Browsing by Subject "OPERATOR"

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  • Nedic, Mitja (2021)
    In this paper, we give several characterizations of Herglotz-Nevanlinna functions in terms of a specific type of positive semi-definite functions called Poisson-type functions. This allows us to propose a multidimensional analogue of the classical Nevanlinna kernel and a definition of generalized Nevanlinna functions in several variables. Furthermore, a characterization of the symmetric extension of a Herglotz-Nevanlinna function is also given. The subclass of Loewner functions is discussed as well, along with an interpretation of the main result in terms of holomorphic functions on the unit polydisk with non-negative real part.
  • Markkanen, Johannes; Ylä-Oijala, Pasi (2016)
    We study and compare spectral properties of various volume-integral-equation formulations. The equations are written for the electric flux, current, field, and potentials, and discretized with basis functions spanning the appropriate function spaces. Each formulation leads to eigenvalue distributions of different kind due to the effects of discretization procedure, namely, the choice of basis and testing functions. The discrete spectrum of the potential formulation reproduces the theoretically predicted spectrum almost exactly while the spectra of other formulations deviate from the ideal one. It is shown that the potential formulation has the spectral properties desired from the preconditioning perspective. (C) 2016 Elsevier Ltd. All rights reserved.
  • Markkanen, Johannes; Ylä-Oijala, Pasi; Järvenpää, Seppo (IEEE, 2016)
    URSI International Symposium on Electromagnetic Theory
    Spectral properties of current-based volume integral equation of electromagnetic scattering are investigated in the case of isotropic and bi-isotropic objects. Using Helmholtz decomposition the spectrum is derived separately for the solenoidal, irrotational, and harmonic subspaces. Based on this analysis, preconditioning strategies of the matrix equation are discussed.
  • Hytonen, Tuomas; Petermichl, Stefanie; Volberg, Alexander (2019)
    We prove the matrix A(2) conjecture for the dyadic square function, that is, an estimate of the form vertical bar vertical bar S-w vertical bar vertical bar(L2cd(w)-> Lr2) less than or similar to [W](A2), where the focus is on the sharp linear dependence on the matrix A(2) constant. Moreover, we give a mixed estimate in terms of A(2) and A(infinity) constants. The key to the proof is a sparse domination of a process inspired by the integrated form of the matrix-weighted square function.
  • Morgunova, Ekaterina; Yin, Yimeng; Das, Pratyush K.; Jolma, Arttu; Zhu, Fangjie; Popov, Alexander; Xu, You; Nilsson, Lennart; Taipale, Jussi (2018)
    Most transcription factors (TFs) can bind to a population of sequences closely related to a single optimal site. However, some TFs can bind to two distinct sequences that represent two local optima in the Gibbs free energy of binding (Delta G). To determine the molecular mechanism behind this effect, we solved the structures of human HOXB13 and CDX2 bound to their two optimal DNA sequences, CAATAAA and TCGTAAA. Thermodynamic analyses by isothermal titration calorimetry revealed that both sites were bound with similar Delta G. However, the interaction with the CAA sequence was driven by change in enthalpy (Delta H), whereas the TCG site was bound with similar affinity due to smaller loss of entropy (Delta S). This thermodynamic mechanism that leads to at least two local optima likely affects many macromolecular interactions, as Delta G depends on two partially independent variables Delta H and Delta S according to the central equation of thermodynamics, Delta G = Delta H - T Delta S.
  • Kian, Yavar; Kurylev, Yaroslav; Lassas, Matti; Oksanen, Lauri (2019)
    We consider a restricted Dirichlet-to-Neumann map Lambda(T)(S, R) associated with the operator partial derivative(2)(t) - Delta(g) + A + q where Delta(g) is the Laplace-Beltrami operator of a Riemannian manifold (M, g), and A and q are a vector field and a function on M. The restriction Lambda(T)(S, R) corresponds to the case where the Dirichlet traces are supported on (0, T) x S and the Neumann traces are restricted on (0, T) x R. Here S and R are open sets, which may be disjoint, on the boundary of M. We show that Lambda(T)(S, R) determines uniquely, up the natural gauge invariance, the lower order terms A and q in a neighborhood of the set R assuming that R is strictly convex and that the wave equation is exactly controllable from S in time T/2. We give also a global result under a convex foliation condition. The main novelty is the recovery of A and q when the sets R and S are disjoint. We allow A and q to be non-self-adjoint, and in particular, the corresponding physical system may have dissipation of energy. Crown Copyright (C) 2019 Published by Elsevier Inc. All rights reserved.