A nonparametric regression setting is considered with a real-valued covariate and responses from metric space. One may approach this via Fréchet regression, where the value of function at each point estimated mean calculated an objective function. second geodesic which builds upon fitting geodesics to observations by least squares method. These approaches are applied transform two most importan...

Let k be a field of char(k) 6= 2, and suppose that q ∈ k is not a root of unity. The associated quantum plane [5, §IV.1], denoted by kq[x, y], is defined to be the free k-algebra k{x, y} generated by x and y, modulo the relation yx = qxy. The set of monomials {xy}i, j≥0 is a basis for the underlying k-vector space, and for every pair (i, j) of nonnegative integers, we have yx = qxy . There is a...

This is an overview of a few possibilities that are open by model theory in applied mathematics. Most attention is paid to the present state and frontiers of the Cauchy method of majorants, approximation of operator equations with finite-dimensional analogs, and the Lagrange multiplier principle in multiobjective decision making. 1. Agenda The union of functional analysis and applied mathematic...

We consider an optimal control problem with indeenite cost for an abstract model which covers in particular hyperbolic and hyperbolic-like systems in a general bounded domain. Necessary and suucient conditions are given for the synthesis of the optimal control, which is given in terms of the Riccati operator arising from a nonstandard Riccati equation. The theory also extends a nite-dimensional...