A wide class of structural models on multivariate normal covariance matrices can be expressed using symmetries. For example, a multivariate normal vector has the intraclass correlation structure (where all variances are equal, and all covariances are equal) if the covariance matrix is invariant under permutation of the components, and the components are independent if the covariance matrix in i...

A measure of the absorption of elastic waves is the specific absorption coe•cient 1/Q. In dispersive mediums, whether the dispersion is due to geometry, inhomogeneity, or both, measurements are often made outside the body and the measurements must be interpreted as to the distribution of values of 1/Q within the body. Two definitive experiments of this type are those performed using standing wa...

background when a primary radiation interacts with a medium, the secondary radiations are produced, that the contribution of these secondary radiation should considered in the calculation of dose. build-up factor is a dosimetric correction factor to assume effect of secondary radiation in calculation of dose. calculation of this factor is very difficult and time consuming. due to significance o...

We discuss the local behaviour of vector fields in the plane R around a regular singular point, using recently introduced reduced normal forms, i.e. Poincaré and Lie renormalized forms [30, 31, 32]. We give a complete classification, and provide explicit formulas, using Poincaré renormalized forms for non-degenerate cases, and Lie ones for certain degenerate cases. Both schemes are completely a...

If L1 and L2 are linear equations, then the disjunctive Rado number of the set {L1, L2} is the least integer n, provided that it exists, such that for every 2-coloring of the set {1, 2, . . . , n} there exists a monochromatic solution to either L1 or L2. If such an integer n does not exist, then the disjunctive Rado number is infinite. In this paper, it is shown that for all integers a 1 and b ...

A normal form is derived for Hamiltonian–Hopf bifurcations of solitary waves in nonlinear Schrödinger equations with general external potentials. This normal form is a simple second-order nonlinear ordinary differential equation (ODE) that is asymptotically accurate in describing solution dynamics near Hamiltonian–Hopf bifurcations. When the nonlinear coefficient in this normal form is complex,...