scholarly journals VARIATION PROBLEM CONTAINING SECOND DERIVATIVES OF UNKNOWN FUNCTIONS

2021 ◽  
Vol 6 (1(34)) ◽  
pp. 30-42
Author(s):  
Misraddin Allahverdi oglu Sadigov
Keyword(s):  
Variational Problem ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Necessary Condition ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Variation Problem ◽  
Second Derivatives ◽  
Necessary And Sufficient ◽  
Derivatives Of

The property subdifferential of an integral and terminal functional in a space of the type of absolutely continuous functions is studied. Necessary and sufficient conditions for an extremum for a variational problem containing the second derivatives of unknown functions are obtained. With the help of the subdifferential introduced by the author, a nonconvex generalized variational problem containing the second derivatives of unknown functions is considered, and the necessary condition for an extremum is obtained.

scholarly journals Approximation by generalized positive linear Kantorovich operators

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4353-4368 ◽  
Author(s):  
Minakshi Dhamija ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Continuous Functions ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of ◽  
Kantorovich Operators

In the present article, we introduce generalized positive linear-Kantorovich operators depending on P?lya-Eggenberger distribution (PED) as well as inverse P?lya-Eggenberger distribution (IPED) and for these operators, we study some approximation properties like local approximation theorem, weighted approximation and estimation of rate of convergence for absolutely continuous functions having derivatives of bounded variation.

scholarly journals ON THE EXACT PENALTY OF HIGH ORDER FOR EXTREME PROBLEMS OF DIFFERENTIAL INCLUSIONS

2021 ◽  
Vol 6 (2(52)) ◽  
pp. 75-86
Author(s):  
Misraddin Allahverdi oglu Sadygov
Keyword(s):  
Distance Function ◽  
Differential Inclusions ◽  
Continuous Functions ◽  
Extremal Problems ◽  
High Order ◽  
Necessary Condition ◽  
Exact Penalty ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Locally Lipschitz

In this paper, using theorems on the continuous dependence of the solution of differential inclusions on the perturbation, we obtain high-order exact penalty theorems for nonconvex extremal problems of differential inclusions in the space of Banach-valued absolutely continuous functions. Using the type of the distance function in the classes of 𝜙 − (𝜙, 𝜙, 𝜙, 𝜙, 𝜙) locally Lipschitz functions, the nonconvex extremal problem for differential inclusions is reduced to a variational problem and the necessary condition for the extremum of a high-order is obtained. The paper also shows that the used functions type of distance function satisfy the 𝜙 − (𝜙, 𝜙, 𝜙, 𝜙, 𝜙) locally Lipschitz conditions.

On identifiability in the autopsy model of reliability theory

1993 ◽  
Vol 30 (04) ◽  
pp. 913-930 ◽  
Author(s):  
Robin Antoine ◽  
Hani Doss ◽  
Myles Hollander
Keyword(s):  
Failure Time ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Coherent System ◽  
System Failure ◽  
Absolutely Continuous ◽  
Failure Times ◽  
Life Distributions ◽  
Parametric Families ◽  
Necessary And Sufficient

A coherent system is observed until it fails. At the instant of system failure, the set of failed components and the failure time of the system are noted. The failure times of the components are not known. We consider whether the component life distributions can be determined from the distributions of the observed data. Meilijson (1981) gave a condition on the structure of the system that was sufficient for the identifiability of the component distributions, under the assumption that the component life distributions are continuous and have common essential extrema. Nowik (1990) gave necessary and sufficient conditions for identifiability under the more restrictive condition that the component distributions have atoms at their common essential infimum and are mutually absolutely continuous. We give a necessary condition for identifiability, which we show to be equivalent to Nowik's condition, under the assumption that the distributions are continuous and strictly increasing. We derive a sufficient condition for identifiability, more general than Meilijson's, for the case in which the component distributions are assumed to be analytic. We also show that our necessary condition for identifiability is both necessary and sufficient when the component life distributions are assumed to belong to certain parametric families.

scholarly journals Rate of convergence of beta operators of second kind for functions with derivatives of bounded variation

2005 ◽  
Vol 2005 (23) ◽  
pp. 3827-3833 ◽  
Author(s):  
Vijay Gupta ◽  
Ulrich Abel ◽  
Mircea Ivan
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Function Of Bounded Variation ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of

We study the approximation properties of beta operators of second kind. We obtain the rate of convergence of these operators for absolutely continuous functions having a derivative equivalent to a function of bounded variation.

On identifiability in the autopsy model of reliability theory

1993 ◽  
Vol 30 (4) ◽  
pp. 913-930 ◽  
Author(s):  
Robin Antoine ◽  
Hani Doss ◽  
Myles Hollander
Keyword(s):  
Failure Time ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Coherent System ◽  
System Failure ◽  
Absolutely Continuous ◽  
Failure Times ◽  
Life Distributions ◽  
Parametric Families ◽  
Necessary And Sufficient

A coherent system is observed until it fails. At the instant of system failure, the set of failed components and the failure time of the system are noted. The failure times of the components are not known. We consider whether the component life distributions can be determined from the distributions of the observed data.Meilijson (1981) gave a condition on the structure of the system that was sufficient for the identifiability of the component distributions, under the assumption that the component life distributions are continuous and have common essential extrema. Nowik (1990) gave necessary and sufficient conditions for identifiability under the more restrictive condition that the component distributions have atoms at their common essential infimum and are mutually absolutely continuous. We give a necessary condition for identifiability, which we show to be equivalent to Nowik's condition, under the assumption that the distributions are continuous and strictly increasing. We derive a sufficient condition for identifiability, more general than Meilijson's, for the case in which the component distributions are assumed to be analytic. We also show that our necessary condition for identifiability is both necessary and sufficient when the component life distributions are assumed to belong to certain parametric families.

Embedding derivatives of weighted Hardy spaces into Lebesgue spaces

1994 ◽  
Vol 116 (1) ◽  
pp. 151-166 ◽  
Author(s):  
Daniel Girela ◽  
María Lorente ◽  
María Dolores Sarrión
Keyword(s):  
Hardy Space ◽  
Sufficient Conditions ◽  
Studia Math ◽  
Necessary Condition ◽  
Weighted Hardy Spaces ◽  
Borel Measures ◽  
Negative Function ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Derivatives Of

AbstractLet 1 ≤ p < ∞ and let ω be a non-negative function defined on the unit circle T which satisfies the Ap condition of Muckenhoupt. The weighted Hardy space Hp(ω) consists of those functions f in the classical Hardy space H1 whose boundary values belong to Lp(ω). Recently McPhail (Studia Math. 96, 1990) has characterized those positive Borel measures μ on the unit disc Δ for which Hp(ω) is continuously contained in Lp(dμ). In this paper we study the question of finding necessary and sufficient conditions on a positive Borel measure μ on Δ for the differentiation operator D defined by Df = f′ to map Hp(ω) continuously into Lp(dμ). We prove that a necessary condition is that there exists a positive constant C such thatwhere for any interval I ⊂ T,We prove that this condition is also sufficient in some cases, namely for 2 ≤ p < ∞ and ω(et0) = |θ|α, (|θ| ≤ π), – 1 < α < p – 1, but not in general. In the general case we prove the sufficiency of a condition which is slightly stronger than (A).

scholarly journals IDENTIFICATION OF LINEAR REGRESSIONS WITH ERRORS IN ALL VARIABLES

2020 ◽  
pp. 1-31
Author(s):  
Dan Ben-Moshe
Keyword(s):  
Measurement Errors ◽  
Generalized Method Of Moments ◽  
Sufficient Conditions ◽  
Firm Investment ◽  
Second Derivatives ◽  
Method Of Moments Estimator ◽  
Classical Linear Regression ◽  
Necessary And Sufficient ◽  
Derivatives Of ◽  
Linear Regressions

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not identified if and only if an independent normally distributed linear combination of regressors can be transferred from the regressors to the errors. Second, we introduce a new estimator for the coefficients using a continuum of moments that are based on second derivatives of the log characteristic function of the observables. In Monte Carlo simulations, the estimator performs well and is robust to the amount of measurement error and number of mismeasured regressors. In an application to firm investment decisions, the estimates are similar to those produced by a generalized method of moments estimator based on third to fifth moments.

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