arXiv subjects
Publications and source records attributed to Mircea Neagu.
In this paper we develop, via the least squares variational method, the Lagrange-Hamilton geometry (in the sense of nonlinear connections, d-torsions and Lagrangian Yang-Mills electromagnetic-like energy) produced by a dynamical system governing the spreading of COVID-19 disease. The Jacobi stability of this dynamical system is also discussed.
The aim of this paper is to develop, via the least squares variational method, the Lagrange-Hamilton geometry (in the sense of nonlinear connections, d-torsions and Lagrangian Yang-Mills electromagnetic-like energy) produced by a Lotka-Volterra dynamical system, a simple model of the population dynamics of species competing for some common resource. From a geometrical point of view, the Jacobi stability of this system is discussed.
Our paper reviews some key concepts in chemical reaction network theory and mathematical epidemiology, and examines their intersection, with three goals. The first is to make the case that mathematical epidemiology (ME), and also related sciences like population dynamics, virology, ecology, etc., could benefit by adopting the universal language of essentially non-negative kinetic systems as developed by chemical reaction network (CRN) researchers. In this direction, our investigation of the relations between CRN and ME lead us to propose for the first time a definition of ME models, stated in Open Problem 1. Our second goal is to inform researchers outside ME of the convenient next generation matrix (NGM) approach for studying the stability of boundary points, which do not seem suficiently well known. Last but not least, we want to help students and researchers who know nothing about either ME or CRN to learn them quickly, by offering them a Mathematica package "BootCamp", located at https://github.com/adhalanay/epidemiology_crns, including illustrating notebooks (and certain sections below will contain associated suggested notebooks; however, readers with experience may safely skip the bootcamp). We hope that the files indicated in the titles of various sections will be helpful, though of course improvement is always possible, and we ask the help of the readers for that.
This essay reviews some key concepts in mathematical epidemiology and examines the intersection of this field with related scientific disciplines, such as chemical reaction network theory and Lagrange-Hamilton geometry. Through a synthesis of theoretical insights and practical perspectives, we underscore the significance of essentially non-negative kinetic systems in the development and implementation of robust epidemiological models. Our purpose is to make the case that currently mathematical modeling of epidemiology is focusing too much on simple particular cases, and maybe not enough on more complex models, whose challenges would require cooperation with scientific computing experts and with researchers in the "sister disciplines" involving essentially nonnegative kinetic systems (like virology, ecology, chemical reaction networks, population dynamics, etc).
In this paper, via the least squares variational method, we develop the Lagrange geometry (in the sense of nonlinear connection, d-torsions and the deviation curvature tensor) and the KCC theory for a given dynamical system. Further, a result on the Jacobi stability of the solutions of this dynamical system is also obtained.
The aim of this paper is to obtain on the dual 1-jet space J^{1*}(R;M) the main geometrical objects used in the dual jet geometry of time-dependent Hamiltonians. We talk about distinguished (d-) tensors, time-dependent semisprays, nonlinear connections and their mathematical connections.
For a space endowed with a general quadratic multi-time Lagrangian and an associated non-linear connection, the paper constructs the main Riemann-Lagrange distinguished geometric objects (linear connection, torsion and curvature).
In this paper we present the m-th root Finsler geometries of the three and four dimensional Bogoslovsky-Goenner metrics (good Finslerian anisotropic models in Special Relativity), in the sense of their Cartan torsion and curvature distinguished tensors or vertical Einstein-like equations.
In this paper we develop the Riemann-Lagrange geometry, in the sense of nonlinear connection, d-torsions, d-curvatures and jet Yang-Mills entity, associated with the dynamical system concerning social interaction in colonial organisms.
In this paper we parametrize the symmetry group of the n-dimensional Berwald-Moor metric. Some properties of this Lie group are studied, and its corresponding Lie algebra is computed.
In this paper we expose on the dual 1-jet space J^{1*}(R,M^4) the distinguished (d-) Riemannian geometry (in the sense of d-connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models) for the (t,x)-conformal deformed Berwald-Moor Hamiltonian metric of order four.
The aim of this paper is to develop on the 1-jet space J^1(R, M^n) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models) attached to the (t,x)-conformal deformation of the Berwald-Moor metric.
In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.
The aim of this paper is to create a large geometrical background on the dual 1-jet space J^{1*}(T,M) for a multi-time Hamiltonian approach of the electromagnetic and gravitational physical fields. Our geometric-physical construction is achieved starting only from a given quadratic Hamiltonian function of polymomenta H, which naturally produces a canonical nonlinear connection N, a canonical Cartan N-linear connection CΓ(N) and their corresponding local distinguished (d-) torsions and curvatures. In such a context, we construct some geometrical electromagnetic-like and gravitational-like field theories which are characterized by some natural geometrical Maxwell-like and Einstein-like equations. Some abstract and geometrical conservation laws for the multi-time Hamiltonian gravitational physical field are also given.
In this paper we construct a distinguished Riemannian geometrization on the dual 1-jet space J^{1*}(T,M) for the multi-time quadratic Hamiltonian functions. Our geometrization includes a nonlinear connection N, a generalized Cartan canonical N-linear connection (together with its local d-torsions and d-curvatures), naturally provided by a given quadratic Hamiltonian function depending on polymomenta.
In this paper we describe the local Ricci and Bianchi identities for an h-normal N-linear connection DΓ(N) on the dual 1-jet space J^{1*}(T,M). To reach this aim, we firstly give the expressions of the local distinguished (d-) adapted components of torsion and curvature tensors produced by DΓ(N), and then we analyze their attached local Ricci identities. The derived deflection d-tensor identities are also presented. Finally, we expose the local expressions of the Bianchi identities (in the particular case of an h-normal N-linear connection of Cartan type), which geometrically connect the local torsion and curvature d-tensors of the linear connection DΓ(N).
In this paper we construct some natural geometrical objects on the 1-jet space J^1(R,R^3), like a nonlinear connection, a Cartan linear connection (together with its d-torsions and d-curvatures), a jet "electromagnetic" d-field and its geometric "electromagnetic" Yang-Mills energy, starting from a given dynamical system governing the three-dimensional motion of the knee in the mathematical model introduced by Grood and Suntay. The corresponding Yang-Mills energetic surfaces of constant level (produced by this knee dynamical system) are studied.
The paper develops the Finsler-like geometry on the 1-jet space for the jet conformal Minkowski (JCM) metric, which naturally extends the Minkowski metric in the Chernov-Pavlov framework. To this aim there are determined the nonlinear connection, distinguished (d-) Cartan linear connection, d-torsions and d-curvatures. The field geometrical gravitational and electromagnetic d-models based on the JCM metric are discussed.