We investigate dynamical system having a special structure namely a codimension-one invariant manifold that is preserved under the variation of parameters. We derive conditions such that bifurcations of codimension-one and of codimension-two occur in the system. The normal forms of these bifurcations are derived explicitly. Both local and global bifurcations are analysed and yield the transcrit...

Results on three-nucleon (3N) elastic scattering below the pion production threshold are discussed with emphasis on the need for a three-nucleon force (3NF). The large discrepancies found between a theory based on numerical solutions of 3N Faddeev equations with (semi)phenomenological NN potentials only and data point to the need for 3NF’s. This is further supported since another possible reaso...

A square-ordered field, also called Hilbert field of type (A), is understood to be an ordered field all of whose positive elements are squares. The problem of classifying, up to isomorphism, all 4-dimensional quadratic division algebras over a square-ordered field k is shown to be equivalent to the problem of finding normal forms for all pairs (X, Y ) of 3× 3-matrices over k, X being antisymmet...

The ‘Alfvén Paradox’ is that as resistivity decreases, the discrete eigenmodes do not converge to the generalized eigenmodes of the ideal Alfvén continuum. To resolve the paradox, the -pseudospectrum of the RMHD operator is considered. It is proven that for any , the pseudospectrum contains the Alfvén continuum for sufficiently small resistivity. Formal − pseudoeigenmodes are constructed using ...

The fact that low intensity light has certain therapeutic effect has been proven through a number of research studies. There are studies that showed the applied electromagnetic radiation (EMR) in the visible and infrared light range can modulate protein and cellular activity. Here we have evaluated experimentally the hypothesis of the Resonant Recognition Model (RRM) that selectivity of protein...

A family of satisfiable benchmark instances in conjunctive normal form is introduced. The instances are constructed by transforming a random regular graph into a system of linear equations followed by clausification. Schemes for introducing nonlinearity to the instances are developed, making the instances suitable for benchmarking solvers with equivalence reasoning techniques. An extensive expe...

pd capture processes at various energies have been analyzed based on solutions of 3N-Faddeev equations and using modern NN forces. The application of the Siegert theorem is compared to the explicit use of πand ρ-like exchange currents connected to the AV18 NN interaction. Overall good agreement with cross sections and spin observables has been obtained but leaving room for improvement in some c...

Cauchy problem in a product space (that may be particularly involved). For example, consider the heat equation  ∂u ∂t (t, x) = ∆u(t, x), t ≥ 0, x ∈ Ω, ∂w ∂t (t, z) = − ∂w ∂n (t, z), t ≥ 0, z ∈ ∂Ω, w(t, z) = u(t, z), t ≥ 0, z ∈ ∂Ω, where − ∂ ∂n denotes the outer normal derivative. This can be written as U ′(t) = ( ∆ 0 − ∂ ∂n 0 ) U(t), where U = ( u u|∂Ω ) . Observe that a relationship between ...

This paper deals with global well-posedness of the following free boundary problem for the Navier-Stokes equations. Let Ω be an exterior domain in the N dimensional Eucledian space RN occupied by an incompressible viscous fluid. Let Γ be the boundary of Ω that is a C2 compact hyper surface with the unit outer normal n. Let t Ω be the evolution of Ω at time t. Let t Γ be the boundary of t Ω with...

Time-resolved pump–probe spectra of 1,18,3,3,38,38-hexamethyl-4,48,5,58-dibenzo-2,28indotricarbocyanine ~HDITC!, a cyanine dye, in ethylene glycol are obtained using 11 fs and 90 fs duration pulses and analyzed in order to study its potential energy surfaces and vibrational dynamics. Ten oscillatory frequencies ranging from 30 cm to 1400 cm are observed in the 11 fs duration wavelength-resolved...