of compressible gas dynamics are presented that show the effect of the (formal) order of accuracy and the use of triangles or rectangles, on the quality of the approximation.

We study a plane circular model of a frictional fault using numerical methods. The model is dynamic since we specify the effective stress at the fault. In one model we assume that the fault appears instantaneously in the medium; in another, that the rupture nucleates at the center and that rupture

As a consequence of optimal investment choices, a firm’s assets and growth options change in predictable ways. Using a dynamic model, we show that this imparts predictability to changes in a firm’s systematic risk, and its expected return. Simulations show that the model simultaneously reproduces

of information in case representations, (v) its non-parametric nature, (vi) reasonably good results on unknown words without morphological analysis, and (vii) fast learning and tagging. In this paper we show that a large-scale application of the memory-based approach is feasible: we obtain a tagging accuracy

BRIEF NOTES pendent generalized coordinates qt, q2, and q3. The relation between the Cartesian velocities v '~, v'y, v' z Since gyroscopic coupling may exist between the coordinate pairs (ql, q2), (q2, q3), and (q3, ql), we evaluate the modulus in Eq. (12) for each of the cases

a velocity field �v. This velocity can depend on position, time, the geometry of the interface and the external physics. The interface is captured for later time as the zero level set of a smooth (at least Lipschitz continuous) function ϕ(�x,t), i.e., Γ(t)={�x|ϕ(�x,t)=0}. ϕ is positive inside Ω

In this article we develop Poincaré ideas about a heat balance of ideal gas considered as a collisionless continuous medium. We obtain the theorems on diffusion in nondegenerate completely integrable systems. As a corollary we show that for any initial distribution the gas will be eventually irreversibly and uniformly distributed over all volume, although every particle during this process approaches arbitrarily close to the initial position indefinitely many times. However, such individual returnability is not uniform, which results in diffusion in a reversible and conservative system. Balancing of pressure and internal energy of ideal gas is proved, the formulas for limit values of these quantities are given and the classical law for ideal gas in a heat balance is deduced. It is shown that the increase of entropy of gas under the adiabatic extension follows from the law of motion of a collisionless continuous medium. 1. Heat balance The establishment of heat balance of gas in a vessel is one of the central problems of nonequilibrium statistical mechanics. The conventional model is Boltzmann–Gibbs gas: ensemble of a large (but finite) number of identical solid balls elastically colliding with each other and with the walls of the vessel. According to the classical approach based on the Boltzmann kinetic equation the process starts with practically instantaneous establishment of the Maxwell velocity distribution, and then (not so fast and with oscillations) the gas density becomes balanced [1].

It is described how the standard Poisson bracket formulas should be modified in order to incorporate integrals of divergences into the Hamiltonian formalism and why this is necessary. Examples from Einstein gravity and Yang-Mills gauge field theory are given. 1.

, there is often the need to deal with data whose type cannot be determined at compile time. To handle such situations safely, we propose to add a type Dynamic whose values are pairs of a value v andatype tag T where v has the type denoted by T. Instances of Dynamic are built with an explicit tagging construct

to simple dynamic motions and events. The ®nal sections of this review generalize these issues beyond vision science, to other modalities and ®elds such as auditory objects of attention and the infant's `object concept'. q 2001 Elsevier Science B.V. All rights reserved.