Special functions for the study of economic dynamics : The case of the Lucas-Uzawa model

The special functions are intensively used in mathematical physics to solve differential systems. We argue that their use should be most useful in economic dynamics, notably in the assessment of the transtion dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of the variables in level. In contrast to the preexisting approaches, our method is global and does not rely on dimension reductionSpecial functions; hypergeometric functions; optimal control; Lucas-Uzawa model; economic dynamics

Indices of the iterates of R3R^3-homeomorphisms at Lyapunov stable fixed points

Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we construct orientation preserving homeomorphisms (f:{\Bbb R}^3 \to {\Bbb R}^3) such that (Fix(f)=Per(f)=\{0\}), (0) is Lyapunov stable and (\limsup \frac{|i(f^m, 0)|}{c_m}= \infty). We will use our results to discuss and to point out some strong differences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.Comment: 19 pages, 8 figure

A 10-way power divider based on a transducer and a radial junction operating in the circular TM01 mode

This work presents a 10-way Ku-band power divider using a mode transducer and a radial junction connected by an overmoded circular waveguide operating in the TM 01 mode. The circular symmetry of this mode has been exploited to obtain a power divider with the rectangular output ports radially distributed along the broad wall of the waveguides in H-plane configuration. This topology provides the same amplitude and phase for all the output ports. At the same time, a compact profile has been obtained, introducing a simple manufacturing for the two components of the divider. The first component is a mode transducer converting the TE 10 mode in the rectangular waveguide to the TM 01 mode in the circular waveguide. It is based on a novel topology providing a very high purity in the mode conversion with an attenuation for the other propagating mode, the TE 11c , higher than 60 dB. The second component is a 10-way radial junction that must work under the excitation of the TM 01 , whose special features, since this mode is not the fundamental one of the circular waveguide, will be highlighted. The final design has been validated with an experimental prototype, proposing a manufacturing based on four simple parts. This has been the key to obtain an experimental prototype with specifications in the state-of-the-art. The measured efficiency is better than 96.5% in a 16.7% relative frequency bandwidth from 11 GHz to 13 GHz, with return losses better than 25 dB in the common port. The measured difference between the signals at the output ports of the prototype is ±0.3 dB for the amplitudes and ±0.45° for the phases. A comparison of the obtained results with another divider based on the TE 01 mode shows the potential of the presented design for becoming an alternative to the more extended TE 01 -based power dividersThis work was supported by the Spanish Government through the Agencia Estatal de Investigacion, Fondo Europeo de Desarrollo Regional (AEI/FEDER, UE), under Grant TEC2016-76070-C3-1/2-R (ADDMATE

Physical Conditions in the Inner Narrow-Line Region of the Seyfert 2 Galaxy NGC 1068

The physical conditions in the inner narrow line region (NLR) of the Seyfert 2 galaxy, NGC 1068, are examined using ultraviolet and optical spectra and photoionization models. The spectra are Hubble Space Telescope (HST) Harchive data obtained with the Faint Object Spectrograph (FOS). We selected spectra of four regions, taken through the 0.3" FOS aperture, covering the full FOS 1200A to 6800A waveband. Each region is approximately 20 pc in extent, and all are within 100 pc of the apparent nucleus of NGC 1068. The spectra show similar emission-line ratios from wide range of ionization states for the most abundant elements. After extensive photoionization modeling, we interpret this result as an indication that each region includes a range of gas densities, which we included in the models as separate components. Supersolar abundances were required for several elements to fit the observed emission line ratios. Dust was included in the models but apparently dust to gas fraction varies within these regions. The low ionization lines in these spectra can be best explained as arising in gas that is partially shielded from the ionizing continuum. Although the predicted line ratios from the photoionization models provide a good fit to the observed ratios, it is apparent that the model predictions of electron temperatures in the ionized gas are too low. We interpret this as an indication of additional collisional heating due to shocks and/or energetic particles associated with the radio jet that traverses the NLR of NGC 1068. The density structure within each region may also be the result of compression by the jet.Comment: 38 pages, Latex, includes 5 figures (postscript), to appear in Ap

Development of a high-performance W-band duplexer for plasma diagnosis using a single band with dual circular polarization

Discrepancia entre la información que aparece en el artículo que indica que el copyright es de Elsevier, y la información que aparece en la página de la revista y en el Copyright Clearance Center que indican © 2019 The Authors. Published by Elsevier B.V., así como que el artículo está publicado en Open Access under a Creative Commons licenceThis work presents the design and experimental validation of a high performance, compact, waveguide duplexer operating from 91.5 to 96.5 GHz for its integration in diverse W-band microwave equipment as in plasma diagnosis applications. It uses a single frequency band, with two signals discriminated by different orthogonal circular polarization, which is generated by means of a septum orthomode transducer (OMT) polarizer. Moreover, this component is optimized loaded with the horn antenna for improving the overall system performance. It is explained how these two components are integrated into a very compact duplexer, designed using efficient numerical algorithms. The manufacturing process by mean of high precision milling, and including electrical discharge machining (EDM) has led to excellent performances. The measured return loss level and isolation are higher than 30 dB, and the insertion loss level is below 0.3 dB. Finally, the key parameter in this device, which reflects the symmetry in the manufacturing process, i.e., the axial ratio, is lower than 0.6 dB for both polarizations, an excellent result showing the potential of the presented designThis work was supported by the Spanish government under grants (ADDMATE) TEC2016-76070-C3-1/2-R (Agencia Estatal de Investigación, Spain, Fondo Europeo de Desarrollo Regional: AEI/FEDER/UE) and the program of Comunidad de Madrid, Spain S2013/ICE-3000 (SPADERADARCM

High-performance 16-way Ku-band radial power combiner based on the TE01-circular waveguide mode

This work presents a 16-way Ku-band radial power combiner for high power and high frequency applications, using the very low loss TE01 circular waveguide mode. The accomplished design shows an excellent performance: the experimental prototype has a return loss better than 30 dB, with a balance for the amplitudes of ( 0.15 dB) and ( 2.5 ) for the phases, in a 16.7% fractional bandwidth (2 GHz centered at 12 GHz). For obtaining these outstanding specifications, required, for instance, in highfrequency amplification or on plasma systems, a rigorous step-by-step procedure is presented. First, a high-purity mode transducer has been designed, from the TE10 mode in the rectangular waveguide to the TE01 mode in the circularwaveguide, with very high attenuation (>50 dB) for the other propagating and evanescent modes in the circularwaveguide. This transducer has been manufactured and measured in a back-to-back configuration, validating the design process. Second, an E-plane 16-way radial power divider has been designed, where the power is coupled from the 16 non-reduced-height radial standardwaveguides into the TE01 circularwaveguide mode, improving the insertion loss response and removing the usual tapered transformers of previous designs limiting the power handling. Finally, both the transducer and the divider have been assembled to make the final radial combiner. The prototype has been carefully manufactured, showing very good agreement between the measurements and the full-wave simulationsThe authors would like to thank INMEPRE S.A., the diligence in the manufacturing process. This work was supported by the Spanish government under Grant (ADDMATE) No. TEC2016-76070-C3-1/2-R (AEI/FEDER/UE) and the program of Comunidad de Madrid S2013/ICE-3000 (SPADERADARCM

LICOR-Liquid Columns' Resonances

The aim of the experiment LICOR was the investigation of the axial resonances oi cylindrical liquid columns supported by equal circular coaxiaJ disks. In preparation ot the D-2 experiment a •heoreiical model has been developed, which exactly describes the small amplitude oscillations of finite cylindrical columns between coaxial circular disks. In addition, in terrestrial experiments the resonance frequencies of small liquid columns with up to 5 mm in diameter have been determined and investigations with density-matched liquids (silicon oil in a waierlmethanol mixture) have been performed. For the D-2 experiment LICOR the front disk and the rear disk lor use in the AFPM have been constructed and equipped with pressure sensors and the necessary electronics. The pressure exerted by the oscillating liquid column on trie supporting disks vsas as low as 10 Pa. Since the data downlink of the Materials Research Laboratory was just one signal oer second and channel, it was necessary to determine amplitude and phase of the pressure already in the LICOR disks. The D-2 experiment has been successfully performed. It has fully confirmed the theoretical models and remarkably supplements the experiments on small liquid columns and on density-matched columns

Convex formulation for multi-task L1-, L2-, and LS-SVMs

Quite often a machine learning problem lends itself to be split in several well-defined subproblems, or tasks. The goal of Multi-Task Learning (MTL) is to leverage the joint learning of the problem from two different perspectives: on the one hand, a single, overall model, and on the other hand task-specific models. In this way, the found solution by MTL may be better than those of either the common or the task-specific models. Starting with the work of Evgeniou et al., support vector machines (SVMs) have lent themselves naturally to this approach. This paper proposes a convex formulation of MTL for the L1-, L2- and LS-SVM models that results in dual problems quite similar to the single-task ones, but with multi-task kernels; in turn, this makes possible to train the convex MTL models using standard solvers. As an alternative approach, the direct optimal combination of the already trained common and task-specific models can also be considered. In this paper, a procedure to compute the optimal combining parameter with respect to four different error functions is derived. As shown experimentally, the proposed convex MTL approach performs generally better than the alternative optimal convex combination, and both of them are better than the straight use of either common or task-specific modelsWith partial support from Spain’s grant TIN2016-76406-P. Work supported also by the UAM–ADIC Chair for Data Science and Machine Learning