A generalized Persidskii-like theorem is derived and shown to be applicable to the stability analysis of a class of gradient dynamical systems with discontinuous right hand sides. These dynamical systems arise from the steepest descent technique applied to a variety of problems suitably formulated as constrained minimization problems. The problems susceptible to this approach include linear pro...

We will show that ζK(s, x) extends for all s ∈ C and is analytic everywhere except at s = 1 where it has a simple pole. It turns out that the special values ζK(1 − k, x) can be written as a polynomial in x, thus giving a generalization of the Bernoulli polynomials (in the case K is totally real). This work had its genesis in looking for simple proofs of the well-known formula ζ(1−k) = −Bk/k, wh...

We formulate the theory of nearly autoparallel maps (generalizing conformal transforms) of locally anisotropic spaces and define the nearly autoparallel integration as the inverse operation to both covariant derivation and deformation of connections by nearly autoparallel maps. By using this geometric formalism we consider a variant of solution of the problem of formulation of conservation laws...

We give an algorithm of decomposition for a finite-dimensional Lie algebra over a field of characteristic 0 permitting to generalize the derivation tower theorem of Lie algebras.

LetN be a zero-symmetric left near-ring, not necessarily with amultiplicative identity element; and letZ be its multiplicative center. DefineN to be 3-prime if for all a, b ∈ N\{0}, aNb / {0}; and callN 2-torsion-free if N, has no elements of order 2. A derivation onN is an additive endomorphism D of N such that D xy xD y D x y for all x, y ∈ N. A generalized derivation f with associated deriva...