Results 211 to 220 of about 3,084 (253)

Dual neuromodulatory dynamics underlie birdsong learning. [PDF]

open access: yesNature
Qi J   +4 more
europepmc   +1 more source

Regularized Trace of the Cauchy Transform

Integral Equations and Operator Theory, 2012
The author discusses the regularized trace of the Cauchy transform \(C_{\Omega}\). He provides a more explicit formula for the regularized trace of the operator \(C_{\Omega}^{*}C_{\Omega}\). A detailed proof of the main theorem is given.
exaly   +3 more sources

The Norm and Regularized Trace of the Cauchy Transform

Mathematical Notes, 2005
Let \(D\) be the unit disk, the Cauchy transform is defined to be \[ \mathcal C_\omega f(z):=-\frac 1\pi \int_{D}\frac{f(\xi)}{\xi-z}d\mu(\xi) , \] where \(f\in L^2(D,d\mu)\), \(d\mu = \omega(| z| )dA(z)\), with \(dA\) being the Lebesgue measure and \(\omega \in C^1(0,1)\) being a positive function such that \[ \frac {\omega(x)}x\int_0^xt\omega(t)dt\in
exaly   +2 more sources

Regularized trace of the Dirac operator

Mathematical Notes, 2015
In this paper, the author considers one-dimensional Dirac operators in \(L_2((0,\pi); \mathbb{C}^2)\) with \(L_2\)-potential and periodic, antiperiodic and Dirichlet boundary conditions, particularly in the non-selfadjoint case. By using similarity transforms and Fourier techniques, formulas for the regularized trace are derived.
exaly   +3 more sources

Regular and context-free nominal traces

Acta Informatica, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DEGANO, PIERPAOLO   +2 more
openaire   +3 more sources

Regularized traces of integrodifferential operators

Mathematical Notes of the Academy of Sciences of the USSR, 1988
Let T be a self-adjoint operator with discrete spectrum \(\{\lambda_ n\}\) in a separable Hilbert space and let \(\sum_{| \lambda_ n| \leq \lambda}1=O(\lambda^ p)\) as \(\lambda\) \(\to \infty\) with ...
Lyubishkin, V. A., Tsopanov, I. D.
openaire   +3 more sources

Weak $ω$-Regular Trace Languages

CoRR, 2014
Mazurkiewicz traces describe concurrent behaviors of distributed systems. Trace-closed word languages, which are "linearizations" of trace languages, constitute a weaker notion of concurrency but still give us tools to investigate the latter. In this vein, our contribution is twofold.
Namit Chaturvedi, Marcus Gelderie
openaire   +2 more sources

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