Related papers: Model Theory of Scattered Piecewise Interpretable …
We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lower and upper bounds on the dimension of this space by…
This paper provides robust estimators for the first canonical correlation and directions of random elements on Hilbert separable spaces by using robust association and scale measures combined with basis expansion and/or penalizations as a…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored…
We give an overview of certain aspects of tractability analysis of multivariate problems. This paper is not intended to give a complete account of the subject, but provides an insight into how the theory works for particular types of…
An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
We consider matrix problems in Hilbert spaces (orthoscalar representations of quivers and posets). A criterion of tameness of the problem of classification of indecomposable orthoscalar representations of a quiver is given.
We give a description of the value of a finitary localizing invariant, such as algebraic $K$-theory, on the category of sheaves on a locally coherent space $X$. This in particular includes all spaces that arise as spectra of commutative…
Semi-cosimplicial objects in the category of Hilbert spaces with isometries which are motivated by non-commutative probability theory, in particular by the distributional symmetry of spreadability, are introduced and systematically…
In a series of papers published in this Journal (J. Math. Phys.), a discussion was started on the significance of a new definition of projective representations in quaternionic Hilbert spaces. The present paper gives what we believe is a…
We develop a Hilbert space framework for a number of general multi-scale problems from dynamics. The aim is to identify a spectral theory for a class of systems based on iterations of a non-invertible endomorphism. We are motivated by the…
We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…
The work lays the foundations of the theory of changeable sets. In author opinion, this theory, in the process of it's development and improvement, can become one of the tools of solving the sixth Hilbert problem least for physics of…
In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g.…
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…
We find certain relations between flag Hilbert schemes of points on plane curves and moduli spaces of one-dimensional plane sheaves. We show that some of these moduli spaces are unirational.
We compare the concept of triplet of closely embedded Hilbert spaces with that of generalised triplet of Hilbert spaces in the sense of Berezanskii by showing when they coincide, when they are different, and when starting from one of them…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
The aim of this paper is to present the technique (and its linkage with physics) of overcoming problems connected to modeling social structures, which are typically hierarchical. Hierarchical Linear Models provide a conceptual and…
We consider the multigraded Hilbert scheme corresponding to the Hilbert function of a finite number of points in general position in a smooth projective complex toric variety. We develop several criteria for a point of that parameter space…