The main objective of the present paper is to solve the several long standing divergence problems related to the logarithmic means of Fourier series in context of general orthonormal systems.
We prove weighted versions of the 2D Restriction Conjecture for the unit sphere in $\mathbb{R}^2$. Our results involve the weight functions $(1+|x|)^α(1+|y|)^β$ and $(1+|x|+|y|)^γ$ with $α,β,γ\geq 0$.
In the note, a local regularity condition for axisymmetric solutions to the non-stationary 3D Navier-Stokes equations is proven. It reads that axially symmetric energy solutions to the Navier-Stokes equations have no Type I blowups.
We prove that, for some irrational torus, the flow map of the periodic fifth-order KP-I equation is not locally uniformly continuous on the energy space, even on the hyperplanes of fixed x-mean value.
“Archaeology for Whom?” A situation where this question gainsparticular importance is the case of rescue archaeology projects,especially those facing big economic projects. It is the purpose ofthis article to propose a reflective attitude towards our practice.Thus, I will focus on the case of the site of Roșia Montană (Romania).Here, the contentious topic of a proposed cyanide gold miningexploitation brought forward a series of relevant questions: what isheritage, for whom it is meaningful (and in what way), and what isthe relationship between heritage and sustainable development ofa contemporary community.
In this paper, Hardy's uncertainty principle and unique continuation properties of abstract Schrödinger equations in vector-valued classes are obtained
The last 40 years have seen an increase in outreach activities, many primarily targeted to children, in archaeology. This outreach has benefited both the discipline of archaeology as well as public education. Several projects have pioneered the development of ‘archaeology for children’ in recent decades and have narrowed the gap between heritage and the public.An overview of these developments is presented in this paper. Particular reference is made to the work undertaken in schools and museums, by associations and archaeological companies, as well as the promotion of archaeology through the media. Examples are drawn especially from the United Kingdom and Spain.
Operator-type estimates of homogenization are obtained for elliptic operators of arbitrary even order equal or greater than two. Operators under consideration are non-selfadjoint with lower-order terms.
We prove Strichartz-type estimates for Schroedinger's equation with time-dependent potentials. The time derivative of the potentials need not be integrable, so the total variation of the potentials may be infinite.
The paper is devoted to the study of transmission problem between two Herschel-Bulkley fluids with different viscosities, yield limits and power law index.
We prove Berezin--Li--Yau-type lower bounds with additional term for the eigenvalues of the Stokes operator and improve the previously known estimates for the Laplace operator. Generalizations to higher-order operators are given.
We present a construction of biorthogonal wavelets using a compact operator which allows to preserve or increase some properties: regularity/vanishing moments, parity, compact supported. We build then a simple algorithm which computes new filters.
We derive some new inf-sup and sup-inf formulae for the so-called effective multiplication factor arising in the study of reactor analysis. We treat in a same formalism the transport equation and the energy-dependent diffusion equation.