Constantin Udrişte - Academia.edu (original) (raw)

Papers by Constantin Udrişte

Tools from Riemannian geometry (suitable Riemannian metric, exponential map, search along geodesi... more Tools from Riemannian geometry (suitable Riemannian metric, exponential map, search along geodesics, covariant differentiation, sectional curvature, etc) are now used in Mathematical Programming to obtain deeply theoretical results and practical algorithms [3]-[11]. §1 lists basic propositions appearing in the numerical finding of a critical point of a real function defined on a Riemannian manifold. 2-3 develop the steplength analysis in terms of geodesics and Riemannian version of Taylor formula (which contains the parallel translation along geodesics), insisting on sufficient decrease principle. 4 analyses the strong influence of the sectional curvature on descent algorithms. 5 proves that the central path of a convex program is in fact a minus gradient line with respect to a suitable Riemannian metric. The main theorems refer to the convergence of the sequence x i+1 = exp x i (ω i t i X i), produced by a descent method, to a critical point of a function f , the convergence of the sequence {df (x i)(e i) | e i = X i / X i } to zero, and the convergence of the sequence of distances {d(xi, xi+1)} to zero.

arXiv: General Finance, 2018

We recall the similarities between the concepts and techniques of Thermodynamics and Roegenian Ec... more 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 ideas can be used to improve our knowledge and understanding of the nature of development and evolution of Roegenian economic systems.

This mathematical essay brings together ideas from Economics, Geobiodynamics and Thermodynamics. ... more 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 Geobiodynamics and Roegenian Economy. In this context, we discuss the isomorphism between the concepts and techniques of Thermodynamics and Economics. Then we describe a Roegenian economic system like a Carnot group. After we analyse the phase equilibrium for two heterogeneous economic systems. The European Union Economics appears like Cartesian product of Roegenian economic systems and its Balance is analysed in details. The Phase Diagram for an economic system highlights a triple point. A Section at the end describes the "economic black holes" as small parts of a a global economic system in which national income is so great that it causes others poor enrichment. These ideas can be used to improve our knowledge and understanding of the nature of development and evolution of thermodynamic-economic systems.

The aim of this paper is three-fold: (i) To explain the meaning of ”multitime”. (ii) To formulate... more The aim of this paper is three-fold: (i) To explain the meaning of ”multitime”. (ii) To formulate and solve problems concerning the most important non-linear multiple recurrence equation, called multitime logistic map recurrence. (iii) To define the Feigenbaum constant for a twoparameter multiple map. M.S.C. 2010: 65Q10, 65Q30.

arXiv: Optimization and Control, 2015

Geometric modeling of multivariate reliability polynomials is based on algebraic hypersurfaces, c... more Geometric modeling of multivariate reliability polynomials is based on algebraic hypersurfaces, constant level sets, rulings etc. The solved basic problems are: (i) find the reliability polynomial using the Maple and Matlab software environment; (ii) find restrictions of reliability polynomial via equi-reliable components; (iii) how should the reliability components linearly depend on time, so that the reliability of the system be linear in time? The main goal of the paper is to find geometric methods for analysing the reliability of electric systems used inside aircrafts.

Journal of Optimization Theory and Applications, 2015

Semivectorial bilevel optimization H. Bonnel Introduction Preliminary results A useful equivalent... more Semivectorial bilevel optimization H. Bonnel Introduction Preliminary results A useful equivalent form for the (SVBσ) Optimality Conditions An existence result for the pessimistic problem Outline 1 Introduction 2 Preliminary results 3 A useful equivalent form for the (SVB σ) 4 Optimality Conditions 5 An existence result for the pessimistic problem Semivectorial bilevel optimization H. Bonnel Introduction Preliminary results A useful equivalent form for the (SVBσ) Optimality Conditions An existence result for the pessimistic problem bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel Pessimistic case = the followers may chose a worst solution for the leader among their best responses Semivectorial bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel Semivectorial bilevel optimization H. Bonnel

The purpose of this paper is twofold: (i) a description of standing waves, (ii) revealing the inf... more The purpose of this paper is twofold: (i) a description of standing waves, (ii) revealing the informational origin of gravity. Waves are achieved by imposing a special form of solutions of the system of partial differential equations (PDE) describing electromag-netic waves. One obtains a frequency dependent EDP system. This system can be solved using two methods: (i) eigenvalues eigenvectors, (ii) three-dimensional Fourier transform. Information theory is a branch of applied mathematics, electrical engineering, bioinformatics, and computer science involving the quan-tification of information. A key measure of information is entropy, which is usually expressed by the average number of bits needed to store or communicate one symbol in a message. Entropy quantifies the uncertainty involved in predicting the value of a random variable. Entropy is a measure of unpredictability or information content. From entropy, energy and temperature we obtain the Newton Law, the New-ton Law of Masses...

Recall that a vector field on an n-dimensional differentiable manifold M is a mapping X defined o... more Recall that a vector field on an n-dimensional differentiable manifold M is a mapping X defined on M with values in the tangent bundle TM that assigns to each point xinMx\in MxinM a vector X(x) in the tangent space TxMT_x MTxM. A vector field may be interpreted alternatively as the right-hand side of an autonomous system of first-order ordinary differential

Lagrange and Finsler Geometry, 1996

In §1 the basic notions of the theory of phase portraits and critical elements of magnetic fields... more In §1 the basic notions of the theory of phase portraits and critical elements of magnetic fields are presented; §2 and §3 describe the symmetries of phase portraits and of the critical points sets respectively, for the magnetic field generated by unitary currents which traverse coplanar angular wires. §4 presents computer experiments. In §5, the associated magnetic field lines are shown to be solutions of a potential conservative system, and also geodesics for a certain Riemannian metric on the space surrounding the wires.

The pseudo-Riemannian Geometry is utilized in Mathematical Optimization, Thermodynamics or in Sta... more The pseudo-Riemannian Geometry is utilized in Mathematical Optimization, Thermodynamics or in Statistics as an important tool for recent research. Given a pseudo-Riemannian manifold (M, g) and a smooth function f : M → R, whose Hessian with respect to g is non-degenerate, one can define on M the associated pseudo-Riemannian Hessian metric h = Hess g f. In the following, we apply this methodology for describing the geometrical properties of some interesting mathematical objects like the higher dimensional Reissner-Nördstrom black holes. The paper is organized as follows. Section 1 reviews the history of pseudo-Riemannian Geometry and points out which Hessian is more convenient for physical problems. Section 2 gives the Christoffel symbols and the system of geodesics of pseudo-Riemannian manifold (M, h = Hess g f), establishes the relation between the components of the curvature tensors field of (M, h) and (M, g), and determines the PDEs representing the coincidence between the Christoffel symbols of (M, h) and the Christoffel symbols of (M, g). The last section presents the comparison of null-length curves trajectories obtained with the two metrics for a 5-dimensional RN black hole.

Section 1 reviews the history of Differential Geometry derived from a fundamental tensor of type ... more Section 1 reviews the history of Differential Geometry derived from a fundamental tensor of type (0, 2) and points out which Hessian is more convenient to be fundamental tensor. Section 2 starts with the fundamental tensor h = Hess g f , gives the Christoffel symbols and the system of geodesics, establishes the relation between the components of the curvature tensors field of h and (R n , g), and determines the PDEs representing the coincidence between the Christoffel symbols of h and the Christoffel symbols of g. Section 3 analyses the Reissner-Nordstrom black hole from Pidokrajt point of view and from our point of view, underlying the physical characteristics of the geometrical models via fundamental tensor, Christoffel symbols, geodesics and curvature. The physical geometric models are total different, the most important differences being the degeneration curves, the null length curves and the sign of sectional curvature.

Arxiv preprint arXiv:1110.4745, 2011

Some optimization problems coming from the Differential Geometry, as for example, the minimal sub... more Some optimization problems coming from the Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control problems. Section 1 underlines some science domains where appear multitime optimal control problems. Section 2 (Section 3) recalls the multitime maximum principle for optimal control problems with multiple (curvilinear) integral cost functionals and m-flow type constraint evolution. Section 4 shows that there exists a multitime maximum principle approach of multitime variational calculus. Section 5 (Section 6) proves that the minimal submanifolds (harmonic maps) are optimal solutions of multitime evolution PDEs in an appropriate multitime optimal control problem. Section 7 uses the multitime maximum principle to show that of all solids having a given surface area, the sphere is the one having the greatest volume. Section 8 studies the minimal area of a multitime linear flow as optimal control problem. Section 9 contains commentaries.

Appl. Sci, 1999

The paper determines the magnetic field and its vector and scalar potentials for spatial piecewis... more The paper determines the magnetic field and its vector and scalar potentials for spatial piecewise rectilinear configurations. Several applications for configurations which generate open magnetic lines, plane angular circuits and properties of the magnetic lines and surfaces, are provided.

edumanager.ro

Proiectul are ca obiectiv adaptarea programelor de studii ale disciplinelor matematice la cerinte... more Proiectul are ca obiectiv adaptarea programelor de studii ale disciplinelor matematice la cerintele pietei muncii si crearea de mecanisme si instrumente de extindere a oportunitatilor de ınvatare. Evaluarea nevoilor educationale obiective ale cadrelor didactice si studentilor ...