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The paper deals with the economic measurements of the market value of enterprise assets, which are of great importance for their effective management. The use of more accurate economic measurements is an integral part of an optimal strategy to manage business assets. Therefore, reduction of evaluation results uncertainty is a necessary condition for effective management. To achieve mentioned goals, the paper aims to determine the mathematical base for the assets valuation methodology of value/depreciation that change over time, which can be applied to its dynamic objective quantitative analysis. The basic hypothesis suggests that all tangible assets, characterized by removable depreciation, are inclined to a negative periodic depreciation during short inter-service periods when remedial repair works are carried out to eliminate depreciation. The methodical approaches concerning a mathematical description of assets value/depreciation dynamics are considered. It is shown that both traditional, progressive and regressive value/depreciation dynamics models change over time. They do not correspond to the actual state since they do not take into account increased objects value and negative periodic depreciation. To evaluate value/depreciation change over time more precisely, a new kind of mathematical model is proposed, which equations take into account the opposite signs of periodic depreciation during operational service periods and non-operational inter-service periods. It is proved that the actual indicators of fair market value and periodic depreciation of enterprise assets can be determined with higher reliability based on a new mathematical model.
AcknowledgmentsComments from the editor and anonymous referees have been gratefully acknowledged. The authors are grateful to the Ministry of Education and Science of Ukraine for financial support, which made it possible to carry out this study within the state budget topic "Value estimation and assessing technology readiness for transfer from universities to the business environment" (2019–2021).

More than sixty-five years have passed since Michal Kalecki (1935) published one of the first formal mathematical models of business cycles. His paper presents a closed-form analytic solution. This characteristic, among others, sets Kalecki's work apart from that of contemporary literary business cycle theorists such as Friedrich A. Hayek (1935) and John Maynard Keynes (1936).

Recent campaigns have demonstrated the importance of dynamic elements in affecting the selection of presidential nominees. This paper develops a mathematical model to analyze these dynamics. The heart of the model is the assumed relationship between the ability to acquire resources and success in primaries and caucuses. The expenditure of resources leads to greater electoral success, while greater electoral success (in particular, exceeding expectations in a primary or caucus) leads to greater resource-gathering capabilities. A difference equation model of these relationships is proposed. I prove that any campaign of this form is necessarily unstable, which implies that most candidates will be "winnowed out" necessarily, while only a very few, but at least one candidate, will necessarily "have momentum." This result is true whether there are two or many contenders. However, I also argue that the larger the number of candidates, the stronger the dynamic forces, and thus the more rapid the "winnowing out" process.

The current world financial scene indicates at an intertwined and interdependent relationship between financial market activity and economic health. This book explains how the economic messages delivered by the dynamic evolution of financial asset returns are strongly related to option prices. The Black Scholes framework is introduced and by underlining its shortcomings, an alternative approach is presented that has emerged over the past ten years of academic research, an approach that is much more grounded on a realistic statistical analysis of data rather than on ad hoc tractable continuous time option pricing models. The reader then learns what it takes to understand and implement these option pricing models based on time series analysis in a self-contained way. The discussion covers modeling choices available to the quantitative analyst, as well as the tools to decide upon a particular model based on the historical datasets of financial returns. The reader is then guided into numerical deduction of option prices from these models and illustrations with real examples are used to reflect the accuracy of the approach using datasets of options on equity indices.

The proposition is tested that the more libertarian a nation, the less its internal, foreign, & dyadic violence. The macrotheory concerning the social field of libertarianism & the antifield of totalitarianism is presented, along with an associated mathematical model. This model is used to explain the inverse relationship between libertarianism & collective violence. The microtheory comprising the conflict helix -- a movement from peaceful relations to social conflict & back, with progressively shorter periods of conflict -- is described conceptually, & the catastrophe theory model is presented to define the precise relationship of libertarianism to the conflict helix. 1 Table, 7 Figures, 15 References. AA

Intro -- Contents -- Cover -- Title -- Acknowledgments -- Foreword, Prólogo, Préface -- Executive Summary, Résumen, Résumé Analytique -- Abbreviations and Acronyms -- 1 The MDGs as a Benchmark for Development Effectiveness -- 2 Country Programs and the MDGs -- 3 Sector Programs and the MDGs -- 4 Global Programs and the MDGs -- 5 Conclusions -- Appendix -- Annexes -- Endnotes -- Bibliography -- Boxes -- Figures -- Tables.