Unified Growth Theory contradicted by Latin American economic data.
problem Unified Growth Theory fails to explain Latin American economic growth.
method Analysis of historical economic growth data from Maddison.
result Unified Growth Theory is inconsistent with Latin American data.
Historical economic growth in countries of the former USSR is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used, but not analysed, during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malt…
Unified Growth Theory disproved by lack of economic takeoffs.
problem The absence of economic takeoffs from stagnation to growth.
method Analysis of historical economic growth data.
result Takeoffs from stagnation to growth never occurred.
Historical economic growth in Asia (excluding Japan) is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used (but not analysed) during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malthusian…
Unified Growth Theory debunked: economic growth is insecure and unsustainable.
problem The mystery of the great divergence in income per capita.
method Analysis of economic data to show that growth trajectories are increasing vertically over time.
result Unified Growth Theory is incorrect and promotes misleading concepts.
The Unified Growth Theory is a puzzling collection of myths based on illusions created by hyperbolic distributions. Some of these myths are discussed. The examination of data shows that the three stages of growth (Malthusian Regime, Post-Malthusian Regime and Modern Growth Regime) did not exist and that Industrial Revo…
One of the fundamental postulates of the Unified Growth Theory is the claimed existence of three distinctly different regimes of economic growth governed by three distinctly different mechanisms of growth. However, Galor also proposed that the timing of these regimes is different for developed countries and for less-de…
Mathematical study of excess growth rate connects info theory with finance.
problem Understanding the excess growth rate in portfolio theory.
method Axiomatic characterization theorems of excess growth rate in terms of relative entropy, Jensen's inequality gap, and logarithmic divergence.
result Established rich connections between information theory and finance.
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and "shape". We show t…
Galor's mysterious income growth rate is debunked, revealing data manipulation.
problem Mysterious sudden spurt in income per capita growth rate.
method Mathematical analysis of historical world economic growth data.
result The sudden spurt in income per capita growth rate is an artifact of data presentation.
Study preferences over uncertain time payments, finds growth-optimality better than expected utility theory.
problem Understanding how people make decisions with uncertain timing of payments.
method Normative model of growth-optimality, revisiting experimental evidence on time lotteries.
result Growth-optimality better explains experimental data on time lotteries than expected discounted utility theory.
Estimates growth of reciprocal classes in Hecke groups.
problem Estimating the growth of reciprocal conjugacy classes in Hecke groups.
method Using free product structure and word lengths of reciprocal elements, with tools from basic probability theory.
result Estimates the asymptotic growth of reciprocal conjugacy classes in Hecke groups.
Mathematical properties of the historical GDP/cap distributions are discussed and explained. These distributions are frequently incorrectly interpreted and the Unified Growth Theory is an outstanding example of such common misconceptions. It is shown here that the fundamental postulates of this theory are contradicted …
Study local control of a specific mechanism with growth vector (4,7).
problem Local control of a mechanism with a specific growth vector.
method Controllability and extremal trajectories on the nilpotent approximation.
result Solutions of the system and examples of local extremal trajectories.
Geometric group theory explores groups through their geometric properties.
problem Understanding groups via geometric properties.
method Cayley and Schreier graphs, ping-pong lemma, quasi-isometries, growth of groups, hyperbolicity.
result Gromov's theorem on groups of polynomial growth and amenability.
The paper defines higher invariants for groups of polynomial growth and proves their convergence.
problem Defining and proving convergence of higher invariants for groups of polynomial growth.
method Using delocalized cyclic cocycles and a determinant map construction.
result A well-defined pairing between delocalized cyclic cocyles and K-theory classes of C*-algebraic secondary higher invariants.
Sharp growth tightness proven for group quotients.
problem Growth behavior of group quotients by confined subgroups.
method Statistically convex-cocompact action with contracting elements.
result Sharp growth tightness proven, with applications to uniformly recurrent subgroups.
We study the growth dynamics of the size of manufacturing firms considering competition and normal distribution of competency. We start with the fact that all components of the system struggle with each other for growth as happened in real competitive bussiness world. The detailed quantitative agreement of the theory w…
New potential theory on minimal hypersurfaces shows stable growth of solutions near singularities.
problem Analyzing potential theory on minimal hypersurfaces.
method Introducing Hardy structures to study classical operators and showing stable growth of solutions.
result Minimal growth of positive solutions of Lw = 0 is stable and persists under perturbations or blow-ups.
Historical income per capita data follow hyperbolic growth patterns.
problem Economic stagnation and Malthusian traps in historical data.
method Fitting hyperbolic distributions to GDP/capita and population data.
result Income per capita growth was monotonic and without transitions.
New proof linking scalar curvature to volume growth on 3-manifolds.
problem Relating scalar curvature to volume growth on 3-manifolds.
method Theory of μ-bubbles and almost splitting theorem.
result New proof of recent result by Munteanu--Wang.
Lie groups applied to tech progress in economic growth.
problem Understanding the impact of technical progress on economic growth.
method Application of Lie theory and economic modeling.
result Estimation of GDP function for Viet Nam, highlighting tech progress impact.
Unified theory explains housing cycle across metros, showing credit expansion impacts.
problem Puzzling correlations between income and mortgage growth across ZIP codes and metros.
method Unified credit expansion theory, double differences, instrumental variables.
result Credit expansion drives housing cycle, affecting boom, bust, and recovery phases.
The study applies Dimensional Analysis to the neoclassical economic growth model.
problem Inconsistency in the neoclassical economic growth model.
method Dimensional Analysis was used to evaluate and adjust the model.
result An adjustment to the neoclassical economic growth model is required to satisfy the principle of dimensional homogeneity.
The paper analyzes growth rates and volatility in the 20th century.
problem Understanding the relationship between economic growth and volatility.
method Analyzes historical data of GDP per capita growth rates and volatility.
result A significant negative scale-relation between volatility and size of countries emerged after 1956.
This study assesses how share capital affects financial growth of non-financial firms listed at NSE.
problem Non-financial firms listed at NSE struggle with financial growth due to declining performance and lack of investor interest.
method Descriptive and panel data analysis of 45 non-financial firms over 10 years.
result Share capital positively and significantly influences financial growth, explaining 32.73% and 11.62% of variations in earnings per share and market capitalization growth, respectively.
Detailed empirical studies of publicly traded business firms have established that the standard deviation of annual sales growth rates decreases with increasing firm sales as a power law, and that the sales growth distribution is non-Gaussian with slowly decaying tails. To explain these empirical facts, a theory is dev…
Study subgroup growth in RAAGs and RAAGs with Coxeter relations.
problem Understanding subgroup growth in RAAGs and RAAGs with Coxeter relations.
method Analyzing the independence number of defining graphs for RAAGs and conjecturing for RAAGs with Coxeter relations.
result Subgroup growth rate depends on the independence number of the defining graph for RAAGs and a conjecture for RAAGs with Coxeter relations.
Study shows long-term debt impacts financial growth of non-financial firms listed at Nairobi Securities Exchange.
problem Declining financial performance and reluctance to lend to non-financial firms listed at Nairobi Securities Exchange.
method Descriptive and panel data analysis of 45 non-financial firms over 10 years.
result Long-term debt positively and significantly influences financial growth measured by earnings per share and market capitalization.
We will show that for a polynomially contractible manifold of bounded geometry and of polynomial volume growth every coarse and rough cohomology class pairs continuously with the K-theory of the uniform Roe algebra. As an application we will discuss non-vanishing of rough index classes of Dirac operators over such mani…
New Morse lemma handles functions going to negative infinity.
problem Deforming functions with negative infinity behavior.
method Generalized Morse Theory lemma for functions going to negative infinity.
result Valid for functions with suitable growth condition.
Study assesses short-term debt's impact on non-financial firms' financial growth.
problem Declining financial performance and reluctance to lend to non-financial firms listed at Nairobi Securities Exchange.
method Explanatory research design, descriptive statistics, and panel data analysis.
result Short-term debt positively and significantly influences financial growth.
Alternative proof of flatness for Ricci-pinched 3-manifolds.
problem Hamilton's pinching conjecture for 3-manifolds.
method Nonlinear potential theory with superquadratic volume growth.
result Flatness of Ricci-pinched 3-manifolds with superquadratic volume growth.
Random quotients of hyperbolic cubulated groups remain cubulated.
problem Understanding properties of random quotients of hyperbolic cubulated groups.
method Cubical small-cancellation theory, exponential growth of conjugacy classes, and hyperplane stabilizers' growth.
result Low-density random quotients of cubulated hyperbolic groups are cubulated and hyperbolic.
Study optimizes growth rate for investors with long-only constraints.
problem Maximizing growth rate under drift uncertainty and long-only constraints.
method Developed a finite dimensional approximation for concave functionally generated portfolios.
result Proved uniqueness and existence for optimal portfolios under long-only constraints.
Optimal stock portfolio strategy using information theory and Tsallis statistics.
problem Finding the optimal stock portfolio growth rate.
method Developed a strategic optimal portfolio based on information theory and Tsallis statistics.
result The wealth growth is modeled by a q-exponential function. Let M be a complete Kähler manifold with nonnegative bisectional curvature. Suppose the universal cover does not split and M admits a nonconstant holomorphic function with polynomial growth, we prove M must be of maximal volume growth. This confirms a conjecture of Ni. There are two essential ingredients in the p…
A strategy ensures maximal wealth growth in competitive asset markets.
problem Maximizing wealth growth in competitive asset markets.
method Game-theoretic model and proof of existence of a submartingale strategy.
result Existence and uniqueness of a submartingale strategy that maximizes wealth growth.
Simplifies analysis of hyperbolic distributions in demographic and economic research.
problem Fundamental postulates of demographic and economic research contradicted by data.
method Simple method of reciprocal values for identifying and analyzing hyperbolic distributions.
result Fundamental postulates of demographic and economic research are incorrect.
We give a new proof of Gromov's theorem that any finitely generated group of polynomial growth has a finite index nilpotent subgroup. Unlike the original proof, it does not rely on the Montgomery-Zippin-Yamabe structure theory of locally compact groups.
We present a quantitative characterisation of the fluctuations of the annualized growth rate of the real US GDP per capita growth at many scales, using a wavelet transform analysis of two data sets, quarterly data from 1947 to 2015 and annual data from 1800 to 2010. Our main finding is that the distribution of GDP grow…
New insights into knot homology growth, extending previous results.
problem Understanding the growth of homology torsion in knot exteriors.
method Analyzing meromorphic continuation of generating functions for knot homology.
result New proofs of Silver-Williams asymptotic, Fried's theorem, and Gordon's theorem.
Groups grow faster than their subgroups, proven using special tools.
problem Growth rates of subgroups within hyperbolic groups.
method Automatic structures, Perron-Frobenius theory, growth tightness, rotating families.
result Non-elementary hyperbolic groups grow exponentially faster than their quasiconvex subgroups.
Investigates how growth and risk balance in populations, revealing a trade-off.
problem Balancing growth and risk in populations under uncertain environments.
method Revisits a common growth model over general graphs to uncover the trade-off between risks and returns.
result Optimal growth strategies often lead to risky positions, but geometry of space can alleviate this tension.
Study adds memory effect to Solow-Swan model for more accurate economic growth modeling.
problem Inaccuracies in classical Solow-Swan model in capturing long-term dynamics.
method Introduced fractional calculus with Caputo derivative into Solow-Swan framework.
result Fractional-order model shows significant impact on capital accumulation and stability.
We introduce a simple agent-based model which allows us to analyze three stylized facts: a fat-tailed size distribution of companies, a `tent-shaped' growth rate distribution, the scaling relation of the growth rate variance with firm size, and the causality between them. This is achieved under the simple hypothesis th…
Survey on handlebody groups and their properties.
problem Understanding handlebody groups and their properties.
method Survey and recent trends in geometric group theory.
result Application of the cheap α-rebuilding property to handlebody group homology growth. Firm foundation theory estimates a security's firm fundamental value based on four determinants: expected growth rate, expected dividend payout, the market interest rate and the degree of risk. In contrast, other views of decision-making in the stock market, using alternatives such as human psychology and behavior, bou…