scholarly journals Vanishing pseudo–Schur complements, reverse order laws, absorption laws and inheritance properties

2017 ◽  
Vol 66 (1) ◽  
pp. 167-183
Author(s):  
Kavita Bisht ◽  
K. C. Sivakumar
2015 ◽  
Vol 30 ◽  
Author(s):  
K. Sivakumar ◽  
Ravindran G. ◽  
Kavita Bisht

Extensions of the Schur complement and the principal pivot transform, where the usual inverses are replaced by the Moore-Penrose inverse, are revisited. These are called the pseudo Schur complement and the pseudo principal pivot transform, respectively. First, a generalization of the characterization of a block matrix to be an M-matrix is extended to the nonnegativity of the Moore-Penrose inverse. A comprehensive treatment of the fundamental properties of the extended notion of the principal pivot transform is presented. Inheritance properties with respect to certain matrix classes are derived, thereby generalizing some of the existing results. Finally, a thorough discussion on the preservation of left eigenspaces by the pseudo principal pivot transformation is presented.


Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 937-947
Author(s):  
Zhiping Xiong

The relationship between generalized inverses of AB and the product of generalized inverses of A and B have been studied in this paper. The necessary and sufficient conditions for a number of mixed-type reverse order laws of generalized inverses of two matrix products are derived by using the maximal ranks of the generalized Schur complements.


2020 ◽  
Author(s):  
Mane Kara-Yakoubian ◽  
Alexander C. Walker ◽  
Constantine Sharpinskyi ◽  
Garni Assadourian ◽  
Jonathan Albert Fugelsang

The Keats heuristic suggests that people find aesthetically pleasing expressions more accurate than mundane expressions. We test this notion with chiastic statements. Chiasmus is a stylistic phenomenon in which at least two linguistic constituents are repeated in reverse order, following an A-B-B-A pattern. Our study focuses on the specific form of chiasmus known as antimetabole, in which the reverse-repeated constituents are words (e.g., “all for one and one for all”). In 3 out of 4 experiments (N = 797), we find evidence that people judge antimetabolic statements (e.g., “Success is getting what you want. Happiness is wanting what you get.”) as more accurate than semantically equivalent non-antimetabolic statements (e.g., “Success is getting what you wish. Happiness is wanting what you receive.”). Furthermore, we evaluate fluency as a potential mechanism explaining the observed accuracy benefit afforded to antimetabolic statements, finding that the increased speed (i.e., fluency) with which antimetabolic statements were processed was misattributed by participants as evidence of greater accuracy. Overall, the current work demonstrates that stylistic factors bias assessments of truth, with information communicated using aesthetically pleasing stylistic devices (e.g., antimetabole) being perceived as more truthful.


2018 ◽  
Vol 23 (1) ◽  
pp. 303-316
Author(s):  
Jung-Sik Choi ◽  
Keyword(s):  

Languages ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 76
Author(s):  
Susan E. Kalt

Variation among closely related languages may reveal the inner workings of language acquisition, loss and innovation. This study of the existing literature and of selected interviews from recent narrative corpora compares the marking of evidentiality and epistemic modality in Chuquisaca, Bolivian Quechua with its closely related variety in Cuzco, Peru and investigates three hypotheses: that morpho-syntactic attrition proceeds in reverse order of child language acquisition, that convergence characterizes the emergence of grammatical forms different from L1 and L2 in contact situations, and that the Quechua languages are undergoing typological shift toward more isolating morphology. It appears that reportive -sis disappeared first in Bolivia, with eyewitness/validator -min retaining only the validator function. This finding seems to concord with reverse acquisition since it has previously been claimed that epistemic marking is acquired earlier than evidential marking in Cuzco. Meanwhile, Spanish and Quechua in nearby Cochabamba are claimed to mark reportive evidentiality via freestanding verbs of saying. I explore the reportive use of ñiy ‘to say’ in Chuquisaca as compared to Cochabamba and Cuzco and suggest the need for comparative statistical studies of evidential and epistemic marking in Southern Quechua.


2021 ◽  
Vol 57 (1) ◽  
pp. 59-83
Author(s):  
Liljana Mitkovska

Abstract This paper analyses a number of constructions with a reflexive marker on the verb and a dative argument, using the framework of Construction Grammar. In these constructions the predication is ascribed in various modes to the experiencer argument. We focus on these constructions in the South Slavic languages in which they have a wide distribution, Macedonian, Bulgarian and Bosnian/Croatian/Serbian (BCS). The following basic types are identified: Emotional processes and states, Accidental, Perception/Cognition and Stative Reflexive-Dative Construction (SRDC). The specific clusters of features in each one are due to the inheritance properties from a reflexive construction, indicating a valence reduction, in combination with the features of affectedness and lack of control, characteristic of a dative argument. This results in varied but multiply linked patterns that create a complex network of constructions. The study aims at defining the relations between these constructions and in particular at determining the place of SRDC in this network.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zdeněk Dostál ◽  
Tomáš Brzobohatý ◽  
Oldřich Vlach

Abstract Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of “floating” clusters arising from the discretization of 3D Laplacian on a cube decomposed into cube subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m × m × m cube subdomains connected by face and optionally edge averages increases proportionally to m. The estimates support scalability of unpreconditioned H-FETI-DP (hybrid FETI dual-primal) method. Though the research is most important for the solution of variational inequalities, the results of numerical experiments indicate that unpreconditioned H-FETI-DP with large clusters can be useful also for the solution of huge linear problems.


2019 ◽  
Vol 4 (1) ◽  
pp. e000190
Author(s):  
Gustavo Ricci Malavazzi ◽  
Jonathan Clive Lake ◽  
Eduardo Sone Soriano ◽  
Walton Nose

ObjectiveTo implement a method to train residents in the performance of phacoemulsification surgery, with the steps completed in reverse chronological order and with the easiest step being undertaken first.Methods and analysisWe created a method for training ophthalmology residents in which we taught phacoemulsification surgery in a series of steps learnt in reverse order. Each resident advanced through the teaching modules only after being approved in the final step and then progressed to the complete performance of surgeries. We analysed the rates of complications in the 2 years after introducing the new method.ResultsThe new method allowed for a standardised approach that enabled replicated teaching of phacoemulsification regardless of instructor or student. After implementing the new method, residents performed 1817 phacoemulsification surgeries in the first year and 1860 in the second year, with posterior capsule rupture rates of 8.42% and 7.9%, respectively.ConclusionsTeaching residents to perform the steps of phacoemulsification in a standardised reverse order resulted in low rates of complications.


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