Related papers: Cicho\'n's maximum with evasion number

Extending the partition function multiplicatively to a function on partitions, we show that it has a unique maximum at an explicitly given partition for any $n\neq 7$. The basis for this is an inequality for the partition function which…

We analyze the non-stationary ideal and the club filter at aleph_1 under MM.

In this note, we apply some techniques developed in [1]-[3] to give a particular construction of bivariate Abelian Codes from cyclic codes, multiplying their dimension and preserving their apparent distance. We show that, in the case of…

The Duffin-Schaeffer conjecture is a central open problem in metric number theory. Let $\psi~\mathbb{N} \mapsto \mathbb{R}$ be a non-negative function, and set $\mathcal{E}_n :=\bigcup \left( \frac{a - \psi(n)}{n},\frac{a+\psi(n)}{n}…

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…

We revisit a well-known divide-and-conquer maximin recurrence $f(n) = \max(\min(n_1,n_2) + f(n_1) + f(n_2))$ where the maximum is taken over all proper bipartitions $n = n_1+n_2$, and we present a new characterization of the pairs…

The Torsion Anomalous Conjecture states that an irreducible variety $V$ embedded in a semi-abelian variety contains only finitely many maximal $V$-torsion anomalous varieties. In this paper we consider an irreducible variety embedded in a…

We confirm the eventual evasiveness of several classes of monotone graph properties under widely accepted number theoretic hypotheses. In particular we show that Chowla's conjecture on Dirichlet primes implies that (a) for any graph $H$,…

We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain,…

We give upper bounds for the number $\Phi_\ell(G)$ of matchings of size $\ell$ in (i) bipartite graphs $G=(X\cup Y, E)$ with specified degrees $d_x$ ($x\in X$), and (ii) general graphs $G=(V,E)$ with all degrees specified. In particular,…

We prove that every odd number $N$ greater than 1 can be expressed as the sum of at most five primes, improving the result of Ramar\'e that every even natural number can be expressed as the sum of at most six primes. We follow the circle…

Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions,…

CZF + Separation is shown to be equiconsistent with second-order arithmetic, using realizability.

We expand the classic variational formulation of $-\log\mathbb{E}\left[e^{-f}\right]$ to the case where f depends on a diffusion, and not only a on Brownian motion, while decreasing the integrability hypothesis on f. We also give an…

We prove it consistent relative to ZFC that all nontrivial forcings of size $\aleph _1$ add a Cohen real.

Motivated by the study of the maximal operator for the Schr\"{o}dinger equation on the one-dimensional torus $ \mathbb{T}^1 $, it is conjectured that for any complex sequence $ \{b_n\}_{n=1}^N $, $$ \left\| \sup_{t\in [0,N^2]}…

Let $\eta^*_n$ denote the maximum, at time $n$, of a nonlattice one-dimensional branching random walk $\eta_n$ possessing (enough) exponential moments. In a seminal paper, Aidekon demonstrated convergence of $\eta^*_n$ in law, after…

In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of $O(n^{-1/5})$ for…

The extremal coefficient function (ECF) of a max-stable process $X$ on some index set $T$ assigns to each finite subset $A\subset T$ the effective number of independent random variables among the collection $\{X_t\}_{t\in A}$. We introduce…

We prove that a strongly compact cardinal is an upper bound for a Hanf number for amalgamation, etc. in AECs using both semantic and syntactic methods. To syntactically prove non-disjoint amalgamation, a different presentation theorem than…