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Academic literature on the topic 'Constrained BV functions'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Constrained BV functions"

1

Bellettini, Giovanni, Maurizio Paolini, Franco Pasquarelli, and Giuseppe Scianna. "Covers, soap films and BV functions." Geometric Flows 3, no. 1 (March 1, 2018): 57–75. http://dx.doi.org/10.1515/geofl-2018-0005.

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Abstract In this paper we review the double covers method with constrained BV functions for solving the classical Plateau’s problem. Next, we carefully analyze some interesting examples of soap films compatible with covers of degree larger than two: in particular, the case of a soap film only partially wetting a space curve, a soap film spanning a cubical frame but having a large tunnel, a soap film that retracts to its boundary, and various soap films spanning an octahedral frame.
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2

Amato, Stefano, Giovanni Bellettini, and Maurizio Paolini. "Constrained BV functions on covering spaces for minimal networks and Plateau’s type problems." Advances in Calculus of Variations 10, no. 1 (January 1, 2017): 25–47. http://dx.doi.org/10.1515/acv-2015-0021.

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AbstractWe link covering spaces with the theory of functions of bounded variation, in order to study minimal networks in the plane and Plateau’s problem without fixing a priori the topology of solutions. We solve the minimization problem in the class of (possibly vector-valued) $\mathrm{BV}$ functions defined on a covering space of the complement of an ${(n-2)}$-dimensional compact embedded Lipschitz manifold S without boundary. This approach has several similarities with Brakke’s “soap films” covering construction. The main novelty of our method stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. In the case of networks, the constraint is defined using a suitable subset of transpositions of m elements, m being the number of points of S. The model avoids all issues concerning the presence of the boundary S, which is automatically attained. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on Γ-convergence.
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3

ARCANGELIS, RICCARDO DE, ANTONIO GAUDIELLO, and GABRIELLA PADERNI. "SOME CASES OF HOMOGENIZATION OF LINEARLY COERCIVE GRADIENT CONSTRAINED VARIATIONAL PROBLEMS." Mathematical Models and Methods in Applied Sciences 06, no. 07 (November 1996): 901–40. http://dx.doi.org/10.1142/s0218202596000377.

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A homogenization problem for integral functionals defined on Lipschitz functions verifying pointwise oscillating constraints on the gradient is studied in the case in which the constraint takes only the values 0 and +∞. Such situation is of interest in some problems in electrostatics and elastic-plastic torsion theory. An integral representation result on BV-spaces for the “homogenized functional”, and convergence results for minimum values and solutions of Dirichlet and Neumann problems, are proved without assuming any geometrical condition on the set of the zeroes of the constraint and under mild assumptions on the integrands. An application to a concrete problem in electrostatics is also given.
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Bredies, Kristian, and David Vicente. "A perfect reconstruction property for PDE-constrained total-variation minimization with application in Quantitative Susceptibility Mapping." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 83. http://dx.doi.org/10.1051/cocv/2018009.

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We study the recovery of piecewise constant functions of finite bounded variation (BV) from their image under a linear partial differential operator with unknown boundary conditions. It is shown that minimizing the total variation (TV) semi-norm subject to the associated PDE-constraints yields perfect reconstruction up to a global constant under a mild geometric assumption on the jump set of the function to reconstruct. The proof bases on establishing a structural result about the jump set associated with BV-solutions of the homogeneous PDE. Furthermore, we show that the geometric assumption is satisfied up to a negligible set of orthonormal transformations. The results are then applied to Quantitative Susceptibility Mapping (QSM) which can be formulated as solving a two-dimensional wave equation with unknown boundary conditions. This yields in particular that total variation regularization is able to reconstruct piecewise constant susceptibility distributions, explaining the high-quality results obtained with TV-based techniques for QSM.
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5

Cattaneo, Alberto S., Pavel Mnev, and Konstantin Wernli. "Quantum Chern–Simons Theories on Cylinders: BV-BFV Partition Functions." Communications in Mathematical Physics, December 5, 2022. http://dx.doi.org/10.1007/s00220-022-04513-8.

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AbstractWe compute partition functions of Chern–Simons type theories for cylindrical spacetimes $$I \times \Sigma $$ I × Σ , with I an interval and $$\dim \Sigma = 4l+2$$ dim Σ = 4 l + 2 , in the BV-BFV formalism (a refinement of the Batalin–Vilkovisky formalism adapted to manifolds with boundary and cutting–gluing). The case $$\dim \Sigma = 0$$ dim Σ = 0 is considered as a toy example. We show that one can identify—for certain choices of residual fields—the “physical part” (restriction to degree zero fields) of the BV-BFV effective action with the Hamilton–Jacobi action computed in the companion paper (Cattaneo et al., Constrained systems, generalized Hamilton–Jacobi actions, and quantization, arXiv:2012.13270), without any quantum corrections. This Hamilton–Jacobi action is the action functional of a conformal field theory on $$\Sigma $$ Σ . For $$\dim \Sigma = 2$$ dim Σ = 2 , this implies a version of the CS-WZW correspondence. For $$\dim \Sigma = 6$$ dim Σ = 6 , using a particular polarization on one end of the cylinder, the Chern–Simons partition function is related to Kodaira–Spencer gravity (a.k.a. BCOV theory); this provides a BV-BFV quantum perspective on the semiclassical result by Gerasimov and Shatashvili.
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Cattaneo, Alberto S., Pavel Mnev, and Konstantin Wernli. "Constrained systems, generalized Hamilton-Jacobi actions, and quantization." Journal of Geometric Mechanics, 2022, 0. http://dx.doi.org/10.3934/jgm.2022010.

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<p style='text-indent:20px;'>Mechanical systems (i.e., one-dimensional field theories) with constraints are the focus of this paper. In the classical theory, systems with infinite-dimensional targets are considered as well (this then encompasses also higher-dimensional field theories in the hamiltonian formalism). The properties of the Hamilton–Jacobi (HJ) action are described in details and several examples are explicitly computed (including nonabelian Chern–Simons theory, where the HJ action turns out to be the gauged Wess–Zumino–Witten action). Perturbative quantization, limited in this note to finite-dimensional targets, is performed in the framework of the Batalin–Vilkovisky (BV) formalism in the bulk and of the Batalin–Fradkin–Vilkovisky (BFV) formalism at the endpoints. As a sanity check of the method, it is proved that the semiclassical contribution of the physical part of the evolution operator is still given by the HJ action. Several examples are computed explicitly. In particular, it is shown that the toy model for nonabelian Chern–Simons theory and the toy model for 7D Chern–Simons theory with nonlinear Hitchin polarization do not have quantum corrections in the physical part (the extension of these results to the actual cases is discussed in the companion paper [<xref ref-type="bibr" rid="b21">21</xref>]). Background material for both the classical part (symplectic geometry, generalized generating functions, HJ actions, and the extension of these concepts to infinite-dimensional manifolds) and the quantum part (BV-BFV formalism) is provided.</p>
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7

Hafemeyer, D., and F. Mannel. "A path-following inexact Newton method for PDE-constrained optimal control in BV." Computational Optimization and Applications, May 11, 2022. http://dx.doi.org/10.1007/s10589-022-00370-2.

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AbstractWe study a PDE-constrained optimal control problem that involves functions of bounded variation as controls and includes the TV seminorm of the control in the objective. We apply a path-following inexact Newton method to the problems that arise from smoothing the TV seminorm and adding an $$H^1$$ H 1 regularization. We prove in an infinite-dimensional setting that, first, the solutions of these auxiliary problems converge to the solution of the original problem and, second, that an inexact Newton method enjoys fast local convergence when applied to a reformulation of the auxiliary optimality systems in which the control appears as implicit function of the adjoint state. We show convergence of a Finite Element approximation, provide a globalized preconditioned inexact Newton method as solver for the discretized auxiliary problems, and embed it into an inexact path-following scheme. We construct a two-dimensional test problem with fully explicit solution and present numerical results to illustrate the accuracy and robustness of the approach.
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8

Tiwari, Ruchi, Gaurav Tiwari, Akanksha Lahiri, Vadivelan Ramachandran, and Awani Rai. "Melittin: A Natural Peptide with Expanded Therapeutic Applications." Natural Products Journal 10 (December 10, 2020). http://dx.doi.org/10.2174/2210315510999201210143035.

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Background: Apis mellifera, European honey bee venom (BV) is a complex combination of chemical compounds comprising proteins, peptides, enzymes, and other small molecules. Melittin (MEL), which is the key component of BV is considered as an alternative for treatment of various infections. MEL is an amphipathic, cell-penetrating, 26-residue, ahelical anti-hepatoma peptide derived from BV. However, owing to its initial conformational strength and poor stability, melittin is constrained in use as a medication. Objective: The study focused on collective data of therapeutic activities of Bee venom component, MEL. Method: Regardless of its broad variety of biological and possible therapeutic uses, there has been increasing concern in the use of MEL. According to literature, MEL revealed range of activities started from Anti- cancer activity, Anti- microbial activity, Anti- viral activity, Anti-inflammatory activity to Anti- diabetic activity. Present review article summarized therapeutic applications of MEL, their mechanism of action along with recent research progress in field of its delivery. Conclusion: It could be concluded that MEL exerts multiple effects on cellular functions of infected cells.
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9

Davoli, Elisa, Rita Ferreira, and Carolin Kreisbeck. "Homogenization in BV of a model for layered composites in finite crystal plasticity." Advances in Calculus of Variations, October 1, 2019. http://dx.doi.org/10.1515/acv-2019-0011.

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Abstract In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin horizontal strips of an elastically rigid component and a softer one with one active slip system. The energies arising from these modeling assumptions are of integral form, featuring linear growth and non-convex differential constraints. We approach this non-standard homogenization problem via Gamma-convergence. A crucial first step in the asymptotic analysis is the characterization of rigidity properties of limits of admissible deformations in the space BV of functions of bounded variation. In particular, we prove that, under suitable assumptions, the two-dimensional body may split horizontally into finitely many pieces, each of which undergoes shear deformation and global rotation. This allows us to identify a potential candidate for the homogenized limit energy, which we show to be a lower bound on the Gamma-limit. In the framework of non-simple materials, we present a complete Gamma-convergence result, including an explicit homogenization formula, for a regularized model with an anisotropic penalization in the layer direction.
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