Conservation of the numbers of characteristic values of polynomial and entire matrix pencils inside and outside a circle under perturbations

2019 ◽  
Vol 13 (05) ◽  
pp. 2050097
Author(s):  
Michael Gil’
Keyword(s):  
Complex Argument ◽  
Matrix Pencils ◽  
Entire Matrix ◽  
Characteristic Values

Let [Formula: see text] and [Formula: see text] be entire matrix-valued functions of a complex argument [Formula: see text] (entire matrix pencils) and [Formula: see text]. Let [Formula: see text] and [Formula: see text] denote the numbers of the characteristic values of [Formula: see text] taken with their multiplicities located inside and outside [Formula: see text], respectively. Besides [Formula: see text] can be infinite. We consider the following problem: how “close” should be [Formula: see text] and [Formula: see text] in order to provide the equalities [Formula: see text] and [Formula: see text]? We restrict ourselves by the entire pencils of order not more than two. Our results are new even for polynomial pencils.

BOUNDS FOR THE SPECTRUM OF ANALYTIC QUASINORMAL OPERATOR PENCILS

2003 ◽  
Vol 05 (01) ◽  
pp. 101-118 ◽  
Author(s):  
M. I. GIL'
Keyword(s):  
Hilbert Space ◽  
Differential Operators ◽  
Separable Hilbert Space ◽  
Integral Operators ◽  
Infinite Matrix ◽  
Complex Argument ◽  
Matrix Pencils ◽  
Nonlinear Spectrum ◽  
Operator Pencils

We consider a class of pencils (operator valued functions of a complex argument) in a separable Hilbert space. Bounds for the λ-nonlinear spectrum are suggested. Applications to differential operators, integral operators with delay and infinite matrix pencils are also discussed.

scholarly journals Code Calibration of the Eurocodes

2021 ◽  
Vol 11 (12) ◽  
pp. 5474
Author(s):  
Tuomo Poutanen
Keyword(s):  
High Reliability ◽  
High Accuracy ◽  
Variable Load ◽  
Reliability Model ◽  
Safety Factors ◽  
Rounding Errors ◽  
Code Calibration ◽  
Load Factors ◽  
Characteristic Values

This article addresses the process to optimally select safety factors and characteristic values for the Eurocodes. Five amendments to the present codes are proposed: (1) The load factors are fixed, γG = γQ, by making the characteristic load of the variable load changeable, it simplifies the codes and lessens the calculation work. (2) Currently, the characteristic load of the variable load is the same for all variable loads. It creates excess safety and material waste for the variable loads with low variation. This deficiency can be avoided by applying the same amendment as above. (3) Various materials fit with different accuracy in the reliability model. This article explains two options to reduce this difficulty. (4) A method to avoid rounding errors in the safety factors is explained. (5) The current safety factors are usually set by minimizing the reliability indexes regarding the target when the obtained codes include considerable safe and unsafe design cases with the variability ratio (high reliability/low) of about 1.4. The proposed three code models match the target β50 = 3.2 with high accuracy, no unsafe design cases and insignificant safe design cases with the variability ratio 1.07, 1.03 and 1.04.

scholarly journals Early prognostication of COVID-19 to guide hospitalisation versus outpatient monitoring using a point-of-test risk prediction score

Thorax ◽  
2021 ◽  
pp. thoraxjnl-2020-216425
Author(s):  
Felix Chua ◽  
Rama Vancheeswaran ◽  
Adrian Draper ◽  
Tejal Vaghela ◽  
Matthew Knight ◽  
...  
Keyword(s):  
Operating Characteristic ◽  
Predictive Accuracy ◽  
Fatal Outcome ◽  
Individual Characteristics ◽  
Adverse Outcomes ◽  
Hospital Death ◽  
Outpatient Monitoring ◽  
Characteristic Values ◽  
Large Random Sample ◽  
Mortality Predictors

IntroductionRisk factors of adverse outcomes in COVID-19 are defined but stratification of mortality using non-laboratory measured scores, particularly at the time of prehospital SARS-CoV-2 testing, is lacking.MethodsMultivariate regression with bootstrapping was used to identify independent mortality predictors in patients admitted to an acute hospital with a confirmed diagnosis of COVID-19. Predictions were externally validated in a large random sample of the ISARIC cohort (N=14 231) and a smaller cohort from Aintree (N=290).Results983 patients (median age 70, IQR 53–83; in-hospital mortality 29.9%) were recruited over an 11-week study period. Through sequential modelling, a five-predictor score termed SOARS (SpO2, Obesity, Age, Respiratory rate, Stroke history) was developed to correlate COVID-19 severity across low, moderate and high strata of mortality risk. The score discriminated well for in-hospital death, with area under the receiver operating characteristic values of 0.82, 0.80 and 0.74 in the derivation, Aintree and ISARIC validation cohorts, respectively. Its predictive accuracy (calibration) in both external cohorts was consistently higher in patients with milder disease (SOARS 0–1), the same individuals who could be identified for safe outpatient monitoring. Prediction of a non-fatal outcome in this group was accompanied by high score sensitivity (99.2%) and negative predictive value (95.9%).ConclusionThe SOARS score uses constitutive and readily assessed individual characteristics to predict the risk of COVID-19 death. Deployment of the score could potentially inform clinical triage in preadmission settings where expedient and reliable decision-making is key. The resurgence of SARS-CoV-2 transmission provides an opportunity to further validate and update its performance.

scholarly journals Preliminary evaluation for quality of dimension lumber in four common softwoods in Mongolia

2020 ◽  
Vol 66 (1) ◽  
Author(s):  
Murzabyek Sarkhad ◽  
Futoshi Ishiguri ◽  
Ikumi Nezu ◽  
Bayasaa Tumenjargal ◽  
Yusuke Takahashi ◽  
...  
Keyword(s):  
Pinus Sylvestris ◽  
Modulus Of Rupture ◽  
Preliminary Evaluation ◽  
Pinus Sibirica ◽  
Bending Properties ◽  
Picea Obovata ◽  
Dimension Lumber ◽  
Commercial Species ◽  
Characteristic Values

Abstract The quality of dimension lumber (2 by 4 lumber) was preliminarily investigated in four common Mongolian softwoods: Pinus sylvestris L., Pinus sibirica Du Tour, Picea obovata Ledeb., and Larix sibirica Ledeb. to produce high quality dimension lumber for structural use. In total 61, 39, 67, and 37 pieces of lumber were prepared for Pinus sylvestris, Pinus sibirica, Picea obovata, and L. sibirica, respectively. The lumber was visually graded and then tested in static bending to obtain the 5% lower tolerance limits at 75% confidence level (f0.05) of the modulus of elasticity (MOE) and the modulus of rupture (MOR). In addition, the effects of sawing patterns on bending properties were also analyzed. The f0.05 of the MOE and MOR were 4.75 GPa and 15.6 MPa, 3.39 GPa and 11.0 MPa, 3.78 GPa and 11.7 MPa, and 6.07 GPa and 22.3 MPa for Pinus sylvestris, Pinus sibirica, Picea obovata, and L. sibirica, respectively. These results suggested that with a few exceptions, characteristic values of MOR in the four common Mongolian softwoods resembled those in similar commercial species already used. In visual grading, over 80% of total lumber was assigned to select structural and No. 1 grades in Pinus sylvestris and Pinus sibirica, whereas approximately 40% of total lumber in L. sibirica was No. 3 and out of grades. Sawing patterns affected bending properties in Pinus sylvestris and L. sibirica, but did not affect Pinus sibirica and Picea obovata. Dynamic Young's modulus was significantly correlated with bending properties of dimension lumber for the four species. Based on the results, it was concluded that dimension lumber for structural use can be produced from the four common Mongolian softwoods.

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