Related papers: Continuous growth models in terms of generalized l…
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamics models into a simple formula. A physical interpretation is given to…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on…
We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As…
We discuss a general growth curve including several parameters, whose choice leads to a variety of models including the classical cases of Malthusian, Richards, Gompertz, Logistic and some their generalizations. The advantage is to obtain a…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
Criteria are given that kappa-deformed logarithmic and exponential functions should satisfy. With a pair of such functions one can associate another function, called the deduced logarithmic function. It is shown that generalized…
Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…
Equilibrium statistical physics is considered from the point of view of statistical estimation theory. This involves the notions of statistical model, of estimators, and of exponential family. A useful property of the latter is the…
We present a general growth model based on non-extensive statistical physics is presented. The obtained equation is expressed in terms of nonadditive $q$ entropy. We show that the most common unidimensional growth laws such as power law,…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
We survey recent work on normal functions, including limits and singularities of admissible normal functions, the Griffiths-Green approach to the Hodge conjecture, algebraicity of the zero-locus of a normal function, Neron models, and…
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on…
We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
Asymptotic expansions for generalised trigonometric integrals are obtained in terms of elementary functions, which are valid for large values of the parameter $a$ and unbounded complex values of the argument. These follow from new…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…