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Papers by Gabriel Dimitriu

Springer eBooks, 2005

In this paper we present an approximation framework and convergence results for the identificatio... more In this paper we present an approximation framework and convergence results for the identification of a nonlinear damping function in a thermoelastic system. A functional technique is used to demonstrate that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem. An example and numerical studies are discussed.

Journal of Computational and Applied Mathematics, 2017

Nucleation and Atmospheric Aerosols, 2016

Motivated by the fact that bounded variation (often discontinuous) functions frequently appear wh... more Motivated by the fact that bounded variation (often discontinuous) functions frequently appear when studying integral equations that describe physical phenomena, we focus on the existence of bounded variation solutions for Urysohn integral measure driven equations. Due to numerous applications of Urysohn integral equations in various domains, problems of this kind have been extensively studied in literature, under more restrictive assumptions. Our approach concerns the framework of Kurzweil-Stieltjes integration, which allows the occurrence of high oscillatory features on the right hand side of the equation. A discussion about interesting consequences of our main result (given by particular cases of the measure driving the equation) is presented. Finally, we show the generality of our results by investigating two examples of impulsive type problems (from both theoretical and numerical perspective) and giving an application in electronics industry concerning polarization properties of ferroelectric materials.

Springer eBooks, May 13, 2007

Springer eBooks, Nov 11, 2005

This study analyzes some mathematical aspects of data assimilation for atmospheric chemistry mode... more This study analyzes some mathematical aspects of data assimilation for atmospheric chemistry models based on variational approaches. Of interest here are the so called adjoint methods which are particularly efficient to mathematically solve the variational problem. Details concerning operator splitting, adjoint and gradient computations are also discussed.

PubMed, Feb 11, 2014

Measurement of arterial stiffness is an accurate method of assessment of endothelial dysfunction,... more Measurement of arterial stiffness is an accurate method of assessment of endothelial dysfunction, together with other noninvasive methods, in the diagnosis of atherosclerotic burden in patients with MetS. Material and methods: The study included 63 patients: MetS group (18 men, 20 women, mean age 58.86 +/- 8.86 years) and the control group (14 men, 11 women, mean age 59.68 +/- 10.0 years). They underwent the following examinations: assessment of arterial stiffness--pulse wave velocity (PWVao), augmentation index of brachial artery (Aixbr) and aorta (Aixao), central systolic blood pressure (SBPao); carotid ultrasound for detection of plaques and measurement of intima-media thickness (IMT); echocardiography--left ventricular hypertrophy (LVH); ankle-brachial index (ABI); biochemical parameters: C-reactive protein (CRP), fibrinogen (Fb), cholesterol (Col), HDLcol, LDLcol and triglycerides. Results: MetS patients had higher PWVao (10.06 +/- 2.12 m/s vs 8.29 +/- 1.33 m/s, p = 0.0001) and SBPao (135.06 +/- 19.80 mmHg vs. 121.76 +/- 18.62 mmHg, p = 0.009). Carotid IMT was higher in MetS group (0.92 +/- 0.11 vs. 0.83 +/- 0.10 mm, p = 0.003). Almost all MetS patients were hypertensive (94.7% vs. 52%, p = 0.01); LVH was present in 57.9% of MetS patients and 20% of the controls (p = 0.05). The MetS group presented higher Col (208.76 +/- 38.41 vs. 176.20 +/- 30.08 mg/dl, p = 0.0003) and CRP levels (0.872 +/- 0.852 mg/dl vs. 0.476 +/- 0.392 mg/dl, p = 0.01). Conclusions: In MetS patients the most reliable marker of arterial stiffness was PWVao, followed by SBPao. Higher values of carotid IMT are also parameters of high atherosclerotic risk. CRP and Col can be considered biomarkers of high risk in MetS.

Lecture Notes in Computer Science, 2008

Computers & mathematics with applications, Jul 1, 2014

Computers & mathematics with applications, May 1, 2008

Kalman filtering has become a powerful framework for solving data assimilation problems. Of inter... more Kalman filtering has become a powerful framework for solving data assimilation problems. Of interest here are the low-rank filters which are computationally efficient for solving large-scale data assimilation problems. Together with theoretical aspects on the basis of which some common low-rank filters are designed, the paper also presents numerically comparative results of data assimilation using an air pollution model. The performance of such filters, as depending on the distance between the measurement locations and emission points, is investigated.

Springer eBooks, 2006

In the past decade the variational methods (3D-var, 4D-var) have been successfully applied in met... more In the past decade the variational methods (3D-var, 4D-var) have been successfully applied in meteorological data assimilation and showed promising results for atmospheric chemistry models. In this paper we describe adjoint computations in data assimilation problems using a 4-stage Rosenbrock method. The order 4 formula is L-stable and has an embedded order 3 formula for error control.

Lecture Notes in Computer Science, 2001

In this paper we establish a convergence rate result for a parameter identification problem. We s... more In this paper we establish a convergence rate result for a parameter identification problem. We show that the convergence rate of a convection parameter in an elliptic equation with Dirichlet boundary conditions is O( Ö{d&lt;/font &gt;} ) \mathcal{O}\left( {\sqrt \delta } \right) , where δ is a norm bound for the noise in the data.

Nucleation and Atmospheric Aerosols, 2019

International Journal of Computer Mathematics, 1998

An optimal control problem for a parabolic equation closely related to an identification problem ... more An optimal control problem for a parabolic equation closely related to an identification problem is considered. This is an application of an abstract existence result of Barbu and Seidman [1]. An approximation scheme based on a discretization using finite differences and an algorithm are presented. Numerical results and conclusions drawn from the computational studies are reported.