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Unconditionally convergent series of operators and narrow operators on $L_1$  [PDF]
Vladimir Kadets,Nigel Kalton,Dirk Werner
Mathematics , 2003,
Abstract: We introduce a class of operators on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$ into a space with an unconditional basis belongs to this class.
Convergent Iterative Solutions of Schroedinger Equation for a Generalized Double Well Potential  [PDF]
R. Friedberg,T. D. Lee,W. Q. Zhao
Physics , 2007, DOI: 10.1016/j.aop.2007.09.006
Abstract: We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with a generalized double well potential $V=\frac{g^2}{2}(x^2-1)^2(x^2+a)$. The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameter $a$ are discussed.
Can any unconditionally convergent multiplier be transformed to have the symbol (1) and Bessel sequences by shifting weights?  [PDF]
Diana T. Stoeva,Peter Balazs
Mathematics , 2011, DOI: 10.1016/j.jmaa.2012.10.007
Abstract: Multipliers are operators that combine (frame-like) analysis, a multiplication with a fixed sequence, called the symbol, and synthesis. They are very interesting mathematical objects that also have a lot of applications for example in acoustical signal processing. It is known that bounded symbols and Bessel sequences guarantee unconditional convergence. In this paper we investigate necessary and equivalent conditions for the unconditional convergence of multipliers. In particular we show that, under mild conditions, unconditionally convergent multipliers can be transformed by shifting weights between symbol and sequence, into multipliers with symbol (1) and Bessel sequences.
Shape Deformations in Atomic Nuclei  [PDF]
Ikuko Hamamoto,Ben R. Mottelson
Physics , 2011, DOI: 10.4249/scholarpedia.10693
Abstract: The ground states of some nuclei are described by densities and mean fields that are spherical, while others are deformed. The existence of non-spherical shape in nuclei represents a spontaneous symmetry breaking.
Muhammad Raza,Farooq Ahmad,Sifat Hussain
Academic Research International , 2012,
Abstract: In this paper we present fourth-order convergent two-step iterative algorithm for solving non-linear equations. This algorithm is refinement of the existing iterative algorithms. Numerical experiment shows this fact.
Iterative Solution for Generalized Sombrero-shaped Potential in $N$-dimensional Space  [PDF]
W. Q. Zhao
Physics , 2007,
Abstract: An explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with generalized $N$-dimensional Sombrero-shaped potential is presented. The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameters are discussed.
A Convergent Iterative Solution of the Quantum Double-well Potential  [PDF]
R. Friedberg,T. D. Lee,W. Q. Zhao,A. Cimenser
Physics , 2001, DOI: 10.1006/aphy.2001.6187
Abstract: We present a new convergent iterative solution for the two lowest quantum wave functions $\psi_{ev}$ and $\psi_{od}$ of the Hamiltonian with a quartic double well potential $V$ in one dimension. By starting from a trial function, which is by itself the exact lowest even or odd eigenstate of a different Hamiltonian with a modified potential $V+\delta V$, we construct the Green's function for the modified potential. The true wave functions, $\psi_{ev}$ or $\psi_{od}$, then satisfies a linear inhomogeneous integral equation, in which the inhomogeneous term is the trial function, and the kernel is the product of the Green's function times the sum of $\delta V$, the potential difference, and the corresponding energy shift. By iterating this equation we obtain successive approximations to the true wave function; furthermore, the approximate energy shift is also adjusted at each iteration so that the approximate wave function is well behaved everywhere. We are able to prove that this iterative procedure converges for both the energy and the wave function at all $x$.
When Shape Matters: Deformations of Tiling Spaces  [PDF]
Alex Clark,Lorenzo Sadun
Mathematics , 2003,
Abstract: We investigate the dynamics of tiling dynamical systems and their deformations. If two tiling systems have identical combinatorics, then the tiling spaces are homeomorphic, but their dynamical properties may differ. There is a natural map ${\mathcal I}$ from the parameter space of possible shapes of tiles to $H^1$ of a model tiling space, with values in $\R^d$. Two tiling spaces that have the same image under ${\mathcal I}$ are mutually locally derivable (MLD). When the difference of the images is ``asymptotically negligible'', then the tiling dynamics are topologically conjugate, but generally not MLD. For substitution tilings, we give a simple test for a cohomology class to be asymptotically negligible, and show that infinitesimal deformations of shape result in topologically conjugate dynamics only when the change in the image of ${\mathcal I}$ is asymptotically negligible. Finally, we give criteria for a (deformed) substitution tiling space to be topologically weakly mixing.
Research on Convergent Speed of Iterative Learning Control

WEI Yan-ding,

控制理论与应用 , 2001,
Abstract: Convergent speed of iterative leaming control (ILC) is discussed from three factors of learning law, learning law's parameters and output errors. Some useful conclusions are gotten for improving convergent speed of this kind of algorithm.
Convergent Iterative Solutions for a Sombrero-Shaped Potential in Any Space Dimension and Arbitrary Angular Momentum  [PDF]
R. Friedberg,T. D. Lee,W. Q. Zhao
Physics , 2005, DOI: 10.1016/j.aop.2005.11.009
Abstract: We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with an $N$-dimensional radial potential $V=\frac{g^2}{2}(r^2-1)^2$ and an angular momentum $l$. For $g$ large, the rate of convergence is similar to a power series in $g^{-1}$.
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