Related papers: Partial isometries in an absolute order unit space
We propose a theoretical framework under which preference profiles can be meaningfully compared. Specifically, given a finite set of feasible allocations and a preference profile, we first define a ranking vector of an allocation as the…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of…
An ordered semiring is a commutative semiring equipped with a compatible preorder. Ordered semirings generalise both distributive lattices and commutative rings, and provide a convenient framework to unify certain aspects of lattice theory…
In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…
A new linear mapping of the linear vector space (LVS) of the octonions is suggested as an approach to the co-ordinatization of space-time. This approach resolves some perplexing issues concerning the validity of certain pre-metric notions…
We investigate a relations of almost isometric embedding and almost isometry between metric spaces and prove that with respect to these relations: (1) There is a countable universal metric space. (2) There may exist fewer than continuum…
The conditions under which a linear anisotropic polarization element orthogonalizes several polarization states of input totally polarized light were studied in the paper. The criterion for orthogonalization was obtained in the form of…
Different notions for order convergence have been considered by various authors. Associated to every notion of order convergence corresponds a topology, defined by taking as the closed sets those subsets of the poset satisfying that no net…
Orthogonal matrices which are linear combinations of permutation matrices have attracted enormous attention in quantum information and computation. In this paper, we provide a complete parametric characterization of all complex, real and…
For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the…
Order unit property of a positive element in a $C^{*}$-algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary $C^{*}$-subalgebras of a $C^{*}$-algebra are…
The note describes the cones in the Euclidean space admitting isotonic metric projection with respect to the coordinate-wise ordering. As a consequence it is showed that the metric projection onto the regression cone (the cone defined by…
This paper presents a new version of boundary on coarse spaces. The space of ends functor maps coarse metric spaces to uniform topological spaces and coarse maps to uniformly continuous maps.
A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous…
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…
While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.