Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of real...

The recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing the Earth’s gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies, i.e. two iterative met...

Krust established that all conjugate and associate surfaces of a minimal graph over a convex domain are also graphs. Using a convolution theorem from the theory of harmonic univalent mappings, we generalize Krust’s theorem to include the family of convolution surfaces which are generated by taking the Hadamard product or convolution of mappings. Since this convolution involves convex univalent ...

A new variational (dis)continuous Galerkin finite element method is presented for linear free surface gravity water wave equations. In this method, the space-time finite element discretization is based on a discrete variational formulation analogous to a version of Luke’s variational principle. The finite element discretization results into a linear algebraic system of equations with a symmetri...

In this paper we study the following two problems: first, given a rational parametrization P(z) = (p1(z), p2(z)) ∈ C(z)2 of a complex curve C in C, to determine algorithmically, if C has an infinite number of real points (i.e. if the trace of C in R is a real curve). If this is the case, then we would like to find another parametrization mapping of the same curve, but this time with real ration...

It is shown that a canonical time observable may be defined for any quantum system having a discrete set of energy eigenvalues, thus significantly generalising the known case of time observables for periodic quantum systems (such as the harmonic oscillator). The general case requires the introduction of almost-periodic probability operator measures (POMs), which allow the expectation value of a...

We propose a reaction path‐based Hamiltonian in terms of the reaction coordinate, the curvature coordinate, the remaining 3N−8 transverse normal coordinates (whose directions are orthogonal to the path tangent and curvature vectors), and their conjugate momenta, for an Natomic reaction system. The 3N−8 transverse vibrational modes are independent of the motion along the reaction path, although ...

a classical result of neumann characterizes the groups in which each subgroup has finitely many conjugates only as central-by-finite groups. if x is a class of groups, a group g is said to have x-conjugate classes of subgroups if g/coreg(ng(h)) 2 x for each subgroup h of g. here we study groups which have soluble minimax conjugate classes of subgroups, giving a description in terms of g/z(g). w...

We study testing properties of functions on finite groups. First we consider functions of the form f : G → C, where G is a finite group. We show that conjugate invariance, homomorphism, and the property of being proportional to an irreducible character is testable with a constant number of queries to f , where a character is a crucial notion in representation theory. Our proof relies on represe...

I develop simple thermodynamic relations for a system of noninteracting classical particles confined in an isotropic harmonic trap. The volume occupied by the particles in such a trap is not well defined, and the pressure varies with position, indicating that the thermodynamic relations should be expressed in terms of more appropriate variables. I use the effective spring constant of the trap a...