2013
DOI: 10.4208/jcm.1210-m4082
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On the Nonlinear Matrix Equation X<sup>s</sup> + A<sup>*</sup>F(X)A = Q with S≥ 1

Abstract: This work is concerned with the nonlinear matrix equation X s + A * F (X)A = Q with s ≥ 1. Several sufficient and necessary conditions for the existence and uniqueness of the Hermitian positive semidefinite solution are derived, and perturbation bounds are presented.Mathematics subject classification: 15A24, 47H10, 47H14, 47J05.

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Cited by 31 publications
(37 citation statements)
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References 32 publications
(43 reference statements)
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“…Recently, high-resolution structures of the 20S complex have been obtained by taking advantage of the remarkable advances in cryo electron microscopy ( Figure 2H). 20,57 The resolution of these structures range between 7 and 10 Å , i.e., sufficient to build detailed structural models in conjunction with crystallographic data. As discussed above, NSF has a three-layered structure with the bottom layer (the most distal layer from the SNARE complex) consisting of the D2 domain hexamer.…”
Section: Mechanistic Insights Into the Disassembly Reactionmentioning
confidence: 99%
“…Recently, high-resolution structures of the 20S complex have been obtained by taking advantage of the remarkable advances in cryo electron microscopy ( Figure 2H). 20,57 The resolution of these structures range between 7 and 10 Å , i.e., sufficient to build detailed structural models in conjunction with crystallographic data. As discussed above, NSF has a three-layered structure with the bottom layer (the most distal layer from the SNARE complex) consisting of the D2 domain hexamer.…”
Section: Mechanistic Insights Into the Disassembly Reactionmentioning
confidence: 99%
“…[11] Within 2D materials, MXenes are unique because they are both hydrophilic and typically synthesized from a top-down selective etching procedure. [12] MXenes are a class of 2D transition metal carbides, nitrides, and carbonitrides that are primarily synthesized from M n þ 1 AX n (MAX) precursor materials, [13] although different precursors, including Mo 2 Ga 2 C [14] and M n þ 1 A x X n þ x [15] have also been used. For MAX phase materials, M is an early transition metal (V, Ti, Mo, Ta, etc.…”
Section: Introductionmentioning
confidence: 99%
“…The supramolecular columns formed by disc shaped molecules not only act as model system for the study of energy and charge migration in self-organized systems but also as functional materials in organic electronic and optoelectronic devices such as light emitting diodes (LEDs) (215,216), field effect transistors (FETs) (217)(218)(219)(220), and photovoltaic (PV) solar cells (221)(222)(223)(224)(225). Furthermore, the columnar phases are remarkably well-defined nanostructures with fascinating 1D semiconducting characteristics.…”
Section: Applications Of Liquid Crystalsmentioning
confidence: 99%