On linked Jordan curves in $R^{3}$

M. Mateljević

Displaying similar documents to “On linked Jordan curves in $R^{3}$ ”

On the Jordan model $C_{0}$ operators

Hari Bercovici (1977)

Studia Mathematica

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Product of operators and numerical range preserving maps

Chi-Kwong Li, Nung-Sing Sze (2006)

Studia Mathematica

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Let V be the C*-algebra B(H) of bounded linear operators acting on the Hilbert space H, or the Jordan algebra S(H) of self-adjoint operators in B(H). For a fixed sequence (i₁, ..., iₘ) with i₁, ..., iₘ ∈ 1, ..., k, define a product of $A ₁, . . ., A_{k} \in V$ by $A ₁ * \dots * A_{k} = A_{i ₁} \dots A_{i ₘ}$ . This includes the usual product $A ₁ * \dots * A_{k} = A ₁ \dots A_{k}$ and the Jordan triple product A*B = ABA as special cases. Denote the numerical range of A ∈ V by W(A) = (Ax,x): x ∈ H, (x,x) = 1. If there is a unitary operator U and a scalar μ satisfying $μ^{m} = 1$ such that ϕ: V → V has...

Equidecomposability of Jordan domains under groups of isometries

M. Laczkovich (2003)

Fundamenta Mathematicae

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Let $G_{d}$ denote the isometry group of $ℝ^{d}$ . We prove that if G is a paradoxical subgroup of $G_{d}$ then there exist G-equidecomposable Jordan domains with piecewise smooth boundaries and having different volumes. On the other hand, we construct a system $ℱ_{d}$ of Jordan domains with differentiable boundaries and of the same volume such that $ℱ_{d}$ has the cardinality of the continuum, and for every amenable subgroup G of $G_{d}$ , the elements of $ℱ_{d}$ are not G-equidecomposable; moreover, their interiors are not G-equidecomposable...

Jordan isomorphisms and maps preserving spectra of certain operator products

Jinchuan Hou, Chi-Kwong Li, Ngai-Ching Wong (2008)

Studia Mathematica

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Let ₁, ₂ be (not necessarily unital or closed) standard operator algebras on locally convex spaces X₁, X₂, respectively. For k ≥ 2, consider different products $T ₁ * \dots * T_{k}$ on elements in $_{i}$ , which covers the usual product $T ₁ * \dots * T_{k} = T ₁ \dots T_{k}$ and the Jordan triple product T₁ ∗ T₂ = T₂T₁T₂. Let Φ: ₁ → ₂ be a (not necessarily linear) map satisfying $σ (Φ (A ₁) * \dots * Φ (A_{k})) = σ (A ₁ * \dots * A_{k})$ whenever any one of $A_{i}$ ’s has rank at most one. It is shown that if the range of Φ contains all rank one and rank two operators then Φ must be a Jordan isomorphism multiplied...

Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree

Nazar Arakelian, Herivelto Borges (2015)

Acta Arithmetica

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For each integer s ≥ 1, we present a family of curves that are $_{q}$ -Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case s=2, we give necessary and sufficient conditions for such curves to be $_{q}$ -Frobenius nonclassical with respect to the linear system of conics. In the $_{q}$ -Frobenius nonclassical cases, we determine the exact number of $_{q}$ -rational points. In the remaining cases, an upper bound for the number of $_{q}$ -rational points will follow from Stöhr-Voloch...

The operation $A B A$ in operator algebras

Marcell Gaál (2020)

Commentationes Mathematicae Universitatis Carolinae

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The binary operation $a b a$ , called Jordan triple product, and its variants (such as e.g. the sequential product $\sqrt{a} b \sqrt{a}$ or the inverted Jordan triple product $a b^{- 1} a$ ) appear in several branches of operator theory and matrix analysis. In this paper we briefly survey some analytic and algebraic properties of these operations, and investigate their intimate connection to Thompson type isometries in different operator algebras.

Generalized Higher Derivations on Lie Ideals of Triangular Algebras

Mohammad Ashraf, Nazia Parveen, Bilal Ahmad Wani (2017)

Communications in Mathematics

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Let $𝔄 = (\begin{matrix} 𝒜 & ℳ \\ ℬ \end{matrix})$ be the triangular algebra consisting of unital algebras $𝒜$ and $ℬ$ over a commutative ring $R$ with identity $1$ and $ℳ$ be a unital $(𝒜, ℬ)$ -bimodule. An additive subgroup $𝔏$ of $𝔄$ is said to be a Lie ideal of $𝔄$ if $[𝔏, 𝔄] \subseteq 𝔏$ . A non-central square closed Lie ideal $𝔏$ of $𝔄$ is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on $𝔄$ , every generalized Jordan triple higher derivation of $𝔏$ into $𝔄$ is a generalized higher derivation of $𝔏$ into $𝔄$ . ...

On the characterization of certain additive maps in prime $*$ -rings

Mohammad Ashraf, Mohammad Aslam Siddeeque, Abbas Hussain Shikeh (2024)

Czechoslovak Mathematical Journal

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Let $𝒜$ be a noncommutative prime ring equipped with an involution ‘ $*$ ’, and let $𝒬_{m s} (𝒜)$ be the maximal symmetric ring of quotients of $𝒜$ . Consider the additive maps $ℋ$ and $𝒯 : 𝒜 \to 𝒬_{m s} (𝒜)$ . We prove the following under some inevitable torsion restrictions. (a) If $m$ and $n$ are fixed positive integers such that $(m + n) 𝒯 (a^{2}) = m 𝒯 (a) a^{*} + n a 𝒯 (a)$ for all $a \in 𝒜$ and $(m + n) ℋ (a^{2}) = m ℋ (a) a^{*} + n a 𝒯 (a)$ for all $a \in 𝒜$ , then $ℋ = 0$ . (b) If $𝒯 (a b a) = a 𝒯 (b) a^{*}$ for all $a, b \in 𝒜$ , then $𝒯 = 0$ . Furthermore, we characterize Jordan left $τ$ -centralizers in semiprime rings admitting an anti-automorphism $τ$ . As applications, we find the...

Rational points on $X_{0}^{+} (p^{r})$

Yuri Bilu, Pierre Parent, Marusia Rebolledo (2013)

Annales de l’institut Fourier

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Using the recent isogeny bounds due to Gaudron and Rémond we obtain the triviality of $X_{0}^{+} (p^{r}) (ℚ)$ , for $r > 1$ and $p$ a prime number exceeding $2 \cdot 10^{11}$ . This includes the case of the curves $X_{split} (p)$ . We then prove, with the help of computer calculations, that the same holds true for $p$ in the range $11 \leq p \leq 10^{14}$ , $p \neq 13$ . The combination of those results completes the qualitative study of rational points on $X_{0}^{+} (p^{r})$ undertook in our previous work, with the only exception of $p^{r} = 13^{2}$ .

An index inequality for embedded pseudoholomorphic curves in symplectizations

Michael Hutchings (2002)

Journal of the European Mathematical Society

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Let $Σ$ be a surface with a symplectic form, let $φ$ be a symplectomorphism of $Σ$ , and let $Y$ be the mapping torus of $φ$ . We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in $ℝ \times 𝕐$ , with cylindrical ends asymptotic to periodic orbits of $φ$ or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to...

On ramified covers of the projective plane II: Generalizing Segre’s theory

Michael Friedman, Rebecca Lehman, Maxim Leyenson, Mina Teicher (2012)

Journal of the European Mathematical Society

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The classical Segre theory gives a necessary and sufficient condition for a plane curve to be a branch curve of a (generic) projection of a smooth surface in $ℙ^{3}$ . We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, $B$ and $E$ , we give a necessary and sufficient condition for $B$ to be the branch curve of a surface $X$ in $ℙ^{N}$ and $E$ to be the image of the double curve of a $ℙ^{3}$ -model of $X$ . In the classical Segre theory, a...

Product decompositions of quasirandom groups and a Jordan type theorem

Nikolay Nikolov, László Pyber (2011)

Journal of the European Mathematical Society

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We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If $k$ is the minimal degree of a representation of the finite group $G$ , then for every subset $B$ of $G$ with $| B | > | G | / k^{1 / 3}$ we have $B^{3} = G$ . We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan’s theorem which implies that if $k \geq 2$ , then $G$ has a...

Why Jordan algebras are natural in statistics: quadratic regression implies Wishart distributions

G. Letac, J. Wesołowski (2011)

Bulletin de la Société Mathématique de France

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If the space $𝒬$ of quadratic forms in $ℝ^{n}$ is splitted in a direct sum $𝒬_{1} \oplus ... \oplus 𝒬_{k}$ and if $X$ and $Y$ are independent random variables of $ℝ^{n}$ , assume that there exist a real number $a$ such that $E (X | X + Y) = a (X + Y)$ and real distinct numbers $b_{1}, . . ., b_{k}$ such that $E (q (X) | X + Y) = b_{i} q (X + Y)$ for any $q$ in $𝒬_{i} .$ We prove that this happens only when $k = 2$ , when $ℝ^{n}$ can be structured in a Euclidean Jordan algebra and when $X$ and $Y$ have Wishart distributions corresponding to this structure.

On invariants of elliptic curves on average

Amir Akbary, Adam Tyler Felix (2015)

Acta Arithmetica

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We prove several results regarding some invariants of elliptic curves on average over the family of all elliptic curves inside a box of sides A and B. As an example, let E be an elliptic curve defined over ℚ and p be a prime of good reduction for E. Let $e_{E} (p)$ be the exponent of the group of rational points of the reduction modulo p of E over the finite field $_{p}$ . Let be the family of elliptic curves $E_{a, b} : y^{2} = x^{3} + a x + b$ , where |a| ≤ A and |b| ≤ B. We prove that, for any c > 1 and k∈ ℕ, $1 / | | \sum_{E \in} \sum_{p \leq x} e_{E}^{k} (p) = C_{k} l i (x^{k + 1}) + O ((x^{k + 1}) / {(l o g x)}^{c}$ )as x → ∞, as long...

Complete pluripolar curves and graphs

Tomas Edlund (2004)

Annales Polonici Mathematici

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It is shown that there exist $C^{\infty}$ functions on the boundary of the unit disk whose graphs are complete pluripolar. Moreover, for any natural number k, such functions are dense in the space of $C^{k}$ functions on the boundary of the unit disk. We show that this result implies that the complete pluripolar closed $C^{\infty}$ curves are dense in the space of closed $C^{k}$ curves in ℂⁿ. We also show that on each closed subset of the complex plane there is a continuous function whose graph is complete pluripolar. ...

Quantum Singularity Theory for $A_{(r - 1)}$ and $r$ -Spin Theory

Huijun Fan, Tyler Jarvis, Yongbin Ruan (2011)

Annales de l’institut Fourier

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We give a review of our construction of a cohomological field theory for quasi-homogeneous singularities and the $r$ -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity $W$ of type $A$ our construction of the stack of $W$ -curves is canonically isomorphic to the stack of $r$ -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an $r$ -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine...

On a theorem of Lindelof

Vladimir Ya. Gutlyanskii, Olli Martio, Vladimir Ryazanov (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We give a quasiconformal version of the proof for the classical Lindelof theorem: Let $f$ map the unit disk $𝔻$ conformally onto the inner domain of a Jordan curve $𝒞$ : Then $𝒞$ is smooth if and only if arg $f^{'} (z)$ has a continuous extension to $\bar{𝔻}$ . Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.

On covering and quasi-unsplit families of curves

Laurent Bonavero, Cinzia Casagrande, Stéphane Druel (2007)

Journal of the European Mathematical Society

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Given a covering family $V$ of effective 1-cycles on a complex projective variety $X$ , we find conditions allowing one to construct a geometric quotient $q : X \to Y$ , with $q$ regular on the whole of $X$ , such that every fiber of $q$ is an equivalence class for the equivalence relation naturally defined by $V$ . Among other results, we show that on a normal and $ℚ$ -factorial projective variety $X$ with canonical singularities and $dim X \leq 4$ , every covering and quasi-unsplit family $V$ of rational curves generates a geometric...

Displaying similar documents to “On linked Jordan curves in R 3 ”

Displaying similar documents to “On linked Jordan curves in $R^{3}$ ”