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This is a preface introducing a Special Issue on the topic of "Guided-Wave Optics" published by Applied Sciences. The Special Issue is a collection of 20 original and review articles dealing with various fundamental and applied aspects of…
In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as…
In this document a review of the author's method of Fourier disentangling of spectra of binary and multiple stars is presented for the purpose of the summer school organized at Ondrejov observatory in September 2008. Related methods are…
This is a review article on the development of the probe and enclosure methods from past to present, focused on their central ideas together with various applications.
A prototype ultrahigh resolution spectrograph has been built with an adaptive optics telescope. It provides $250,000$ resolving power, 300 \AA\ wavelength coverage and 0.8\% efficiency.
Tiny fluctuations of the Cosmic Microwave Background as well as various observable quantities obtained by spin raising and spin lowering of the effective gravitational lensing potential of distant galaxies and galaxy clusters, are described…
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.
Beginning with a historical account of the spectral classification, its refinement through additional criteria is presented. The line strengths and ratios used in two dimensional classifications of each spectral class are described. A…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
This article is devoted to the construction of pseudomodes of one-dimensional biharmonic operators with the complex-valued potentials via the WKB method. As a by-product, the shape of pseudospectrum near infinity can be described. This is a…
Spectral lines of heavy atomic elements in the ejecta of supernovae and neutron star mergers can have important contribution to the opacity of the ejecta matter even when the abundance of the elements is very small. Under favorable…
The mirror extensions for vertex operator algebras are studied. Two explicit examples which are not simple current extensions of some affine vertex operator algebras of type $A$ are given.
This editorial from the PASP Special Focus Issue "Techniques and Methods for Astrophysical Data Visualization" summarizes contributions from authors, their software and tutorials, video abstracts, and 3D content. PASP and IOP have made this…
This paper presents a brief survey of the evolution of knowledge about diffraction gratings. After recalling some basic facts, historically and physically, we introduce the concept of Wood anomalies. Next, we present some recent works in…
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
This text is a commentary on the paper "On some ideals of differentiable functions" of Ren{\'e} Thom which appeared in Volume II of his "Oeuvres Math{\'e}matiques" published by the Soci{\'e}t{\'e} math{\'e}matique de France, s{\'e}rie…
We study the geometry of the set of closed extensions of index 0 of an elliptic cone operator and its model operator in connection with the spectra of the extensions, and give a necessary and sufficient condition for the existence of rays…
An overview of the Nordic Optical Telescope (NOT) is presented. Emphasis is on current capabilities of direct interest to the scientific user community, including instruments. Educational services and prospects and strategies for the future…
This is a survey recent works on topological extensions of the Tutte polynomial.