vulvar cancer is a rare gynecological malignancy with mainly lymphatic spread. sentinel node mapping plays an important role in the management of this gynecological malignancy. in the current study, we reported our experience in sentinel node mapping of vulvar cancer and review the literature accordingly. since the introduction of sentinel node mapping to the surgical oncology community of our ...

A theorem of Glimm states that representation theory of an NGCR C∗-algebra is always intractable, and the Cuntz algebra ON is a case in point. The equivalence classes of irreducible representations under unitary equivalence cannot be captured with a Borel cross section. Nonetheless, we prove here that wavelet representations correspond to equivalence classes of irreducible representations of ON...

An equigenerated monomial ideal [Formula: see text] in the polynomial ring is a Freiman if text], where analytic spread of and least number generators text]. In this paper, we classify certain classes Borel-type ideals, including Borel ideals with multiple principal text]-Borel which are Freiman.

Title of dissertation: THE BOREL COMPLEXITY OF ISOMORPHISM FOR SOME FIRST-ORDER THEORIES Richard Rast, Doctor of Philosophy, 2016 Dissertation directed by: Professor Michael C. Laskowski Department of Mathematics In this work we consider several instances of the following problem: “how complicated can the isomorphism relation for countable models be?” Using the Borel reducibility framework from...

See [Oli04]. In [AdKech00], Adams and Kechris showed that the relation of equality on Borel sets (and therefore, any Borel equivalence relation whatsoever) is Borel reducible to the equivalence relation of Borel bireducibility. (In somewhat finer terms, they showed that the partial order of inclusion on Borel sets is Borel reducible to the quasi-order of Borel reducibility.) Their technique was...

We prove a classification theorem of the “Glimm–Effros” type for Borel order relations: a Borel partial order on the reals either is Borel linearizable or includes a copy of a certain Borel partial order ≤0 which is not Borel linearizable. Notation. A binary relation 4 on a set X is a partial quasi-order , or p.q.-o. in brief, on X, iff x 4 y∧y 4 z ⇒ x 4 z, and x 4 x for any x ∈ X. In this case...

The problem of extrapolating the perturbation series for dilute Fermi gas in three dimensions to unitary limit infinite scattering length and into BEC region is considered, using available strong-coupling information constrain extrapolation problem. In this constrained (CEP), goal find classes approximants that give well-converged results already low perturbative truncation orders. First, it sh...

We show that Hausdorff measures of different dimensions are not Borel isomorphic; that is, the measure spaces (R, B, H) and (R, B, H) are not isomorphic if s 6= t, s, t ∈ [0, 1], where B is the σ-algebra of Borel subsets of R and H is the d-dimensional Hausdorff measure. This answers a question of B. Weiss and D. Preiss. To prove our result, we apply a random construction and show that for ever...

In this paper we give some characterizations of topological extreme amenability. Also we answer a question raised by Ling [5]. In particular we prove that if T is a Borel subset of a locally compact semigroup S such that M(S)* has a multiplicative topological left invariant mean then T is topological left lumpy if and only if there is a multiplicative topological left invariant mean M on M(S)* ...