We present some properties regarding Darboux property, non-atomicity, regular fuzziness of multimeasures taking values in the family of all closed nonvoid subsets of a real normed space. Key–words: Darboux property, fuzzy multimeasure, atom, non-atomic, regular, diffused.

In this paper we study planar polynomial differential systems of this form: dX dt = Ẋ = A(X, Y ), dY dt = Ẏ = B(X, Y ), where A, B ∈ Z[X, Y ] and degA ≤ d, degB ≤ d, ‖A‖∞ ≤ H and ‖B‖∞ ≤ H. A lot of properties of planar polynomial differential systems are related to irreducible Darboux polynomials of the corresponding derivation: D = A(X, Y )∂X + B(X, Y )∂Y . Darboux polynomials are usually comp...

A minimal sufficient condition for global optimality involving the Darboux point, analogous to the minimal sufficient condition of local optimality involving the conjugate point, is presented. The Darboux point is then characterized for optimal control problems with linear dynamics, cost functionals with a general terminal state term and an integrand quadratic in the state and control, and gene...

The paper introduces a new kind of special ruled surface. base each surface is taken to be one the Smarandache curves given curve according Frenet frame, and generator (ruling) chosen corresponding unit Darboux vector. characteristics these newly defined surfaces are investigated by means first second fundamental forms their curvatures. An example provided considering both helix Viviani’s curve.

A Darboux-transformed surface gravitational acceleration of the constant gravitational acceleration for a body endowed with an atmospheric layer is shown to turn the atmospheric free fall with quadratic resistance in the opposite motion, i.e., a free rising. Although the atmosphere of such a body may look completely normal, it is the time dependence of its gravitational field that produces this...

It is well known that if a scalar second order hyperbolic partial differential equation in two independent variables is Darboux integrable, then its local Cauchy problem may be solved by ordinary differential equations. In addition, such an equation has infinitely many non-trivial conservation laws. Moreover, Darboux integrable equations have properties in common with infinite dimensional compl...

In this paper we consider the problems connected with the continuity of Darboux transformations and the monotonicity of the restrictions of these transformations. We show that it becomes possible to give answers to many questions concerning these problems if our considerations are connned to the family of c-functions which is deened in the paper. In paper DG] (1875), the rst example of a discon...

In this paper we show that there are explicit Yang-Baxter maps with Darboux-Lax representation between Grassmann extensions of algebraic varieties. Motivated by some recent results on noncommutative extensions of Darboux transformations, we first derive a Darboux matrix associated with the Grassmann-extended derivative Nonlinear Schrödinger (DNLS) equation, and then we deduce novel endomorphism...

Using as an illustrative example the p=1 operator-ordered Wheeler-DeWitt equation for a closed, radiation-filled Friedmann-Robertson-Walker universe, we introduce and discuss the supersymmetric double Darboux method in quantum cosmology. A one-parameter family of " quantum " universes and the corresponding " wavefunctions of the universe " for this case are presented. Many interesting results h...

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the BirkhoffGustavson(BG)-normalization: In solving an inverse problem of the BGnormalization on computer algebra, it is shown that if the perturbed harmonic oscillators with a homogeneous cubic-polynomial potential and with a homogeneous quartic-polynomial potenti...