On optimal recovery of values of linear operators from information, known with stochastic error

2021 ◽  
Vol 212 (11) ◽  
Author(s):  
Kirill Yurevich Krivosheev
Keyword(s):  
Optimal Recovery ◽  
Linear Operators ◽  
Stochastic Error

Studies on the Fibrinolytic System in Human Plasma: Quantitative Determination of Plasminogen Activators and Proactivators

1979 ◽  
Vol 41 (02) ◽  
pp. 365-383 ◽  
Author(s):  
C Kluft
Keyword(s):  
Pilot Study ◽  
Plasma Level ◽  
Human Plasma ◽  
Plasminogen Activators ◽  
Venous Occlusion ◽  
Quantitative Information ◽  
Optimal Recovery ◽  
Dextran Sulphate ◽  
Baseline Levels

SummaryEffects due to plasma plasminogen activators and proactivators are usually studied in assay systems where inhibitors influence the activity and where the degree of activation of proactivators is unknown. Quantitative information on activator and proactivator levels in plasma is therefore not availableStudies on the precipitating and activating properties of dextran sulphate in euglobulin fractionation presented in this paper resulted in the preparation of a fraction in which there was optimal recovery and optimal activation of a number of plasminogen activators and proactivators from human plasma. The quantitative assay of these activators on plasminogen-rich fibrin plates required the addition of flufenamate to eliminate inhibitors. The response on the fibrin plates (lysed zones) could be coverted to arbitrary blood activator units (BAU). Consequently, a new activator assay which enables one to quantitatively determine the plasma level of plasminogen activators and proactivators together is introduced.Two different contributions could be distinguished: an activity originating from extrinsic activator and one originating from intrinsic proactivators. The former could be assayed separately by means of its resistance to inhibition by Cl-inactivator. Considering the relative concentrations of extrinsic and intrinsic activators, an impression of the pattern of activator content in plasma was gained. In morning plasma with baseline levels of fibrinolysis, the amount of extrinsic activator was negligible as compared to the level of potentially active intrinsic activators. Consequently, the new assay nearly exclusively determines the level of intrinsic activators in morning plasma. A pilot study gave a fairly stable level of 100 ± 15 BAU/ml (n = 50). When fibrinolysis was stimulated by venous occlusion (15 min), the amount of extrinsic activator was greatly increased, reaching a total activator level of 249 ± 27 BAU/ml (n = 7).

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

Industrial Ecology of the Paper Industry

1999 ◽  
Vol 40 (11-12) ◽  
pp. 21-24
Author(s):  
Tapio Pento
Keyword(s):  
Systems Engineering ◽  
Industrial Ecology ◽  
Raw Materials ◽  
Paper Industry ◽  
Waste Recycling ◽  
Optimal Recovery ◽  
Natural Systems ◽  
Earth Systems ◽  
Controversial Area ◽  
Recycling Systems

Industrial ecology (IE) is a biological concept applied to industrial structures. The basic concepts of IE include regional, intra-firm and product-based waste recycling systems as well as the principle of upward and downward cascading. In best current examples of regional systems, several parties are in an industrial waste re-use symbiosis. Paper industry has learned to arrange the recovery and re-use of its products on distant markets, even up to a level where indications of exceeding optimal recovery and re-use rates already exist through deteriorated fibre and product quality. Such occurrences will take place in certain legislative-economic situations. Paper industry has many cascade levels, each with their internal recovery and recycling, as well as many intra-firm, regional, and life cycle ecology structures. As an example of prospects for individual cascading routes, sludges may continue to be incinerated, but the route to landfills will be closed. The main obstacles of legislative drive toward better IE systems are in many cases existing laws and political considerations rather than economic or technical aspects. The study and practice of engineering human technology systems and related elements of natural systems should develop in such a way that they provide quality of life by actively managing the dynamics of relevant systems to reduce the risk and scale of undesirable behavior and outcomes. For the paper industry, earth systems engineering offers several development routes. One of them is the further recognition of and research on the fact that the products of the industry are returned back to the carbon cycle of the natural environment. Opportunities for modifying current earth systems may also be available for the industry, e.g. genetically modified plants for raw materials or organisms for making good quality pulp out of current raw materials. It is to be recognized that earth systems engineering may become a very controversial area, and that very diverse political pressures may determine its future usefulness to the paper industry.

On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3749-3760 ◽  
Author(s):  
Ali Karaisa ◽  
Uğur Kadak
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Bernstein Operator ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Inclusion Relations ◽  
Prior Investigation

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

Cline’s formula for g-Drazin inverses in a ring

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2249-2255
Author(s):  
Huanyin Chen ◽  
Marjan Abdolyousefi
Keyword(s):  
Operator Theory ◽  
Spectral Properties ◽  
Associative Ring ◽  
Linear Operators ◽  
Drazin Inverse ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

Sign in / Sign up

Export Citation Format

Share Document