Let 1 < p ̸= 2 < ∞, ε > 0 and let T : lp(l2) into → Lp[0, 1] be an isomorphism Then there is a subspace Y ⊂ lp(l2), (1 + ε)-isomorphic to lp(l2), such that: T|Y is an (1+ ε)-isomorphism and T (Y ) is Kp-complemented in Lp [0, 1], with Kp depending only on p. Moreover, Kp ≤ (1 + ε)γp if p > 2 and Kp ≤ (1 + ε)γp/(p−1) if 1 < p < 2, where γr is the Lr norm of a standard Gaussian variable.

This paper studies the following two non-Newtonian equations with nonlinear boundary conditions. Firstly, we show that finite time blow up occurs on and get a rate an estimate for of equation $k_{t}=(\left \vert k_{x}\right ^{r-2}k_{x})_{x}$, $(x,t)\in (0,L)\times (0,T)\ $with $k_{x}(0,t)=k^{\alpha }(0,t)$, $k_{x}(L,t)=k^{\beta }(L,t)$,$\ t\in $and initial function $k\left(x,0\right) =k_{0}\lef...

background: it has been hypothesized that the body's response to anesthesia techniques can increase risk of cancer recurrence and metastatic disease after surgery and also can modulate immune responses. some acute inflammatory markers have been measured to survey the immunomodulatory effect of anesthesia, but in this research, we studied the plasma level of cd30 and ykl-40 gene expression which...