In this paper the single cycle T-functions are studied. Making use of the explicit formulas of sum and product of 2-adic integers, we present the necessary and sufficient conditions on the generalized polynomial p̃(x) = a0⊕a1x + ⊕ · · · + ⊕adx d(mod2n) being a single cycle T-function. Furthermore, for any given generalized polynomial, we can deduce some expressions about its coefficients by whic...

in this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. we use some natural constraints and the ljusternik-schnirelman critical point theory on c1-manifolds, to prove our main results.

A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...