Background
Udriste, Constantin Nicolae was born on January 22, 1940 in Turceni, Gorj, Romania. Son of Nicolae C. and Dumitra (Iordache) University.
(Geometric dynamics is a tool for developing a mathematica...)
Geometric dynamics is a tool for developing a mathematical representation of real world phenomena, based on the notion of a field line described in two ways: -as the solution of any Cauchy problem associated to a first-order autonomous differential system; -as the solution of a certain Cauchy problem associated to a second-order conservative prolongation of the initial system. The basic novelty of our book is the discovery that a field line is a geodesic of a suitable geometrical structure on a given space (Lorentz-Udri~te world-force law). In other words, we create a wider class of Riemann-Jacobi, Riemann-Jacobi-Lagrange, or Finsler-Jacobi manifolds, ensuring that all trajectories of a given vector field are geodesics. This is our contribution to an old open problem studied by H. Poincare, S. Sasaki and others. From the kinematic viewpoint of corpuscular intuition, a field line shows the trajectory followed by a particle at a point of the definition domain of a vector field, if the particle is sensitive to the related type of field. Therefore, field lines appear in a natural way in problems of theoretical mechanics, fluid mechanics, physics, thermodynamics, biology, chemistry, etc.
http://www.amazon.com/gp/product/9401058229/?tag=prabook0b-20
(The object of this book is to present the basic facts of ...)
The object of this book is to present the basic facts of convex functions, standard dynamical systems, descent numerical algorithms and some computer programs on Riemannian manifolds in a form suitable for applied mathematicians, scientists and engineers. It contains mathematical information on these subjects and applications distributed in seven chapters whose topics are close to my own areas of research: Metric properties of Riemannian manifolds, First and second variations of the p-energy of a curve; Convex functions on Riemannian manifolds; Geometric examples of convex functions; Flows, convexity and energies; Semidefinite Hessians and applications; Minimization of functions on Riemannian manifolds. All the numerical algorithms, computer programs and the appendices (Riemannian convexity of functions f:R ~ R, Descent methods on the Poincare plane, Descent methods on the sphere, Completeness and convexity on Finsler manifolds) constitute an attempt to make accesible to all users of this book some basic computational techniques and implementation of geometric structures. To further aid the readers,this book also contains a part of the folklore about Riemannian geometry, convex functions and dynamical systems because it is unfortunately "nowhere" to be found in the same context; existing textbooks on convex functions on Euclidean spaces or on dynamical systems do not mention what happens in Riemannian geometry, while the papers dealing with Riemannian manifolds usually avoid discussing elementary facts. Usually a convex function on a Riemannian manifold is a real valued function whose restriction to every geodesic arc is convex.
http://www.amazon.com/gp/product/0792330021/?tag=prabook0b-20
(The object of this book is to present the basic facts of ...)
The object of this book is to present the basic facts of convex functions, standard dynamical systems, descent numerical algorithms and some computer programs on Riemannian manifolds in a form suitable for applied mathematicians, scientists and engineers. It contains mathematical information on these subjects and applications distributed in seven chapters whose topics are close to my own areas of research: Metric properties of Riemannian manifolds, First and second variations of the p-energy of a curve; Convex functions on Riemannian manifolds; Geometric examples of convex functions; Flows, convexity and energies; Semidefinite Hessians and applications; Minimization of functions on Riemannian manifolds. All the numerical algorithms, computer programs and the appendices (Riemannian convexity of functions f:R ~ R, Descent methods on the Poincare plane, Descent methods on the sphere, Completeness and convexity on Finsler manifolds) constitute an attempt to make accesible to all users of this book some basic computational techniques and implementation of geometric structures. To further aid the readers,this book also contains a part of the folklore about Riemannian geometry, convex functions and dynamical systems because it is unfortunately "nowhere" to be found in the same context; existing textbooks on convex functions on Euclidean spaces or on dynamical systems do not mention what happens in Riemannian geometry, while the papers dealing with Riemannian manifolds usually avoid discussing elementary facts. Usually a convex function on a Riemannian manifold is a real valued function whose restriction to every geodesic arc is convex.
http://www.amazon.com/gp/product/904814440X/?tag=prabook0b-20
Udriste, Constantin Nicolae was born on January 22, 1940 in Turceni, Gorj, Romania. Son of Nicolae C. and Dumitra (Iordache) University.
Diploma, University Timisoara, Romania, 1963. Doctor of Mathematics, Babes-Bolyai University, Cluj-Napoca, 1971.
Teacher mathematics high school, Bucharest, Romania, 1963-1964. Assistant professor mathematics Polytechnic University Bucharest, 1964-1970, lecturer, 1970-1976. Professor Polytechnic University, Bucharest, since 1976.
Senate member University Polytechnic, Bucharest.
(Geometric dynamics is a tool for developing a mathematica...)
(The object of this book is to present the basic facts of ...)
(The object of this book is to present the basic facts of ...)
Deputy Popular Council Nicolae Balcescu, Bucharest, 1965-1970. Member Society Mathematics Sciences Romania, Tensor Society Japan, professors' Council Transport Faculty, American Mathematics Society, Balkan Society Geometers (vice president since 1994).
Married Aneta Anghel, August 21, 1965. Children: Daniel Ion, Sorin Adrian.