In a normed linear space X, consider a nonempty closed set K which has the property that for some r > 0 there exists a set of points xo € X\K, d(xoK) > r, which have closest points p(xo) € K and where the set of points xo — r((xo — p(xo))/\\xo — p(zo)||) is dense in X\K. If the norm has sufficiently strong differentiability properties, then the distance function d generated by K has similar dif...

In one of the most important methods in Density Functional Theory – the FullPotential Linearized Augmented Plane Wave (FLAPW) method – dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly correlated to the next one in the sequence. We propose a novel approach which exploits such correlation through the use of an eigensolver based on subspace it...

We construct accurate central difference stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh, and with an easily obtained bound on the dispersion error. This is done by demonstrating that the problem of constructing central difference stencils that have minimal dispersion error in the infinity norm can ...

Let Γ be an embeddable non-degenerate polar space of finite rank n≥2. Assuming that admits the universal embedding (which is true for all spaces except grids order at least 5 and certain generalized quadrangles defined over quaternion division rings), let ε:Γ→PG(V) Γ. S a subspace suppose S, regarded as space, has 2. We shall prove ε-preimage projective PG(V).

In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra  integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...

The paper contains three results, the common feature of which is that they deal with the Schatten p class. The first is a presentation of a new complemented subspace of Cp in the reflexive range (and p ̸= 2). This construction answers a question of Arazy and Lindestrauss from 1975. The second result relates to tight embeddings of finite dimensional subspaces of Cp in C n p with small n and shows...

In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...

Small-scale temperature and conductivity variations have been measured in the upper 100 m of the northeast Atlantic during the STRATIPHYT-II cruise (Las Palmas– Reykjavik, 6 April–3 May 2011). The measurements were done at midday and comprised 2 to 15 vertical profiles at each station. The derived turbulent quantities show a transition between weakly-stratified (mixed layer depth, MLD, <100) an...

We analyze a homogenization limit for the linear wave equation of second order. The spatial operator is assumed to be of divergence form with an oscillatory coefficient matrix aε that is periodic with characteristic length scale ε; no spatial symmetry properties are imposed. Classical homogenization theory allows to describe solutions uε well by a non-dispersive wave equation on fixed time inte...

For a large class, containing the Kato class, of real-valued Radon measures m on R the operators −∆ + ε∆ + m in L(R, dx) tend to the operator −∆ +m in the norm resolvent sense, as ε tends to zero. If d ≤ 3 and a sequence (μn) of finite real-valued Radon measures on R converges to the finite real-valued Radon measure m weakly and, in addition, supn∈N μ ± n (R) < ∞, then the operators −∆ + ε∆ + μ...