We define a set of orthogonal functions on the complex projective space CPN−1, and compute their Clebsch-Gordan coefficients as well as a large class of 6–j symbols. We also provide all the needed formulae for the generation of high-temperature expansions for U(N)-invariant spin models defined on CPN−1.

It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pse...

Child cortical bone tissue is rarely studied because of the difficulty of obtaining samples. Yet the preparation and ultrasonic characterization of the small samples available, while challenging, is one of the most promising ways of obtaining information on the mechanical behavior of non-pathological children׳s bone. We investigated children׳s cortical bone obtained from chirurgical waste. 22 f...

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor–dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the...

Accuracy of the quarter-point and transition elements is investigated on oneand two-dimensional problems with inverse square-root singularity. It is demonstrated that most coefficients of the stiffness matrix of the quarter-point element are unbounded. However, numerical integration produces finite values of these coefficients. Influence of several parameters on the error in determining the str...

This article concerns the stability of a model for mass-spring systems with positive damping and negative stiffness. It is well known that when the coefficients are frozen in time the system is unstable. Here we find conditions on the variable coefficients to prove stability. In particular, we disprove the believe that if the eigenvalues of the system change slowly in time the system remains un...