In this work, we consider the Lie's method of infinitesimal transformation groups and discrete symmetries method for Burgers equation with time dependent flux at the origin. Following the Lie's
method of infinitesimal transformation groups we determine the symmetry reductions and similarity solutions of the governing equation. By applying discrete symmetries analysis we have obtained three groups of discrete symmetries which lead to new symmetry reductions and similarity solutions of our problem. The analytical solutions which are obtained using symmetries and discrete symmetries are summarized in table form.

In this work, we consider the Lie's method of infinitesimal transformation groups and discrete symmetries method for Burgers equation with time dependent flux at the origin. Following the Lie's
method of infinitesimal transformation groups we determine the symmetry reductions and similarity solutions of the governing equation. By applying discrete symmetries analysis we have obtained three groups of discrete symmetries which lead to new symmetry reductions and similarity solutions of our problem. The analytical solutions which are obtained using symmetries and discrete symmetries are summarized in table form.

Systemic lupus erythematosus (SLE) is a prototypic autoimmune disease characterized by an imbalanced redox state and increased apoptosis. Tropical infections, particularly malaria, may confer protection against SLE. Oxidative stress is a hallmark of SLE. We have measured changes in the levels of nitric oxide (NO), hydrogen peroxide (H2O2), malondialdehyde (MDA), and reduced glutathione (GSH) in both kidney and liver tissues of female BWF1 lupus mice, an experimental model of SLE, after infection with either live or gamma-irradiated malaria. We observed a decrease in NO, H2O2, and MDA levels in kidney tissues after infection of lupus mice with live malaria. Similarly, the levels of NO and H2O2 were significantly decreased in the liver tissues of lupus mice after infection with live malaria. Conversely, GSH levels were obviously increased in both kidney and liver tissues after infection of lupus mice with either live or gamma-irradiated malaria. Liver and kidney functions were significantly altered after infection of lupus mice with live malaria. We further investigated the ultrastructural changes and detected the number of apoptotic cells in kidney and liver tissues in situ by electron microscopy and TUNEL assays. Our data reveal that infection of lupus mice with malaria confers protection against lupus nephritis.

the forced convenection heat transfer to the power law non-Neetonian nanofluid from the stretching surface has been investigated numerically. this is the first paper on non-Newtonian with stratching sheet in nanofluids .the stretching of the surface velocity and the prescribed surface tempertaure is assumed to vary as alinear function of the distance of the distance from the origin .A similarity solution is presented which depends on nanoparticle volume fraction φ power law index n; buoyancy convenction parameter λ and the modified prandtl number NPr. velocity and temperature variations as well as the variation of skin friction and nusselt number with the parameters govern the problem is presented and discussed . different types of nanoparticles are tested.

The current paper outlines a new algorithm, which is used to determine the exact solutions of
ODEs and the similarity transformations of PDEs whose the invariant groups are known. Three groups of
formulations (named by HAMAD Formulations) are presented: (I) Formulations for the exact solutions of
ODE. (II) Formulations for similarity transformations of PDEs contains two independent variables. (III)
Formulations for similarity transformations of PDEs contains three independent variables. By using these
formulations enable readers can calculate the similarity transformations which transform PDEs to ODEs
and also can calculate exact solutions of ODEs . Some examples are presented.

The current paper outlines a new algorithm, which is used to determine the exact solutions of
ODEs and the similarity transformations of PDEs whose the invariant groups are known. Three groups of
formulations (named by HAMAD Formulations) are presented: (I) Formulations for the exact solutions of
ODE. (II) Formulations for similarity transformations of PDEs contains two independent variables. (III)
Formulations for similarity transformations of PDEs contains three independent variables. By using these
formulations enable readers can calculate the similarity transformations which transform PDEs to ODEs
and also can calculate exact solutions of ODEs . Some examples are presented.

The current paper outlines a new algorithm, which is used to determine the exact solutions of
ODEs and the similarity transformations of PDEs whose the invariant groups are known. Three groups of
formulations (named by HAMAD Formulations) are presented: (I) Formulations for the exact solutions of
ODE. (II) Formulations for similarity transformations of PDEs contains two independent variables. (III)
Formulations for similarity transformations of PDEs contains three independent variables. By using these
formulations enable readers can calculate the similarity transformations which transform PDEs to ODEs
and also can calculate exact solutions of ODEs . Some examples are presented.