Related papers: Nonexistence of Euler Boxes with Semiprime Sides

We prove that a finite von Neumann algebra ${\mathcal A}$ is semisimple if the algebra of affiliated operators ${\mathcal U}$ of ${\mathcal A}$ is semisimple. When ${\mathcal A}$ is not semisimple, we give the upper and lower bounds for the…

The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing. The original proof, announced in 1998 and published in 2006, is long and…

According to Euler's relation any polytope P has as many faces of even dimension as it has faces of odd dimension. As a generalization of this fact one can compare the number of faces whose dimension is congruent to i modulo m with the…

We study certain typical semilinear elliptic equations in Euclidean space $\bR^{n}$ or on a closed manifold $M$ with nonnegative Ricci curvature. Our proof is based on a crucial integral identity constructed by the invariant tensor method.…

We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo-finite fields over A. Assuming GCH, we generalise this result to \kappa-prime models, for \kappa a regular uncountable cardinal or…

Bell's theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the…

In this article, we disprove a conjecture of F. Alarc\'on and D. Anderson and give a complete classification of the prime ideals in the one variable polynomial semiring with coefficients in Boolean semifield. We group the prime ideals of…

We prove an Alexander type theorem for the spectral unit ball $\Omega_n$ showing that there are no non-trivial proper holomorphic mappings in $\Omega_n$, $n\geq 2$.

We consider semilinear elliptic equations with double power nonlineaities. The condition to assure the existence of positive solutions is well-known. In the present paper, we remark that the additional condition to assure uniqueness…

In this short note, we prove the non-existence of slow and fast small nontrivial compact solutions for the Euler-Poisson system in $1$D. The proof is based on the virial estimate which provides local in space average decay of bounded small…

We give a new proof of the fact that Barker polynomials of even degree greater than 12, and hence Barker sequences of odd length greater than 13 do not exist. This is intimately tied to irreducibility questions and proved as a consequence…

Non-existence and uniqueness results are proved for several local and non-local supercritical bifurcation problems involving a semilinear elliptic equation depending on a parameter. The domain is star-shaped but no other symmetry assumption…

Let $K=\mathbb{Q}(\sqrt{-p})$ be a quadratic field for an odd prime $p$. We show that there exist infinitely many primes $p$ for which no elliptic curve $E/\mathbb{Q}$ has torsion subgroup $\mathbb{Z}/2\mathbb{Z}\times…

For a commutative ring $R$, in contrast to the completion in the sense of Bousfield and Kan at just a prime integer, there cannot exist spaces which are good and bad in an arbitrary way.

In this work we prove that for a compact odd-dimensional orbifold its Euler characteristic is half of the Euler characteristic of its boundary.

We prove that any polar action on a separable Hilbert space by a connected Hilbert Lie group does not have exceptional orbits. This generalizes a result of Berndt, Console and Olmos in the finite dimensional Euclidean case. As an…

In this paper we use the results of our previous work in order to compute the phase of the torsion of an Euler structure in terms of its characteristic class. Also, we introduce here a new notion of an absolute torsion, which does not…

We consider box spaces of finitely generated, residually finite groups $G$, and try to distinguish them up to coarse equivalence. We show that, for $n\geq 2$, the group $SL_n(\mathbb{Z})$ has a continuum of box spaces which are pairwise…

We derive some 1-D symmetry and uniqueness or non-existence results for nonnegative solutions of some elliptic system in the halfspace $\R^N_+$ in low dimension. Our method is based upon a combination of Fourier series and Liouville…

Euler showed that if an odd perfect number $N$ exists, it must consist of two parts $N=q^k n^2$, with $q$ prime, $q \equiv k \equiv 1 \pmod{4}$, and gcd$(q,n)=1$. Dris conjectured that $q^k < n$. We first show that $q<n$ for all odd perfect…