The Order Structure of Positive Operators

2006 ◽  
pp. 1-77 ◽  
Author(s):  
Charalambos D. Aliprantis ◽  
Owen Burkinshaw
2017 ◽  
Vol 60 (2) ◽  
pp. 289-305 ◽  
Author(s):  
ZSIGMOND TARCSAY ◽  
TAMÁS TITKOS

AbstractThe main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on *-algebras. We describe the extreme points of order intervals, and give a non-trivial sufficient condition to decide whether or not the infimum of two representable functionals exists. To this aim, we offer a suitable approach to the Lebesgue decomposition theory, which is in complete analogy with the one developed by Ando in the context of positive operators. This tight analogy allows to invoke Ando's results to characterize uniqueness of the decomposition, and solve the infimum problem over certain operator algebras.


Author(s):  
J.M. Guilemany ◽  
F. Peregrin

The shape memory effect (SME) shown by Cu-Al-Mn alloys stems from the thermoelastic martensitic transformation occuring between a β (L2,) metastable phase and a martensitic phase. The TEM study of both phases in single and polycrystalline Cu-Al-Mn alloys give us greater knowledge of the structure, order and defects.The alloys were obtained by vacuum melting of Cu, Al and Mn and single crystals were obtained from polycrystalline alloys using a modified Bridgman method. Four different alloys were used with (e/a) ranging from 1.41 to 1.46 . Two different heat treatments were used and the alloys also underwent thermal cycling throughout their characteristic temperature range -Ms, Mf, As, Af-. The specimens were cut using a low speed diamond saw and discs were mechanically thinned to 100 μm and then ion milled to perforation at 4 kV. Some thin foils were also prepared by twin-jet electropolishing, using a (1:10:50:50) urea: isopropyl alcohol: orthophosphoric acid: ethanol solution at 20°C. The foils were examinated on a TEM operated at 200 kV.


Author(s):  
A. Thust ◽  
K. Urban

The alloy of composition Ni4Mo develops, at temperatures below 860 °C, an ordered Dla-structure which is based on the fcc-lattice. This alloy has been widely investigated with respect to its physical properties and its ordering behaviour. High resolution studies are rare and concentrated mainly on its short-range order structure. The aim of the present work was to develop a detailed understanding of image contrast and to apply the results to antiphase-boundary studies in ordered Ni4Mo by means of a JEOL 4000 EX electron microscope.In high-resolution electron microscopy, depending on defocus and foil thickness, a large variety of different images is obtained. Only a few of these allow a direct interpretation concerning the location and the type of the atoms. By computing a through-focus/through-thickness map (TFTT map) before starting experimental work it is possible to determine the proper conditions at which images can be obtained which are closely related to the projected potential.


2012 ◽  
Vol 28 (1) ◽  
pp. 25-31 ◽  
Author(s):  
Paula Elosua ◽  
Alicia López-Jáuregui

In this study the Eating Disorder Inventory-3 was adapted to Spanish and analyzed the internal psychometric properties of the test in a clinical sample of females with eating disorders. The results showed a high internal consistency of the scores as well as high temporal stability. The factor structure of the scale composites was analyzed using confirmatory factor analysis. The results supported the existence of a second-order structure beyond the psychological composites. The second-order factor showed high correlation with the factor related to eating disorders. Overall, the Spanish version of the EDI-3 showed good psychometric qualities in terms of internal consistency, temporal stability and internal structure.


2020 ◽  
Vol 36 (4) ◽  
pp. 670-680 ◽  
Author(s):  
Bojana M. Dinić ◽  
Aleksandar Vujić

Abstract. The aim of this research was to explore measurement invariance across samples from Serbia and the USA (Study 1) and to further validate the Serbian adaptation of the Pathological Narcissism Inventory – PNI (Study 2). The results supported the original seven-factor first-order structure as well as the hierarchical structure of the PNI with Narcissistic grandiosity and vulnerability as the second-order factors. Further, scalar invariance between the two versions of the PNI was achieved. Relations between Narcissistic grandiosity and vulnerability and other measures of grandiose and hypersensitive narcissism supported the validity of their scores. Among HEXACO traits, both Narcissistic grandiosity and vulnerability showed substantial negative correlations with Honesty-Humility. The main distinctions between the two aspects of narcissism lie in the positive relations with Neuroticism and negative relations with self-esteem, both of which are higher for Narcissistic vulnerability. The results support good psychometric properties of the PNI scores and add to the PNI’s cross-cultural validity.


2012 ◽  
Author(s):  
Xin Liu ◽  
Xiaobin Zhou ◽  
Jing-Jen Wang ◽  
Jianjun Zhu

2020 ◽  
Author(s):  
Viraj kirinda ◽  
Scott Hartley

The self-assembly of foldamers into macrocycles is a simple approach to non-biological higher-order structure. Previous work on the co-assembly of ortho-phenylene foldamers with rod-shaped linkers has shown that folding and self-assembly affect each other; that is, the combination leads to new emergent behavior, such as access to otherwise unfavorable folding states. To this point this relationship has been passive. Here, we demonstrate control of self-assembly by manipulating the foldamers’ conformational energy surfaces. A series of o-phenylene decamers and octamers have been assembled into macrocycles using imine condensation. Product distributions were analyzed by gel-permeation chromatography and molecular geometries extracted from a combination of NMR spectroscopy and computational chemistry. The assembly of o-phenylene decamers functionalized with alkoxy groups or hydrogens gives both [2+2] and [3+3] macrocycles. The mixture results from a subtle balance of entropic and enthalpic effects in these systems: the smaller [2+2] macrocycles are entropically favored but require the oligomer to misfold, whereas a perfectly folded decamer fits well within the larger [3+3] macrocycle that is entropically disfavored. Changing the substituents to fluoro groups, however, shifts assembly quantitatively to the [3+3] macrocycle products, even though the structural changes are well-removed from the functional groups directly participating in bond formation. The electron-withdrawing groups favor folding in these systems by strengthening arene–arene stacking interactions, increasing the enthalpic penalty to misfolding. The architectural changes are substantial even though the chemical perturbation is small: analogous o-phenylene octamers do not fit within macrocycles when perfectly folded, and quantitatively misfold to give small macrocycles regardless of substitution. Taken together, these results represent both a high level of structural control in structurally complex foldamer systems and the demonstration of large-amplitude structural changes as a consequence of a small structural effects.


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