preserving Message Forwarding Framework with key caching for low latency

For exchanging messages over opportunistic exchanges in cloud calculating-empowered Internet of Things (IoT), opportunistic Cloud of Things (CoT) is encouraging for customers by means of an emergent conveying policy. In recent times, for predicting upcoming interactions by the determination of enlightening message promoting effectiveness as well as system quantity, several informally-awake structures have been placed onward, influencing consumers’ communal features as well as interaction account. Nevertheless, in the extrapolation procedure as well as communication phase of unprincipled CoT distinct secrecy remains commonly ignored. Towards assuring distinct secrecy as well as improving communication effectiveness, in this broadsheet, we develop a secrecy preservative communication promoting context aimed at unprincipled CoT. For improving transmission effectiveness of incurable customers, we mainly assemble twofold-level design of a cloud server. The proposed method can efficiently safeguard distinct secrecy through incorporating a safety-centered flexibility extrapolation procedure using an overpowering assessment procedure. This paper also introduces data key caching to reduce the latency during the transmission process. The proposed method outperforms the conventional methods.

A Privacy-Preserving Message Forwarding Framework with Key Caching for Low Latency Cloud of Things

For exchanging messages over opportunistic exchanges in cloud calculating-empowered Internet of Things (IoT), opportunistic Cloud of Things (CoT) is encouraging for customers by means of an emergent conveying policy. In recent times, for predicting upcoming interactions by the determination of enlightening message promoting effectiveness as well as system quantity, several informally-awake structures have been placed onward, influencing consumers’ communal features as well as interaction account. Nevertheless, in the extrapolation procedure as well as communication phase of unprincipled CoT distinct secrecy remains commonly ignored. Towards assuring distinct secrecy as well as improving communication effectiveness, in this broadsheet, we develop a secrecy preservative communication promoting context aimed at unprincipled CoT. For improving transmission effectiveness of incurable customers, we mainly assemble twofold-level design of a cloud server. The proposed method can efficiently safeguard distinct secrecy through incorporating a safety-centered flexibility extrapolation procedure using an overpowering assessment procedure. This paper also introduces data key caching to reduce the latency during the transmission process. The proposed method outperforms the conventional methods.

Embedding Approach to Modeling Electromagnetic Fields in a Complex Two-Dimensional Environment

An approach is presented to combine the response of a two-dimensionally inhomogeneous dielectric object in a homogeneous environment with that of an empty inhomogeneous environment. This allows an efficient computation of the scattering behavior of the dielectric cylinder with the aid of the CGFFT method and a dedicated extrapolation procedure. Since a circular observation contour is adopted, an angular spectral representation can be employed for the embedding. Implementation details are discussed for the case of a closed 434 MHz microwave scanner, and the accuracy and efficiency of all steps in the numerical procedure are investigated. Guidelines are proposed for choosing computational parameters such as truncation limits and tolerances. We show that the embedding approach does not increase the CPU time with respect to the forward problem solution in a homogeneous environment, if only the fields on the observation contour are computed, and that it leads to a relatively small increase when the fields on the mesh are computed as well.

Blow-up phenomena in the model of a space charge stratification in semiconductors: numerical analysis of original equation reduction to a differential-algebraic system

Показана эффективность одной из методик численной диагностики разрушения решения на примере решения нелинейного уравнения cоболевского типа, описывающего стратификацию объемного заряда в полупроводниках. В процессе численного исследования этой задачи использовался подход, основанный на сведении исходного уравнения в частных производных к дифференциально-алгебраической системе с последующим решением этой системы с помощью одностадийной схемы Розенброка с комплексным коэффициентом. Численная диагностика разрушения точного решения указанного уравнения основывалась на методике вычисления апостериорной асимптотически точной оценки погрешности, получаемой при вычислении приближенного решения на последовательно сгущающихся сетках. The efficiency of one of the methods for the numerical diagnostics of solution's blow-up is shown using the example of solving a nonlinear Sobolev-type equation that describes a space charge stratification in semiconductors. An approach to reduce the original partial differential equation to a differential-algebraic system is used. This system is solved by the Rosenbrock scheme with a complex coefficient. The numerical diagnostics of solution's blow-up is based on the Richardson extrapolation procedure.

Generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions

Purpose – The purpose of this paper is to present outcomes of efforts made over the last 20 years to extend the applicability of the Richardson extrapolation procedure to numerical predictions of multidimensional, steady and unsteady, fluid flow and heat transfer phenomena in regular and irregular calculation domains. Design/methodology/approach – Pattern-preserving grid-refinement strategies are proposed for mathematically rigorous generalizations of the Richardson extrapolation procedure for numerical predictions of steady fluid flow and heat transfer, using finite volume methods and structured multidimensional Cartesian grids; and control-volume finite element methods and unstructured two-dimensional planar grids, consisting of three-node triangular elements. Mathematically sound extrapolation procedures are also proposed for numerical solutions of unsteady and boundary-layer-type problems. The applicability of such procedures to numerical solutions of problems with curved boundaries and internal interfaces, and also those based on unstructured grids of general quadrilateral, tetrahedral, or hexahedral elements, is discussed. Findings – Applications to three demonstration problems, with discretizations in the asymptotic regime, showed the following: the apparent orders of accuracy were the same as those of the numerical methods used; and the extrapolated results, measures of error, and a grid convergence index, could be obtained in a smooth and non-oscillatory manner. Originality/value – Strict or approximate pattern-preserving grid-refinement strategies are used to propose generalized Richardson extrapolation procedures for estimating grid-independent numerical solutions. Such extrapolation procedures play an indispensable role in the verification and validation techniques that are employed to assess the accuracy of numerical predictions which are used for designing, optimizing, virtual prototyping, and certification of thermofluid systems.

Multinational Production: Data and Stylized Facts

We present a comprehensive data set on the bilateral activity of multinational firms, with focus on two variables: affiliate revenues and the number of affiliates across country pairs. Our basic data are from UNCTAD and include 59 countries, an average over 1996-2001. We implement an extrapolation procedure that fills in missing values using, alternately, FDI stocks and the bilateral number of M&A transactions. Our dataset allows for the analysis of new patterns of multinational production activities across countries, by taking into account firm rather than balance of payment variables, and both the intensive and extensive margins of multinational activities.