On the properties of the limit q-Bernstein operator

2011 ◽  
Vol 48 (2) ◽  
pp. 160-179 ◽  
Author(s):  
Sofiya Ostrovska
Keyword(s):  
Entire Function ◽  
Linear Operator ◽  
Energy Distribution ◽  
Slow Growth ◽  
Probabilistic Interpretation ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Shape Preserving ◽  
Boson Theory ◽  
The Impact

The limit q-Bernstein operator Bq = B∞,q: C[0, 1] → C[0, 1] emerges naturally as a q-version of the Szász-Mirakyan operator related to the q-deformed Poisson distribution. The latter is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state.The limit q-Bernstein operator has been widely studied lately. It has been shown that Bq is a positive shape-preserving linear operator on C[0, 1] with ‖Bq‖ = 1. Its approximation properties, probabilistic interpretation, behavior of iterates, and the impact on the smoothness have been examined.In this paper, it is shown that the possibility of an analytic continuation of Bqf into {z: |z| < R}, R > 1, implies the smoothness of f at 1, which is stronger when R is greater. If Bqf can be extended to an entire function, then f is infinitely differentiable at 1, and a sufficiently slow growth of Bqf implies analyticity of f in {z: |z − 1| < δ}, where δ is greater when the growth is slower. Finally, there is a bound for the growth of Bqf which implies f to be an entire function.

scholarly journals A Survey of Results on the Limit -Bernstein Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sofiya Ostrovska
Keyword(s):  
Approximation Theory ◽  
Probabilistic Interpretation ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Shape Preserving ◽  
The Past ◽  
Boson Theory ◽  
Complete Bibliography ◽  
The Impact ◽  
Exemplary Model

The limit -Bernstein operator emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution, which is used in the -boson theory to describe the energy distribution in a -analogue of the coherent state. At the same time, this operator bears a significant role in the approximation theory as an exemplary model for the study of the convergence of the -operators. Over the past years, the limit -Bernstein operator has been studied widely from different perspectives. It has been shown that is a positive shape-preserving linear operator on with . Its approximation properties, probabilistic interpretation, the behavior of iterates, and the impact on the smoothness of a function have already been examined. In this paper, we present a review of the results on the limit -Bernstein operator related to the approximation theory. A complete bibliography is supplied.

scholarly journals The Functional-Analytic Properties of the Limitq-Bernstein Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Sofiya Ostrovska
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Dimensional Subspace ◽  
Probabilistic Interpretation ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Shape Preserving ◽  
Infinite Dimensional ◽  
Boson Theory ◽  
Infinite Dimensional Subspace

The limitq-Bernstein operatorBq,0<q<1, emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution. The latter is used in theq-boson theory to describe the energy distribution in aq-analogue of the coherent state. Lately, the limitq-Bernstein operator has been widely under scrutiny, and it has been shown thatBqis a positive shape-preserving linear operator onC[0,1]with∥Bq∥=1. Its approximation properties, probabilistic interpretation, eigenstructure, and impact on the smoothness of a function have been examined. In this paper, the functional-analytic properties ofBqare studied. Our main result states that there exists an infinite-dimensional subspaceMofC[0,1]such that the restrictionBq|Mis an isomorphic embedding. Also we show that each such subspaceMcontains an isomorphic copy of the Banach spacec0.

scholarly journals The Impact of COVID-19 on the Romanian Hospitals’ Expenses. A Case Study Toward the Financial Resilience after the Pandemic

2021 ◽  
pp. 22-36
Author(s):  
Attila GYÖRGY ◽  
◽  
Liliana SIMIONESCU ◽  
Keyword(s):  
Human Resources ◽  
Slow Growth ◽  
Growth Potential ◽  
High Scale ◽  
Monthly Basis ◽  
Goods And Services ◽  
Almost All ◽  
Medical Infrastructure ◽  
The Impact

The Coronavirus disease 2019 (COVID-19) affect­ed almost all activities worldwide. The medical sec­tor was one of those which were most significantly impacted because the medical infrastructure was not sized for such a high scale shock, specialized human resources and medical infrastructure prov­ing to be much undersized and with slow growth potential. Many changes were required, important financial resources being mobilized in order to mo­tivate medical staff, offer treatments for the most severely affected patients, but also to create new fa­cilities where the increasing number of sick persons could be cured. In our research we want to offer a hospital cost perspective based on empirical analysis of the COVID-19 impact on different categories of expens­es made by Romanian hospitals that treated patients with COVID-19 in different stages of their disease. The period analyzed was January 2019 to December 2020 on a monthly basis. Our results showed that expenses with goods and services, drugs, reagents and human resources are influenced by COVID-19 in a significant manner.

Grid Quality Measures for PEBI Grids

2021 ◽  
Author(s):  
Ilya Mishev ◽  
Ruslan Rin
Keyword(s):  
Flow Behavior ◽  
Quality Measures ◽  
Approximation Properties ◽  
Approximation Quality ◽  
Flux Approximation ◽  
The Matrix ◽  
Eventual Loss ◽  
Dynamic Measures ◽  
The Impact

Abstract Combining the Perpendicular Bisector (PEBI) grids with the Two Point Flux Approximation (TPFA) scheme demonstrates a potential to accurately model on unstructured grids, conforming to the geological and engineering features of real grids. However, with the increased complexity and resolution of the grids, the PEBI conditions will inevitably be violated in some cells and the approximation properties will be compromised. The objective is to develop accurate and practical grid quality measures that quantify such errors. We critically evaluated the existing grid quality measures and found them lacking predictive power in several areas. The available k-orthogonality measures predict error for flow along the strata, although TPFA provides an accurate approximation. The false-positive results are not only misleading but can overwhelm further analysis. We developed the so-called "truncation error" grid measure which is probably the most accurate measure for flow through a plane face and accurately measures the error along the strata. We also quantified the error due to the face curvature. Curved faces are bound to exist in any real grid. The impact of the quality of the 2-D Delaunay triangulation on TPFA approximation properties is usually not taken into account. We investigate the impact of the size of the smallest angles that can cause considerable increase of the condition number of the matrix and an eventual loss of accuracy, demonstrated with simple examples. Based on the analysis, we provide recommendations. We also show how the size of the largest angles impacts the approximation quality of TPFA. Furthermore, we discuss the impact of the change of the permeability on the TPFA approximation. Finally, we present simple tools that reservoir engineers can use to incorporate the above-mentioned grid quality measures into a workflow. The grid quality measures discussed up to now are static. We also sketch the further extension to dynamic measures, that is, how the static measures can be used to detect change in the flow behavior, potentially leading to increased error. We investigate a comprehensive set of methods, several of them new, to measure the static grid quality of TPFA on PEBI grids and possible extension to dynamic measures. All measures can be easily implemented in production reservoir simulators and examined using the suggested tools in a workflow.

scholarly journals Some local properties of the solutions of second-order differential equations

1995 ◽  
Vol 59 (2) ◽  
pp. 255-265
Author(s):  
Jiuyi Cheng ◽  
John Rossi
Keyword(s):  
Entire Function ◽  
Differential Equations ◽  
Slow Growth ◽  
Classical Case ◽  
Second Order ◽  
Zero Distribution ◽  
Second Order Differential Equations ◽  
Local Properties

AbstractWe investigate the asymptotics and zero distribution of solutions of ω″ + Aω = 0 where A is an entire function of very slow growth. The results parallel the classical case when A is assumed to be a polynomial.

scholarly journals On the Numerical Solution of Fractional Boundary Value Problems by a Spline Quasi-Interpolant Operator

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 61
Author(s):  
Francesca Pitolli
Keyword(s):  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Numerical Experiments ◽  
Boundary Value ◽  
Bernstein Operator ◽  
Explicit Formulas ◽  
Shape Preserving ◽  
Engineering Control ◽  
Shape Preserving Properties ◽  
Fractional Boundary Value Problems

Boundary value problems having fractional derivative in space are used in several fields, like biology, mechanical engineering, control theory, just to cite a few. In this paper we present a new numerical method for the solution of boundary value problems having Caputo derivative in space. We approximate the solution by the Schoenberg-Bernstein operator, which is a spline positive operator having shape-preserving properties. The unknown coefficients of the approximating operator are determined by a collocation method whose collocation matrices can be constructed efficiently by explicit formulas. The numerical experiments we conducted show that the proposed method is efficient and accurate.

scholarly journals The VLA-COSMOS 3 GHz Large Project: Average radio spectral energy distribution of highly star-forming galaxies

2019 ◽  
Vol 621 ◽  
pp. A139 ◽  
Author(s):  
K. Tisanić ◽  
V. Smolčić ◽  
J. Delhaize ◽  
M. Novak ◽  
H. Intema ◽  
...  
Keyword(s):  
Survival Analysis ◽  
Energy Distribution ◽  
Power Law ◽  
Rest Frame ◽  
Spectral Energy Distribution ◽  
Spectral Energy ◽  
Radio Luminosity ◽  
Star Forming ◽  
The Impact ◽  
Frame Frequency

We construct the average radio spectral energy distribution (SED) of highly star-forming galaxies (HSFGs) up to z ∼ 4. Infrared and radio luminosities are bound by a tight correlation that is defined by the so-called q parameter. This infrared–radio correlation provides the basis for the use of radio luminosity as a star-formation tracer. Recent stacking and survival analysis studies find q to be decreasing with increasing redshift. It was pointed out that a possible cause of the redshift trend could be the computation of rest-frame radio luminosity via a single power-law assumption of the star-forming galaxies’ (SFGs) SED. To test this, we constrained the shape of the radio SED of a sample of HSFGs. To achieve a broad rest-frame frequency range, we combined previously published Very Large Array observations of the COSMOS field at 1.4 GHz and 3 GHz with unpublished Giant Meterwave Radio Telescope (GMRT) observations at 325 MHz and 610 MHz by employing survival analysis to account for non-detections in the GMRT maps. We selected a sample of HSFGs in a broad redshift range (z ∈ [0.3, 4],  SFR ≥ 100 M⊙ yr−1) and constructed the average radio SED. By fitting a broken power-law, we find that the spectral index changes from α1 = 0.42 ± 0.06 below a rest-frame frequency of 4.3 GHz to α2 = 0.94 ± 0.06 above 4.3 GHz. Our results are in line with previous low-redshift studies of HSFGs ( SFR >  10 M⊙  yr−1) that show the SED of HSFGs to differ from the SED found for normal SFGs ( SFR <  10 M⊙ yr−1). The difference is mainly in a steeper spectrum around 10 GHz, which could indicate a smaller fraction of thermal free–free emission. Finally, we also discuss the impact of applying this broken power-law SED in place of a simple power-law in K-corrections of HSFGs and a typical radio SED for normal SFGs drawn from the literature. We find that the shape of the radio SED is unlikely to be the root cause of the q − z trend in SFGs.

The impact of energy distribution on data quality and cost of 3D seismic survey over Bu Hasa Onshore Field in Abu Dhabi, UAE

2000 ◽  
Author(s):  
Abu Baker Al Jeelani ◽  
Samer Marmash ◽  
Abdulsalam Bin Ishaq ◽  
Ahmad Al‐Shaikh ◽  
Erik Kleiss ◽  
...  
Keyword(s):  
Energy Distribution ◽  
Data Quality ◽  
Seismic Survey ◽  
Abu Dhabi ◽  
3D Seismic ◽  
The Impact

Voronovskaja’s theorem, shape preserving properties and iterations for complex q-Bernstein polynomials

2011 ◽  
Vol 48 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Sorin Gal
Keyword(s):  
Convergence Theorem ◽  
Analytic Functions ◽  
Quantitative Estimate ◽  
Bernstein Polynomials ◽  
Exact Order ◽  
Approximation Properties ◽  
Shape Preserving ◽  
Voronovskaja’S Theorem ◽  
Shape Preserving Properties ◽  
Compact Disks

In this paper, first we prove Voronovskaja’s convergence theorem for complex q-Bernstein polynomials, 0 < q < 1, attached to analytic functions in compact disks in ℂ centered at origin, with quantitative estimate of this convergence. As an application, we obtain the exact order in approximation of analytic functions by the complex q-Bernstein polynomials on compact disks. Finally, we study the approximation properties of their iterates for any q > 0 and we prove that the complex qn-Bernstein polynomials with 0 < qn < 1 and qn → 1, preserve in the unit disk (beginning with an index) the starlikeness, convexity and spiral-likeness.

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