During modern era of critical phenomena, several inequalities between critical exponents have been derived. However most of these inequalities depend on some assumptions. Beside this, some of these inequalities can be replaced by equalities. Several solved classical models as well as some recent theories have helped us to check the validity of these inequalities. To check these inequalities in ...

Abstract We prove that under the log-Hölder continuity condition of variable exponent $$p(\cdot )$$ p ( · ) , a new type maximal operators, $$U_{\gamma ,s}$$ U γ , s<...

The exponent P that describes the sinusoidally modulate d * paramagnetic phase transition crosses over from a value of 0.39 near TN to a mean field value away from TN. Electrical resistivity measurements near TN are given for the c axis and the critical behaviour is discussed. Erbium orders below its NBel temperature TN= 85 K with its spins directed along the c axis of the hcp crystal and with ...

Existence and uniqueness of a specific self-similar solution is established for the following reaction-diffusion equation with Hardy singular potential?tu=?um+|x|?2up,(x,t)?RN×(0,?), in range exponents 1?p0 p?[1,?). As an applica...