Related papers: p-adic tight wavelet frames
A formal methodology for developing variational principles corresponding to a given nonlinear PDE system is discussed. The scheme is demonstrated in the context of the incompressible Navier-Stokes equations, systems of first-order…
In this article, we develop a general method for constructing wavelets {|det A_j|^{1/2} g(A_jx-x_{j,k}): j in J, k in K}, on irregular lattices of the form X={x_{j,k} in R^d: j in J, k in K}, and with an arbitrary countable family of…
We present the applications of methods from nonlinear local harmonic analysis for calculations in nonlinear collective dynamics described by different forms of Vlasov-Maxwell-Poisson equations. Our approach is based on methods provided the…
The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or…
The general procedure of constructing a consistent covariant Dirac-type bracket for models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial…
Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by…
We construct a notion of p-adic measure on Artin n-stacks which are strongly of finite type over the ring of p-adic integers. We also prove the rationality of of the Poincare series and the Serre series associated with such stacks. Finally,…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
Synthetic turbulence models are a useful tool that provide realistic representations of turbulence, necessary to test theoretical results, to serve as background fields in some numerical simulations, and to test analysis tools. Models of 1D…
We present an algorithm for construction step wavelets on local fields of positive characteristic.
The integral of the top dimensional term of the multiplicative sequence of Pontryagin forms associated to an even formal power series is calculated for special Riemannian metrics on the unit ball of a hermitean vector space. Using this…
p-Adic wavelet transform is considered as a possible tool for the description of hierarchic quantum systems
We extend the approach of wall modeling via function enrichment to detached-eddy simulation. The wall model aims at using coarse cells in the near-wall region by modeling the velocity profile in the viscous sublayer and log-layer. However,…
The aim of the paper is to investigate the structure of plurifinely open sets. As an application, we will prove an equality on complex Monge-Amp\`ere measures in plurifinely open sets.
Time-modulated arrays (TMAs) can effectively perform beamsteering over the first positive harmonic pattern by applying progressively delayed versions of stair-step approximations of a sine waveform to the antenna excitations. In this…
We present a new approach to absolute continuity of laws of Poisson functionals. The theoretical framework is that of local Dirichlet forms as a tool to study probability spaces. The method gives rise to a new explicit calculus that we show…
A multivariate biorthogonal wavelet system can be obtained from a pair of multivariate biorthogonal refinement masks in Multiresolution Analysis setup. Some multivariate refinement masks may be decomposed into lower dimensional refinement…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
We propose a simple, intuitive alternative method of deriving the rule for connecting asymptotic wave function amplitudes to scattering probabilities. This is illustrated using the standard example of a 1-D particle reflecting or…