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Let X⊂ℙr be an integral and non-degenerate complex variety. For any q∈ℙr let rX(q) be its X-rank and S(X,q) the set of all finite subsets of X such that |S|=rX(q) and q   ∈  〈S〉, where 〈〉 denotes the linear span. We consider the case |S(X,q)|>1 (i.e. when q is not X -identifiable) and study the set W(X)q:=∩ S∈S(X,q)〈S〉, which we call the non-uniqueness set of q. We study the case dimX=1 and the case X a Veronese embedding of ℙn. We conclude the paper with a few remarks concerning this problem over the reals.

In this work, a user-friendly Java-based open-source software has been developed for internal radiation dosimetry. Based on values published by the International Commission on Radiological Protection (ICRP), the software calculates the estimated absorbed dose for each organ and also the estimated effective dose, this for about forty of the most known radioactive drugs. In addition, the present software offers many features which include: 1) a very friendly graphical user-interface (GUI) designed to facilitate the process of selecting mandatory input data such as radiopharmaceutical product, administered activity and patient's data, 2) a tool for generating a medical report, which can be exported as PDF file or printed directly and then incorporated into the patient's record, 3) a SQLite database for storing patient's specific and dosimetric data. We believe that the present software can be a useful tool for nuclear medicine workers. It is freely available for download on GitHub (https://github.com/EL-Bakkali-Jaafar/RadioPharmaDose).

Negative disclosure tone in 10-K annual reports has economic consequences, yet relatively little is known about how it is generated. Boards of directors play an important governance role with respect to mandatory disclosures and personally sign off on Form 10-K, leading us to expect directors to influence financial reporting narratives. This study investigates whether the negative tone of firms' narrative annual report disclosures is associated with the human and social capital of its board of directors.

Multivariate regression analyses of negative disclosure tone (Loughran and McDonald, 2011) on board members' average age, gender, education, financial expertise and turnover is performed. A host of supplemental tests to corroborate our primary analysis, including using Sarbanes-Oxley's financial expert mandate as an exogenous shock to board composition, impact threshold for a confounding variable, placebo analysis, portfolio tests of more and less negative disclosing firms and portfolio tests of “loud” versus “quiet” boards are conducted.

Evidence that directors' gender, education, financial expertise and board turnover are associated with more negative disclosure tone, while directors' age is associated with less negative disclosure tone is found. The study also looked within the board to differentiate whether these findings are driven by characteristics of inside directors or outside directors serving on the audit committee, or both, as these are the specific groups of directors we would expect to play a role in disclosure. It was found that negative disclosure tone is associated with a lower bid-ask spread, so this study interpreted more negative tone as containing more descriptive information.

This study helps decode the “black box” of annual report disclosure tone, which Loughran and McDonald (2011) show has important economic implications. The results help inform stakeholders such as policymakers, executives and capital market participants as to how board member traits are associated with disclosure. The findings are particularly important as this study bears witness to the increasing prominence of gender/diversity mandates (e.g. Israel, Norway, California) and financial expertise mandates (e.g. Sarbanes-Oxley).