Products of spaces by $[0,1]$

Poenaru, V.

Displaying similar documents to “Products of spaces by $[0, 1]$ ”

A proof of the Grünbaum conjecture

Bruce L. Chalmers, Grzegorz Lewicki (2010)

Studia Mathematica

Similarity:

Let V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N ∈ N with N ≥ n define $λ ₙ^{N} = s u p λ (V) : d i m (V) = n, V \subset l_{\infty}^{(N)}$ , λₙ = supλ(V): dim(V) = n. A well-known Grünbaum conjecture [Trans. Amer. Math. Soc. 95 (1960)] says that λ₂ = 4/3. König and Tomczak-Jaegermann [J. Funct. Anal. 119 (1994)] made an attempt to prove this conjecture. Unfortunately, their Proposition 3.1, used in the proof, is incorrect. In this paper a complete proof of the Grünbaum conjecture is presented ...

Dynamically defined Cantor sets under the conditions of McDuff's conjecture

Jorge Iglesias, Aldo Portela (2010)

Colloquium Mathematicae

Similarity:

We prove that if the Cantor set K, dynamically defined by a function $S \in C^{1 + α}$ , satisfies the conditions of McDuff’s conjecture then it cannot be C¹-minimal.

On the generalized vanishing conjecture

Zhenzhen Feng, Xiaosong Sun (2019)

Czechoslovak Mathematical Journal

Similarity:

We show that the GVC (generalized vanishing conjecture) holds for the differential operator $Λ = (\partial_{x} - Φ (\partial_{y})) \partial_{y}$ and all polynomials $P (x, y)$ , where $Φ (t)$ is any polynomial over the base field. The GVC arose from the study of the Jacobian conjecture.

Homotopy invariance of higher signatures and $3$ -manifold groups

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch (2008)

Bulletin de la Société Mathématique de France

Similarity:

For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable $3$ -manifolds, including the “piecewise geometric” ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable $3$ -manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients...

Two remarks on the Suita conjecture

Nikolai Nikolov (2015)

Annales Polonici Mathematici

Similarity:

It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with $C^{1 + ε}$ -smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely connected planar domain.

Coarse topology, enlargeability, and essentialness

Bernhard Hanke, Dieter Kotschick, John Roe, Thomas Schick (2008)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the $K$ -theory of the corresponding reduced $C^{*}$ -algebras. Our proofs do not depend on the Baum–Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.

A new proof of the $L^{p}$ -conjecture for locally compact abelian groups

David L. Johnson (1982)

Colloquium Mathematicae

Similarity:

Order of the smallest counterexample to Gallai's conjecture

Fuyuan Chen (2018)

Czechoslovak Mathematical Journal

Similarity:

In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Zamfirescu conjectured that the smallest counterexample to Gallai’s conjecture is a graph on 12 vertices. We prove that Gallai’s conjecture is true for every connected graph $G$ with $α^{'} (G) \leq 5$ , which implies that Zamfirescu’s conjecture is true.

A note on Nakai’s conjecture for the ring $K [X ₁, . . ., X ₙ] / (a ₁ X ₁^{m} + \dots + a ₙ X ₙ^{m})$

Paulo Roberto Brumatti, Marcelo Oliveira Veloso (2011)

Colloquium Mathematicae

Similarity:

The strength of the projective Martin conjecture

C. T. Chong, Wei Wang, Liang Yu (2010)

Fundamenta Mathematicae

Similarity:

We show that Martin’s conjecture on Π¹₁ functions uniformly $\leq_{T}$ -order preserving on a cone implies Π¹₁ Turing Determinacy over ZF + DC. In addition, it is also proved that for n ≥ 0, this conjecture for uniformly degree invariant $Π ¹_{2 n + 1}$ functions is equivalent over ZFC to $Σ ¹_{2 n + 2}$ -Axiom of Determinacy. As a corollary, the consistency of the conjecture for uniformly degree invariant Π¹₁ functions implies the consistency of the existence of a Woodin cardinal.

On the Brocard-Ramanujan problem and generalizations

Andrzej Dąbrowski (2012)

Colloquium Mathematicae

Similarity:

Let $p_{i}$ denote the ith prime. We conjecture that there are precisely 28 solutions to the equation $n ² - 1 = p ₁^{α ₁} \dots p_{k}^{α_{k}}$ in positive integers n and α₁,..., $α_{k}$ . This conjecture implies an explicit description of the set of solutions to the Brocard-Ramanujan equation. We also propose another variant of the Brocard-Ramanujan problem: describe the set of solutions in non-negative integers of the equation n! + A = x₁²+x₂²+x₃² (A fixed).

A geometric construction for spectrally arbitrary sign pattern matrices and the $2 n$ -conjecture

Dipak Jadhav, Rajendra Deore (2023)

Czechoslovak Mathematical Journal

Similarity:

We develop a geometric method for studying the spectral arbitrariness of a given sign pattern matrix. The method also provides a computational way of computing matrix realizations for a given characteristic polynomial. We also provide a partial answer to $2 n$ -conjecture. We determine that the $2 n$ -conjecture holds for the class of spectrally arbitrary patterns that have a column or row with at least $n - 1$ nonzero entries.

Greenberg’s conjecture for $ℤ_{p}^{d}$ -extensions

Andrea Bandini (2003)

Acta Arithmetica

Similarity:

On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function

Ke-Pao Lin, Xue Luo, Stephen S.-T. Yau, Huaiqing Zuo (2014)

Journal of the European Mathematical Society

Similarity:

It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function $ψ (x, y)$ which is the number of positive integers $\leq x$ and free of prime factors $> y$ . Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional ( $n \geq 3$ ) real right-angled simplices. In this...

A proof of the Livingston conjecture for the fourth and the fifth coefficient of concave univalent functions

Karl-Joachim Wirths (2004)

Annales Polonici Mathematici

Similarity:

Let D denote the open unit disc and f:D → ℂ̅ be meromorphic and injective in D. We further assume that f has a simple pole at the point p ∈ (0,1) and an expansion $f (z) = z + \sum_{n = 2}^{\infty} a ₙ (f) z ⁿ$ , |z| < p. In particular, we consider f that map D onto a domain whose complement with respect to ℂ̅ is convex. Because of the shape of f(D) these functions will be called concave univalent functions with pole p and the family of these functions is denoted by Co(p). It is proved that for p ∈ (0,1) the domain of variability...

A counterexample to a conjecture of Bass, Connell and Wright

Piotr Ossowski (1998)

Colloquium Mathematicae

Similarity:

Let F=X-H: $k^{n}$ → $k^{n}$ be a polynomial map with H homogeneous of degree 3 and nilpotent Jacobian matrix J(H). Let G=(G1,...,Gn) be the formal inverse of F. Bass, Connell and Wright proved in [1] that the homogeneous component of $G_{i}$ of degree 2d+1 can be expressed as $G_{i}^{(d)} = \sum_{T} α {(T)}^{- 1} σ_{i} (T)$ , where T varies over rooted trees with d vertices, α(T)=CardAut(T) and $σ_{i} (T)$ is a polynomial defined by (1) below. The Jacobian Conjecture states that, in our situation, $F$ is an automorphism or, equivalently, $G_{i}^{(d)}$ is zero for sufficiently...

Displaying similar documents to “Products of spaces by [ 0 , 1 ] ”

Displaying similar documents to “Products of spaces by $[0, 1]$ ”