Related papers: A Non explicit counterexample to a problem of quas…

G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this…

It is stated equicontinuity and normality of families $\frak{F}^{\Phi}$ of the so--called homeomorphisms with finite distortion on conditions that $K_{f}(z)$ has finite mean oscillation, singularities of logarithmic type or integral…

Let $A$ be a matrix with nonnegative real entries. A nonnegative factorization of size $k$ is a representation of $A$ as a sum of $k$ nonnegative rank-one matrices. The space of all such factorizations is a bounded semialgebraic set, and we…

R. Fehlmann and M. Vuorinen proved in 1988 that Mori's constant $M(n,K)$ for $K$-quasiconformal maps of the unit ball in $\mathbf{R}^n$ onto itself keeping the origin fixed satisfies $M(n,K) \to 1$ when $K\to 1 .$ We give here an…

In this paper, we construct a counterexample to the Liouville property of some nonlocal reaction-diffusion equations of the form$$ \int\_{\mathbb{R}^N\setminus K} J(x-y)\,( u(y)-u(x) )\mathrm{d}y+f(u(x))=0, \quad x\in\R^N\setminus K,$$where…

Our main result is a new upper bound for the size of k-uniform, L-intersecting families of sets, where L contains only positive integers. We characterize extremal families in this setting. Our proof is based on the Ray-Chaudhuri--Wilson…

Peter Lappan in [9] proved that for each $n\in \mathbb{N}=\{1,2,3,\dots\}$, let $f_{1,n}, f_{2,n}$ and $f_{3,n}$ be three continuous functions on $\mathbb{D}:=\{z\in \mathbb{C} : |z| < 1\}$ such that for each $j=1,2,3,$ the sequence…

Let $A$ and $B$ be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.

We consider vanishing properties of exponential sums of the Liouville function $\lambda$ of the form $$ \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup_{\alpha\in C}\bigg|\frac{1}{H}\sum_{h\leq…

Let $p \in (0, \infty)$ be a constant and let $\{\xi_n\} \subset L^p(\Omega, {\mathcal F}, \P)$ be a sequence of random variables. For any integers $m, n \ge 0$, denote $S_{m, n} = \sum_{k=m}^{m + n} \xi_k$. It is proved that, if there…

A Riemann surface $M$ is said to be $K$-quasiconformally homogeneous if for every two points $p,q \in M$, there exists a $K$-quasiconformal homeomorphism $f \colon M \rightarrow M$ such that $f(p) = q$. In this paper, we show there exists a…

We establish the following uniformization result for metric spaces $X$ of finite Hausdorff 2-measure. If $X$ is homeomorphic to a smooth 2-manifold $M$ with non-empty boundary, then we show that $X$ admits a quasiconformal almost…

In this paper, we will consider normality and uniqueness property of a family $\mathcal{F}$ of meromorphic functions when $[Q(f)]^{(k)}$ and $[Q(g)]^{(k)}$ share $\alpha$ ignoring multiplicities, for any $f,g\in \mathcal{F}$, where $Q$ is a…

A result of Simonovits and S\'os states that for any fixed graph $H$ and any $\epsilon > 0$ there exists $\delta > 0$ such that if $G$ is an $n$-vertex graph with the property that every $S \subseteq V(G)$ contains $p^{e(H)} |S|^{v(H)} \pm…

Our primary result is that a demi-normal quasi-projective variety can be embedded in a demi-normal projective variety. Recall that a demi-normal variety $X$ is a variety with properties $S_2$, $G_1$, and seminormality. Equivalently, $X$ has…

In graph theory, the Szemer\'edi regularity lemma gives a decomposition of the indicator function for any graph $G$ into a structured component, a uniform part, and a small error. This result, in conjunction with a counting lemma that…

A little-known and highly economical characterization of the real interval [0, 1], essentially due to Freyd, states that the interval is homeomorphic to two copies of itself glued end to end, and, in a precise sense, is universal as such.…

Chmieli\'{n}ski has proved in the paper [4] the superstability of the generalized orthogonality equation $|< f(x), f(y) >| = |< x, y >|$. In this paper, we will extend the result of Chmieli\'{n}ski by proving a theorem: Let $D_{n}$ be a…

If $X$ is Frobenius split, then so is its normalization and we explore conditions which imply the converse. To do this, we recall that given an $\mathcal{O}_X$-linear map $\phi : F_* \mathcal{O}_X \to \mathcal{O}_X$, it always extends to a…

We consider the asymptotic normalcy of families of random variables $X$ which count the number of occupied sites in some large set. We write $Prob(X=m)=p_mz_0^m/P(z_0)$, where $P(z)$ is the generating function $P(z)=\sum_{j=0}^{N}p_jz^j$…