We introduce a novel multi-resolution localized orthogonal decomposition (LOD) for time-harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The method merges concepts of LOD and operator-adapted wavelets (gamblets) proves its applicability class complex-valued, non-hermitian, indefinite problems. It computes hierarchical bases block-diagonalize operator thereby ...

It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbert -space. This ”modular localization” is not only useful in order to construct interactionfree nets of local algebras without using non-unique ”free field coordinates”, but also permits the study of propertie...

MOTIVATION Nucleo-cytoplasmic trafficking of proteins is a core regulatory process that sustains the integrity of the nuclear space of eukaryotic cells via an interplay between numerous factors. Despite progress on experimentally characterizing a number of nuclear localization signals, their presence alone remains an unreliable indicator of actual translocation. RESULTS This article introduce...

glioblastoma is the most common and the most lethal primary brain cancer. this malignancy is highly locally invasive, rarely metastatic and resistant to current therapies. little is known about the distinct molecular biology of glioblastoma multiforme (gbm) in terms of initiation and progression. so far, several molecular mechanisms have been suggested to implicate in gbm development. homeodoma...

this paper presents characterizations of m-fuzzifying matroids bymeans of two kinds of fuzzy operators, called m-fuzzifying derived operatorsand m-fuzzifying difference derived operators.

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties , in terms of Dirac's position operator x. It is shown that, although x is not an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the 4-vector density (ρ(x, t), j(x, t)/c) is observable , and can be localized arbitrar...

We study localization and chirality properties of eigenvectors of the lattice Dirac operator. In particular we focus on the dependence of our observables on the size of the corresponding eigenvalue, which allows us to study the transition of a near-zero mode into a bulk mode. We analyze ensembles of quenched SU(3) configurations using a Dirac operator which is a systematic expansion in path len...

We study localization and chirality properties of eigenvectors of the lattice Dirac operator. In particular we focus on the dependence of our observables on the size of the corresponding eigenvalue, which allows us to study the transition of a near-zero mode into a bulk mode. We analyze ensembles of quenched SU(3) configurations using a Dirac operator which is a systematic expansion in path len...

In this paper we use results on reducibility, localization and duality for the Almost Mathieu operator, (Hb,φx)n = xn+1 + xn−1 + b cos (2πnω + φ) xn on l2(Z) and its associated eigenvalue equation to deduce that for b 6= 0,±2 and ω Diophantine the spectrum of the operator is a Cantor subset of the real line. This solves the so-called “Ten Martini Problem” for these values of b and ω. Moreover, ...