Encoding algebraic power series

Algebraic power series are formal power series which satisfy a univariate polynomial equation over the polynomial ring in n variables. This relation determines the series only up to conjugacy. Via the Artin-Mazur theorem and the implicit function theorem it is possible to describe algebraic series completely by a vector of polynomials in n+p variables. This vector will be the code of the series. In the paper, it is then shown how to manipulate algebraic series through their code. In particular, the Weierstrass division and the Grauert-Hironaka-Galligo division will be performed on the level of codes, thus providing a finite algorithm to compute the quotients and the remainder of the division.Comment: 35 page

Continuum discretized BCS approach for weakly bound nuclei

The Bardeen-Cooper-Schrieffer (BCS) formalism is extended by including the single-particle continuum in order to analyse the evolution of pairing in an isotopic chain from stability up to the drip line. We propose a continuum discretized generalized BCS based on single-particle pseudostates (PS). These PS are generated from the diagonalization of the single-particle Hamiltonian within a Transformed Harmonic Oscillator (THO) basis. The consistency of the results versus the size of the basis is studied. The method is applied to neutron rich Oxygen and Carbon isotopes and compared with similar previous works and available experimental data. We make use of the flexibility of the proposed model in order to study the evolution of the occupation of the low-energy continuum when the system becomes weakly bound. We find a larger influence of the non-resonant continuum as long as the Fermi level approaches zero.Comment: 20 pages, 16 figures, to be submitte

Intrinsic structure of two-phonon states in the interacting boson model

A general study of excitations up to two-phonon states is carried out using the intrinsic-state formalism of the Interacting Boson Model (IBM). Spectra and transitions for the different dynamical symmetries are analyzed and the correspondence with states in the laboratory frame is established. The influence of multi-phonon states is discussed. The approach is useful in problems where the complexity of the IBM spectrum renders the analysis in the laboratory frame difficult.Comment: 22 pages, TeX (ReVTeX). 7 eps figures. Submitted to Nucl. Phys.

Critical point symmetries in boson-fermion systems. The case of shape transition in odd nuclei in a multi-orbit model

We investigate phase transitions in boson-fermion systems. We propose an analytically solvable model (E(5/12)) to describe odd nuclei at the critical point in the transition from the spherical to $\gamma$-unstable behaviour. In the model, a boson core described within the Bohr Hamiltonian interacts with an unpaired particle assumed to be moving in the three single particle orbitals j=1/2,3/2,5/2. Energy spectra and electromagnetic transitions at the critical point compare well with the results obtained within the Interacting Boson Fermion Model, with a boson-fermion Hamiltonian that describes the same physical situation.Comment: Phys. Rev. Lett. (in press

Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex

Neural-Network Vector Controller for Permanent-Magnet Synchronous Motor Drives: Simulated and Hardware-Validated Results

This paper focuses on current control in a permanentmagnet synchronous motor (PMSM). The paper has two main objectives: The first objective is to develop a neural-network (NN) vector controller to overcome the decoupling inaccuracy problem associated with conventional PI-based vector-control methods. The NN is developed using the full dynamic equation of a PMSM, and trained to implement optimal control based on approximate dynamic programming. The second objective is to evaluate the robust and adaptive performance of the NN controller against that of the conventional standard vector controller under motor parameter variation and dynamic control conditions by (a) simulating the behavior of a PMSM typically used in realistic electric vehicle applications and (b) building an experimental system for hardware validation as well as combined hardware and simulation evaluation. The results demonstrate that the NN controller outperforms conventional vector controllers in both simulation and hardware implementation

Switchable Lightweight Anti-symmetric Processing (SLAP) with CNN Outspeeds Data Augmentation by Smaller Sample -- Application in Gomoku Reinforcement Learning

To replace data augmentation, this paper proposed a method called SLAP to intensify experience to speed up machine learning and reduce the sample size. SLAP is a model-independent protocol/function to produce the same output given different transformation variants. SLAP improved the convergence speed of convolutional neural network learning by 83% in the experiments with Gomoku game states, with only one eighth of the sample size compared with data augmentation. In reinforcement learning for Gomoku, using AlphaGo Zero/AlphaZero algorithm with data augmentation as baseline, SLAP reduced the number of training samples by a factor of 8 and achieved similar winning rate against the same evaluator, but it was not yet evident that it could speed up reinforcement learning. The benefits should at least apply to domains that are invariant to symmetry or certain transformations. As future work, SLAP may aid more explainable learning and transfer learning for domains that are not invariant to symmetry, as a small step towards artificial general intelligence.Comment: Change title; 6 pages, 8 figure

Survey for Emission-Line Galaxies: Universidad Complutense de Madrid List 3

A new low-dispersion objective-prism search for low-redshift (z<0.045) emission-line galaxies (ELG) has been carried out by the Universidad Complutense de Madrid with the Schmidt Telescope at the Calar-Alto Observatory. This is a continuation of the UCM Survey, which was performed by visual selection of candidates in photographic plates via the presence of the Halpha+[NII]6584 blend in emission. In this new list we have applied an automatic procedure, fully developed by us, for selecting and analyzing the ELG candidates on the digitized images obtained with the MAMA machine. The analyzed region of the sky covers 189 square degrees in nine fields near R.A.=14h & 17h, Dec=25 deg. The final sample contains 113 candidates. Special effort has been made to obtain a large amount of information directly from our uncalibrated plates by using several external calibrations. The parameters obtained for the ELG candidates allow for the study of the statistical properties for the sample.Comment: 13 pages, 18 PostScript figures, 6 JPEG figures, Table 2 corrected. Accepted for publication in Astrophysical Journal Supplements, also available at http://www.ucm.es/info/Astrof/opera/LIST3_ApJS99

A note on the combustion of blends of diesel and soya, sunflower and rapeseed vegetable oils in a light boiler

Producción CientíficaThis paper deals with the study of the vegetable oils (VO) used as fuel for heating. The properties of sunflower, rape and soya oils are studied and these are compared with the properties of C-diesel fuel (used for heating domestic purposes in Spain). The mixtures of VO and diesel are studied and characterized and, finally, the results of a series of combustion trials of the mixtures in a conventional heating installation with a mechanical pulverization burner are presented. The results show that viscosity of VO limits the use of blends up to 40% of them, and the oxygen present in their structures contributes to an efficiency gai