Thompson’s partition of a cyclic subnormal operator into normal and completely non-normal components is combined with non-commutative calculus for hyponormal operators separating outliers from the cloud, in rather general point distributions plane. The main result provides exact transformation formulas power moments prescribed distribution uniform mass carried by cloud. proposed algorithm solel...

Study of smut fungi on Liliaceae resulted to propose a new genus and three new combinations: Vankya Ershad, type V. ornithogali (Schmidt et Kunze) Ershad, based on Uredo ornithogali Schmidt et Kunze, V. heufleri (Fuckel) Ershad, based on Ustilago heufleri Fuckel, and V. vaillantii (L.-R. et C. Tulasne) Ershad, based on Ustilago vaillantii L.-R. et C. Tulasne.

In this paper, we have investigated the dependence of the spectral entanglement and indistinguishability of photon pairs produced by the spontaneous parametric down-conversion (SPDC) procedure on the bandwidth of spectral filters used in the detection setup. The SPDC is a three-wave mixing process which occurs in a nonlinear crystal and generates entangled photon pairs and utilizes as one of th...

A Helson matrix is an infinite $A = (a_{m,n})_{m,n\geq1}$ such that the entry $a_{m,n}$ depends only on product $mn$. We demonstrate orthogonal projection from Hilbert--Schmidt class $\mathcal{S}_2$ onto subspace of matrices does not extend to a bounded operator Schatten $\mathcal{S}_q$ for $1 \leq q \neq 2 < \infty$. In fact, we prove more general result showing large natural projections are u...

In these notes we provide an introduction to compact linear operators on Banach and Hilbert spaces. These operators behave very much like familiar finite dimensional matrices, without necessarily having finite rank. For more thorough treatments, see [RS, Y]. Definition 1 Let X and Y be Banach spaces. A linear operator C : X → Y is said to be compact if for each bounded sequence {xi}i∈IN ⊂ X , t...

‎‎for any group $g$‎, ‎we define an equivalence relation $thicksim$ as below‎: ‎[forall g‎, ‎h in g gthicksim h longleftrightarrow |g|=|h|]‎ ‎the set of sizes of equivalence classes with respect to this relation is called the same-order type of $g$ and denote by $alpha{(g)}$‎. ‎in this paper‎, ‎we give a partial answer to a conjecture raised by shen‎. ‎in fact‎, ‎we show that if $g$ is a nilpot...

Let G denote a locally compact Hausdorff abelian group. Then a bounded linear operator T from L^2(G) into L^2(G) is a bounded multiplier operator if, under the Fourier transform on L^2(G ), for each function f in L^2(G), T(f) changes into a bounded function U times the Fourier transform of f. Then U is called the multiplier of T. An unbounded multiplier operator has a similar definition, but it...

In these notes we provide an introduction to compact linear operators on Banach and Hilbert spaces. These operators behave very much like familiar finite dimensional matrices, without necessarily having finite rank. For more thorough treatments, see [RS, Y]. Definition 1 Let X and Y be Banach spaces. A linear operator C : X → Y is said to be compact if for each bounded sequence {xi}i∈IN ⊂ X , t...