Search results for "Vector"
showing 10 items of 2660 documents
Extension of the line element-less method to dynamic problems
2020
The line element-less method is an efficient approach for the approximate solution of the Laplace or biharmonic equation on a general bidimensional domain. Introducing generalized harmonic polynomials as approximation functions, we extend the line element-less method to the inhomogeneous Helmholtz equation and to the eigenvalue problem for the Helmholtz equation. The obtained approximate solutions are critically discussed and advantages as well as limitations of the approach are pointed out.
Monotonicity and local uniqueness for the Helmholtz equation
2017
This work extends monotonicity-based methods in inverse problems to the case of the Helmholtz (or stationary Schr\"odinger) equation $(\Delta + k^2 q) u = 0$ in a bounded domain for fixed non-resonance frequency $k>0$ and real-valued scattering coefficient function $q$. We show a monotonicity relation between the scattering coefficient $q$ and the local Neumann-Dirichlet operator that holds up to finitely many eigenvalues. Combining this with the method of localized potentials, or Runge approximation, adapted to the case where finitely many constraints are present, we derive a constructive monotonicity-based characterization of scatterers from partial boundary data. We also obtain the local…
Dimension bounds in monotonicity methods for the Helmholtz equation
2019
The article [B. Harrach, V. Pohjola, and M. Salo, Anal. PDE] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems. The monotonicity inequality states that if two scattering coefficients satisfy $q_1 \leq q_2$, then the corresponding Neumann-to-Dirichlet operators satisfy $\Lambda(q_1) \leq \Lambda(q_2)$ up to a finite-dimensional subspace. Here we improve the bounds for the dimension of this space. In particular, if $q_1$ and $q_2$ have the same number of positive Neumann eigenvalues, then the finite-dimensional space is trivial. peerReviewed
Behavior of a Short preS1 Epitope on the Surface of Hepatitis B Core Particles
1999
The major immunodominant region of hepatitis B core particles is widely recognized as the most prospective target for the insertion of foreign epitopes, ensuring their maximal antigenicity and immunogenicity. This region was mapped around amino acid residues 79-81, which were shown by electron cryo-microscopy to be located on the tips of the spikes protruding from the surface of hepatitis B core shells. Here we tried to expose a model sequence, the short immunodominant hepatitis B preS1 epitope 31-DPAFR-35, onto the tip of the spike, with simultaneous deletion of varying stretches from the major immunodominant region of the HBc molecule. Accessibility to the monoclonal anti-preS1 antibody M…
Overexpression of STAT-1 by adenoviral gene transfer does not inhibit hepatitis B virus replication.
2006
Objectives Interferons are known to inhibit the replication of hepatitis B viruses (HBV) in several animal models in vitro and in vivo as well in humans. The STAT-1 protein plays a central role in the biological activity of both type I and type II interferons. The lack of functional STAT-1 renders cells and organisms susceptible to bacterial and viral infectious agents. We analysed whether the overexpression of STAT-1 protein enhances the biological interferon response and whether it elicits antiviral acitivity against HBV in vitro. Methods To achieve an efficient STAT-1 overexpression in primary liver cells and hepatoma cells, we generated a recombinant, replication-deficient adenovirus ex…
The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials
2003
We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansa…
Are most of the stationary points in a molecular association minima? Application of Fraga's potential to benzene-benzene
1993
The importance of characterizing the stationary points of the intermolecular potential by means of Hessian eigenvalues is illustrated for the calculation of the benzene–benzene interaction using an atom-to-atom pair potential proposed by Fraga (FAAP). Two models, the standard one-center-per atom and another using three-centers-per atom due to Hunter and Sanders, are used to evaluate the electrostatic contributions and the results are compared. It is found in both cases that although using low-gradient thresholds allows optimization procedures to avoid many stationary points that are not true minima computing time considerations makes the usual procedure of using high-gradient thresholds [sa…
AMYR 2: A new version of a computer program for pair potential calculation of molecular associations
1998
AMYR is a computer program for the calculation of molecular associations using Fraga's pairwise atom-atom potential. The interaction energy is evaluated through a 1R expansion. The electrostatic energy is calculated through either the one-centre-per atom or the three-centres-per atom model by Hunter and Sanders. A pairwise dispersion energy term is included in the potential and corrected by a damping function. The program carries out energy minimizations through variable metric methods. The new version allows for the stationary point analysis of the intermolecular potential by means of the Hessian eigenvalues. Although using low-gradient thresholds optimization procedures to avoid many stat…
Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids
2018
The critical points analysis of electron density,i.e. ρ(x), fromab initiocalculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points,i.e. such that ∇ρ(xc) = 0 and λ1, λ2, λ3≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) atxc], towards degenerate critical points,i.e. ∇ρ(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood ofxcand allo…
Comparison results for Hessian equations via symmetrization
2007
where the λ’s are the eigenvalues of the Hessian matrix D2u of u and Sk is the kth elementary symmetric function. For example, for k = 1, S1(Du) = 1u, while, for k = n, Sn(D 2u) = detD2u. Equations involving these operators, and some more general equations of the form F(λ1, . . . , λn) = f in , (1.2) have been widely studied by many authors, who restrict their considerations to convenient cones of solutions with respect to which the operator in (1.2) is elliptic. Following [25] we define the cone 0k of ellipticity for (1.1) to be the connected component containing the positive cone 0 = {λ ∈ R : λi > 0 ∀i = 1, . . . , n} of the set where Sk is positive. Thus 0k is an open, convex, symmetric…