The ramifications of endocrine and neural senescence converge in the hippocampus, particularly with respect to glutamatergic synapses. In this review, we will focus on current literature suggesting that potential synaptic alterations induced by estrogen in the hippocampus are mediated through interactions between ER-alpha and NMDA receptors. In addition, we will examine the data suggesting that...

In this paper, we investigate the sums of multiple zeta(-star) values height one: $$Z_{\pm }(n)=\sum _{a+b=n} (\pm 1)^b\zeta (\{1\}^a,b+2)$$ , }^{\star ^{\star }(\{1\}^a,b+2)$$ . particular, prove that weighted sum $$\begin{aligned}\sum _{\begin{array}{c} 0\le m\le p\\ m: \mathrm{even} \end{array}} \sum _{\mid \varvec{\alpha }\mid =p+3} 2^{\alpha _{m+1}+1}\zeta (\alpha _0,\alpha _1,\ldots ,\alp...

In this paper, we study the existence and non-existence of normalized solutions to lower critical Choquard equation with a local perturbation $ \begin{equation*} \begin{cases} -\Delta u+\lambda u = \gamma (I_{\alpha}\ast|u|^{\frac{N+\alpha}{N}})|u|^{\frac{N+\alpha}{N}-2}u+\mu |u|^{q-2}u, \quad {\rm{in}}\ \mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx c^2, \end{cases} \end{equation*} where \gamma, ...

Abstract For an integer $$p\ge 2$$ p ≥ 2 , let $$\{x_n\}_{n\in {\mathbb {N}}}\subset {T}}$$ { x n } ∈ N ⊂ <mml:...

We study the asymptotic behaviour of number solutions $$(m, n)\in \mathbb{N}^2$$ , to inequality $$| \alpha^n - \beta^m | \leq x$$ when x tends infinity. Here $$\alpha, \beta$$ are given multiplicatively independent complex numbers with $$|\alpha| > 1 {\rm and} |\beta|>1$$ .