Related papers: A User's Guide: Relative Thom Spectra via Operadic…
Optical spectroscopy techniques such as differential reflectance and transmittance have proven to be very powerful techniques to study 2D materials. However, a thorough description of the experimental setups needed to carry out these…
In this paper we investigate the spectral expansion for the asymptotically spectral differential operators generated in all real line by ordinary differential expression of arbitrary order with periodic matrix-valued coefficients
In this paper, we investigate Li-Yorke composition operators and some of their variations on Lorentz spaces. Further, we also study expansive composition operators on these spaces. The work of the paper is essentially based on the work in…
The article is designed to explain to commutative algebraists what spectra (in the sense of algebraic topology) are, why they were originally defined, and how they can be useful for commutative algebra.
In this short notes we propose a new notion of contractibility for coloured $\omega$-operad defined in the article published in Cahiers de Topologie et de G{\'e}om{\'e}trie Diff{\'e}rentielle Cat{\'e}gorique (2011), volume 4. We propose…
This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.
While the methodology of band structure unfolding has appeared in several publications, the original derivations of the unfolding formulas can be considerably simplified by using the $k$-projection method. In this work, more transparent…
This paper introduces the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We then show that the condition of local spectral expansion for a complex yields various…
Expository notes about spectral sequences, filtered spectra, and synthetic spectra. We focus on the $\tau$-formalism as it arises in filtered spectra.
This is an introductory article to the theory of multiple gaps.
This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…
Functional version for the so-called Furuta parametric relative operator entropy is here investigated. Some related functional inequalities are also discussed. The theoretical results obtained by our functional approach immediately imply…
Optical link tomography (OLT) is a rapidly evolving field that allows the multi-span, end-to-end visualization of optical power along fiber links in multiple dimensions from network endpoints, solely by processing signals received at…
This is a survey on Drinfeld associators and their generalizations, where we focus on operadic aspects.
Theoretical calculations of one- and two-hole spectral functions for the O16 nucleus are still failing to describe some of the important features observed experimentally. Of critical importance for the solution of these issues is to obtain…
Elements of a vector theory of open resonators and experiments on excitation of a fundamental mode with transverse and longitudinal polarization in such resonators are discussed.
This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006).
This paper is a review of recent mathematical and computational advances in optical tomography. We discuss the physical foundations of forward models for light propagation on microscopic, mesoscopic and macroscopic scales. We also consider…
We establish some asymptotic expansions for infinite weighted convolutions of distributions having light subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs…
This book is a manual for the course of electrodynamics and theory of relativity. It is recommended primarily for students of mathematical departments. This defines its style: I use elements of vectorial and tensorial analysis, differential…