Vladimir Balan

Deviations of Geodesics in Fibered Finslerian Approach

In §1 the authors introduce basic notions for developing the fibered Finslerian approach, considering the case of a vector bundle endowed with a non-linear connection, a (h, v) metric and a d — connection. In §2 the generalized equations of stationary curves for G.S. Asanov’s Lagrangian [1, 2] and for the classical one are derived, and in §3 the equations for deviations of geodesics for the given context are obtained in brief and explicit form. §4 contains applications to particular cases (generalized Lagrange, Lagrange, Finsler and Riemannian cases), emphasizing the relationships of extended results to known classical ones.

SYNGE-BEIL AND RIEMANN-JACOBI JET STRUCTURES WITH APPLICATIONS TO PHYSICS

In the framework of geometrized first-order jet approach, we study the SyngeBeil generalized Lagrange jet structure, derive the canonic nonlinear and Cartan connections, and infer the Einstein-Maxwell equations with sources; the classical ansatz is emphasized as a particular case. The Lorentz-type equations are described and the attached Riemann-Jacobi structures for two certain uniparametric cases are presented. 2000 Mathematics Subject Classification: 58A20, 58A30, 53B15, 53B50, 53C80. 1. Preliminaries. Let (T , hαβ) and (M, γij) be two ∞ pseudo-Riemannian manifolds of dimensions m and n, respectively. We denote by ζ = (E = j 1 (T , M), π,T × M) the first-order jet bundle of mappings ϕ : T → M ,w ith the local coordinates

Research of Gravitation in Flat Minkowski Space

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor φ, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the n-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order c−2.

Magnetic dynamical systems

§1 contains a brief exposition of elementary notions of phase portrait theory; §2 describes the magnetic field generated by a basic plane configuration. §3 gives a selective list of the plain configurations of piece wise rectilinear circuits, primarily investigated by Sabba Ştefănescu, and develops new properties of the Schlumberger magnetic field. Finally, two computer experiments regarding Runge-Kutta approximations of magnetic lines are detailed.

Versal deformation and static bifurcation diagrams for the cancer cell population model

The paper studies the existence of rest-points and the static bifurcation diagrams of a given nonlinear differential system modeling the cancer cell population evolution from biology. To this aim, the nullclines, the equilibrium points, the transient set, the static bifurcation equation and the associated versal deformation are investigated. The results are further discussed in view of potential applications to cancer therapy.

Distinguished geodesics and jacobi fields on first order jet spaces

In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized. The main geometric objects and the paths are described and, in the case when the vertical metric is independent of fiber coordinates, the first two variations of energy and the extended Jacobi field equations are derived.

Variational problems in the geometrized first‐order jet framework

In the framework of geometrized jet spaces of first order endowed with a Lagrange structure, is discussed the existence of Lagrangian canonic nonlinear connections. The Euler‐Lagrange equations for certain Kronecker‐type Lagrangian cases are derived, and extensions of the known results are provided.

Fuzzy T-map estimates of complex circuit reliability

The fuzzy T — norms and T — conorms offer alternatives to compute the classical structural polynomial of a complex circuit. The reliability of a special complex 4-node circuit were evaluated, and it is show that, among a certain family of classic T — norms, the Frank T-norm provides a T — map emerging from the structural polynomial, which proves to be the best estimate for this reliability. Illustrative plots contain the 2 — parameter reliability map and the optimal fuzzy approximate — the best candidate T-map.