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The Improper and Dominated Integrals
In Chap. 6 we discuss the improper and dominated integrals; in particular, the latter addresses the question as to when a function is majorized by a...
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A SUPG formulation augmented with shock-capturing for solving convection-dominated reaction–convection–diffusion equations
In this computational study, stabilized finite element solutions of convection-dominated stationary and linear reaction–convection–diffusion...
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The Anisotropic Total Variation and Surface Area Measures
We prove a formula for the first variation of the integral of a log-concave function, which allows us to define the surface area measure of such a...
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Experimental Investigation of Spanwise-Periodic Surface Heating for Control of Crossflow-Dominated Laminar-Turbulent Transition
An actuation concept for control of crossflow-dominated laminar-turbulent transition is investigated which has not received much attention in this...
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Examples of Finite Quadratic Variation Processes
This chapter focuses on the class of finite quadratic variation processes and provides several examples. Among them one can find the Föllmer-Wu-Yor...
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Hyper-reduction for parametrized transport dominated problems via adaptive reduced meshes
We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential...
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Metric Approximation of Set-Valued Functions of Bounded Variation by Integral Operators
We introduce an adaptation of integral approximation operators to set-valued functions (SVFs, multifunctions), map** a compact interval [ a , b ] into...
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It \( {\hat{\text{o}}} \) Integration and Quadratic Variation
Local and finite-variation martingales, completeness, covariation, continuity, norm comparison, uniform integrability, Cauchy-type inequalities,...
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Bounded Variation Solution for a Class of Kirchhoff Type Problem Involving the 1-Laplacian Operator
In this work, we study the existence of a nontrivial bounded variation solution to a class of nonlocal elliptic problems of Kirchhoff type involving...
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Quasiconformal deformation of the chordal Loewner driving function and first variation of the Loewner energy
We derive the variational formula of the Loewner driving function of a simple chord under infinitesimal quasiconformal deformations with Beltrami...
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Linear Instability of Shock-Dominated Laminar Hypersonic Separated Flows
The self-excited spanwise homogeneous perturbations arising in shock-wave/boundary-layer interaction (SWBLI) system formed in a hypersonic flow of...
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On the definition of solution to the total variation flow
We show that the notions of weak solution to the total variation flow based on the Anzellotti pairing and the variational inequality coincide under...
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High-dimensional estimation of quadratic variation based on penalized realized variance
In this paper, we develop a penalized realized variance (PRV) estimator of the quadratic variation (QV) of a high-dimensional continuous Itô...
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A new space of generalised functions with bounded variation motivated by fracture mechanics
We introduce a new space of generalised functions with bounded variation to prove the existence of a solution to a minimum problem that arises in the...