Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups

Let $S(A)$ denote the orbit of a complex or real matrix $A$ under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix $A_0$ by the sum of matrices in $S(A_1), ..., S(A_N)$ in the sense of finding the Euclidean least-squares distance $$\min \{\|X_1+ ... + X_N - A_0\|: X_j \in S(A_j), j = 1, >..., N\}.$$ Connections of the results to different pure and applied areas are discussed

Blood diamonds: an analysis of the state of affairs and the effectiveness of the Kimberley Process

In an era when corporate responsibility and sustainability are gaining momentum, and growing access to information and communication has empowered consumers to make more socially responsible purchasing decisions, the diamond industry remains opaque. The Kimberley Process was established to monitor the rough diamond trade with the objective of stemming the flow of conflict diamonds. The definition of conflict diamonds, however, often excludes human rights abuses, which has led to mounting criticism. The purpose of this paper is to examine the prevalence, magnitude, and scope of ethical issues affecting sourcing conditions in the diamond industry. The research found that ethical issues were reported in the diamond industries of several African nations, with Angola topping the list. Child labour and slavery are the most prevalent human rights abuses. In 2017, one in five diamonds in terms of volume and one in ten diamonds in terms of value may have been produced under conditions that cannot be regarded as sustainable or ethical

Multi-field modelling and simulation of large deformation ductile fracture

In the present contribution we focus on a phase-field approach to ductile fracture applied to large deformation contact problems. Phase-field approaches to fracture allow for an efficient numerical investigation of complex three-dimensional fracture problems, as they arise in contact and impact situations. To account for large deformations the underlying formulation is based on a multiplicative decomposition of the deformation gradient into an elastic and plastic part. Moreover, we make use of a fourth-order crack regularization combined with gradient plasticity. Eventually, a demonstrative example shows the capability of the proposed framework

Lepton Mass Effects in Single Pion Production by Neutrinos

We reconsider the Feynman-Kislinger-Ravndal model applied to neutrino-excitation of baryon resonances. The effects of lepton mass are included, using the formalism of Kuzmin, Lyubushkin and Naumov. In addition we take account of the pion-pole contribution to the hadronic axial vector current. Application of this new formalism to the reaction nu(mu) + p --> mu + Delta at E(nu) approx 1 GeV gives a suppressed cross section at small angles, in agreement with the screening correction in Adler's forward scattering theorem. Application to the process nu(tau) + p --> tau + Delta at E(nu) approx 7 GeV leads to the prediction of right-handed tau polarization for forward-going leptons, in line with a calculation based on an isobar model. Our formalism represents an improved version of the Rein-Sehgal model, incorporating lepton mass effects in a manner consistent with PCAC.Comment: 14 pages, 5 figures. Typos in eq. 9 and 27 corrected. Numbers in table I for coherent cross sections (RSA and RSC) corrected (normalization error). Figs 3 and 4 changed accordingly. These corrections also apply to the published version PRD 76, 113004 (2007

Polarimetric Evidence of Non-Spherical Winds

Polarization observations yield otherwise unobtainable information about the geometrical structure of unresolved objects. In this talk we review the evidences for non-spherically symmetric structures around Luminous Hot Stars from polarimetry and what we can learn with this technique. Polarimetry has added a new dimension to the study of the envelopes of Luminous Blue Variables, Wolf-Rayet stars and B[e] stars, all of which are discussed in some detail.Comment: 8 pages, 2 encapsulated Postscript figures, uses lamuphys.sty. Invited review to appear in IAU Coll. 169, Variable and Non-Spherical Stellar Winds in Luminous Hot Stars, eds. B. Wolf, A.Fullerton and O. Stahl (Springer

GN&C Sequencing for Orion Rendezvous, Proximity Operations, and Docking

As part of the Artemis program to return humans to the lunar surface, the National Aeronautics and Space Administration is planning to use the Orion Multi- Purpose Crew Vehicle to transport crew to a small orbital platform called Gate- way in cislunar space. To facilitate this activity, Orion is required to perform Rendezvous, Proximity Operations, and Docking (RPOD) with both the Gate- way and the launch vehicle upper stage. The Orion spacecraft uses sequencing in the form of Phases, Segments, Activities, and Modes (PSAM) to configure Guidance, Navigation, & Control (GN&C) software during each portion of the mission. Significant updates to Orion PSAM definitions are required for RPOD. This paper describes the process of defining these new sequencing elements, implementing them in prototype flight software, and testing them in an integrated simulation environment. First, requirements are specified to determine the nominal and off-nominal sequencing behavior necessary to complete the mission. These requirements also specify which software functions should be fully autonomous and which functions require manual interactions from crew or ground operators. Next, the RPOD concept of operations is defined with detailed events listed in a mission timeline. Third, a state machine diagram is developed to show all PSAM states, including all possible transitions between them. After this, the PSAM states and transitions are entered into a sequencing software emulator and parameter values and modes are defined for GN&C software elements. Finally, the PSAM architecture is tested within an integrated simulation environment by connecting it with prototypes of relevant GN&C flight software elements and with detailed vehicle models. After the sequencing design has been finalized and tested, it is implemented in flight software

CC56-139 Poultry Profit Pointers: Marketing Eggs

The egg represents the marketable, finished produce from the laying flock. Poultry raisers should be familiar with eggs and do everything possible to maintain egg quality. Eggs are a valuable human food because they are rich in protein, vitamins and minerals. Like other important protein foods, eggs should be properly handled to protect their quality. This campaign circular discusses what to look for in the size eggs and how to handle them before taking them market