Related papers: The distributivity numbers of of P(om) /fin and it…

We give upper bounds on the size of the gap between the constant term and the next non-zero Fourier coefficient of an entire modular form of given weight for \Gamma_0(2). Numerical evidence indicates that a sharper bound holds for the…

In this article we investigate the dual-shattering cardinal H, the dual-splitting cardinal S and the dual-reaping cardinal R, which are dualizations of the well-known cardinals h (the shattering cardinal, also known as the distributivity…

We provide examples of multiplicative functions $f$ supported on the $k$-free integers such that at primes $f(p)=\pm 1$ and such that the partial sums of $f$ up to $x$ are $o(x^{1/k})$. Further, if we assume the Generalized Riemann…

In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by…

We investigate the low-frequency dynamics for transmission or reflection of a wave by a cavity with chaotic scattering. We compute the probability distribution of the phase derivative phi'=d phi/d omega of the scattered wave amplitude,…

We introduce a new method for building models of CH, together with $\Pi_2$ statements over $H(\omega_2)$, by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only $\aleph_1$-many of…

The paper is devoted to the spreading of a message within the random graph evolving by the Norros-Reittu preferential attachment model. The latter model forms random Poissonian numbers of edges between newly added nodes and existing ones.…

In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2^omega = omega_2 and that…

We show how to compute the probability distributions of the order parameter of the $O(n)$ model at two-loop order of perturbation theory generalizing the methods developed for computing the same in case of the Ising model…

We consider the probability hierarchy for Popperian FINite learning and study the general properties of this hierarchy. We prove that the probability hierarchy is decidable, i.e. there exists an algorithm that receives p_1 and p_2 and…

Let $(M,g_0)$ be a compact Riemmanian manifold of dimension $n$. Let $P_0 (\h) := -\h^2\Delta_{g}+V$ be the semiclassical Schr\"{o}dinger operator for $\h \in (0,\h_0]$, and let $E$ be a regular value of its principal symbol…

We consider the time dependent two point function, <\phi_q (t) \phi_-q (0)> in non-linear stochastic field theories, for which the KPZ equation serves as a prototype. In particular we consider the small q's and long times such that \omega_q…

Let $v,~\omega_1, ~\omega_2$ be weights and $1<p_1, ~p_2<\infty.$ Suppose that $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$ and $(\omega_1, \omega_2)\in RH(p_1, p_2).$ For the multisublinear maximal operator $\mathfrak{M}$ in martingale…

Let $f, g^1, \dots, g^d : \mathbb{R}^d \longrightarrow \mathbb{R}$ be H\"older continuous functions. If the H\"older exponents of these functions are less than $1$ but sufficiently large, we use the integral introduced by Z\"ust to…

We prove a H\"{o}rmander type multiplier theorem for multilinear Fourier multipiers with multiple weights. We also give weighted estimates for their commutators with vector $BMO$ functions.

In this paper, we get the sharp bound for $|G/O_p(G)|_p$ under the assumption that either $p^2 \nmid \chi(1)$ for all $\chi \in {\rm Irr}(G)$ or $p^2 \nmid \phi(1)$ for all $\phi \in {\rm IBr}_p(G)$. This would settle two conjectures raised…

We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…

Let chi be the minimum cardinal of a subset of 2^omega that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of creature forcing we show that s<chi is consistent. We thus answer a question by…

In a previous paper, we derived a recursive formula determining the weight distributions of the [n=(q^m-1)/(q-1)] Hamming code H(m,q), when (m,q-1)=1. Here q is a prime power. We note here that the formula actually holds for any positive…

Let $\alpha$ be a Steinhaus or a Rademacher random multiplicative function. For a wide class of multiplicative functions $f$ we show that the sum $\sum_{n \le x}\alpha(n) f(n)$, normalised to have mean square $1$, has a non-Gaussian…