Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems

We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family of admissible trajectories may lack important compactness properties. In the first part of the paper we show that the existence of a $p_0$-minimum restraint function provides not only global asymptotic controllability (despite non-transversality) but also a state-dependent upper bound for the value function (provided $p_0>0$). This extends to unbounded dynamics a former result which heavily relied on the compactness of the control set. In the second part of the paper we apply the general result to the case when the system is polynomial in the control variable. Some elementary, algebraic, properties of the convex hull of vector-valued polynomials' ranges allow some simplifications of the main result, in terms of either near-affine-control systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344

Moving constraints as stabilizing controls in classical mechanics

The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms which are linear or quadratic w.r.t.time derivatives of the control functions. After reviewing the basic equations, we explain the significance of the quadratic terms, related to geodesics orthogonal to a given foliation. We then study the problem of stabilization of the system to a given point, by means of oscillating controls. This problem is first reduced to the weak stability for a related convex-valued differential inclusion, then studied by Lyapunov functions methods. In the last sections, we illustrate the results by means of various mechanical examples.Comment: 52 pages, 4 figure

Observing System Simulation Experiments for the assessment of temperature sampling strategies in the Mediterranean Sea

International audienceFor the first time in the Mediterranean Sea various temperature sampling strategies are studied and compared to each other by means of the Observing System Simulation Experiment technique. Their usefulness in the framework of the Mediterranean Forecasting System (MFS) is assessed by quantifying their impact in a Mediterranean General Circulation Model in numerical twin experiments via univariate data assimilation of temperature profiles in summer and winter conditions. Data assimilation is performed by means of the optimal interpolation algorithm implemented in the SOFA (System for Ocean Forecasting and Analysis) code. The sampling strategies studied here include various combinations of eXpendable BathyThermograph (XBT) profiles collected along Volunteer Observing Ship (VOS) tracks, Airborne XBTs (AXBTs) and sea surface temperatures. The actual sampling strategy adopted in the MFS Pilot Project during the Targeted Operational Period (TOP, winter-spring 2000) is also studied. The data impact is quantified by the error reduction relative to the free run. The most effective sampling strategies determine 25?40% error reduction, depending on the season, the geographic area and the depth range. A qualitative relationship can be recognized in terms of the spread of information from the data positions, between basin circulation features and spatial patterns of the error reduction fields, as a function of different spatial and seasonal characteristics of the dynamics. The largest error reductions are observed when samplings are characterized by extensive spatial coverages, as in the cases of AXBTs and the combination of XBTs and surface temperatures. The sampling strategy adopted during the TOP is characterized by little impact, as a consequence of a sampling frequency that is too low. Key words. Oceanography: general (marginal and semi-enclosed seas; numerical modelling

HJ Inequalities Involving Lie Brackets and Feedback Stabilizability with Cost Regulation

With reference to an optimal control problem where the state has to approach asymptotically a closed target while paying a non-negative integral cost, we propose a generalization of the classical dissipative relation that defines a Control Lyapunov Function to a weaker differential inequality. The latter involves both the cost and the iterated Lie brackets of the vector fields in the dynamics up to a certain degree k = 1, and we call any of its (suitably defined) solutions a degree -k Minimum Restraint Function. We prove that the existence of a degree -k Minimum Restraint Function allows us to build a Lie-bracket-based feedback which sample stabilizes the system to the target while regulating (i.e., uniformly bounding) the cost

Optical properties of the NGC 5328 group of galaxies

We present the results of a photometric and spectroscopic study of seven members of the NGC 5328 group of galaxies, a chain of galaxies spanning over 200 kpc (H_0 = 70 km/s/Mpc). We analyze the galaxy structure and study the emission line properties of the group members looking for signatures of star formation and AGN activity. We finally attempt to infer, from the modeling of line-strength indices, the stellar population ages of the early-type members. We investigate also the presence of a dwarf galaxy population associated with the bright members. The group is composed of a large fraction of early-type galaxies including NGC 5328 and NGC 5330, two bona fide ellipticals at the center of the group. In both galaxies no recent star formation episodes are detected by the H_beta vs. MgFe indices of these galaxies. 2MASX J13524838-2829584 has extremely boxy isophotes which are believed to be connected to a merging event: line strength indices suggest that this object probably had a recent star formation episode. A warped disc component emerges from the model subtracted image of 2MASX J13530016-2827061 which is interpreted as a signature of an ongoing interaction with the rest of the group. Ongoing star formation and nuclear activity is present in the projected outskirts of the group. The two early-type galaxies 2MASX J13523852-2830444 and 2MASX J13525393-2831421 show spectral signatures of star formation, while a Seyfert 2 type nuclear activity is detected in MCG -5-33-29.Comment: 18 pages, 12 figures, accepted for publication in MNRA

Nearby early-type galaxies with ionized gas.II. Line-strength indices for 18 additional galaxies

Rampazzo et al. 2005 (Paper I) presented a data-set of line-strength indices for 50 early-type galaxies in the nearby Universe. The galaxy sample is biased toward galaxies showing emission lines, located in environments corresponding to a broad range of local galaxy densities, although predominantly in low density environments. The present addendum to Paper I enlarges the above data-set of line-strength indices by analyzing 18 additional early-type galaxies (three galaxies, namely NGC 3607, NGC 5077 and NGC 5898 have been already presented in the previous set). As in Paper I, we measured 25 line-strength indices, defined by the Lick IDS "standard" system (Trager et al. 1998; Worthey & Ottaviani 1997), for 7 luminosity weighted apertures and 4 gradients of each galaxy. This paper presents the line-strength data-set and compares it with the available data in the literature.Comment: 18 pages, A&A in pres

Galaxy evolution in nearby groups. II. Galaxy evolution in nearby loose groups. II. Photometric and kinematic characterization of USGC U268 and USGC U376 group members in the Leo cloud

We present the photometric and kinematic characterization of two groups, USGC U268 and USGC U376 located in different regions of the Leo cloud. U268, composed of 10 catalogued members and 11 new added members, has a small fraction (~24%) of early-type galaxies (ETGs). U376 has 16 plus 8 new added members, with ~38% of ETGs. We find the presence of significant substructures in both groups suggesting that they are likely accreting galaxies. U268 is located in a more loose environment than U376. For each member galaxy, broad band integrated and surface photometry have been obtained in far-UV and near-UV with GALEX, and in u,g, r, i, z (SDSS) bands. H_alpha imaging and 2D high resolution kinematical data have been obtained using PUMA Scanning Fabry-Perot interferometer at the 2.12 m telescope in San Pedro M\'artir, (Baja California, M\'exico). We improved the galaxy classification and we detected morphological and kinematical distortions that may be connected to either on-going and/or past interaction/accretion events or environmental induced secular evolution. U268 appears more active than U376, with a large fraction of galaxies showing interaction signatures (60% vs. 13%). The presence of bars among late-type galaxies is ~10% in U268 and ~$29% in U376. The cumulative distribution of (FUV - NUV) colours of galaxies in U268 is significantly different than that in U376 with galaxies in U268 bluer than those in U376. In the (FUV-r vs. M_r) and (NUV-r vs. M_r) planes no members of U268 are found in the `red sequence', even early-type galaxies lie in the `blue sequence' or in the `green valley'. Most (80%) of the early-type members in U376 inhabits the `red sequence, a large fraction of galaxies, of different morphological types, are located in the `green valley', while the `blue sequence' is under-populated with respect to U268.Comment: 27 pages, 11 figures, 8 tables, accepted for publication in MNRAS (abridged abstract

Cell Cycle-dependent Metabolism of Pyrimidine Deoxynucleoside Triphosphates in CEM Cells

We incorporated 3H-labeled thymidine, deoxycytidine, or cytidine into dNTPs and DNA of exponentially growing CEM cells. G1 and S phase cells were separated by centrifugal elutriation, and the size and specific activity of dNTP pools were determined to study the cell cycle-dependent regulation of specific dNTP synthesizing enzymes in their metabolic context. With [3H]thymidine, we confirm the earlier demonstrated S phase specificity of thymidine kinase. Incorporation of radioactivity from [5-3H]deoxycytidine into dCTP occurred almost exclusively in G1 cells. During S phase, de novo synthesis by ribonucleotide reductase was switched on, resulting in a 70-fold dilution of [3H]dCTP, confirming that ribonucleotide reductase is an S phase-specific enzyme, whereas deoxycytidine kinase is not. [5-3H]Cytidine appeared in dCTP almost to the same extent in G1 as in S phase, despite the S phase specificity of ribonucleotide reductase. During S phase, DNA replication greatly increased the turnover of dCTP, requiring a corresponding increase in ribonucleotide reductase activity. During G1, the enzyme maintained activity to provide dNTPs for DNA repair and mitochondrial DNA synthesis. The poor incorporation of isotope from deoxycytidine into DNA earlier led to the suggestion that the nucleoside is used only for DNA repair (Xu, Y-Z., Peng, H., and Plunkett, W. (1995) J. Biol. Chem. 270, 631-637). The poor phosphorylation of deoxycytidine in S phase provides a better explanation