On some separation axioms and $$-closure

D. Janković

Displaying similar documents to “On some separation axioms and -closure”

Characterizations of some bitopological separation axioms in terms of $i j - θ$ - closure operator

S. K. Sen, J. N. Nandi, M. N. Mukherjee (1992)

Matematički Vesnik

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On geodesics of phyllotaxis

Roland Bacher (2014)

Confluentes Mathematici

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Seeds of sunflowers are often modelled by $n ⟼ ϕ_{θ} (n) = \sqrt{n} e^{2 i π n θ}$ leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance $2 π θ$ for $θ$ the golden ratio. We associate to such a map $ϕ_{θ}$ a geodesic path $γ_{θ} : ℝ_{> 0} ⟶ {PSL}_{2} (ℤ) ∖ ℍ$ of the modular curve and use it for local descriptions of the image $ϕ_{θ} (ℕ)$ of the phyllotactic map $ϕ_{θ}$ .

Sums of Three Prime Squares

Hiroshi Mikawa, Temenoujka Peneva (2007)

Bollettino dell'Unione Matematica Italiana

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Let $A,\epsilon>0$ be arbitrary. Suppose that $x$ is a sufficiently large positive number. We prove that the number of integers $n\in(x,x+x^{\theta}]$ , satisfying some natural congruence conditions, which cannot be written as the sum of three squares of primes is $\ll x^{\theta}(\log x)^{-A}$ , provided that $\frac{7}{16}+\epsilon\leq\theta\leq 1$ .

On weakly $θ$ -continuous functions

F. Commaroto, T. Noiri (1986)

Matematički Vesnik

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Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations

Katarzyna Horbacz (2006)

Bollettino dell'Unione Matematica Italiana

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We consider the stochastic differential equation ${}dX(t)=a(X(t);\xi(t))\,dt+\int_{\Theta}b(X(t);\theta)\mathcal{N}_{p}(dt;d\theta)$ for $t\geq 0$ with the initial condition $X(0)=x_{0}$ . We give sufficient conditions for the asymptotic stability of the semigroup $\{P^{t}\}_{t\geq 0}$ generated by the stochastic differential equation (1).

Some remarks on the interpolation spaces $A^{θ}, A_{θ}$

Mohammad Daher (2016)

Commentationes Mathematicae Universitatis Carolinae

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Let $(A_{0}, A_{1})$ be a regular interpolation couple. Under several different assumptions on a fixed $A^{β}$ , we show that $A^{θ} = A_{θ}$ for every $θ \in (0, 1)$ . We also deal with assumptions on ${\bar{A}}^{β}$ , the closure of $A^{β}$ in the dual of ${(A_{0}^{*}, A_{1}^{*})}_{β}$ .

Comments on the fractional parts of Pisot numbers

Toufik Zaïmi, Mounia Selatnia, Hanifa Zekraoui (2015)

Archivum Mathematicum

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Let $L (θ, λ)$ be the set of limit points of the fractional parts ${λ θ^{n}}$ , $n = 0, 1, 2, \dots$ , where $θ$ is a Pisot number and $λ \in ℚ (θ)$ . Using a description of $L (θ, λ)$ , due to Dubickas, we show that there is a sequence ${(λ_{n})}_{n \geq 0}$ of elements of $ℚ (θ)$ such that $Card (L (θ, λ_{n})) < Card (L (θ, λ_{n + 1}))$ , $\forall$ $n \geq 0$ . Also, we prove that the fractional parts of Pisot numbers, with a fixed degree greater than 1, are dense in the unit interval.

The local index density of the perturbed de Rham complex

Jesús Álvarez López, Peter B. Gilkey (2021)

Czechoslovak Mathematical Journal

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A perturbation of the de Rham complex was introduced by Witten for an exact 1-form $Θ$ and later extended by Novikov for a closed 1-form on a Riemannian manifold $M$ . We use invariance theory to show that the perturbed index density is independent of $Θ$ ; this result was established previously by J. A. Álvarez López, Y. A. Kordyukov and E. Leichtnam (2020) using other methods. We also show the higher order heat trace asymptotics of the perturbed de Rham complex exhibit nontrivial dependence...

Linearly-invariant families and generalized Meixner–Pollaczek polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The extremal functions $f_{0} (z)$ realizing the maxima of some functionals (e.g. $max | a_{3} |$ , and $max a r g f^{^{'}} (z)$ ) within the so-called universal linearly invariant family $U_{α}$ (in the sense of Pommerenke [10]) have such a form that $f_{0}^{^{'}} (z)$ looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials $P_{n}^{λ} (x; θ, ψ)$ of a real variable $x$ as coefficients of $G^{λ} (x; θ, ψ; z) = \frac{1}{{(1 - z e^{i θ})}^{λ - i x} {(1 - z e^{i ψ})}^{λ + i x}} = \sum_{n = 0}^{\infty} P_{n}^{λ} (x; θ, ψ) z^{n}, | z | < 1,$ where the parameters $λ$ , $θ$ , $ψ$ satisfy the conditions:...

Singularities of theta divisors and the geometry of $𝒜_{5}$

Gavril Farkas, Samuele Grushevsky, Salvati R. Manni, Alessandro Verra (2014)

Journal of the European Mathematical Society

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We study the codimension two locus $H$ in $𝒜_{g}$ consisting of principally polarized abelian varieties whose theta divisor has a singularity that is not an ordinary double point. We compute the class $[H] \in C H^{2} (𝒜_{g})$ for every $g$ . For $g = 4$ , this turns out to be the locus of Jacobians with a vanishing theta-null. For $g = 5$ , via the Prym map we show that $H \subset 𝒜_{5}$ has two components, both unirational, which we describe completely. We then determine the slope of the effective cone of $\bar{𝒜_{5}}$ and show that the component $\bar{N_{0}^{'}}$ of the Andreotti-Mayer...