Ionel Ţevy
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Optimal Control Problem for Minimization of Net Energy Consumption at Metro Open
The optimal control currently decides the minimum energy consumption within the problems attached to subways. Among other things, we formulate and solve an optimal bi-control problem, the two controls being the acceleration and the feed-ba…
Information Geometry in Roegenian Economics Open
We characterise the geometry of the statistical Roegenian manifold that arises from the equilibrium distribution of an income of noninteracting identical economic actors. The main results for ideal income are included in three subsections:…
Train Bi-Control Problem on Riemannian Setting Open
This article refers to the optimization of the energy consumption of guided traction rails, such as those used for electric trains (including subway electric units), railcars, locomotives, and trams, in a Riemannian framework. The proposed…
Economic Cycles of Carnot Type Open
Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of…
Minimum Time Problem Controlled by Affine Connection Open
Geometrically, the affine connection is the main ingredient that underlies the covariant derivative, the parallel transport, the auto-parallel curves, the torsion tensor field, and the curvature tensor field on a finite-dimensional differe…
Properties of Hamiltonian in free final multitime problems Open
"In single-time autonomous optimal control problems, the Hamiltonian is constant on optimal evolution. In addition, if the final time is free, the optimal Hamiltonian vanishes on the hole interval of evolution. The purpose of this paper is…
Riccati PDEs That Imply Curvature-Flatness Open
In this paper the following three goals are addressed. The first goal is to study some strong partial differential equations (PDEs) that imply curvature-flatness, in the cases of both symmetric and non-symmetric connection. Although the cu…
Flow, Wind, and Stochastic Connectivity Modeling Infectious Diseases Open
We study in this paper the trends of the evolution of different infections using a SIR flow (first‐order ODE system), completed by a differential inclusion, a geodesic motion in a gyroscopic field of forces, and a stochastic SIR perturbati…
Least Squares Approximation of Flatness on Riemannian Manifolds Open
The purpose of this paper is fourfold: (i) to introduce and study the Euler–Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on Ri…
Least Squares Approximation of Flatness on Riemannian Manifolds Open
The purpose of this paper is threefold: (i) to introduce and study the Euler-Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on R…
Minirobots Moving at Different Partial Speeds Open
In this paper, we present the mathematical point of view of our research group regarding the multi-robot systems evolving in a multi-temporal way. We solve the minimum multi-time volume problem as optimal control problem for a group of pla…
Geometric Dynamics on Riemannian Manifolds Open
The purpose of this paper is threefold: (i) to highlight the second order ordinary differential equations (ODEs) as generated by flows and Riemannian metrics (decomposable single-time dynamics); (ii) to analyze the second order partial dif…
Flatness produced by some geometric PDEs Open
This paper has several goals. The first idea is to study the geometric PDEs of connection-flatness, curvature-flatness, Ricci-flatness, scalar curvature-flatness in a modern and rigorous way. Although the idea is not new, our main Theorems…
View article: Entropy of Reissner–Nordström 3D Black Hole in Roegenian Economics
Entropy of Reissner–Nordström 3D Black Hole in Roegenian Economics Open
The subject of this paper is to analyse the Mathematical Principia of Economic 3D Black Holes in Roegenian economics. In detail, we study two main problems: (i) mathematical origin of economic 3D black holes; and (ii) entropy and internal …
View article: Entropy of Reissner-Nordström 3D Hole in Roegenian Economics
Entropy of Reissner-Nordström 3D Hole in Roegenian Economics Open
The subject of this paper is to analyse the Math Principia of Economic 3D Black Holes in Roegenian economics. This idea is totally new in the related literature, excepting our papers. In details, we study two special problems: (i) math ori…
View article: Geobiodynamics and Roegenian Economic Systems
Geobiodynamics and Roegenian Economic Systems Open
This mathematical essay brings together ideas from Economics, Geobiodynamics and Thermodynamics. Its purpose is to obtain real models of complex evolutionary systems. More specifically, the essay defines Roegenian Economy and links Geobiod…
View article: Phase Diagram for Roegenian Economics
Phase Diagram for Roegenian Economics Open
We recall the similarities between the concepts and techniques of Thermodynamics and Roegenian Economics. The Phase Diagram for a Roegenian economic system highlights a triple point and a critical point, with related explanations. These id…
Bilevel Disjunctive Optimization on Affine Manifolds Open
Bilevel optimization is a special kind of optimization where one problem is embedded within another. The outer optimization task is commonly referred to as the upper-level optimization task, and the inner optimization task is commonly refe…
Optimal reliability allocation for redundancy series-parallel systems Open
This paper examines the optimal reliability approaches to allocate the reliability values based on minimization of the total cost for a series-parallel systems. The problem is approached as a nonlinear programming problem and general costs…
Viscosity solutions of divergence type PDEs associated to multitime hybrid games Open
Our original results are associated to a multitime hybrid game, with two equips of players, based on a multiple integral functional and an m- ow as constraint. The aim of this paper is three-fold: (i) to define the multitime lower or upper…
Viscosity solution PDEs in hybrid games with mechanical work payoff Open
In a multitime hybrid differential game with mechanical work payoff, the multitime upper value function and the multitime lower value function are viscosity solutions of original PDEs of type Hamilton-Jacobi-Isaacs.
Multitime hybrid differential games with curvilinear integral functional Open
Multitime differential games are related to the modeling and analysis of cooperation or conflict in the context of a multitime dynamical systems. Their theory involves either a curvilinear integral functional or a multiple integral functio…
Dualities in Nonholonomic Optimization Open
This article deals with optimizing problems whose restrictions are nonholonomic. The central issue relates to dual nonholonomic programs (what they mean and how they are solved?) when the nonholonomic constraints are given by Pfaff equatio…