On the mean convergence of derivatives of Lagrange interpolation

2012 ◽  
pp. 397-404 ◽  
Author(s):  
J. Szabados ◽  
A. K. Varma
Keyword(s):  
Lagrange Interpolation ◽  
Mean Convergence ◽  
The Mean ◽  
Derivatives Of

scholarly journals Mean convergence of derivatives of Lagrange interpolation

1991 ◽  
Vol 34 (3) ◽  
pp. 385-396 ◽  
Author(s):  
Giuseppe Mastroianni ◽  
Paul Nevai
Keyword(s):  
Lagrange Interpolation ◽  
Mean Convergence ◽  
Derivatives Of

Mean Convergence of Derivatives of Extended Lagrange Interpolation with Additional Nodes

1993 ◽  
Vol 163 (1) ◽  
pp. 73-92 ◽  
Author(s):  
Giuliana Criscuolo ◽  
Guiseppe Mastroianni ◽  
Paul Nevai
Keyword(s):  
Lagrange Interpolation ◽  
Mean Convergence ◽  
Derivatives Of

The Mean Convergence of Orthogonal Series

1950 ◽  
Vol 72 (4) ◽  
pp. 792 ◽  
Author(s):  
G. Milton Wing
Keyword(s):  
Orthogonal Series ◽  
Mean Convergence ◽  
The Mean

CERTAIN ISOMETRIES RELATED TO THE BILATERAL LAPLACE TRANSFORM

2006 ◽  
Vol 11 (3) ◽  
pp. 331-346 ◽  
Author(s):  
S. B. Yakubovich
Keyword(s):  
Hilbert Space ◽  
Entire Function ◽  
Laplace Transform ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Inversion Formulas ◽  
Mean Convergence ◽  
The Laplace Transform ◽  
The Mean

We study certain isometries between Hilbert spaces, which are generated by the bilateral Laplace transform In particular, we construct an analog of the Bargmann‐Fock type reproducing kernel Hilbert space related to this transformation. It is shown that under some integra‐bility conditions on $ the Laplace transform FF(z), z = x + iy is an entire function belonging to this space. The corresponding isometrical identities, representations of norms, analogs of the Paley‐Wiener and Plancherel's theorems are established. As an application this approach drives us to a different type of real inversion formulas for the bilateral Laplace transform in the mean convergence sense.

Mean Convergence of Lagrange Interpolation for Exponential weights on [-1, 1]

1998 ◽  
Vol 50 (6) ◽  
pp. 1273-1297 ◽  
Author(s):  
D. S. Lubinsky
Keyword(s):  
Orthogonal Polynomials ◽  
Lagrange Interpolation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Exponential Weights ◽  
Mean Convergence ◽  
Zeros Of Orthogonal Polynomials ◽  
Necessary And Sufficient

AbstractWe obtain necessary and sufficient conditions for mean convergence of Lagrange interpolation at zeros of orthogonal polynomials for weights on [-1, 1], such asw(x) = exp(-(1 - x2)-α), α > 0orw(x) = exp(-expk(1 - x2)-α), k≥1, α > 0,where expk = exp(exp(. . . exp( ) . . .)) denotes the k-th iterated exponential.

scholarly journals An Activity of Thioacyl Derivatives of 4-Aminoquinolinium Salts towards Biofilm Producing and Planktonic Forms of Coagulase-Negative Staphylococci

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Robert D. Wojtyczka ◽  
Andrzej Zięba ◽  
Arkadiusz Dziedzic ◽  
Małgorzata Kępa ◽  
Danuta Idzik
Keyword(s):  
Biofilm Formation ◽  
Hospital Environment ◽  
Initial Assessment ◽  
Coagulase Negative Staphylococci ◽  
Planktonic Form ◽  
The Mean ◽  
New Compounds ◽  
Derivatives Of ◽  
Mean Concentration ◽  
Mic Value

Microorganisms present in different environments have developed specific mechanisms of settling on various abiotic and biotic surfaces by forming a biofilm. It seems to be well justified to search for new compounds enabling biofilm reduction, which is highly resistant to antibiotics. This study was thus an initial assessment of the antibacterial activity of two new quinoline derivatives of a structure of 3-thioacyl 1-methyl 4-arylaminoquinolinium salts against coagulase-negative staphylococci (CoNS) isolated from a hospital environment, in a form of both biofilms and in planktonic form. Thirty-three stains of CoNS isolated from the hospital environment (air, surfaces) and seven reference strains from the ATCC collection were selected for the study. The mean MIC value for 1-methyl-3-benzoylthio-4-(4-chlorophenylamino)quinolinum chloride (4-chlorophenylamino derivative) was 42.60 ± 19.91 μg/mL, and in the case of strains subjected to 1-methyl-3-benzoylthio-4-(4-fluorophenylamino)quinolinum chloride (4-fluorophenylamino derivative) activity, the mean MIC value was 43.20 ± 14.30 μg/mL. The mean concentration of 4-chlorophenylamino derivative that inhibited biofilm formation was 86.18 ± 30.64 μg/mL. The mean concentration of 4-fluorophenylamino derivatives that inhibited biofilm formation was higher and amounted to 237.09 ± 160.57 μg/mL. Based on the results, both derivatives of the examined compounds exhibit high antimicrobial activity towards strains growing both in planktonic and biofilm form.

CRITICAL DIMENSIONS OF SYSTEMS WITH JOINT MULTICRITICAL AND LIFSHITZ-POINT-LIKE BEHAVIOR

2011 ◽  
Vol 25 (22) ◽  
pp. 1839-1845 ◽  
Author(s):  
ARTEM V. BABICH ◽  
LESYA N. KITCENKO ◽  
VYACHESLAV F. KLEPIKOV
Keyword(s):  
Field Theory ◽  
Critical Phenomena ◽  
Critical Points ◽  
Order Parameter ◽  
Mean Field Theory ◽  
Mean Field ◽  
Critical Dimensions ◽  
Lifshitz Point ◽  
The Mean ◽  
Derivatives Of

In this article, we consider a model that allows one to describe critical phenomena in systems with higher powers and derivatives of order parameter. The systems considered have critical points with joint multicritical and Lifshitz-point-like properties. We assess the lower and upper critical dimensions of these systems. These calculation enable us to find the fluctuation region where the mean field theory description does not work.

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