We prove the existence of a Gevrey family of invariant curves for analytic reversible mappings under weaker nondegeneracy condition. The index of the Gevrey smoothness of the family could be any number μ > τ 2, where τ > m − 1 is the exponent in the small divisors condition and m is the order of degeneracy of the reversible mappings. Moreover, we obtain a Gevrey normal form of the reversible ma...

In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.

This paper discusses the variations in the early-age pavement smoothness at different measurement times and locations in three jointed plain concrete pavements ( JPCPs) representing different ranges of construction times. Surface profile measurements were made during the early morning and late afternoon hours at different locations of the instrumented JPCPs during the first 7 d after constructi...

In this paper, X denotes an arbitrary nonempty set, a lattice of subsets of X with ∅, X∈ , A( ) is the algebra generated by and M( ) is the set of nontrivial, finite, and finitely additive measures on A( ), and MR( ) is the set of elements of M( ) which are -regular. It is well known that any μ ∈M( ) induces a finitely additive measure μ̄ on an associated Wallman space. Whenever μ ∈MR( ), μ̄ is c...

We obtain a characterization of modulus of smoothnes of fractional order in the Lebesgue spaces Lω, 1 < p <∞, with weights ω satisfying the Muckenhoupt’s Ap condition. Also, a realization result and equivalence between modulus of smoothness and the Peetre K-functional are proved in Lω for 1 < p <∞ and ω ∈ Ap.

The Cauchy problem for first order system L(t, x, ∂t, ∂x) is known to be well posed in L when a it admits a microlocal symmetrizer S(t, x, ξ) which is smooth in ξ and Lipschitz continuous in (t, x). This paper contains three main results. First we show that a Lipsshitz smoothness globally in (t, x, ξ) is sufficient. Second, we show that the existence of symmetrizers with a given smoothness is e...

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

applying 2d algorithms for inverting the potential field data is more useful and efficient than their 3d counterparts, whenever the geologic situation permits. this is because the computation time is less and modeling the subsurface is easier. in this paper we present a 2d inversion algorithm for interpreting gravity data by employing a set of constraints including minimum distance, smoothness,...