Some necessary conditions for orders to be of finite lattice type. I.

1972 ◽  
Vol 1972 (256) ◽  
pp. 107-129
2019 ◽  
Vol 523 ◽  
pp. 15-33
Author(s):  
Abdolnaser Bahlekeh ◽  
Fahimeh Sadat Fotouhi ◽  
Shokrollah Salarian
Keyword(s):  

1956 ◽  
Vol 9 (2) ◽  
pp. 184 ◽  
Author(s):  
RC Croft

An extension of previous work (Croft 1952) on molecular compounds of graphite has led to the discovery of over 30 new molecular compounds of the layer lattice type. In addition, the experimental data revealed some necessary conditions for compound formation. Thus, intercalation was found to be most probable with multivalent chlorides of the transition metals, but only when the latter are in their higher valence states. Chlorides of all Group IIIA elements can also form molecular compounds with graphite. Intercalation is related to the position of the cation of the test substance in the periodic table. Molecular shape, polarity, and the covalent nature of the test substance have little, if any, relation to its reactivity with graphite. Graphite compounds formed from Group IIIA chlorides are distinguished from those containing transition metal chlorides by the possibility of hydrolysing intercalated cations of the former but not those of the latter. The metal cations of graphite-ZrCl4 and graphite-YCl3 are also capable of hydrolysis in situ. The results of this investigation suggest the possibility of employing graphite compound formation to effect many chemical separations and purifications.


Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Wenyan Han ◽  
Guolin Yu ◽  
Tiantian Gong

This note is devoted to the investigation of optimality conditions for robust approximate quasi weak efficient solutions to a nonsmooth uncertain multiobjective programming problem (NUMP). Firstly, under the extended nonsmooth Mangasarian–Fromovitz constrained qualification assumption, the optimality necessary conditions of robust approximate quasi weak efficient solutions are given by using an alternative theorem. Secondly, a class of generalized convex functions is introduced to the problem (NUMP), which is called the pseudoquasi-type-I function, and its existence is illustrated by a concrete example. Finally, under the pseudopseudo-type-I generalized convexity hypothesis, the optimality sufficient conditions for robust approximate quasi weak efficient solutions to the problem (NUMP) are established.


1972 ◽  
Vol 17 (1) ◽  
pp. 79-84 ◽  
Author(s):  
M. Auslander ◽  
K. W. Roggenkamp
Keyword(s):  

2014 ◽  
Vol 6 (2) ◽  
pp. 1799-1861 ◽  
Author(s):  
E. Kovaleva ◽  
U. Klötzli ◽  
G. Habler ◽  
E. Libowitzky

Abstract. This study examines finite deformation patterns of zircon grains from high-temperature natural shear zones. Various zircon-bearing rocks were collected in the Western Tauern Window, Eastern Alps, where they were deformed under amphibolite facies conditions, and in the Ivrea-Verbano Zone (IVZ), Southern Alps, where deformation is related with granulite-facies metamorphism. Among the sampled rocks are: granitic orthogneisses, meta-lamprophyres and paragneisses, all of which are highly deformed. The investigated zircon grains ranging from 10 to 50 microns were studied in situ using a combination of scanning electron microscope (SEM) techniques, including secondary electron (SE), backscattered electron (BSE), forward scattered electron (FSE), cathodoluminescence (CL) imaging, and crystallographic orientation mapping by electron backscatter diffraction analysis (EBSD), as well as micro-Raman spectroscopy. Energy-dispersive X-ray spectrometry (EDS) was applied to host phases. Microstructural analysis of crystal-plastically deformed zircon grains was based on high-resolution EBSD maps. Three general types of finite lattice distortion patterns were detected: Type (I) is defined by gradual bending of the zircon lattice with orientation changes of about 0.6° to 1.4° per μm without subgrain boundary formation. Type (II) represents local gradual bending of the crystal lattice coupled with the formation of subgrain boundaries that have concentric semicircular shapes in 2-D sections. Cumulative grain-internal orientation variations range from 7° to 40° within single grains. Type (III) is characterized by formation of subgrains separated by a well-defined subgrain boundary network, where subgrain boundaries show a characteristic angular closed contour in 2-D sections. The cumulative orientation variation within a single grain ranges from 3° to 10°. Types (I) and (II) predominate in granulite facies rocks, whereas type (III) is restricted to the amphibolite facies rocks. Investigated microstructures demonstrate that misorientation axes are usually parallel to the ⟨ 001 ⟩ and ⟨ 100 ⟩ crystallographic directions; dominant slip systems operating along tilt boundaries are ⟨ 010 ⟩{001}, ⟨ 010 ⟩{100} and ⟨ 001 ⟩{010}. In case of twist boundaries the slip systems ⟨ 010 ⟩{001} and ⟨ 100 ⟩ {001} are active, whereas in some grains cross-slip takes place. This study demonstrates that activation of energetically preferable slip systems is mostly controlled by the degree of coupling with the host phase and by the viscosity ratio between inclusion and host, and defined by crystallographic and elastic anisotropy of the zircon lattice.


1987 ◽  
Vol 59 (2) ◽  
pp. 187-207 ◽  
Author(s):  
Alfred Wiedemann
Keyword(s):  

1979 ◽  
Vol 33 (1) ◽  
pp. 334-337 ◽  
Author(s):  
Christine Bessenrodt
Keyword(s):  

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