Related papers: The Coase Theorem and Ideal Exchanges
A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence that is weaker than exchangeability, but is equivalent to exchangeability for stationary sequences. In this article we…
A statistical-mechanical treatment of collision leads to a formal connection with transition-state theory, suggesting that collision theory and transition-state theory might be joined ultimately as a collision induced transition state…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
The paper presents a new proof of O'Cinneide's characterization theorem. It is much simpler than the original one and constructive in the sense that we not only show the existence of a phase type representation, but present a procedure…
The change of variable theorem is proved under the sole hypothesis of differentiability of the transformation. Specifically, it is shown under this hypothesis that the transformed integral equals the given one over every measurable subset…
We study the max-plus or tropical analogue of the notion of polar: the polar of a cone represents the set of linear inequalities satisfied by its elements. We establish an analogue of the bipolar theorem, which characterizes all the…
The aim of this paper is to give new representation theorems for extended contact algebras. These representation theorems are based on equivalence relations.
In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are…
We prove a analog of Kurosh theorem for countable Borel equivalence relations giving the structure of sub-relations in free products.
In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.
In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
In this instructional exposition in Portuguese for the popularisation of mathematics, we state and prove the completeness theorem.
Let $S=K[x_1, \ldots,x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $\mathfrak{c}\in\mathbb{Z}_{>0}^n$, the ideal $I_{\mathfrak{c}}$ is the ideal generated by those…
The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.
If $I$ is a monomial ideal with linear quotients, then it has componentwise linear quotients. However, the converse of this statement is an open question. In this paper, we provide two classes of ideals for which the converse of this…
The most powerful formulation of the Central Sets Theorem in an arbitrary semigroup was proved in the work of De, Hindman, and Strauss. The sets which satisfy the conclusion of the above Central Sets Theorem are called $C$-sets. The…
We define a diophantine condition for interval exchange transformations (i.e.t.s). When the number of intervals is two, that is for rotations on the circle, our condition coincides with classical Khinchin condition. We prove for i.e.t.s the…