Volume 17, Issue 2

Stochastic processes with discrete time are considered which are described by one multinomial scheme until the random disorder moment and by another one, after the disorder moment. The problems of optimal in mean square sense filtering and interpolation of disorder moment are investigated and the forecasting estimate for this process is found.

An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G , let X be a G -simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪( G ) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

The geometric properties of quasiconformal mappings and generalized quasiconformal mappings are studied. Inequalities of the Grötzsch–Belinskii type are established to estimate the distortion of p -moduli of ring domains for these classes of mappings.

The present paper deals with the Bézier variant of the Szász–Kantorovich operator. Its approximation properties are studied. A convergence theorem of this type approximation operators for locally bounded functions is established, which subsumes the approximation of functions of bounded variation as a special case.

A class of bases of the space of cusp forms is constructed for any integer k and character mod 8.

In [Int. J. Math. Math. Sci. 2005: 3045–3055] by Liu et al. the common property ( E.A ) for two pairs of hybrid maps is defined. Recently, O'Regan and Shahzad [Acta Math. Sin. (Engl. Ser.) 23: 1601–1610, 2007] have introduced a very general contractive condition and obtained some fixed point results for hybrid maps. We introduce a new property for pairs of hybrid maps that contains the property ( E.A ) and obtain some coincidence and fixed point theorems that extend/generalize some results from the above-mentioned papers.

Some nonlocal problems for one class of second order strictly hyperbolic systems in a strip on the plane are considered in weighted functional spaces. Proceeding from the structure of solutions of hyperbolic systems and using the methods of complex analysis conditions are found for weight exponents of functional spaces which ensure well-posedness of considered problems.

We seek for closed Jordan curves C , for which there exists a pair of analytic functions ƒ, F , where ƒ is analytic in the interior of C , while F in the exterior, except for a given singularity, and with at C .

We study the operad of associative algebras equipped with a derivation. We show that it is determined by polynomials in several variables and substitution. Replacing polynomials by rational functions gives an operad which is isomorphic to the operad of “moulds”. It provides an efficient environment for doing integro-differential calculus. Interesting variations are obtained by using formal group laws. The preceding case corresponds to the additive formal group law. We unravel the notion of homotopy associative algebra with derivation in the spirit of Kadeishvili's work.

Second order nonlinear ordinary differential equations are considered, and a certain boundary value problem on the whole line is studied. Two theorems are obtained as main results. The first theorem is established by the use of the Schauder theorem and concerns the existence of solutions, while the second theorem is concerned with the existence and uniqueness of solutions and is derived by the Banach contraction principle. These two theorems are applied, in particular, to the specific class of second order nonlinear ordinary differential equations of Emden–Fowler type and to the special case of second order linear ordinary differential equations, respectively.

Kadeishvili's proof of theminimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv. 35 :3 (1980), 231–238] induces an algorithm for the inductive computation of an A ∞ -algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A ∞ -algebra structure after a finite amount of computational work.

Let T (ƒ) denote the Littlewood–Paley square operators, including the g -function g (ƒ), Luzin area function S (ƒ) and Stein's function , on the generalized Orlicz–Campanato spaces , where Φ is a N-function satisfying the Δ 2 condition and φ a positive function satisfying the doubling property. It is proved that if T (ƒ)( x 0 ) < ∞ for a single point , then T (ƒ)( x ) exists almost everywhere in , and T (ƒ) is bounded on the spaces .