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At present a number of current or proposed experiments are directed towards a search for a `new physics' by detecting variations of fundamental physical constants or violations of certain basic symmetries. Various problems related to the…
We review some convexity inequalities for Hermitian matrices an add one more to the list.
We give a very brief introduction to the machinery of spectral sequences, including the spectral sequence of a bicomplex. We then briefly introduce a generalisation of the spectral sequences of a bicomplex to the spectral sequences of…
We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial…
In this paper, we study perturbation of Hilbert-Schmidt frames under structured modifications, where the perturbation takes the form of replacing finitely or infinitely many frame elements. We establish explicit criteria under which the…
This paper is concerned with the stability of deficiency indices of Hermitian subspaces (i.e., linear relations) under relatively bounded perturbations in Hilbert spaces. Several results about invariance of deficiency indices of Hermitian…
We study perturbations of linear differential equations, deriving explicit series solutions, using Dyson-type expansions. We analyze the monodromy of deformed solutions in a number of examples, and relate this to cocycles in a cohomological…
The explicit dispersion equation for a one-dimensional periodic structure with alternative layers of left-handed material (LHM) and right-handed material (RHM) is given and analyzed. Some abnormal phenomena such as spurious modes with…
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing…
In this paper we summarize our recent work about perturbative and non-perturbative effects in four-dimensional heterotic strings with $N=2$ space-time supersymmetry.
Light propagation in distributed feedback optical structures with gain/loss regions is shown to provide an accessible laboratory tool to visualize in optics the spectral properties of the one-dimensional Dirac equation with non-Hermitian…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather limited. To that end, it was argued that a recent…
Advances in experiment, theory and phenomenology of hadron spectroscopy are discussed. We focus on specific developments in the meson sector.
We consider "spectral" matrix-functions for Hermitian matrices, where the novelty is that the function applied to the spectrum is allowed to be a vector-field rather than a scalar function (a.k.a isotropic matrix functions). We prove first…
The status of QCD phenomena and open problems are reviewed
We investigate some questions on the construction of $\eta$ operators for pseudo-Hermitian Hamiltonians. We give a sufficient condition which can be exploited to systematically generate a sequence of $\eta$ operators starting from a known…
Though the phenomenon of quantum-mechanical interference has been known for many years, it still has many open questions. The present review discusses specifically how the interference of resonances may and does work. We collect data on the…
This paper explains the theory of spectral sequences via d\'ecalage and the Beilinson t-structure.