Related papers: On the totally positive grassmannian

We show that any Hermiticity and trace preserving continuous semigroup gamma_t in d dimensions is completely positive if and only if the semigroup gamma_t otimes gamma_t is positivity preserving.

An algebraic notion of representational consistency is defined. A theorem relating it to free actions is proved. A metrizability problem of the quotient (a shape space) is discussed. This leads to a new algebraic variety with a…

We discuss the application of the determinantal method to the proof of the Riemann hypothesis. We start from the fact that, if a certain doubly infinite set of determinants are all positive, then the hypothesis is true. This approach…

We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.

We prove a variation of Gronwall's lemma.

We express connected Fermionic Green's functions in terms of completely explicit tree formulas. In contrast with the ordinary formulation in terms of Feynman graphs these formulas allow a completely transparent proof of convergence of the…

We prove two positivity conjectures proposed by Guo for alternating sums and factorial ratios built from Gaussian coefficients. The first result proves the positivity of the odd $q$-super Catalan numbers \[…

We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones.

We explain the motivation for looking for a predicative analogue of the notion of a topos and propose two definitions. For both notions of a predicative topos we will present the basic results, providing the groundwork for future work in…

A positive definite Hermitian lattice is said to be 2-universal if it represents all positive definite binary Hermitian lattices. We find all 2-universal ternary and quaternary Hermitian lattices over imaginary quadratic number fields.

In this note, we give a criteria whether given two Eisenstein polynomials over a padic field define the same extension (Proposition 1.6). In particular, we completely identify Eisenstein polynomials of degree p (Theorem 1.16). This note is…

We descibed all alternative algebras with invertible derivations (the analogue of Bergen-Herstein-Lanski's Theorem) and proved the analogue of Moens's Theorem.

We present a proof of completeness for the implicational propositional calculus, based on a variant of the Lindenbaum procedure.

We derive equivalent conditions for the (local) absolute continuity of two laws of semimartingales on random sets. Our result generalizes previous results for classical semimartingales by replacing a strong uniqueness assumption by a weaker…

We study grassmannians associated with a linear space with a nondegenerate hermitian form. The geometry of these grassmannians allows us to explain the relation between a (pseudo-)riemannian projective geometry and the conformal structure…

We give a proof of a result of D. Peterson's identifying the quantum cohomology ring of a Grassmannian with the reduced coordinate ring of a certain subvariety of $GL_n$. The totally positive part of this subvariety is then constructed and…

Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove an inequality involving the energy and the discriminant and apply it to deduce a result on totally positive…

This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…

Under appropriate spectral assumptions we prove two existence results for positive solutions of Lichnerowicz-type equations on complete manifolds. We also give a priori bounds and a comparison result that immediately yields uniqueness for…

The key result in the present paper is a direct analogue of the celebrated Thurston's Theorem for marked Thurston maps with parabolic orbifolds. Combining this result with previously developed techniques, we prove that every Thurston map…