Related papers: On the history of the Ulam's Conjugacy
We describe the geometry of conjugation within any split subgroup $H$ of the full isometry group $G$ of $n$-dimensional Euclidean space. We prove that for any $h \in H$, the conjugacy class $[h]_H$ of $h$ is described geometrically by the…
We exploit an ansatz in order to construct power series expansions for pairs of conjugate functions defined on domains of Euclidean $3$--space. Convergence properties of the resulting series are investigated. Entire solutions which are not…
We describe complex conjugation on the primitive middle-dimensional algebraic de Rham cohomology of a smooth projective hypersurface defined over a number field that admits a real embedding. We use Griffiths' description of the cohomology…
We consider in this article the properties of the topological conjugacy of the piecewise linear unimodal maps $g:\, [0,\, 1]\rightarrow [0,\, 1]$, all whose kinks belong to the complete pre-image of $0$. We call such maps firm carcass maps.…
We study the harmonic polytope, which arose in Ardila, Denham, and Huh's work on the Lagrangian geometry of matroids. We describe its combinatorial structure, showing that it is a $(2n-2)$-dimensional polytope with…
Various algebraic structures of degenerate four-wave mixing equations of optical phase conjugation are analyzed. Two approaches (the spinorial and the Lax-pair based), complementary to each other, are utilized for a systematic derivation of…
A new inequality, $(x)^{p}+(1-x)^{\frac{1}{p}}\leq1$ for $p \geq 1$ and $\frac{1}{2} \geq x \geq 0$ is found and proved. The inequality looks elegant as it integrates two number pairs ($x$ and $1-x$, $p$ and $\frac{1}{p}$) whose summation…
Let $f,g$ be $C^2$ expanding maps on the circle which are topologically conjugate. We assume that the derivatives of $f$ and $g$ at corresponding periodic points coincide for some large period $N$. We show that $f$ and $g$ are…
In [BGLM] and [GLNP] it was conjectured that if $H$ is a simple Lie group of real rank at least 2, then the number of conjugacy classes of (arithmetic) lattices in $H$ of covolume at most $x$ is $x^{(\gamma(H)+o(1))\log x/\log\log x}$ where…
In this paper we consider a class of conjugate equations, which generalizes de Rham's functional equations. We give sufficient conditions for existence and uniqueness of solutions under two different series of assumptions. We consider…
Given a group G, the conjugacy problem in G is the problem of giving an effective procedure for determining whether or not two given elements f, g of G are conjugate, i.e. whether there exists h belonging to G with fh = hg. This paper is…
We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals with approximate (join) homomorphisms in terms of certain…
We prove that for any nondegenerate dendrite $D$ there exist topologically mixing maps $F : D \to D$ and $f : [0, 1] \to [0, 1]$, such that the natural extensions (aka shift homeomorphisms) $\sigma_F$ and $\sigma_f$ are conjugate, and…
In this paper, we begin with the Lehman-Walsh formula counting one-face maps and construct two involutions on pairs of permutations to obtain a new formula for the number $A(n,g)$ of one-face maps of genus $g$. Our new formula is in the…
In the paper I considered mappings of conjugation of quaternion algebra. I proved the theorem that there is unique expansion of R-linear mapping of quaternion algebra relative to the given set of mappings of conjugation.
We show that evolutionary Hirota type Euler-Lagrange equations in (2+1) dimensions have a symplectic Monge-Amp\`ere form. We consider integrable equations of this type in the sense that they admit infinitely many hydrodynamic reductions and…
We construct sense-preserving univalent harmonic mappings which map the unit disk onto a domain which is convex in the horizontal direction, but with varying dilatation. Also, we obtain minimal surfaces associated with such harmonic…
In this article, we study the properties of conjugacies between polynomial basins. For any conjugacy, there is a quasiconformal conjugacy in the same homotopy class minimizing the dilatation. We compute the precise value of the minimal…
We propose to relax the classic Cauchy-Riemann equations for a mapping. We support the interest of such a proposal by looking at one specific situation in 3D, and proving the existence of pairs of harmonic conjugate functions with respect…
As an application of Cauchy's Theorem we prove that $\int_0^1\arctan\left({\arctanh x-\arctan x\over \pi+\arctanh x-\arctan x}\right) {dx\over x}= {\pi\over 8}\log{\pi^2\over 8}$ answering a question first posted in Mathematics Stack…