scholarly journals Error bounds associated with different versions of Hadamard inequalities of mid-point type

2020 ◽  
Vol 23 (03) ◽  
pp. 213-229
Author(s):  
Muhammad Raees ◽  
Matloob Anwar ◽  
Ghulam Farid
Keyword(s):  
2020 ◽  
Vol 133 (3) ◽  
pp. 800-807 ◽  
Author(s):  
Andreas Fahlström ◽  
Henrietta Nittby Redebrandt ◽  
Hugo Zeberg ◽  
Jiri Bartek ◽  
Andreas Bartley ◽  
...  

OBJECTIVEThe authors aimed to develop the first clinical grading scale for patients with surgically treated spontaneous supratentorial intracerebral hemorrhage (ICH).METHODSA nationwide multicenter study including 401 ICH patients surgically treated by craniotomy and evacuation of a spontaneous supratentorial ICH was conducted between January 1, 2011, and December 31, 2015. All neurosurgical centers in Sweden were included. All medical records and neuroimaging studies were retrospectively reviewed. Independent predictors of 30-day mortality were identified by logistic regression. A risk stratification scale (the Surgical Swedish ICH [SwICH] Score) was developed using weighting of independent predictors based on strength of association.RESULTSFactors independently associated with 30-day mortality were Glasgow Coma Scale (GCS) score (p = 0.00015), ICH volume ≥ 50 mL (p = 0.031), patient age ≥ 75 years (p = 0.0056), prior myocardial infarction (MI) (p = 0.00081), and type 2 diabetes (p = 0.0093). The Surgical SwICH Score was the sum of individual points assigned as follows: GCS score 15–13 (0 points), 12–5 (1 point), 4–3 (2 points); age ≥ 75 years (1 point); ICH volume ≥ 50 mL (1 point); type 2 diabetes (1 point); prior MI (1 point). Each increase in the Surgical SwICH Score was associated with a progressively increased 30-day mortality (p = 0.0002). No patient with a Surgical SwICH Score of 0 died, whereas the 30-day mortality rates for patients with Surgical SwICH Scores of 1, 2, 3, and 4 were 5%, 12%, 31%, and 58%, respectively.CONCLUSIONSThe Surgical SwICH Score is a predictor of 30-day mortality in patients treated surgically for spontaneous supratentorial ICH. External validation is needed to assess the predictive value as well as the generalizability of the Surgical SwICH Score.


2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.


2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.


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