Unusual square roots in the ghost-free theory of massive gravity

A crucial building block of the ghost free massive gravity is the square root function of a matrix. This is a problematic entity from the viewpoint of existence and uniqueness properties. We accurately describe the freedom of choosing a square root of a (non-degenerate) matrix. It has discrete and (in special cases) continuous parts. When continuous freedom is present, the usual perturbation theory in terms of matrices can be critically ill defined for some choices of the square root. We consider the new formulation of massive and bimetric gravity which deals directly with eigenvalues (in disguise of elementary symmetric polynomials) instead of matrices. It allows for a meaningful discussion of perturbation theory in such cases, even though certain non-analytic features arise.Comment: 24 pages; minor changes, final versio

Social Cost of Carbon: What Do the Numbers Really Mean?

Social cost of carbon (SCC) is estimated by integrated assessment models (IAM) and is widely used by government agencies to value climate policy impacts. While there is an ongoing debate about obtained numerical estimates and related uncertainties, little attention has been paid so far to the SCC calculation method itself. This work attempts to fill the gap by providing theoretical background and economic interpretation of the SCC calculation approach implemented in the open-source IAM DICE (Dynamic Integrated model of Climate and the Economy). Our analysis indicates that the present calculation method provides an approximation that might work pretty well in some cases, while in the other cases the estimated value substantially (by the factor of four) deviates from the "true" value. This deviation stems from the inability of the present calculation method to catch the linkages between two key IAM's components -- complex interconnected systems -- climate and economy, both influenced by emission abatement policies. Within the modeling framework of DICE, the presently estimated SCC valuates policy-uncontrolled emissions against economically unjustified consumption, which makes it irrelevant for application in climate-economic policies and, therefore, calls for a replacement by a more appropriate indicator. An apparent SCC alternative, which can be employed for policy formulation is the direct output of the DICE model -- the socially optimal marginal abatement cost (SMAC), which corresponds to technological possibilities at optimal level of carbon emissions abatement. In policy making, because of the previously employed implicit approximation, great attention needs to be paid to the use of SCC estimates obtained earlier

Competence–Based Support of Interaction between Business Network Members

In a complicated business network finding a supplier can be a very time consuming task. The technology of competence management is aimed to support such kind of tasks. The paper presents an approach to support interaction between business network members based on such technologies as competence management and knowledge management. The conceptual models of the context-driven competence management system and production network member competence profile are described. The usage of the competence management system is illustrated via an example from automotive industry

Shadow prices and optimal cost in economic applications

Shadow prices are well understood and are widely used in economic applications. However, there are limits to where shadow prices can be applied assuming their natural interpretation and the fact that they reflect the first order optimality conditions (FOC). In this paper, we present a simple ad-hoc example demonstrating that marginal cost associated with exercising an optimal control may exceed the respective cost estimated from a ratio of shadow prices. Moreover, such cost estimation through shadow prices is arbitrary and depends on a particular (mathematically equivalent) formulation of the optimization problem. These facts render a ratio of shadow prices irrelevant to estimation of optimal marginal cost. The provided illustrative optimization problem links to a similar approach of calculating social cost of carbon (SCC) in the widely used dynamic integrated model of climate and the economy (DICE)

Economic Aspects of Maritime Transport Development

In the article on the basis of the analysis of features of activity of the marine transport of Russia in 2010-2015, dynamics of its key economic indicators are defined tendencies of development of the marine transport in general and its structural components in the fast-changing environmental conditions