Browsing Artikler, rapporter og annet (datateknologi og beregningsorienterte ingeniørfag) by Title
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A sharp boundedness result for restricted maximal operators of VilenkinFourier series on martingale Hardy spaces
(Journal article; Peer reviewed, 20180920)The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p to the Lebesgue space L p for all 0<p≤1 . We also prove that the result is sharp in a particular sense. 
Sharp HpLp type inequalities of weighted maximal operators of VilenkinNörlund means and its applications
(Peer reviewed, 20161001)We prove and discuss some new HpLp type inequalities of weighted maximal operators of VilenkinNörlund 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 VilenkinNörlund means. As applications, both some wellknown and new results are pointed out. 
Shock Tube. Detail overview of equipment and instruments in the shock tube experimental setup
(Book; Bok, 2015)The shock tube is a device in which a normal shock wave is produced by the interaction of fluids at significantly highpressure difference. The shock tube is comprised of two sections known as driver and driven sections. These two sections are interacted with the highspeed valve or a bursting disc. When the interaction happens, a shock wave forms almost instantaneously and propagates into the driven ... 
Singularly perturbed spectral problems in a thin cylinder with fourier conditions on its bases
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019)The paper deals with the bottom of the spectrum of a singularly perturbed second order elliptic operator defined in a thin cylinder and having locally periodic coefficients in the longitudinal direction. We impose a homogeneous Neumann boundary condition on the lateral surface of the cylinder and a generic homogeneous Fourier condition at its bases. We then show that the asymptotic behavior of the ... 
Singularly perturbed spectral problems with Neumann boundary conditions
(Peer reviewed, 20150907)The paper deals with the Neumann spectral problem for a singularly perturbed secondorder elliptic operator with bounded lower order terms. The main goal is to provide a refined description of the limit behaviour of the principal eigenvalue and eigenfunction. Using the logarithmic transformation, we reduce the studied problem to an additive eigenvalue problem for a singularly perturbed Hamilton–Jacobi ... 
Some Fourier inequalities for orthogonal systems in Lorentz–Zygmund spaces
(Journal article; Peer reviewed, 20190613)A number of classical inequalities and convergence results related to Fourier coefficients with respect to unbounded orthogonal systems are generalized and complemented. All results are given in the case of Lorentz–Zygmund spaces. 
Some inequalities for Cesàro means of double VilenkinFourier series
(Journal article; Peer reviewed; Tidsskriftartikkel, 20181219)In this paper, we state and prove some new inequalities related to the rate of Lp approximation by Cesàro means of the quadratic partial sums of double Vilenkin–Fourier series of functions from Lp. 
Some inequalities related to strong convergence of Riesz logarithmic means
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200323)In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the onedimensional Vilenkin–Fourier (Walsh–Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh–Fourier series. 
Some new estimates of the ‘Jensen gap’
(Peer reviewed, 20160201) 
Some new Fourier inequalities for unbounded orthogonal systems in LorentzZygmund spaces
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200320)In this paper we prove some essential complements of the paper (J. Inequal. Appl. 2019:171, 2019) on the same theme. We prove some new Fourier inequalities in the case of the Lorentz–Zygmund function spaces L q,r (logL ) α Lq,r(logL)α involved and in the case with an unbounded orthonormal system. More exactly, in this paper we prove and discuss some new Fourier inequalities of this type for ... 
Some new Hardytype inequalities for RiemannLiouville fractional qintegral operator
(Peer reviewed, 20150924)We consider the qanalog of the RiemannLiouville fractional qintegral operator of order n∈Nn∈N. Some new Hardytype inequalities for this operator are proved and discussed. 
Some new Hardytype inequalities in qanalysis
(Peer reviewed, 201609)We derive necessary and sufficient conditions (of MuckenhouptBradley type) for the validity of q analogs of (r, p) weighted Hardytype inequalities for all possible positive values of the parameters r and p . We also point out some possibilities to further develop the theory of Hardytype inequalities in this new direction. 
SOME NEW REFINEMENTS OF HARDYTYPE INEQUALITIES
(Journal article; Tidsskriftartikkel; Peer reviewed, 20200211)We obtain some further reﬁnements of Hardytype inequalities via superqudraticity technique. Our results both unify and further generalize several results on reﬁnements of Hardytype inequalities in the literature. 
Some new TwoSided Inequalities concerning the Fourier Transform
(Journal article; Peer reviewed; Tidsskriftartikkel, 2017)The classical HausdorffYoung and HardyLittlewoodStein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a twosided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S. [7] (MR 2464253). 
Some sharp inequalities for integral operators with homogeneous kernel
(Peer reviewed, 20160409)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 ... 
Stationary convectiondiffusion equation in an infinite cylinder
(Journal article; Tidsskriftartikkel; Peer reviewed, 20171221)We study the existence and uniqueness of a solution to a linear stationary convection–diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of two semiinfinite cylinders with two different periodic regimes. Depending on the direction of the effective convection in the two semiinfinite cylinders, we ... 
Steady States, FluctuationDissipation Theorems and Homogenization for Reversible Diffusions in a Random Environment
(Journal article; Peer reviewed; Tidsskriftartikkel, 20180402)Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle, we introduce the notions of steady state and weak steady state. We establish the continuity of weak steady states for an ergodic and uniformly elliptic environment. ... 
Steklov Problems in Perforated Domains with a Coefficient of Indefinite Sign
(Journal article; Peer reviewed; Tidsskriftartikkel, 2012) 
Study of Acoustics Properties of SK One Component Polyurethane and its Application in Arctic Marine Structures
(Conference object; Konferansebidrag, 20161208)Marine noise reduction tends to be challenging and requires a comprehensive engineering approach. The soundproofing materials for marine noise reduction are usually exposed to high temperatures, potential fluid or oil spills, engine maintenance and a high airflow environment. This work looks into the acoustic proofing properties of a nontoxic material ‘SK One Component Polyurethane’ developed by ... 
Study of Ice Adhesion Behavior of SK One Component Polyurethane
(Conference object; Konferansebidrag, 201612)Ice adhesion causes many serious problems such as aircraft accidents, navigational issues on ships, and power loss on wind turbines. These challenges are mainly associated with the acute behavior of ice adhesion. The ice adheres when water seeps into the microscopic pores of the material substrate and freezes, thereby, forming an interlocking mechanism. Therefore, surface roughness has a significant ...