The expression for the radial moments $\left\langle r^{n}\right\rangle_{c}$ of nuclear charge density has been discussed under plane wave Born approximation (PWBA) method recently, which is significant to investigate surface thickness and neutron distribution radius. In this paper, we extend studies extracting second-order moment r^{2}\right\rangle_{c}$ fourth-order r^{4}\right\rangle_{c}$ from...

Given $A\subseteq GL_2(\mathbb{F}_q)$, we prove that there exist disjoint subsets $B, C\subseteq A$ such $A = B \sqcup C$ and their additive multiplicative energies satisfying \[ \max\{\,E_{+}(B),\, E_{\times}(C)\,\}\ll \frac{|A|^3}{M(|A|)}, \] where \begin{equation*} \label{eqn:MAminBVPolyLSSS} M(|A|) \min\Bigg\{\,\frac{q^{4/3}}{|A|^{1/3}(\log|A|)^{2/3}},\, \frac{|A|^{4/5}}{q^{13/5}(\log|A|)^{...

We classify the compact quantum groups Au(Q) and Bu(Q) up to isomorphism and analyze their structures. Structures et classifications isomorphiques des groupes quantiques compacts Au(Q) et Bu(Q) Résumé. Nous classifions les groupes quantiques compacts Au(Q) et Bu(Q) à isomorphisme près et analysons leur structures. Version française abrégée Rappelons [5, 4, 3] que pour chaque Q ∈ GL(n,C), le gro...

Construction methods are presented that generate hermite interpolation quaternion curves on SO(3). Two circular curves C 1 (t) and C 2 (t), 0 t 1, are generated that interpolate two orientations q 1 and q 2 , and have boundary angular velocities: C 0 1 (0) = ! 1 and C 0 2 (1) = ! 2 , respectively. They are smoothly blended together on SO(3) to generate a hermite quaternion curve Q(t) 2 SO(3), 0...

In this paper, we study the transcendental entire solutions for nonlinear differential-difference equations of forms: $ \begin{eqnarray*} f^{2}(z)+\widetilde{\omega} f(z)f'(z)+q(z)e^{Q(z)}f(z+c) = u(z)e^{v(z)}, \end{eqnarray*} and class="disp_formula">$ f^{n}(z)+\omega f^{n-1}(z)f'(z)+q(z)e^{Q(z)}f(z+c) p_{1}e^{\lambda_{1} z}+p_{2}e^{\lambda_{2} z}, \quad n\g...

Suppose that Q is a positive defined n×n matrix, and Q[x̲]=x̲TQx̲ with x̲∈Zn. The Epstein zeta-function ζ(s;Q), s=σ+it, defined, for σ>n2, by the series ζ(s;Q)=∑x̲∈Zn∖{0̲}(Q[x̲])−s, it has meromorphic continuation to whole complex plane. Let n⩾4 be even, while φ(t) an increasing differentiable function continuous monotonic bounded derivative φ′(t) such φ(2t)(φ′(t))−1≪t, sequence {aφ(k)} uniformly d...