Given $d\in \mathbb{N}$, $g\in \mathbb{N} \cup\{0\}$, and an integral vector $\kappa=(k_1,\dots,k_n)$ such that $k_i>-d$ $k_1+\dots+k_n=d(2g-2)$, let $\Omega^d\mathcal{M}_{g,n}(\kappa)$ denote the moduli space of meromorphic $d$-differentials on Riemann surfaces genus $g$ whose zeros poles have orders prescribed by $\kappa$. We show carries a canonical volume form is parallel with respect to it...

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...

Let $K$ be a number field and $S$ set of primes $K$. We write $K_S/K$ for the maximal extension unramified outside $G_{K,S}$ its Galois group. In this paper, we answer following question under some assumptions: "For $i=1,2$, let $K_i$ field, $S_i$ (sufficiently large) $\sigma :G_{K_1,S_1}\to G_{K_2,S_2}$ an isomorphism. Is $\sigma$ induced by unique isomorphism between $K_{1,S_1}/K_1$ $K_{2,S_2...

Using 2.93 fb$^{-1}$ of $e^+e^-$ collision data taken with the BESIII detector at a center-of-mass energy 3.773 $\rm \,GeV$, observation $D^0\to K_1(1270)^- e^+\nu_e$ semileptonic decay is presented. The statistical significance greater than $10\sigma$. branching fraction measured to be $(1.09\pm0.13^{+0.09}_{-0.16} \pm 0.12)\times10^{-3}$. Here, first uncertainty statistical, second systematic...

Using 2.93 fb$^{-1}$ of $e^+e^-$ collision data taken with the BESIII detector at a center-of-mass energy 3.773 $\rm \,GeV$, observation $D^0\to K_1(1270)^- e^+\nu_e$ semileptonic decay is presented. The statistical significance greater than $10\sigma$. branching fraction measured to be $(1.09\pm0.13^{+0.09}_{-0.16} \pm 0.12)\times10^{-3}$. Here, first uncertainty statistical, second systematic...

Let $${\mathbb {F}}_{q^n}$$ be a finite field with $$q^n$$ elements and r positive divisor of $$q^n-1$$ . An element $$\alpha \in {\mathbb {F}}_{q^n}^*$$ is called r-primitive if its multiplicative order $$(q^n-1)/r$$ Also, k-normal over {F}}_q$$ the greatest common polynomials $$g_{\alpha }(x) = \alpha x^{n-1}+ ^q x^{n-2} + \ldots ^{q^{n-2}}x ^{q^{n-1}}$$ $$x^n-1$$ in {F}}_{q^n}[x]$$ has degre...

A function $F(s)=\sum_{n=1}^{\infty}a_n\exp\{s\lambda_n\}$ with $0\le\lambda_n\uparrow+\infty$ is called the Hadamard composition of genus $m\ge 1$ functions $F_j(s)=\sum_{n=1}^{\infty}a_{n,j}\exp\{s\lambda_n\}$ if $a_n=P(a_{n,1},...,a_{n,p})$, where$P(x_1,...,x_p)=\sum\limits_{k_1+\dots+k_p=m}c_{k_1...k_p}x_1^{k_1}\cdot...\cdot x_p^{k_p}$ a homogeneous polynomial degree 1$. Let $M(\sigma,F)=\s...