In the present study, buckling problem of nonhomogeneous microbeams with a variable cross-section is analyzed. The microcolumn considered in this study made functionally graded materials longitudinal direction and varies continuously throughout axial direction. Bernoulli–Euler beam theory conjunction modified strain gradient are employed to model structure by considering size effect. Rayleigh–R...

We make use of the Pad e approximants and Krylov's sequence x; Ax; ; : : :; A m?1 x in the projection methods to compute a few Ritz values of a hermitian matrix A of order n. This process consists of approaching the poles of R x () = ((I ?A) ?1 x; x), the mean value of the resolvant of A, by those of m ? 1=m] Rx (), where m ? 1=m] Rx () is the Pad e approximant of order m of the function R x ()...

I have been asked to discuss for you some applications of the Rayleigh-Ritz method in physics. Rather than at tempt to survey the whole of a discouragingly large field I have preferred to restrict my attention to some few topics from the theory of atomic and molecular structure. The application of the Rayleigh-Ritz method in this field has been carried out with some care and persistence, and th...

The article touches on two themes in which Larry Brown has been interested, namely foundations, and mathematical analysis of Bayesian decision theory. In the section on foundations, a new formulation of the problem of testing is given, and is theoretically explored. The formulation strikes a balance between false discoveries and missed discoveries. Basic higher order asymptotic theory for the α...

Ice-sheet modelers tend to be more familiar with the Newtonian, vectorial formulation of continuum mechanics, in which the motion of an ice sheet or glacier is determined by the balance of stresses acting on the ice at any instant in time. However, there is also an equivalent and alternative formulation of mechanics where the equations of motion are instead found by invoking a variational princ...