Related papers: The Splitting Lemma in any Characteristic

Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…

We give a new sufficient condition which allows to test primality of Fermat's numbers. This characterization uses uniquely values at most equal to tested Fermat number. The robustness of this result is due to a strict use of elementary…

We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…

We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a central division algebra, and a description…

We obtain a polynomial criterion for a set to have a small doubling in terms of the common energy of its subsets.

The Nelson-Seiberg theorem relates R-symmetries to F-term supersymmetry breaking, and provides a guiding rule for new physics model building beyond the Standard Model. A revision of the theorem gives a necessary and sufficient condition to…

The (.)_reg construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)_reg which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J-order structure). We show…

We give some details about the stationary phase lemma. We first prove a special case where the high order terms are derived explicitly. Based on that, we prove a more general case by using Morse lemma.

The law of large numbers is one of the most fundamental results in Probability Theory. In the case of independent sequences, there are some known characterizations; for instance, in the independent and identically distributed setting it is…

A number has the "collective" property if the number is the greatest lower bound of a bounded, strictly decreasing sequence on the real line. We prove that numbers with the collective property constitute an empty set.

We show that the Generalized Vanishing Conjecture $$\forall_{m \ge 1} [\Lam^m f^m = 0] \Longrightarrow \forall_{m \gg 0} [\Lam^m (g f^m) = 0]$$ for a fixed differential operator $\Lam \in k[\partial]$ follows from a special case of it,…

We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.

We reexamine the characterization of incentive compatible single-parameter mechanisms introduced in Archer & Tardos(2001). We argue that the claimed uniqueness result, called `Myerson's Lemma' was not well established. We provide an…

An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some appropriate local chart by a differential equation with algebraic coefficients. We show that there exists at least countably many…

We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics…

Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…

Let R be a locally finitely generated algebra over a discrete valuation ring V of mixed characteristic. For any of the homological properties, the Direct Summand Theorem, the Monomial Theorem, the Improved New Intersection Theorem, the…

Pellet's theorem determines when the zeros of a polynomial can be separated into two regions, based on the presence or absence of positive roots of an auxiliary polynomial, but does not provide a method to verify its conditions or to…

Dirichlet's Lemma states that every primitive quadratic Dirichlet character $\chi$ can be written in the form $\chi(n) = (\frac{\Delta}n)$ for a suitable quadratic discriminant $\Delta$. In this article we define a group, the separant class…

We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…