Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.Comment: 19 pages, 1 figur

Nearby early-type galaxies with ionized gas. The UV emission from GALEX observations

We present GALEX far-ultraviolet (FUV, $\lambda_{eff}$=1538 \AA) and near-ultraviolet (NUV, $\lambda_{eff}$=2316 \AA) surface photometry of 40 early-type galaxies (ETGs) selected from a wider sample of 65 nearby ETGs showing emission lines in their optical spectra. We derive FUV and NUV surface brightness profiles, (FUV-NUV) colour profiles and D$_{25}$ integrated magnitudes. We extend the photometric study to the optical {\it r} band from SDSS imaging for 14 of these ETGs. In general, the (FUV-NUV) radial colour profiles become redder with galactocentric distance in both rejuvenated ($\leq 4$ Gyr) and old ETGs. Colour profiles of NGC 1533, NGC 2962, NGC 2974, NGC 3489, and IC 5063 show rings and/or arm-like structures, bluer than the body of the galaxy, suggesting the presence of recent star formation. Although seven of our ETGs show shell systems in their optical image, only NGC 7135 displays shells in the UV bands. We characterize the UV and optical surface brightness profiles, along the major axis, using a Sersic law. The Sersic law exponent, $n$, varies from 1 to 16 in the UV bands. S0 galaxies tend to have lower values of $n$ ($\leq5$). The Sersic law exponent $n=4$ seems to be a watershed: ETGs with $n>4$ tend to have [$\alpha$/Fe] greater than 0.15, implying a short star-formation time scale. We find a significant correlation between the FUV$-$NUV colour and central velocity dispersions $\sigma$, with the UV colours getting bluer at larger $\sigma$. This trend is likely driven by a combined effect of `downsizing' and of the mass-metallicity relation.Comment: Accepted for publication in MNRAS, 33 pages, 7 figure

Comparative Advertising Wars: An Historical Analysis of Their Causes and Consequences

This historical study contributes to the extensive literature on comparative advertising by examining the causes and consequences of comparative advertising wars; that is, when one advertiser responds to a direct or implied attack by another advertiser. Primary and secondary sources consist of articles published in historic and contemporary marketing and advertising trade journals, such as Printers’ Ink, Advertising & Selling, and Advertising Age. The findings reveal that well-publicized advertising wars occurred frequently between major U.S. advertisers throughout the twentieth century and into the twenty-first, and that they most often occurred in product and service markets characterized by intense competition. Many, if not most, advertisers’ principal motive for responding to a comparative advertising attack has been emotional rather than rational. The findings also reveal that advertising wars often became increasingly hostile, leading to negative consequences for all combatants, as well as a broad and negative social consequence in the form of potentially misleading advertising.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline