相关论文: A counterexample to the Arakelyan Conjecture

Two counterexamples, addressing questions raised in \cite{AD} and \cite{PZ}, are provided. Both counterexamples are related to chaoses. Let $F_n=Y_n+Z_n$. It may be that $F_n\overset{a.s.}\longrightarrow 0$,…

If $N={q^k}{n^2}$ is an odd perfect number given in Eulerian form, then the Descartes-Frenicle-Sorli conjecture predicts that $k=\nu_{q}(N)=1$. In this article, we give a short proof for this conjecture.

We provide a counterexample to P.~Olver's freeness conjecture for $C^\omega$ transformations.

We disprove a conjecture of Kuznetsov--Shinder, which posits that $D$-equivalent simply connected varieties are $L$-equivalent, by constructing a counterexample using moduli spaces of sheaves on K3 surfaces.

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.

We give an example of $C^k$-integrable almost complex structure that does not admit a corresponding $C^{k+1}$-complex coordinate system.

We deal with the monadic (second-order) theory of order. We prove all known results in a unified way, show a general way of reduction, prove more results and show the limitation on extending them. We prove (CH) that the monadic theory of…

Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foundational theory for (all of) mathematics that is not weaker…

We give counterexamples for the modification on Malle's Conjecture given by T\"urkelli. T\"urkelli's modification on Malle's conjecture is inspired by an analogue of Malle's conjecture over a function field. As a consequence, our…

In this paper, we show that the minimal model theory does not hold in characteristic two. More precisely, we construct counter-examples to the relative abundance conjecture.

In this paper I introduce a new and intuitive first-order foundational theory (where the concept of set is not primitive) and use it to show that the power set of an infinite set does not exist. In particular, proofs of uncountability of a…

The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…

We argue that Godel's completeness theorem is equivalent to completability of consistent theories, and Godel's incompleteness theorem is equivalent to the fact that this completion is not constructive, in the sense that there are some…

We introduce a concept of a quasi proximate order which is a generalization of a proximate order and allows us to study efficiently analytic functions whose order and lower order of growth are different. We prove an existence theorem of a…

The purpose of this note is to show by constructing counterexamples that two conjectures of M\'{o}ri and Sz\'{e}kely for the Borel-Cantelli lemma are false.

For the Riemann zeta-function on the critical line the terminal estimate have been proved, which had been conjectured by Lindel\"of at the beginning of this Centure. The proof is based on the authors relations which connect the bilinear…

For substructural logics with contraction or weakening admitting cut-free sequent calculi, proof search was analyzed using well-quasi-orders on $\mathbb{N}^d$ (Dickson's lemma), yielding Ackermannian upper bounds via controlled bad-sequence…

We give a counterexample to a conjecture of S.E. Morris by showing that there is a compact plane set X such that R(X) has no non-zero, bounded point derivations but such that R(X) is not weakly amenable. We also give an example of a…

If A/K is an abelian variety over a number field and P and Q are rational points, the original support conjecture asserted that if the order of Q (mod p) divides the order of P (mod p) for almost all primes p of K, then Q is obtained from P…

By suitable examples we illustrate an algorithm for composition of inverse problems.