Variability of stellar granulation and convective blueshift with spectral type and magnetic activity. I. K and G main sequence stars

In solar-type stars, the attenuation of convective blueshift by stellar magnetic activity dominates the RV variations over the low amplitude signal induced by low mass planets. Models of stars that differ from the Sun will require a good knowledge of the attenuation of the convective blueshift to estimate its impact on the variations. It is therefore crucial to precisely determine not only the amplitude of the convective blueshift for different types of stars, but also the dependence of this convective blueshift on magnetic activity, as these are key factors in our model producing the RV. We studied a sample of main sequence stars with spectral types from G0 to K2 and focused on their temporally averaged properties: the activity level and a criterion allowing to characterise the amplitude of the convective blueshift. We find the differential velocity shifts of spectral lines due to convection to depend on the spectral type, the wavelength (this dependence is correlated with the Teff and activity level), and on the activity level. This allows us to quantify the dependence of granulation properties on magnetic activity for stars other than the Sun. The attenuation factor of the convective blueshift appears to be constant over the considered range of spectral types. We derive a convective blueshift which decreases towards lower temperatures, with a trend in close agreement with models for Teff lower than 5800 K, but with a significantly larger global amplitude. We finally compare the observed RV variation amplitudes with those that could be derived from our convective blueshift using a simple law and find a general agreement on the amplitude. Our results are consistent with previous results and provide, for the first time, an estimation of the convective blueshift as a function of Teff, magnetic activity, and wavelength, over a large sample of G and K main sequence stars

On the expressive power of read-once determinants

We introduce and study the notion of read-$k$ projections of the determinant: a polynomial $f \in \mathbb{F}[x_1, \ldots, x_n]$ is called a {\it read-$k$ projection of determinant} if $f=det(M)$, where entries of matrix $M$ are either field elements or variables such that each variable appears at most $k$ times in $M$. A monomial set $S$ is said to be expressible as read-$k$ projection of determinant if there is a read-$k$ projection of determinant $f$ such that the monomial set of $f$ is equal to $S$. We obtain basic results relating read-$k$ determinantal projections to the well-studied notion of determinantal complexity. We show that for sufficiently large $n$, the $n \times n$ permanent polynomial $Perm_n$ and the elementary symmetric polynomials of degree $d$ on $n$ variables $S_n^d$ for $2 \leq d \leq n-2$ are not expressible as read-once projection of determinant, whereas $mon(Perm_n)$ and $mon(S_n^d)$ are expressible as read-once projections of determinant. We also give examples of monomial sets which are not expressible as read-once projections of determinant

Building the Brightrock Brand through Change

Subject area This case allows students to engage with classical marketing tenets of branding, media and communications decisions and content marketing within a management framework. Study level/applicability This case is appropriate for an undergraduate or graduate-level programme in marketing management. Case overview Suzanne Stevens was part of a group of four former senior employees of a large life insurance firm that decided to establish a new and innovative South African insurance company, BrightRock. They identified a gap in a large and highly competitive (albeit generic and opaque) insurance market and developed a distinctive positioning within the market. There was low consumer understanding of the technical aspects of life insurance products, and no existing life insurance product provided an individualized offering. Stevens developed the company’s brand and marketing strategy by drawing on reputation drivers, traditional advertising and a content marketing approach. BrightRock focused on change moments in consumers’ lives, including getting married, having children or getting a new job, and changed the standard insurance product model by launching an individualized flexible product that could adapt with the consumer through their various life stages. The case study documents the first three years of BrightRock’s operations, with a strong focus on brand and product development, distribution and communication. The case dilemma involves choices Stevens faced at the beginning of 2015 about marketing investments across paid, earned and owned media. Expected learning outcomes This study enables to critique the development of a services brand; integrate paid, owned and earned media to increase communication effectiveness and efficiency; and critique a content marketing strategy. Supplementary materials Teaching Notes are available for educators only. Please contact your library to gain login details or email [email protected] to request teaching notes. Subject code CSS 8: Marketing. </jats:sec

Measuring Impression Management in Male Leaders of Color

Companies’ survival depends on their ability to attract and maintain diverse leaders. This research examines the tactics used by male leaders of color to secure management positions. The Jones and Pittman’s Impression Management Taxonomy (1982) was used to explore the impression management phenomenon and the constructs of self-promotion, ingratiation, exemplification, intimidation, and supplication as they relate to gender and ethnicity. The statistical analysis was conducted on 240 valid responses where an exploratory factor analysis and a MANOVA provided insight on the variables’ relationships. The findings convey Black/African–American and Latinos scored similarly in their use of supplication versus White male leaders, which indicates that male leaders of color are more likely to be modest in their approach. Additionally, to some extent, all ethnicities with the exception of Asians tended to use the intimidation tactic in the workplace. While diversity is a growing trend in the workplace, this study confirms that it is imperative to have healthy conversations about ethnicity and gender in professional settings

Semidefinite Representation of the kk-Ellipse

The $k$-ellipse is the plane algebraic curve consisting of all points whose sum of distances from $k$ given points is a fixed number. The polynomial equation defining the $k$-ellipse has degree $2^k$ if $k$ is odd and degree $2^k{-}\binom{k}{k/2}$ if $k$ is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted $k$-ellipses and $k$-ellipsoids in arbitrary dimensions, and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure