Generic rescue: argument alternations and the monotonicity condition

Repairs ◽  
2013 ◽  
Author(s):  
Holden Härtl
Keyword(s):  
Monotonicity Condition

scholarly journals A generalization of the monotonicity condition and applications

2007 ◽  
Vol 115 (3) ◽  
pp. 247-267 ◽  
Author(s):  
D. S. Yu ◽  
S. P. Zhou
Keyword(s):  
Monotonicity Condition

Quasilinearization and boundary value problems at resonance

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Kareem Alanazi ◽  
Meshal Alshammari ◽  
Paul Eloe
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Approximate Solutions ◽  
Monotonicity Condition ◽  
Uniqueness Of Solutions ◽  
Shift Method ◽  
At Resonance ◽  
Problem At Resonance

Abstract A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

scholarly journals Semiparametric Semivariogram Modeling with a Scaling Criterion for Node Spacing: A Case Study of Solar Radiation Distribution in Thailand

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2173
Author(s):  
Sompop Moonchai ◽  
Nawinda Chutsagulprom
Keyword(s):  
Solar Radiation ◽  
Monotonicity Condition ◽  
Ungauged Sites ◽  
Spurious Oscillation ◽  
Geostatistical Interpolation ◽  
Radiation Distribution ◽  
Parametric Functions ◽  
Close Form ◽  
Kriging Approach

Geostatistical interpolation methods, sometimes referred to as kriging, have been proven effective and efficient for the estimation of target quantity at ungauged sites. The merit of the kriging approach relies heavily on the semivariograms in which the parametric functions are prevalently used. In this work, we explore the semiparametric semivariogram where no close-form semivariogram is required. By additionally enforcing the monotonicity condition in order to suppress the presence of spurious oscillation, a scaling of the nodes of the semiparametric kriging is proposed. To this end, the solar radiation estimates across extensive but unmeasured regions in Thailand using three different semivariogram models are undertaken. A cross validation analysis is carried out in order to justify the performance of each approach. The best results are achieved by the semiparametric model with an improvement of around 7–13% compared to those obtained from the parametric semivariograms.

scholarly journals Trigonometric series with a generalized monotonicity condition

2014 ◽  
Vol 30 (8) ◽  
pp. 1289-1296 ◽  
Author(s):  
Lei Feng ◽  
Vilmos Totik ◽  
Song Ping Zhou
Keyword(s):  
Trigonometric Series ◽  
Generalized Monotonicity ◽  
Monotonicity Condition

scholarly journals Constrained Variational-Hemivariational Inequalities on Nonconvex Star-Shaped Sets

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1824
Author(s):  
Stanisław Migórski ◽  
Long Fengzhen
Keyword(s):  
Directional Derivative ◽  
Upper Semicontinuity ◽  
Hemivariational Inequality ◽  
Hemivariational Inequalities ◽  
Strong Monotonicity ◽  
Monotonicity Condition ◽  
Elliptic Type ◽  
Existence Of A Solution ◽  
Locally Lipschitz ◽  
Clarke Subgradient

In this paper, we study a class of constrained variational-hemivariational inequality problems with nonconvex sets which are star-shaped with respect to a certain ball in a reflexive Banach space. The inequality is a fully nonconvex counterpart of the variational-hemivariational inequality of elliptic type since it contains both, a convex potential and a locally Lipschitz one. Two new results on the existence of a solution are proved by a penalty method applied to a variational-hemivariational inequality penalized by the generalized directional derivative of the distance function of the constraint set. In the first existence theorem, the strong monotonicity of the governing operator and a relaxed monotonicity condition of the Clarke subgradient are assumed. In the second existence result, these two hypotheses are relaxed and a suitable hypothesis on the upper semicontinuity of the operator is adopted. In both results, the penalized problems are solved by using the Knaster, Kuratowski, and Mazurkiewicz (KKM) lemma. For a suffciently small penalty parameter, the solution to the penalized problem solves also the original one. Finally, we work out an example on the interior and boundary semipermeability problem that ilustrate the applicability of our results.

scholarly journals INSTRUMENTAL VARIABLE QUANTILE REGRESSION WITH MISCLASSIFICATION

2020 ◽  
pp. 1-36
Author(s):  
Takuya Ura
Keyword(s):  
Quantile Regression ◽  
Instrumental Variable ◽  
Reduced Form ◽  
Outcome Variable ◽  
Annual Review ◽  
Monotonicity Condition ◽  
Treatment Variable ◽  
Treatment Status ◽  
Instrumental Variable Quantile Regression ◽  
Quantile Treatment Effect

This article investigates the instrumental variable quantile regression model (Chernozhukov and Hansen, 2005, Econometrica 73, 245–261; 2013, Annual Review of Economics, 5, 57–81) with a binary endogenous treatment. It offers two identification results when the treatment status is not directly observed. The first result is that, remarkably, the reduced-form quantile regression of the outcome variable on the instrumental variable provides a lower bound on the structural quantile treatment effect under the stochastic monotonicity condition. This result is relevant, not only when the treatment variable is subject to misclassification, but also when any measurement of the treatment variable is not available. The second result is for the structural quantile function when the treatment status is measured with error; the sharp identified set is characterized by a set of moment conditions under widely used assumptions on the measurement error. Furthermore, an inference method is provided in the presence of other covariates.

scholarly journals Definition and Evaluation of the Monotonicity Condition for Preference-based Instruments

Epidemiology ◽  
2015 ◽  
Vol 26 (3) ◽  
pp. 414-420 ◽  
Author(s):  
Sonja A. Swanson ◽  
Matthew Miller ◽  
James M. Robins ◽  
Miguel A. Hernán
Keyword(s):  
Monotonicity Condition

scholarly journals About the infinite dimensional skew and obliquely reflected Ornstein–Uhlenbeck process

2015 ◽  
Vol 18 (04) ◽  
pp. 1550031
Author(s):  
Michael Röckner ◽  
Gerald Trutnau
Keyword(s):  
Real Hilbert Space ◽  
Monotonicity Condition ◽  
Normal Vector ◽  
Reflection Point ◽  
Uhlenbeck Process ◽  
Infinite Dimensional ◽  
Ornstein Uhlenbeck Process ◽  
Integration By Parts Formula ◽  
Regular Convex ◽  
Convex Subsets

Based on an integration by parts formula for closed and convex subsets [Formula: see text] of a separable real Hilbert space [Formula: see text] with respect to a Gaussian measure, we first construct and identify the infinite dimensional analogue of the obliquely reflected Ornstein–Uhlenbeck process (perturbed by a bounded drift [Formula: see text]) by means of a Skorokhod type decomposition. The variable oblique reflection at a reflection point of the boundary [Formula: see text] is uniquely described through a reflection angle and a direction in the tangent space (more precisely through an element of the orthogonal complement of the normal vector) at the reflection point. In case of normal reflection at the boundary of a regular convex set and under some monotonicity condition on [Formula: see text], we prove the existence and uniqueness of a strong solution to the corresponding SDE. Subsequently, we consider an increasing sequence [Formula: see text] of closed and convex subsets of [Formula: see text] and the skew reflection problem at the boundaries of this sequence. We present concrete examples and obtain as a special case the infinite dimensional analogue of the [Formula: see text]-skew reflected Ornstein–Uhlenbeck process.

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