4,853 research outputs found
Statistical approximation properties of Stancu type -Baskakov-Kantorovich operators
In the present paper, we consider Stancu type generalization of
Baskakov-Kantorovich operators based on the q-integers and obtain statistical
and weighted statistical approximation properties of these operators. Rates of
statistical convergence by means of the modulus of continuity and the Lipschitz
type function are also established for said operators. Finally, we construct a
bivariate generalization of the operator and also obtain the statistical
approximation properties.Comment: 16. arXiv admin note: substantial text overlap with arXiv:1508.0586
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
A mixed mimetic spectral element method is applied to solve the rotating
shallow water equations. The mixed method uses the recently developed spectral
element histopolation functions, which exactly satisfy the fundamental theorem
of calculus with respect to the standard Lagrange basis functions in one
dimension. These are used to construct tensor product solution spaces which
satisfy the generalized Stokes theorem, as well as the annihilation of the
gradient operator by the curl and the curl by the divergence. This allows for
the exact conservation of first order moments (mass, vorticity), as well as
quadratic moments (energy, potential enstrophy), subject to the truncation
error of the time stepping scheme. The continuity equation is solved in the
strong form, such that mass conservation holds point wise, while the momentum
equation is solved in the weak form such that vorticity is globally conserved.
While mass, vorticity and energy conservation hold for any quadrature rule,
potential enstrophy conservation is dependent on exact spatial integration. The
method possesses a weak form statement of geostrophic balance due to the
compatible nature of the solution spaces and arbitrarily high order spatial
error convergence
Comparison of some Reduced Representation Approximations
In the field of numerical approximation, specialists considering highly
complex problems have recently proposed various ways to simplify their
underlying problems. In this field, depending on the problem they were tackling
and the community that are at work, different approaches have been developed
with some success and have even gained some maturity, the applications can now
be applied to information analysis or for numerical simulation of PDE's. At
this point, a crossed analysis and effort for understanding the similarities
and the differences between these approaches that found their starting points
in different backgrounds is of interest. It is the purpose of this paper to
contribute to this effort by comparing some constructive reduced
representations of complex functions. We present here in full details the
Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM)
together with other approaches that enter in the same category
Statistical thermodynamics for a non-commutative special relativity: Emergence of a generalized quantum dynamics
There ought to exist a description of quantum field theory which does not
depend on an external classical time. To achieve this goal, in a recent paper
we have proposed a non-commutative special relativity in which space-time and
matter degrees of freedom are treated as classical matrices with arbitrary
commutation relations, and a space-time line element is defined using a trace.
In the present paper, following the theory of Trace Dynamics, we construct a
statistical thermodynamics for the non-commutative special relativity, and show
that one arrives at a generalized quantum dynamics in which space and time are
non-classical and have an operator status. In a future work, we will show how
standard quantum theory on a classical space-time background is recovered from
here.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1106.091
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