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It is well-known that the (a,b)-way Karatsuba algorithm (KA) with a\neq b is used for efficient digit-serial multiplication with subquadratic space complexity architecture. In this paper, based on (a,b)-way KA decomposition, we have derived a novel k-way block recombination KA (BRKA) decomposition for digit-serial multiplication. The proposed k-way BRKA is formed by a power of 2 polynomial decomposition. By theoretical analysis, it is shown that k-way BRKA can provide the necessary tradeoff between space and time complexity. Using (4,2)-way KA to construct the proposed k-way BRKA architecture in GF(2^409), it is shown that the proposed 2-way BRKA approach requires less area, and the proposed 8-way BRKA approach requires less computation time and less area-time product compared to compared the existing (a,b)-way KA decomposition. [ABSTRACT FROM PUBLISHER]

In open-shell atoms and ions, processes such as photoionization, combination (Raman) scattering, electron scattering, and recombination are often mediated by many-electron compound resonances. We show that their interference (neglected in the independent-resonance approximation) leads to a coherent contribution, which determines the energy-averaged total cross sections of electron- and photon-induced reactions obtained using the optical theorem. In contrast, the partial cross sections (e.g., electron recombination or photon Raman scattering) are dominated by the stochastic contributions. Thus, the optical theorem provides a link between the stochastic and coherent contributions of the compound resonances. Similar conclusions are valid for reactions via compound states in molecules and nuclei. [ABSTRACT FROM AUTHOR]

Highly excited eigenstates of atoms and ions with open f shell are chaotic superpositions of thousands, or even millions, of Hartree-Fock determinant states. The interaction between dielectronic and multielectronic configurations leads to the broadening of dielectronic recombination resonances and relative enhancement of photon emission due to opening of thousands of radiative decay channels. The radiative yield is close to 100% for electron energy ≲ 1 eV and rapidly decreases for higher energies due to opening of many autoionization channels. The same mechanism predicts suppression of photoionization and relative enhancement of the Raman scattering. Results of our calculations of the recombination rate are in agreement with the experimental data for W20+ and Au25+ [ABSTRACT FROM AUTHOR]

Ternary electron-assisted collisional radiative recombination (E-CRR) and neutral-assisted radiative recombi-nation (N-CRR) have very strong negative temperature dependencies and hence dominate electron recombination in some plasmas at very low temperatures. However, there are only few data for molecular ions and almost none for atomic ions at temperatures much below 300 K. In this experimental study we used a cryogenic afterglow plasma experiment (Cryo-FALP II) at temperatures from 50 K to 100 K to measure ternary recombination rate coefficients for Ar+ ions in ambient helium gas. The measured magnitudes and the temperature dependencies of the ternary recombination rate coefficients for electron-assisted and neutral-assisted collisional radiative recombination agree well with theoretical predictions (KE-CRR ~ T-4.5 and KHe-CRR ~ T-2.5 to T-2.9) over a broad range of electron and He densities. [ABSTRACT FROM AUTHOR]

We present theoretical studies of high-order harmonic generation (HHG) driven by plasmonic fields in two-electron atomic systems. Comparing the single- and two-electron active approximation models of the hydrogen negative ion, we provide strong evidence that a nonsequential double-electron recombination mechanism appears to be mainly responsible for the HHG cutoff extension. Our analysis is carried out by means of a reduced one-dimensional numerical integration of the two-electron time-dependent Schrödinger equation, and on investigations of the classical electron trajectories, resulting from the Newton's equation of motion. Additional comparisons between the hydrogen negative ion and the helium atom suggest that the double recombination process depends distinctly on the atomic target. Our research paves the way to the understanding of strong field processes in multielectronic systems driven by spatially inhomogeneous fields. [ABSTRACT FROM AUTHOR]