\((1)\)已知集合\(A=\left\{ x\in Z|y={{\log }_{3}}\left( x+5 \right) \right\},B=\left\{ x\in R|{{2}^{x}} < \dfrac{1}{2} \right\}\)，则\(A\bigcap B=\)____________．

\((2)\)过双曲线\(C:\dfrac{{{x}^{2}}}{{{a}^{2}}}-\dfrac{{{y}^{2}}}{{{b}^{2}}}=1\left( a,b > 0 \right)\)的右焦点且垂直于\(x\)轴的直线与\(C\)的渐近线相交于\(A,B\)两点，若\(\Delta AOB(O\)为原点\()\)为正三角形，则\(C\)的离心率是 ____________．

\((3)\) 已知变量\(x,y\)满足约束条件\(\begin{cases} & x+2y-3\leqslant 0, \\ & x+3y-3\geqslant 0, \\ & y-1\leqslant 0, \end{cases}\)则\(F\left( x,y \right)={{\log }_{2}}\left( y+1 \right)+{{\log }_{\frac{1}{2}}}\left( x+1 \right)\)的最小值为___________．

\((4)\)若数列\(\left\{ {{a}_{n}} \right\}\)满足\({{a}_{2}}-{{a}_{1}} > {{a}_{3}}-{{a}_{2}} > {{a}_{4}}-{{a}_{3}} > \cdot \cdot \cdot > {{a}_{n+1}}-{{a}_{n}} > \cdot \cdot \cdot \)，则称数列\(\left\{ {{a}_{n}} \right\}\)为“差递减”数列\(.\)若数列\(\left\{ {{a}_{n}} \right\}\)是“差递减”数列，且其通项\({{a}_{n}}\)与其前\(n\)项和\({{S}_{n}}\left( n\in {{N}^{*}} \right)\)满足\(2{{S}_{n}}=3{{a}_{n}}+2\lambda -1\left( n\in {{N}^{*}} \right)\)，则实数\(\lambda \)的取值范围是__________．