Precise constants in inequalities of Jackson type

1981 ◽  
Vol 29 (5) ◽  
pp. 388-393
Author(s):  
A. N. Davidchik ◽  
A. A. Ligun
Keyword(s):  
Jackson Type

CLINICAL TRIALS IN INFANTS OF ORALLY ADMINISTERED ATTENUATED POLIOMYELITIS VIRUSES

PEDIATRICS ◽  
1959 ◽  
Vol 23 (6) ◽  
pp. 1041-1062
Author(s):  
Stanley Alan Plotkin ◽  
Hilary Koprowski ◽  
Joseph Stokes
Keyword(s):  
Clinical Trials ◽  
Fecal Excretion ◽  
Jackson Type ◽  
Poliomyelitis Virus ◽  
Minor Illness ◽  
The Difference ◽  
Antibody Levels ◽  
Type 3

Forty-six infants, ranging from less than 1 day to 6 months of age, were given more than 100 feedings of living, attenuated poliomyelitis viruses without the occurrence of major or minor illness. The strains used were CHAT (type 1), Wistar (type 1), Jackson (type 2), P-712 (type 2) and Fox (type 3). All strains except the Jackson strain were found to be antigenic on oral administration. Response to vaccination was demonstrated in these infants by the presence after vaccination of antibody levels significantly in excess of those attributable to transplacentally acquired antibodies, and by the detection of fecal excretion of poliomyelitis virus. Infants less than 2 months old were more difficult to immunize than older infants. The evidence suggests that biologic immaturity rather than transplacental antibodies caused the difference. When the three types of poliomyelitis virus were fed at 3-week intervals, responses occurred to all types. No interference between types was observed when they were fed in all possible sequences. Three infants given a second feeding of homotypic, attenuated poliomyelitis virus 3 to 5 months after a successful vaccination showed resistance to intestinal reinfection.

scholarly journals Approximation of positive operators by analytic vectors

2020 ◽  
Vol 12 (2) ◽  
pp. 412-418
Author(s):  
M.I. Dmytryshyn
Keyword(s):  
Banach Space ◽  
Positive Operator ◽  
Invariant Subspaces ◽  
Positive Operators ◽  
Interpolation Spaces ◽  
Jackson Type ◽  
Normalization Factor ◽  
Approximation Spaces ◽  
Similar Role ◽  
Approximation Errors

We give the estimates of approximation errors while approximating of a positive operator $A$ in a Banach space by analytic vectors. Our main results are formulated in the form of Bernstein and Jackson type inequalities with explicitly calculated constants. We consider the classes of invariant subspaces ${\mathcal E}_{q,p}^{\nu,\alpha}(A)$ of analytic vectors of $A$ and the special scale of approximation spaces $\mathcal {B}_{q,p,\tau}^{s,\alpha}(A)$ associated with the complex degrees of positive operator. The approximation spaces are determined by $E$-functional, that plays a similar role as the module of smoothness. We show that the approximation spaces can be considered as interpolation spaces generated by $K$-method of real interpolation. The constants in the Bernstein and Jackson type inequalities are expressed using the normalization factor.

On Comonotone Approximation

1983 ◽  
Vol 26 (2) ◽  
pp. 220-224 ◽  
Author(s):  
R. K. Beatson ◽  
D. Leviatan
Keyword(s):  
Jackson Type ◽  
Monotone Functions ◽  
Piecewise Monotone ◽  
Comonotone Approximation

AbstractJackson type theorems are obtained for the comonotone approximation of piecewise monotone functions by polynomials.

THEOREMS OF JACKSON TYPE IN $ H^p$, $ 0 < p < 1$

1981 ◽  
Vol 17 (1) ◽  
pp. 203-218 ◽  
Author(s):  
È A Storoženko
Keyword(s):  
Jackson Type

Approximations by multivariate perturbed neural network operators

2017 ◽  
Vol 15 (03) ◽  
pp. 413-432 ◽  
Author(s):  
George A. Anastassiou
Keyword(s):  
Neural Network ◽  
Rate Of Convergence ◽  
Activation Function ◽  
Jackson Type ◽  
Partial Derivatives ◽  
Right Hand ◽  
Hidden Layer ◽  
The Right ◽  
Derivatives Of

This article deals with the determination of the rate of convergence to the unit of each of three newly introduced here multivariate perturbed normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the involved multivariate function or its high-order partial derivatives and that appears in the right-hand side of the associated multivariate Jackson type inequalities. The multivariate activation function is very general, especially it can derive from any multivariate sigmoid or multivariate bell-shaped function. The right-hand sides of our convergence inequalities do not depend on the activation function. The sample functionals are of multivariate Stancu, Kantorovich and quadrature types. We give applications for the first partial derivatives of the involved function.

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