 can be gained by visualizing the 3D-QSAR model in the context of one or more ligands in the series
The validation of AD results indicates that the predictions of test set compounds are quite reliable.
The DModX values of all 17 test set compounds are below the critical value of 2.8. Fig. 8 represents the residual SD of X-residuals (DModX) of the test set compounds for the best model.
We carried out docking studies for all molecules and we analyzed the most active molecule and least active molecule in the receptor ligand binding region. Fig. 9a   The performance of the Glide dock program was also evaluated by comparing the docked pose of active and inactive ligand to co-crystallize ligand pose in the 3IOP crystal structure. The co-crystallized ligand was removed from the active site and again re-docked along with compound 7 and compound 32. The rmsd values for heavy atoms between the docked poses of compound 7, compound 32 and the native ligand   Table 3. The combined ligand-based pharmacophore and atom-based 3D-QSAR models were generated using a training set of 65 molecules which consists of six-point pharmacophore hypothesis has led to the development of satisfactory models for predicting the biological activity of new compounds. Understanding the intermolecular interactions of various derivatives with PDK1 was achieved by integrating statistically significant and predictable models. The atom-based 3D-QSAR visualization model in the context of the structure of molecules understudy provides details of the relationship between structure and activity. This will enhance in-depth information related with modifications of some structural side chains which will help in the designing of new analogs with better activity before synthesis. Molecular docking studies also support by validating the Glide program which shows that binding orientation of these 82 inhibitors are correlating with the native ligand present in the PDK1 protein. These reveal that newly synthesizing inhibitory molecules not only possess higher activity (pIC 50 ) and also fit the binding pocket of PDK1 protein. And last, the binding free energy was calculated from the Prime MM-GBSA method to revel the potency of the electrostatic interactions between protein ligand complexes.Streamline Payments provides PCI compliant solutions through a direct link to the Buypass platform, allowing dealers to maximize the cards accepted at the pump. Wright Express, Voyager and other fleet cards are all accepted. Working with micronode technology, we provide high speed transaction capabilities with dial backup, a must for high traffic. Our representatives have experience with the Verifone Ruby and Gilbarco Systems, and strive to minimize downtime during our conversions.\section{Introduction and statement of main results}

In recent years, it has been evidenced that \emph{Sparse Operators} play an important 
role in the weighted bounds for many singular integrals, see for example \cite{La1,Le,CCDO, CR}. Such techniques
have led to advances in sharp estimates within the Calder\'on-Zygmund theory.
The fundamental example is the sparse domination of the one-parameter dyadic maximal function 
\begin{align*}
M_d f (x) \vcentcolon = \sup_{Q \in \mathscr{D}^n \, : \, x \in Q} {1\over |Q|} \int_Q |f(x_1)| \, dx_1
\end{align*}
where the supremum is taken over all dyadic cubes in $\mathbb R^n$ containing $x$, that is,
\begin{align*}
M_d f (x) \leq C \sum_{Q \in \mathscr{S}} \left( {1\over |Q|} \int_Q f(x_1) \, dx_1 \right) \raisebox{2pt}{$\chi$}_Q(x),
\end{align*}
where $\mathscr{S}$ is a sparse collection of dyadic cubes.

Nevertheless, a remarkable recent result (Theorem A in \cite{BCOR}) shows that there is no sparse 
domination in the tensor product setting $\mathbb R^n\times \mathbb R^m$ for the strong dyadic maximal function
\begin{align*}
M_{sd} f (x,y) \vcentcolon = \sup_{R \in \mathscr{D}^{n} \times \mathscr{D}^{m} \, : \, (x,y) \in R} {1\over |R|} \int_R |f(x_1,y_1)| \, dx_1dy_1,
\end{align*}
where the supremum is taken over all dyadic rectangles with sides parallel to the axes containing $(x,y)$. This result suggests that
the sparse domination techniques in the one-parameter setting cannot be expected to work 
with the same approach in the multiparameter setting.

The classical Calder\'on--Zygmund
singular integrals are related to the one-parameter dilation
structure on $\Bbb R^n$, defined by $\delta_o \circ
(x_1,x_2,\ldots, x_n) \vcentcolon = (\delta x_1,\ldots,\delta x_n)$, with
$x\in\mathbb{R}^n$ and $\delta > 0$. Meanwhile the product
dilation structure is defined by $\delta_p \circ (x_1,x_2,\ldots, x_n) \vcentcolon =
(\delta_1 x_1,\ldots,\delta_n x_n)$, $\delta_i > 0$, $i =
1,\ldots,n$. The key difference is that $\delta_o$ maps cubes
to cubes, while $\delta_p$ maps cubes to rectangular prisms
whose side-lengths are independent. Multiparameter dilations
lie between these two extremes: the side-lengths need not be
equal nor be completely independent of each other, but may be mutually dependent. 

With these dilation structures in mind, it is natural to wonder whether it is possible to obtain certain 
sparse domination for multiparameter maximal functions which lie in between
the two extreme cases $M_d$ and $M_{sd}$.

One of the most natural and interesting examples of a group of dilations in $\Bbb R^3$ that lies in between 
the one-parameter and the full product setting is the so-called \emph{Zygmund dilation} defined by
$\rho_{s,t}(x_1,x_2,x_3) = (sx_1, tx_2, stx_3)$ for $s, t > 0$ (see for example \cite{RS,FP}). The 
maximal function corresponding to this Zygmund dilation is  
\begin{align}\label{zygmund maximal}
{\mathcal M}_{\frak z} f (x_1,x_2,x_3) \vcentcolon = \sup_{R \, : \, (x_1,x_2,x_3) \in R} \frac{1}{|R|}\int_{R}|f(u_1,u_2,u_3)| \, du_1du_2du_3,
\end{align}
where the supremum above is taken over all rectangles in $\Bbb R^3$ with edges parallel
to the axes and side-lengths of the form $s, t$, and $st$ (see \cite{Co}). See also \cite{So} for a discussion
of the Zygmund conjecture about the differentiation properties of $k$-parameter bases of rectangular 
prisms in $\mathbb{R}^n$, and \cite{DLOWY2} for the Zygmund type singular integrals and their commutators. The survey paper of R. Fefferman \cite{Fe1} has more information 
about research directions in this setting.

Another very important example in the multiparameter setting is the implicit flag structure.
To be precise, in \cite{MRS,MRS2}, M\"{u}ller, Ricci and Stein studied Marcinkiewicz 
multipliers on the Heisenberg group $\mathbb H^n$  associated with the sub-Laplacian on 
$\mathbb H^n$ and the central invariant vector field, and obtained the $L^p$-boundedness for $1<p<\infty$. 
This is surprising since these multipliers are invariant under a two-parameter
group of dilations on $\mathbb{C}^{n}\times \mathbb{R}$, while there is
\emph{no} two-parameter group of \emph{automorphic} dilations on $\mathbb{H}
^{n}$. Moreover, they showed that Marcinkiewicz multipliers can be characterized by
a convolution operator of the form $f\ast K$ where $K$ is a \emph{flag} convolution kernel, 
which satisfies size and  smoothness conditions lying in between the one-parameter and 
product singular integrals. The complete flag Hardy space theory and the boundedness of the iterated commutator was obtained only recently in \cite{HLLW} and \cite{DLOWY}, respectively.
The fundamental tool in this setting is the  flag maximal function. We state the definition in $\mathbb R\times \mathbb R$
for the sake of simplicity: 
\begin{align}\label{flag maximal}
{\mathcal M}_{\text {flag}} f (x_1,x_2) \vcentcolon = \sup_{R \, : \, (x_1,x_2) \in R}\frac