Related papers: Gaps for the Igusa-Todorov function

Let $\Lambda$ be a finite-dimensional $k$-algebra with $k$ algebraically closed. Bongartz has recently shown that the existence of an indecomposable $\Lambda$-module of length $n > 1$ implies that also indecomposable $\Lambda$-modules of…

Let $L(s,f)$ be an $L$-function associated to a primitive (holomorphic or Maass) cusp form $f$ on GL(2) over $\mathbb{Q}$. Combining mean-value estimates of Montgomery and Vaughan with a method of Ramachandra, we prove a formula for the…

Let $\Gamma$ denote a finite, simple and connected graph. Fix a vertex $x$ of $\Gamma$ which is not a leaf and let $T=T(x)$ denote the Terwilliger algebra of $\Gamma$ with respect to $x$. Assume that the unique irreducible $T$-module with…

We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m-cluster-tilting object in a triangulated m-Calabi-Yau category, where m is any integer greater than 2.

Let $F(y):=\displaystyle\int_t^TL(s, y(s), y'(s))\,ds$ be a positive functional, unnecessarily autonomous, defined on the space $ W^{1,p}([t,T]; \mathbb R^n)$ ($p\ge 1$) of Sobolev functions, possibly with prescribed one or two end point…

We consider the minimization problem of $\phi$-divergences between a given probability measure $P$ and subsets $\Omega$ of the vector space $\mathcal{M}_\mathcal{F}$ of all signed finite measures which integrate a given class $\mathcal{F}$…

We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified.…

In this paper, we establish two finiteness results and propose a conjecture concerning the Pythagoras number $P(A)$ of a finitely generated real algebra $A$. Let $X \hookrightarrow \mathbb{P}^n$ be an integral projective surface over…

Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…

In this note we announce the proof of the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s => 3; this is new for s => 4, the cases s = 1,2,3 having been previously established. More precisely we outline a proof (details of which…

The $p$-adic Littlewood Conjecture due to De Mathan and Teuli\'e asserts that for any prime number $p$ and any real number $\alpha$, the equation $$\inf_{|m|\ge 1} |m|\cdot |m|_p\cdot |\langle m\alpha \rangle|\, =\, 0 $$ holds. Here, $|m|$…

Cai and Hemachandra used iterative constant-setting to prove that Few $\subseteq$ $\oplus$P (and thus that FewP $\subseteq$ $\oplus$P). In this paper, we note that there is a tension between the nondeterministic ambiguity of the class one…

Let $A$ be a connected commutative $\C$-algebra with derivation $D$, $G$ a finite linear automorphism group of $A$ which preserves $D$, and $R=A^G$ the fixed point subalgebra of $A$ under the action of $G$. We show that if $A$ is generated…

It is shown that over an arbitrary countable field, there exists a finitely generated algebra that is nil, infinite dimensional, and has Gelfand-Kirillov dimension at most three.

Let $(X,B_X,\mu,T)$ be a measure-preserving probability system with $T$ is invertible. Suppose that $A\in B_X$ with $\mu(A)>0$ and $\epsilon>0$. For any $m\geq 1$, there exist infinitely many primes $p_0,p_1,\ldots,p_m$ with…

In this paper, we give algorithms for determining the existence of isomorphism between two finite-dimensional Lie algebras and compute such an isomorphism in the affirrmative case. We also provide algorithms for determining algebraic…

The \emph{Filter Dichotomy} says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A function between topological…

Given functions $f,g: [n] \rightarrow [n]$ do there exist $n$ points $A_1,A_2\ldots A_n$ in some metric space such that $A_{f(i)},A_{g(i)}$ are the points closest and farthest from point $A_i$? In this paper we characterize precisely which…

We consider the variety of Filippov ($n$-Lie) algebra structures on an $(n+1)$-dimensional vector space. The group $GL_n(K)$ acts on it, and we study the orbit closures with respect to the Zariski topology. This leads to the definition of…

Within the gossamer numbers which extend the real numbers to include infinitesimals and infinities we prove the Fundamental Theorem of Calculus (FTC). Riemann sums are also considered in the gossamer number system, and their non-uniqueness…