Graph theory, which is used effectively in many fields from science to liberal arts, has very important place our lives. As a result of this, the topological structure graphs studied by researchers. In this paper, we investigate spaces generated graphs. The states being an accumulation point and interior these are examined. It defined that relative topology on subgraph graph. shown different su...

Double blind $T$-private information retrieval (DB-TPIR) enables two users, each of whom specifies an index ($\theta_1, \theta_2$, resp.), to efficiently retrieve a message $W(\theta_1,\theta_2)$ labeled by the indices, from set $N$ servers that store all messages $W(k_1,k_2), k_1\in\{1,2,\cdots,K_1\}, k_2\in\{1,2,\cdots,K_2\}$, such users' indices are kept private any up $T_1,T_2$ colluding se...

The symmetrization map $$\pi :{\mathbb{C}}^2\rightarrow {\mathbb{C}}^2$$ is defined by (z_1,z_2)=(z_1+z_2,z_1z_2).$$ closed symmetrized bidisc $$\Gamma$$ the of unit $$\overline{{\mathbb{D}}^2}$$ , that is, $$\begin{aligned} \Gamma = \pi (\overline{{\mathbb{D}}^2})=\{ (z_1+z_2,z_1z_2)\,:\, |z_i|\le 1, i=1,2 \}. \end{aligned}$$ A pair commuting Hilbert space operators (S, P) for which a spectral...

Найдено предельное совместное распределение статистик $T_1$, $T_2$, $T_3$ следующих трех критериев пакета НИСТ: «Monobit Test», «Frequency Test within a Block» и «Test for the Longest Run of Ones in в ситуации, когда исследуемая последовательность состоит из независимых случайных величин, имеющих Бернулли с параметром $p = \frac12$. Установлены необходимые достаточные условия асимптотической не...

 In Proposition 2.6 in (G‎. ‎Gruenhage‎, ‎A‎. ‎Lutzer‎, ‎Baire and Volterra spaces‎, ‎textit{Proc‎. ‎Amer‎. ‎Math‎. ‎Soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of $D$ is $G_delta$ in $X$ was overlooked‎. ‎So we‎ ‎proved some conditions by which a Baire space is equivalent to a‎ ‎Volterra space‎. ‎In this note we show that if $X$ is a‎ ‎monotonically normal $T_1...

In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

We derive $ab$ $initio$ low-energy effective Hamiltonians (LEH) for high-temperature superconducting (SC) copper oxides Bi$_2$Sr$_2$CuO$_6$ (Bi2201, $N_{\ell}=1$, $T_c^{\rm exp} \sim 10$ K), Bi$_2$Sr$_2$CaCu$_2$O$_8$ (Bi2212, $N_{\ell}=2$, 84$ HgBa$_2$CuO$_4$ (Hg1201, 90$ K) and CaCuO$_2$ (Ca11, $N_{\ell}=\infty$, 110$ with different experimental optimal SC transition temperature exp}$ number $...

We present the structural and magnetic properties of KNaCuP$_2$O$_7$ investigated via x-ray diffraction, magnetization, specific heat, $^{31}$P NMR $^{23}$Na measurements complementary electronic structure calculations. The temperature dependent susceptibility shift could be modeled very well by uniform spin-$1/2$ Heisenberg antiferromagnetic chain model with nearest-neighbour interaction $J/k_...