in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...

Abstract This paper deals with some analytic aspects of GG system introduced by I.M. Gelfand and M.I. Graev: we compute the dimension solution space over field meromorphic functions periodic respect to a lattice. We describe monodromy invariant subspace space. provide connection formula between pair bases consisting $\Gamma $-series solutions associated regular triangulations adjacent each othe...

This paper concerns the problem of output consensus in nonlinear non-minimum phase systems. The main contribution of the paper is to guarantee achieving consensus in the presence of unstable zero dynamics. To achieve this goal, an output redefinition method is proposed. The new outputs of agents are functions of original outputs and internal states and defined such that the dynamics of agents a...

In this paper Lie’s formalism is applied to deduce classes of solutions of a nonlinear partial differential equation (nPDE) of second order with quadratic nonlinearity. The equation has the meaning of a field equation appearing in the formulation of kinetic models. Similarity solutions and transformations are given in a most general form derived to the first time in terms of reciprocal Jacobian...

Invariant assertions play an important role in the analysis and documentation of while loops of imperative programs. Invariant functions and invariant relations are alternative analysis tools that are distinct from invariant assertions but are related to them. In this paper we discuss these three concepts and analyze their relationships. The study of invariant functions and invariant relations ...

We compute the linear metric perturbation to a Schwarzschild black hole generated by spinning compact object, specializing circular equatorial orbits with an (anti-)aligned spin vector. derive two-timescale expansion of field equations, attendant waveform-generation framework, that includes all effects through first postadiabatic order, and we use Regge-Wheeler-Zerilli formalism in frequency do...

The aim of this paper is to present a proof of the hyperbolicity of the family $f_c(x)=c(x-frac{x^3}{3}), |c|>3$, on an its invariant subset of $mathbb{R}$.

In the transformation semigroup (X, S) we introduce the height of a closed nonempty invariant subset of X, define the transformed dimension of nonempty subset S of X and obtain some results and relations.

The generalized Liénard polynomial differential systems are the of form x′ = y, y′ − f(x)y g(x), where f and g polynomials. We characterize all having an invariant algebraic curve. show that first four higher coefficients in variable defining curve, determine completely system. This fact does not hold for arbitrary systems. Primary 34A05. Secondary 34C05, 37C10.