On Funnels of Multis and Their Behavior
On Galilean connections and the first jet bundle
We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations - sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces “laboratory” coordinate systems, and the geodesic equations in this coordinates form a system of second-order...
On Gel'fand's method of chasing for solving multipoint boundary value problems
On general solutions of linear differential equations.
On generalized differential equations in Banach spaces [Book]
On generalized periodic solutions of linear differential equations of order n
On generalized solutions of some differential non-linear equations of order n
On generalized symmetric means and Stirling numbers of the second kind
On generalized Wazewski and Lozinskii inequalities for semilinear abstract differential-delay equations.
On geometric detection of periodic solutions and chaotic dynamics.
On global exponential stability of discrete-time Hopfield neural networks with variable delays.
On global transformations of functional-differential equations of the first order
The paper describes the general form of functional-differential equations of the first order with delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation for is solved on and a method of proof by J. Aczél is applied.
On global transformations of ordinary differential equations of the second order
The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form is solved on for ,
On gradient at infinity of semialgebraic functions
Let f: ℝⁿ → ℝ be a C² semialgebraic function and let c be an asymptotic critical value of f. We prove that there exists a smallest rational number such that |x|·|∇f| and are separated at infinity. If c is a regular value and , then f is a locally trivial fibration over c, and the trivialisation is realised by the flow of the gradient field of f.
On granular derivatives and the solution of a granular initial value problem
Perceptions about function changes are represented by rules like “If X is SMALL then Y is QUICKLY INCREASING.” The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler’s...
On -stability of autonomous systems.
On Hadamard's concepts of correctness
On Halphen and Laguerre-Forsyth canonical forms of linear differential equations
On Hill's equation with a discontinuous coefficient.
On holomorphic foliations without algebraic solutions.