Recurring to some excellent geometric and algebraic properties of Poisson curves, we present an algorithm that generates a developable Poisson surface through a Poisson curve of arbitrary degree. The technique is based on necessary and sufficient conditions for a developable surface, degree elevation formula of a Poisson curve and linear independence of Poisson basis. Some common transcendental...

Ten new exact solutions of the Riccati equation dy/dx = a(x) + b(x)y + c(x)y are presented. The solutions are obtained by assuming certain relations among the coefficients a(x), b(x) and c(x) of the Riccati equation, in the form of some integral or differential expressions, also involving some arbitrary functions. By appropriately choosing the form of the coefficients of the Riccati equation, w...

The closure conditions, which make a finite set of moment equations equivalent to the collisionless Boltzmann equation, are investigated for Gaussian and ellipsoidal velocity distributions working from the complete mathematical expression for the n-order stellar hydrodynamic equation, which was explicitly obtained depending on the comoving moments in a previous paper. First, for a Schwarzschild...

We identify the cotangent bundle Lie algebroid of a Poisson homogeneous space G/H of a Poisson Lie group G as a quotient of a transformation Lie algebroid over G. As applications, we describe the modular vector fields of G/H , and we identify the Poisson cohomology of G/H with coefficients in powers of its canonical line bundle with relative Lie algebra cohomology of the Drinfeld Lie algebra as...

We propose an approximation to full relativity that captures the main gravitational effects of dynamical importance in supernovae. The conceptual link between this formalism and the Newtonian limit is such that it could likely be implemented relatively easily in existing multidimensional Newtonian gravitational hydrodynamics codes employing a Poisson solver. As a test of the formalism’s utility...

We have modeled the electric potential profile, across the membranes of the ganglion neuron and neuroblastoma cells. We considered the resting and action potential states, and analyzed the influence of fixed charges of the membrane on the electric potential of the surface of the membranes of these cells, based on experimental values of membrane properties. The ganglion neuron portrays a healthy...

We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space Hn. This enables us to find asymptotic properties of the kernel. Our starting point is the formula for its Fourier transform. When n = 3, 4 or 6 we give an explicit formula for the Poisson kernel itself. In the general case we give various asymptotics and show convergence to the Poi...

We consider a gas in a horizontal slab in which the top and bottom walls are kept at different temperatures. The system is described by the Boltzmann equation (BE) with Maxwellian boundary conditions specifying the wall temperatures. We study the behavior of the system when the Knudsen number e. is small and the temperature difference between the walls as well as the velocity field is of order ...

Let ω(·) = ω(·, x) denote the harmonic measure associated to the Laplace operator and defined with respect to Ω and x ∈ Ω. A classical result concerning the harmonic measure, due to Lavrentiev [22], states that if Ω ⊂ R is a chord arc domain, then ω is mutually absolutely continuous with respect to σ, i.e., dω = kdσ, where k is the associated Poisson kernel. Moreover, Lavrentiev [22] proved tha...

In this paper we consider the Gaussian Besov-Lipschitz B α p,q (γ d) and Gaussian Triebel-Lizorkin F α p,q (γ d) spaces, for any α > 0, studying the inclusion relations among them, proving that the Gaussian Sobolev spaces L p α (γ d) are contained in them, giving some interpolation results and studying the continuity properties of the Ornstein-Uhlenbeck semigroup, the Poisson-Hermite semigroup ...