1,721,107 research outputs found
Benford' law: a number -theoretical perspective
Full text linkThe historical journey of the Benford’s law and its most important definitions and properties are shortly reviewed. Firstly, we define a new class of numbers based on the first-digit law. Secondly, we investigate the relation between Benford’s sequence and normal numbers
A geometric characterization of ves and kadiyala-type production functions
Full text linkThe basic concepts of the differential geometry are shortly reviewed and applied to the study of VES production function in the spirit of the works of Vîlcu and collaborators. A similar characterization is given for a more general production function, namely the Kadiyala production function, in the case of developable surfaces
NOTES ON A CONFORMAL CHARACTERIZATION OF 2-DIMENSIONAL LORENTZIAN MANIFOLDS WITH CONSTANT RICCI SCALAR CURVATURE
Full text linkWe present a characterization of 2-dimensional Lorentzian manifolds with con-stant Ricci scalar curvature. It is well known that every 2-dimensional Lorentzian manifolds is conformally flat, so we rewrite the Ricci scalar curvature in terms of the conformal factor and we study the solutions of the corresponding differential equations. Several remarkable examples are provided
Exact solutions for a Solow-Swan model with non-constant returns to scale
Full text linkThe Solow-Swan model is shortly reviewed from a mathematical point of view. By considering non-constant returns to scale, we obtain a general solution strategy. We then compute the exact solution for the Cobb-Douglas production function, for both the classical model and the von Bertalanffy model. Numerical results are eventually provided
Global stability of SAIRS epidemic models
Full text linkWe study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission patterns of the disease. We provide a global stability analysis for the model. We determine the value of the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable if R01, the disease free equilibrium is unstable and a unique endemic equilibrium exists. We investigate the global stability of the endemic equilibrium for some variations of the original model under study and answer an open problem proposed in Ansumali et al. (2020). In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when R0=1. We provide a thorough numerical exploration of our model to illustrate our analytical results
How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks
Full text linkWith the premise that social interactions are described by power-law distributions, we study the stochastic dynamics of SIR (Susceptible-Infected-Removed) compartmental models on static scale-free random networks generated via the configuration model. We compare simulations of our model to analytical results, providing a closed formula and a lower bound for the probability of having a minor epidemic of the disease. We explore the variability in disease spread by stochastic simulations. In particular, we demonstrate how important epidemic indices change as a function of the contagiousness of the disease and the connectivity of the network. Our results quantify the role of the starting node’s degree in determining these indices, commonly used to describe epidemic spread. Our results and implementation set a baseline for studying epidemic spread on networks, showing how analytical methods can help in the interpretation of stochastic simulations
Global stability of multi-group SAIRS epidemic models
Full text linkWe study a multi-group SAIRS-type epidemic model with vaccination. The role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission pattern of the disease among the groups in which the population is divided. This is a natural extension of the homogeneous mixing SAIRS model with vaccination studied in Ottaviano et. al (2021) to a network of communities. We provide a global stability analysis for the model. We determine the value of the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable if R01, the disease-free equilibrium is unstable and a unique endemic equilibrium exists. First, we investigate the local asymptotic stability of the endemic equilibrium and subsequently its global stability, for two variations of the original model. Last, we provide numerical simulations to compare the epidemic spreading on different networks topologies
A generalization of unaimed fire Lanchester’s model in multi-battle warfare
Full text linkThe classical Lanchester’s model is shortly reviewed and analysed, with particular attention to the critical issues that intrinsically arise from the mathematical formalization of the problem. We then generalize a particular version of such a model describing the dynamics of warfare when three or more armies are involved in the conflict. Several numerical simulations are provided
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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