We review the status of a quasi degenerate doublets in nuclei, called pseudospin doublets, which were discovered about thirty years ago and the origins of which have remained a mystery, until recently. We show that pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian which occurs when the scalar and vector potentials are opposite in sign but equal in magnitude. Furtherm...

Matrix fixed-point iterations zn+1 = ψ(zn) defined by a rational function ψ are considered. For these iterations a new proof is given that matrix convergence is essentially reduced to scalar convergence. It is shown that the principal Padé family of iterations for the matrix sign function and the matrix square root is a special case of a family of rational iterations due to Ernst Schröder. This...

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...

Scalar implicatures have been a subject of much debate concerning their place as part of either the grammatical computation of the semantics of a sentence or as post-compositional pragmatic reasoning. This paper describes three experiments addressing the semantic/pragmatic question of scalar implicatures from a developmental perspective, one in English and two in American Sign Language (ASL). T...

We present a general L stability result for a generic finite volume method for hyperbolic scalar equations coupled with a large class of reconstruction. We show that the stability is obtained if the reconstruction respects two fundamental properties: the convexity property and the sign inversion property. We also introduce a new MUSCL technique, the multislope MUSCL technique, based on the appr...

Following some ideas in the Landau’s book, some corrections about errors in the old literature on scalar gravitational waves are given and discussed. Even if such errors can be considered not important from the point of view of observations, because they do not alter the interferometric response function for scalar gravitational waves, the presented analysis is due and very important for a sake...

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wavelike behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term r...

We consider a massless scalar Bose field interacting with two particles, one of them infinitely heavy. Neither an infrared nor an ultraviolet cutoff is imposed. In case the charge of the particles is of the same sign and sufficiently small, we prove the existence of a ground state.

In this paperwe consider a linear scalar differential equationwith variable delays andgive conditions to ensure that the zero solution is asymptotically stable bymeans of fixedpoint theory.These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved. 2...

We obtain the existence of infinitely many solutions with prescribed nodal properties for some boundary value problems associated to the second order scalar equation ẍ+ q(t)g(x) = 0, where g(x) has superlinear growth at infinity and q(t) changes sign.