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Numerical simulation of the dynamic response in pulse-loaded fibre–metal-laminated plates
(Journal article; Tidsskriftartikkel; Peer reviewed, 2016-07-27)
This article presents a three-dimensional constitutive model to replicate the dynamic response of blast-loaded fibre–metal laminates made of 2024-0 aluminium alloy and woven composite (glass fibre–reinforced polypropylene). Simulation of the dynamic response is challenging when extreme localised loads are of concern and requires reliable material constitutive models as well as accurate modelling ...
Resolvent bounds for jump generators
(Journal article; Peer reviewed; Tidsskriftartikkel, 2016-12-02)
The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially, we prove a number of lower and upper bounds for the resolvent of such operators. In particular we focus on sharp estimates of the resolvent kernel for small values of the spectral parameter. We consider two applications of these results. First we obtain pointwise ...
Boundedness and compactness of a class of Hardy type operators
(Journal article; Tidsskriftartikkel; Peer reviewed, 2016-12-13)
We establish characterizations of both boundedness and of compactness of a general
class of fractional integral operators involving the Riemann-Liouville, Hadamard, and
Erdelyi-Kober operators. In particular, these results imply new results in the theory of
Hardy type inequalities. As applications both new and well-known results are pointed
out.
Sharp Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-10-01)
We prove and discuss some new Hp-Lp type inequalities of weighted maximal
operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved
that these inequalities are the best possible in a special sense. We also apply these
results to prove strong summability for such Vilenkin-Nörlund means. As applications,
both some well-known and new results are pointed out.
Weighted Hardy type inequalities for supremum operators on the cones of monotone functions
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-09-28)
The complete characterization of the weighted L<sup>p</sup>-L<sup>r</sup> inequalities of supremum operators on the cones of monotone functions for all 0 < p, r≤∞ is given.
Some new estimates of the ‘Jensen gap’
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-02-01)
Some new Hardy-type inequalities in q-analysis
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-09)
We derive necessary and sufficient conditions (of Muckenhoupt-Bradley type) for the validity of q -analogs of (r, p) -weighted Hardy-type inequalities for all possible positive values of the parameters r and p . We also point out some possibilities to further develop the theory of Hardy-type inequalities in this new direction.
Osmosis for non-electrolyte solvents in permeable periodic porous media
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-08)
The paper gives a rigorous description, based on mathematical homogenization theory, for flows of solvents with not charged solute particles under osmotic pressure for periodic porous media permeable for solute particles. The effective Darcy type equations for the flow under osmotic pressure distributed within the porous media are derived. The effective Darcy law contains an additional flux term ...
Some sharp inequalities for integral operators with homogeneous kernel
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-04-09)
One goal of this paper is to show that a big number of inequalities for functions in Lp(R+), p ≥ 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and ...
A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016)
In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in [14], and so ...