We show that the quantum stochastic Langevin model for continuous in time measurements provides an exact formulation of the Heisenberg uncertainty error-disturbance principle. Moreover, as it was shown in the 80’s, this Markov model induces all stochastic linear and non-linear equations of the phenomenological ”quantum trajectories” such as quantum state diffusion and spontaneous localization b...

The question of uniqueness for linearized problems describing interaction of submerged bodies with an ideal unbounded fluid is far from its final resolution. In the present work a new criterion of uniqueness is suggested based on Green’s integral identity and maximum principles for elliptic differential equations. The criterion is formulated as an inequality involving integrals of the Green fun...

This paper presents additional unpublished aspects related to a recenty published method to calculate equilibrium formation temperatures, under spherical flow conditions in geothermal reservoirs. This method considers that the evolution of equilibrium bottom-hole temperatures following a cold fluid circulation time during drilling, follows a radialspherical pattern. F'rom the mathematical solut...

This paper deals with the approximate solution ofhnear 4th-order elhptic boundaryvalue problems by thefimte element method For a displacement method using the nonconforming plate element of M orley and for a mixed method known as Herrmann-Miyoshi-scheme quasi optimal Land L^-error estimâtes are denved The proof essenüally uses L-estimâtes for regularized Green's functwns and then disaere amiloq...

In this article, we discuss the existence of solutions for a boundaryvalue problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented. 1. Formulation ...

The study of the Dirichlet problem with arbitrary measurable data for harmonic functions in unit disk ???? is due to dissertation Luzin. Later on, known monograph Vekua was devoted boundary-value problems only Hölder continuous generalized analytic functions, i.e., complex-valued f(z) complex variable z = x + iy first partial derivatives by Sobolev satisfying equations form $$ {\partial}_{\over...

The residual-free bubble method (RFB) is a parameter-free stable finite element method that has been successfully applied to a wide range of boundaryvalue problems exhibiting multiple-scale behaviour. If some local features of the solution are known a priori, the approximation properties of the RFB finite element space can be improved by enriching it on selected edges of the partition by edgebu...

The Hodge theory of the de Rham complex in the setting of the Sobolev topology is studied. As a result, a new elliptic boundaryvalue problem is obtained. Next, the Hodge theory of the @-Neumann problem in the Sobolev topology is studied. A new @-Neumann boundary condition is obtained, and the corresponding subelliptic estimate derived. The classical Hodge theory on a domain in R N+1 (or, more g...