A direct application of Zorn’s lemma gives that every Lipschitz map f : X ⊂ Qp → Qp has an extension to a Lipschitz map f̃ : Qp → Qp . This is analogous to, but easier than, Kirszbraun’s theorem about the existence of Lipschitz extensions of Lipschitz maps S ⊂ Rn → R`. Recently, Fischer and Aschenbrenner obtained a definable version of Kirszbraun’s theorem. In this paper, we prove in the p-adic ...

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of infinite families of QP codes which includes all binary, ternary and quaternary codes known to is. We continue further with a list of sporadic examples of binary ...

An isometric immersion f : Mn ? ?Mm from an n-dimensional Riemannian manifold into almost Hermitian of complex dimension m is called pointwise slant if its Wirtinger angles define a function defined on Mn. In this paper we establish the Existence and Uniqueness Theorems for immersions manifolds space form ?Mn(c) constant holomorphic sectional curvature c, which extend proved by B.-Y. Chen L. Vr...

For a Tychonoff space $X$, we denote by $C_p(X)$ the of all real-valued continuous functions on $X$ with topology pointwise convergence.  We study functional characterization covering property Hurewicz.

Given a compact orientable surface Σ, let S(Σ) be the set of isotopy classes of essential simple loops on Σ. We determine a complete set of relations for a function from S(Σ) to Z to be a geometric intersection number function. As a consequence, we obtain explicit equations in R S(Σ) and P (R S(Σ)) defining Thurston's space of measured laminations and Thurston's compactification of the Teichmül...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived

For a linear group G acting on an absolutely irreducible variety X over Q, we describe the orbits of X(Qp) under G(Qp) and of X(Fp((t))) under G(Fp((t))) for p big enough. This allows us to show that the degree of a wide class of orbital integrals over Qp or Fp((t)) is ≤ 0 for p big enough, and similarly for all finite field extensions of Qp and Fp((t)).

In this letter, we present an approach for learning a neural implicit signed distance function expressed in joint space coordinates, that efficiently computes distance-to-collisions arbitrary robotic manipulator configurations. Computing such distances is long standing problem robotics as approximate representations of the robot and environment geometry can lead to overly conservative constrain...

For a linear group G acting on an absolutely irreducible variety X over Q, we describe the orbits of X(Qp) under G(Qp) and of X(Fp((t))) under G(Fp((t))) for p big enough. This allows us to show that the degree of a wide class of orbital integrals over Qp or Fp((t)) is ≤ 0 for p big enough, and similarly for all finite field extensions of Qp and Fp((t)).

Sequences with ultrashort echo times enable new applications of MRI, including bone, tendon, ligament, and dental imaging. In this article, a sequence is presented that achieves the shortest possible encoding time for each k-space point, limited by pulse length, hardware switching times, and gradient performance of the scanner. In pointwise encoding time reduction with radial acquisition (PETRA...