Olivines in angrite LEW 87051: Phenos or xenos

Nyquist et al. recently reported the presence of live Mn-53 in angrite LEW 86010 when it crystallized. Hence, melting must have occurred within approx. 10 Ma of the accretion of the angrite parent body, and LEW 86010 is the oldest known differentiated meteorite. This discovery has made it even more desirable to understand teh petrogenesis of angrites, which presumably were all formed at a similar time. As part of the continuing work on angrite petrogenesis, crystallization experiments were conducted on LEW 87051, the other Antarctic angrite, to clarify its petrogenesis. Several aspects of the experimental work is reported. Although the details are not understood, it is clear that the Cr abundance in the experimental olivines must be controlled by spinel crystallization

Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.Comment: 27 page

Large Networks of Diameter Two Based on Cayley Graphs

In this contribution we present a construction of large networks of diameter two and of order $\frac{1}{2}d^2$ for every degree $d\geq 8$, based on Cayley graphs with surprisingly simple underlying groups. For several small degrees we construct Cayley graphs of diameter two and of order greater than $\frac23$ of Moore bound and we show that Cayley graphs of degrees $d\in\{16,17,18,23,24,31,\dots,35\}$ constructed in this paper are the largest currently known vertex-transitive graphs of diameter two.Comment: 9 pages, Published in Cybernetics and Mathematics Applications in Intelligent System

Where My Books Go: Choice and Place in Digital Reading

Digital reading is a topic of rising interest in digital libraries, particularly in terms of optimizing the reading experience. However, there is relatively little data on the patterns of digital reading, including issues of where and what users read, and how they organize, plan and conduct their reading sessions. This paper reports the first data on mobile reading, combining insights from three different studies of users, including diary studies, interviews and ethnomethodological work. The data reveals that reading often depends on highly developed and rehearsed practices, especially when the reading is related to study or research. From this, we are able to identify a number of opportunities for further digital library research to better support the needs of users

Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r) that one usually associates with such a group and hence with a simply-laced Coxeter-Dynkin diagram have a meaningful definition for the non-simply-laced diagrams, too, and as a byproduct we extend Saito's formula for the determinant of the Cartan matrix to all cases. Returning to invariant theory we show that for each irreducible representation i of a binary tetrahedral, octahedral, or icosahedral group one can find a homomorphism into a finite complex reflection group whose defining reflection representation restricts to i.Comment: 19 page

On Birthing Dancing Stars: The Need for Bounded Chaos in Information Interaction

While computers causing chaos is acommon social trope, nearly the entirety of the history of computing is dedicated to generating order. Typical interactive information retrieval tasks ask computers to support the traversal and exploration of large, complex information spaces. The implicit assumption is that they are to support users in simplifying the complexity (i.e. in creating order from chaos). But for some types of task, particularly those that involve the creative application or synthesis of knowledge or the creation of new knowledge, this assumption may be incorrect. It is increasingly evident that perfect order—and the systems we create with it—support highly-structured information tasks well, but provide poor support for less-structured tasks.We need digital information environments that help create a little more chaos from order to spark creative thinking and knowledge creation. This paper argues for the need for information systems that offerwhat we term ‘bounded chaos’, and offers research directions that may support the creation of such interface

Modular Solutions to Equations of Generalized Halphen Type

Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions all uniformize Riemann surfaces of genus zero and have $q$--series with integral coefficients. Rational maps relating these functions are derived, implying subgroup relations between their automorphism groups, as well as symmetrization maps relating the associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.

Nematic liquid crystal director structures in rectangular regions

We consider a shallow rectangular well of nematic liquid crystal subject to weak anchoring on the sides of the well. By considering weak anchoring instead of infinitely strong anchoring, we are able to analyze nematic equilibria in the well without the need to exclude point defects at the corners, as done in previous work in the area. For relatively weak anchoring, we are able to derive analytic expressions for the director alignment angle in terms of an infinite series of modes, involving roots of a transcendental equation. The analytic forms of the director configuration are then used to calculate critical anchoring strengths at which uniform and distorted director structures exchange stability. We also consider the asymptotic behavior of the director structure and energy for very strong anchoring. We show that in both cases—for the transitions from uniform to distorted states and the limit of infinitely strong anchoring—the approximate analytic expansions agree very well with corresponding numerical calculations of the full model