We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second spac...

Contrary to the simple structure of tensor product quaternionic Hilbert space, octonionic situation becomes more involved. It turns out that an space can be decomposed as orthogonal direct sum two subspaces, each them isomorphic a irreducible with real space. As application, we find for given basis, Parseval equality holds if and only basis is weak associative. Fortunately, there always exists ...

It is shown that the Orlicz–Lorentz spaces $\ell ^n_{M,a}$, $n\in \mathbb {N}$, with Orlicz function $M$ and weight sequence $a$ are uniformly isomorphic to subspaces of $L_1$ if norm $\| \cdot \|_{M,a}$ satisfies certain Hardy-type inequalities. This includes embedding some Lorentz $\mathrm {d}^n(a,p)$. The approach based on combinatorial averaging techniques, a new result independent intere...

We study graphs coming from quadratic spaces over finite fields which generalize a recent result given by Bishnoi, Ihringer, and Pepe (2020). More precisely, we the graph Γ□(n,k,q) defined as follows: vertex set is of k-dimensional subspaces fixed space (Fqn,x12+⋯+xn−12+λxn2) isometrically isomorphic to x12+⋯+xk2. Here λ non-square in Fq, two vertices x,y are adjacent if x⊆y⊥.

In this paper we emphasize two different aspects of abduction in Logic Programming (LP): (1) the engineering of LP abduction systems, and (2) application of LP abduction, complemented with other non-monotonic features, to model morality issues. For the LP engineering part, we present an implemented tabled abduction technique in order to reuse priorly obtained (and tabled) abductive solutions, f...

Finding models of logical formulas is a challenging problem. For first-order formulas, a finite model can be found by exhaustive search. For many structured problem instances, there is much isomorphism in the search space. This paper proposes general-purpose techniques for eliminating isomorphic subspaces, which can be helpful when the formulas have many predicates. The techniques are based on ...

We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set A, in the Effros-Borel space of subspaces of C[0, 1], of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space Y , with a Schauder basis, that contains isomorphic copies of every space X in the c...

The paper addresses a problem of sampling discretization integral norms elements finite-dimensional subspaces satisfying some conditions. We prove results under standard assumption formulated in terms the Nikol'skii-type inequality. In particular, we obtain upper bounds on number sample points sufficient for good Lp norms, 1≤p<2, functions from continuous functions. Our new improve upon known t...