We follow a paper by Sedunova regarding Vaughan’s basic mean value Theorem to improve and complete more general demonstration for suitable class of arithmetic functions as started Cojocaru Murty. As an application we derive theorem the von Mangoldt generalized functions.

The conformable derivative and its properties have been recently introduced. In this research work, we propose prove some new results on the calculus. By using definitions derivatives of higher order, generalize theorems mean value which follow same argument as in classical Taylor remainder is obtained through generalized theorem value. Finally, introduce version two interesting multivariable c...

Using local Ward identities and a new correlation inequality, we prove that the mean field transition temperature is an upper bound on the true transition temperature in multicomponent Heisenberg-type classical ferromagnets. (49' = 1 i=1 Given a translation-invariant function J(c~-t3) on Z v x Z ~, we consider for A c Z ~ the Hamiltonian D c~,B~A i = 1 cEA and form the partition function with a...