Related papers: Integrated and differentiated sequence spaces
Two numerical algorithms are proposed for computing an interval matrix containing the matrix gamma function. In 2014, the author presented algorithms for enclosing all the eigenvalues and basis of invariant subspaces of $A \in \mathbb{C}^{n…
In data rich environments we may sometimes deal with time series that are probability density-function valued, such as observations of cross-sectional income distributions over time. To apply the methods of functional time series analysis…
Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in Harmonic Analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have…
An important problem in machine learning theory is to understand the approximation and generalization properties of two-layer neural networks in high dimensions. To this end, researchers have introduced the Barron space…
In this book super interval matrices using the special type of intervals of the form [0, a] are introduced. Several algebraic structures like semigroups, groups, semirings, rings, semivector spaces and vector spaces are introduced. Special…
We introduce a unified method for study of 2-dimensional invariant subspaces of matrices and their corresponding super-eigenvalues. As a novel application to non-commutative algebra, we present a connection between the eigenvalues of…
In these lectures, we discuss two approaches to studying orbit spaces of algebraic Lie groups. Due to algebraic approach orbit space, or quotient, is an algebraic manifold, while from the differential viewpoint a quotient is a differential…
Refined algebraic domains are regions in the plane surrounded by finitely many non-singular real algebraic curves which may intersect with normal crossing. We are interested in shapes of such regions with surrounding real algebraic curves.…
Gaussian and discrete non-Gaussian spatial datasets are common across fields like public health, ecology, geosciences, and social sciences. Bayesian spatial generalized linear mixed models (SGLMMs) are a flexible class of models for…
This paper proposes a framework dedicated to the construction of what we call discrete elastic inner product allowing one to embed sets of non-uniformly sampled multivariate time series or sequences of varying lengths into inner product…
We investigate algebraic structures within sets of surjective and injective linear operators between sequence spaces, completing results of Aron et al.
By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra…
The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…
We combine multi-task learning and semi-supervised learning by inducing a joint embedding space between disparate label spaces and learning transfer functions between label embeddings, enabling us to jointly leverage unlabelled data and…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
We develop further the approach to derived differential geometry introduced in Costello's work on the Witten genus. In particular, we introduce several new examples of L-infinity spaces, discuss vector bundles and shifted symplectic…
A vector space is commonly defined as a set that satisfies several conditions related to addition and scalar multiplication. However, for beginners, it may be hard to immediately grasp the essence of these conditions. There are probably a…
We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we find an interesting duality for such objects. A definition of a quantum…
The f-invariant is an injective homomorphism from the 2-line of the Adams-Novikov spectral sequence to a group which is closely related to divided congruences of elliptic modular forms. We compute the f-invariant for two infinite families…
In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study.…