Optimal recovery of functions and their derivatives from Fourier coefficients prescribed with an error

Abstract

In this work, we have used solvent-free thermo-curable epoxy systems for low-pressure and moderate-temperature nanoimprint lithography (NIL). The curing kinetic parameters and conversion of diglycidyl ether of bisphenol A (DGEBA) resin with different ambient-cure 930 and 954 hardeners were studied by the isothermal DSC technique. They are useful for the study of epoxy resins in the imprinting application. The DGEBA/930 and DGEBA/954 epoxy resists can be imprinted to obtain high-density nano-and micro-scale patterns on a flexible indium tin oxide/poly(ethylene terephthalate) (ITO/PET) substrate. The DGEBA/930 epoxy resin is not only suitable for resist material, but also for plastic mold material. Highly dense nanometer patterns can be successfully imprinted using a UV-curable resist from the DGEBA/930 epoxy mold. Using the replicated DGEBA/930 epoxy mold instead of the expensive master can prevent brittle failure of the silicon molds in the NIL.

Optimal recovery of integral operators and its applications

“…Problems of optimal recovery of operators based on exact information were studied in [27,5,9,20], and on approximate information in [15,19,21,17,16,4]. We also refer the reader to the discussion of closely related questions in [28,20,12,30,24,1,2].…”

“…These research questions have been explored under the theory of optimal recovery of functions and operators, which is an area of Approximation Theory that started to develop in 1970s. More information on the development of the area can be found, for instance, in [20,28,21,12,17,24,25,11].As for specific applications to recovering solutions of boundary and initial value problems, Magaril-Ill'yaev, Osipenko, and co-authors (see, for instance, [16,22,18]) have considered the problem of optimal L 2 -approximation of the solution to the Dirichlet problem for Laplace's and Possion's equations in simple domains (disk, ball, annulus) based on the first N consecutive Fourier coefficients of the boundary function (possibly given with an error). In order to solve this problem they have used methods of Harmonic Analysis and general results from Optimization Theory.…”

“…As for specific applications to recovering solutions of boundary and initial value problems, Magaril-Ill'yaev, Osipenko, and co-authors (see, for instance, [16,22,18]) have considered the problem of optimal L 2 -approximation of the solution to the Dirichlet problem for Laplace's and Possion's equations in simple domains (disk, ball, annulus) based on the first N consecutive Fourier coefficients of the boundary function (possibly given with an error). In order to solve this problem they have used methods of Harmonic Analysis and general results from Optimization Theory.…”

On optimal harmonic synthesis from inaccurate spectral data

“…Thus, if a bounded function m( · ) satisfies the condition A b s (m( · )) = σ 2(k−n) 0 , then the corresponding method is optimal. But it is easy to verify that this condition is equivalent to (2).…”

Наилучшее Восстановление Оператора Лапласа Функции По Ее Неточно Заданному Спектру

“…Представление о дальнейшем развитии тематики, связанной с задачами оптимального восстановления линейных функционалов и операторов по неточной информации можно получить из работ [2]- [8]. Задачи, близкие к той, которая изучается здесь, но для функций одного переменного (периодических и на прямой) рассматривались в работах [9]- [11].…”