In this talk I will present the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [4] follows, and I will show how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and I will give a computer demonstration how importa...

Molecular dynamics (MD) simulations of a Lennard–Jones fluid in an inhomogeneous external field generate steady-state profiles of density and pressure with nanoscopic heterogeneities. The continuum level of mass, momentum, and energy transport balances is capable of reproducing the MD profiles only when the equation of state for pressure as a function of density is extracted directly from the m...

Evidence for human learning without awareness of what is learned has been sought in serial reaction time (SRT) tasks in which, unknown to participants, the locations of stimuli follow a particular rule or sequence (Willingham, Nissen & Bullemer, 1989). A number of criticisms have been levelled at such tasks, including a lack of adequate control for sequential effects and a discrepancy in sensit...

We study the propagation of solitons along the hydrogen bonds of an alpha helix. Modeling the hydrogen and peptide bonds with Lennard-Jones potentials, we show that the solitons can appear spontaneously and have long lifetimes. Remarkably, even if no explicit solution is known for the Lennard-Jones potential, the solitons can be characterized analytically with a good quantitative agreement usin...

In order to improve the description of the N-d vector analyzing powers Ay and iT11 (the so-called Ay puzzle) a spin–orbit three-body force has been introduced. The L · S term in the NN potential has been modified including a two-parameter three-body function depending on the hyperradius ρ. The modification has been performed in channels where the pair of nucleons (i, j) are coupled to spin Sij ...

A review of the properties that bond the particles under Lennard Jones Potential allow to states properties and conditions for building evolutive algorithms using the CB lattice with other different lattices. The new lattice is called CB lattice and it is based on small cubes, such the number of its vertices in a region is always greater than the number of the particles of a cluster or a region...

The previous analysis of the short-range NN repulsion originating from the Goldstone boson exchange hyperfine interaction between constituent quarks is revisited. We study in which respects the repulsion depends on the radial form of the spin-spin quark-quark force. We show that while the radial form affects the structure of the 6Q wave function, the short-range repulsion in the NN system persi...

An investigation into the properties of a two dimensional (2D+1) system of self propelled particles (known as boids) in free space is conducted using a Lagrangian Individual-Based Model. A potential, associated with each boid is specified and a Lagrangian is subsequently derived in order to obtain the equations of motion for each particle in the flock. The Morse potential and the Lennard-Jones ...

Z. Naturforsch. 54 a, 559-569 (1999); received June 1, 1999 The pressure in the gaseous, the isotropic liquid and nematic liquid crystalline states, as well as the isotropic-nematic transition temperature are calculated for a model system composed of non-spherical particles. The potential is a generalization of the Lennard-Jones interaction where the attractive part depends on the relative orie...

A new molecular simulation method for the calculation of vapour-liquid equilibria of mixtures is presented. In this method, the independent thermodynamic variables are temperature and liquid composition. In the first step, one isobaric isothermal simulation for the liquid phase is performed, in which the chemical potentials of all components and their derivatives with respect to the pressure, i...