Investigates quadratic-exponential growth BSDEs with jumps and proves existence and differentiability.
problem Existence and differentiability of solutions to quadratic-exponential growth BSDEs with jumps.
method Proves existence and differentiability of solutions under general quadratic-exponential structure using local Lipschitz continuity and A_gamma-condition.
result Proves existence and differentiability of solutions under general quadratic-exponential structure.
Sharp time analyticity proved for heat equation on Ricci solitons.
problem Analyticity of heat equation solutions on gradient shrinking Ricci solitons.
method Proved analyticity for solutions with quadratic exponential growth.
result Sharp growth condition for analyticity is established.
The paper studies ABSDEs with jumps and various growth drivers.
problem Solving ABSDEs with specific growth conditions.
method Proves existence of unique solution for ABSDEs with jumps and various growth drivers.
result Existence of unique solution for ABSDEs with specific growth conditions.
This paper calculates the growth constant for quantum knot mosaics.
problem Calculating the growth constant for quantum knot mosaics.
method Introduced knot mosaic system, defined quantum knots, and used enumeration to find the growth constant.
result Existence and bounds of the knot mosaic constant δ. The paper calculates subgroup distortions in 3-manifold groups.
problem Understanding subgroup distortions in 3-manifold groups.
method Computed all finitely generated subgroups of finitely generated 3-manifold groups and analyzed their distortions.
result Subgroup distortions in 3-manifold groups are linear, quadratic, exponential, or double exponential.
Computes distortion of surfaces in non-geometric 3-manifolds.
problem Distortion of surfaces in non-geometric 3-manifolds.
method Computes distortion of π1(S) in π1(N) and relates it to separability.
result Distortion is linear, quadratic, exponential, or double exponential.
The paper provides a representation for dynamic risk measures and capital allocations.
problem Representation of dynamic risk measures and capital allocations under Itô-Lévy model.
method Representation theorem for dynamic capital allocation derived from BSDEs with quadratic-exponential growth.
result Derivation of a capital allocation representation for dynamic entropic risk measure and static coherent risk measure.
Investment and insurance strategy optimized under inflation using BSDEs.
problem Optimal investment, consumption, and insurance selection in inflationary environment.
method Theory of quadratic-exponential backward stochastic differential equations (BSDEs) with jumps.
result Explicit solutions for optimal investment strategies under exponential and power utilities.
Unified Growth Theory contradicted by USSR economic data.
problem Unified Growth Theory fails to explain USSR economic growth.
method Analysis of historical USSR economic data.
result USSR economic growth was hyperbolic, not stagnant.
Abstract Coxeter groups have growth rates that are Perron numbers.
problem Understanding growth rates of Coxeter groups.
method Defined a class of Coxeter groups, ∞--spanned, and analyzed their growth rates. result For ∞--spanned Coxeter groups, geodesic growth rate strictly dominates word growth rate and appears to be a Perron number. World GDP growth is predicted to become unsustainable.
problem Predicting the future of world economic growth.
method Analysis of World Bank data on GDP growth rates.
result World economic growth is predicted to become unsustainable.
Unified Growth Theory contradicted by Asian economic data.
problem Unified Growth Theory fails to explain Asian economic growth.
method Analysis of historical economic growth data in Asia.
result Asian economic growth was hyperbolic, not stagnant.
Unified Growth Theory contradicted by African economic data.
problem Contradiction between Unified Growth Theory and African economic growth data.
method Analysis of Galor's data for African countries.
result Data contradicts Unified Growth Theory's claims about economic growth regimes.
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.
Study measures economic growth sources in Iran's mining sector using neoclassical growth accounting.
problem Determining the share of economic growth sources in Iran's mining sector.
method Neoclassical growth accounting approach, using production function and Solow residual equation.
result Average annual growth rate of TFP was 2.94% over 30 years.
Simple math predicts growth trends.
problem Complex growth projections are hard to understand.
method Direct or indirect analysis of growth rates.
result Simple assumptions lead to understandable growth predictions.
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.
Calculates the systolic growth of nilpotent Lie groups, providing new insights.
problem Understanding the growth of systolic volume in nilpotent Lie groups.
method Expressed systolic growth in terms of discrete subrings, developed methods for lower bounds.
result First computations of systolic growth for non-equivalent volume growth cases.
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…
Study confined subgroups in groups with contracting elements, showing their growth rate is strictly greater than half of the ambient growth rate.
problem Understanding the growth rate of confined subgroups in groups with contracting elements.
method Through boundary actions, analyzing the Hopf decomposition and quotient growth.
result Confined subgroups have a growth rate strictly greater than half of the ambient growth rate.
The US GDP per capita growth alternates between high and low rates, with an average growth rate of 1.6% since 1800.
problem Understanding the fluctuations and stability of US GDP growth rates over time.
method Wavelet transform analysis of US GDP per capita data from 1800 to 2010.
result The growth rate of US GDP per capita is bimodal, alternating between high and low rates with an average of 1.6% since 1800.
Growth rates of geodesics on modular orbifolds are studied.
problem Understanding growth rates of geodesics on modular orbifolds.
method Exhaustion of modular orbifold by compact subsurfaces, analysis of low lying geodesics and reciprocal geodesics.
result Growth rates of low lying geodesics and reciprocal geodesics converge to the full set's growth rate.
Data describing historical economic growth are analysed. Included in the analysis is the world and regional economic growth. The analysis demonstrates that historical economic growth had a natural tendency to follow hyperbolic distributions. Parameters describing hyperbolic distributions have been determined. A search …
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.
The study provides volume growth estimates for specific types of manifolds.
problem Estimating volume growth for Ricci solitons and quasi-Einstein manifolds.
method Similar to classical results, the study proves volume growth estimates for gradient Ricci solitons and quasi-Einstein manifolds.
result Sharp volume growth estimates for gradient shrinking Ricci solitons and upper bound volume growth estimates for quasi-Einstein manifolds.
Study growth rates of subgroups in groups with a constricting element.
problem Understanding growth rates of subgroups in groups with a constricting element.
method Examining the spectrum of relative and quotient exponential growth rates of quasi-convex subgroups.
result Determine when growth rates of subgroups are strictly smaller or coincide with the group's growth rate.
Paper reviews and proves volume growth estimates for different types of gradient Ricci solitons.
problem Estimating volume growth for gradient Ricci solitons.
method Survey and prove new volume growth estimates.
result New volume growth estimates for expanding gradient Ricci solitons.
The paper studies stability and area growth of λ-hypersurfaces.
problem Stability and growth of area for λ-hypersurfaces. method Defined a F-functional and studied F-stability. result Lower and upper bounds for area growth of λ-hypersurfaces. New insights into groups with uniform exponential growth.
problem Uniform exponential growth in hierarchically hyperbolic groups.
method Quasi-isometric characterization and new insights into group structure.
result Uniform exponential growth for hierarchically hyperbolic groups.
Study groups with polynomial growth, finding structure and applications.
problem Understanding groups with polynomial growth structure.
method Structure theorem for locally compact groups of polynomial growth.
result Applications on various growth functions and relations to FC-G series.
In many European countries the growth of the real GDP per capita has been linear since 1950. An explanation for this linearity is still missing. We propose that in artificial intelligence we may find models for a linear growth of performance. We also discuss possible consequences of the fact that in systems with linear…
Study ancient caloric functions on graphs, extending a theorem from manifolds.
problem Bounding the dimension of ancient caloric functions on graphs.
method Extending Colding and Minicozzi's theorem to graphs.
result Dimension of ancient caloric functions is bounded by growth degree and graph dimension.
Optimal bounds found for ancient caloric functions on manifolds.
problem Bounding the dimension of ancient caloric functions on manifolds with polynomial volume growth.
method Analyzing polynomial growth and using Yau's conjecture for harmonic functions.
result Sharp bound for the dimension of ancient caloric functions on spaces where Yau's conjecture holds.
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.
New proof shows not all Salem numbers are growth rates of Coxeter groups.
problem Identifying growth rates of Coxeter groups using Salem numbers.
method New proof using spectral radii and Coxeter transformations.
result Not every Salem number is a growth rate of hyperbolic Coxeter groups.
Random 3-manifolds have exponential growth of torsion in covers.
problem Exponential growth of torsion in random 3-manifolds.
method Study of random 3-manifolds with positive first Betti number.
result Exponential growth of torsion in cyclic covers.
Study homology growth in nonpositive curvature spaces, finding examples of torsion.
problem Understanding homology growth in nonpositive curvature spaces.
method Computing mod p homology growth of right-angled Artin groups and closed locally CAT(0) manifolds.
result Homology torsion grows exponentially in the index of subgroups, contradicting rational homology growth.
Study on Monge-Ampère equations with polynomial growth rates.
problem Analyzing solutions to Monge-Ampère equations with polynomial right-hand sides.
method Utilizing polynomial growth analysis to study regularity and growth rates of solutions.
result Translators for sub-affine-critical curvature flows are smooth and convex with specific growth rates.
Proves WPD elements are exponentially generic in acylindrically hyperbolic groups.
problem Growth rates of acylindrically hyperbolic groups.
method Analyzes exponential growth rates of non-WPD and WPD elements.
result WPD elements are exponentially generic in acylindrically hyperbolic groups.
Paper proves volume growth estimate for steady gradient Ricci solitons.
problem Estimating the volume growth of steady gradient Ricci solitons.
method Proved a volume growth estimate using Nash entropy.
result Volume growth rate is no smaller than $r^{ rac{n+1}{2}}$.
Estimates growth loss in fund models and proposes a shrinkage method.
problem Estimating growth loss in fund models under frequentist and Bayesian estimation.
method Proposes a shrinkage method to target maximal growth with minimal deviation.
result Empirical evidence shows shrinkage gives a stable estimate closer to growth potential.
Simple, non-optimized portfolios beat capitalization-weighted indexes due to excess growth, not individual stock growth.
problem Simple investment strategies outperform capitalization-weighted indexes over long periods.
method Decomposed portfolio log-returns into average and excess growth components, using rank-based empirical study.
result Excess growth component, not individual stock growth, explains outperformance of naive portfolios.
Two rigidity theorems for manifolds with nonnegative Ricci curvature and specific volume growth.
problem Characterizing manifolds with nonnegative Ricci curvature and specific volume growth properties.
method Rigidity theorems based on volume growth and existence of harmonic functions.
result Conditions for the Riemannian universal cover to have Euclidean volume growth and existence of nonconstant linear growth harmonic functions.
The paper uses SVAR modeling to analyze how demographic changes affect the current account and economic growth.
problem The impacts of demographic changes on the current account and economic growth.
method SVAR modeling to track dynamic impacts between population growth, current account, and economic growth.
result The long-run net impact on economic growth of the domestic working population growth and demand labor for emigrants is positive.
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.
Bubbles are essential in certain economic models with high growth and low interest rates.
problem Asset price bubbles exceeding fundamental values.
method Developed the Bubble Necessity Theorem in economic models with specific growth and interest rate conditions.
result Bubbles are inevitable in certain economic scenarios with high growth and low interest rates.
Study growth rates of harmonic functions on curved surfaces.
problem Understanding the growth rates of harmonic functions on curved surfaces.
method Gradient estimate and frequency analysis on complete surfaces and manifolds with non-negative curvature.
result Existence and properties of nonconstant polynomial growth harmonic functions on manifolds with maximal volume growth.
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.