213,879 research outputs found
The Muscle-Mechanical Compromise Framework: Implications for the Scaling of Gait and Posture
Many aspects of animal and human gait and posture cannot be predicted from purely mechanical work minimization or entirely based on optimizing muscle efficiency. Here, the Muscle-Mechanical Compromise Framework is introduced as a conceptual paradigm for considering the interactions and compromises between these two objectives. Current assumptions in implementing the Framework are presented. Implications of the compromise are discussed and related to the scaling of running mechanics and animal posture
Instantons, Topological Strings and Enumerative Geometry
We review and elaborate on certain aspects of the connections between
instanton counting in maximally supersymmetric gauge theories and the
computation of enumerative invariants of smooth varieties. We study in detail
three instances of gauge theories in six, four and two dimensions which
naturally arise in the context of topological string theory on certain
non-compact threefolds. We describe how the instanton counting in these gauge
theories are related to the computation of the entropy of supersymmetric black
holes, and how these results are related to wall-crossing properties of
enumerative invariants such as Donaldson-Thomas and Gromov-Witten invariants.
Some features of moduli spaces of torsion-free sheaves and the computation of
their Euler characteristics are also elucidated.Comment: 61 pages; v2: Typos corrected, reference added; v3: References added
and updated; Invited article for the special issue "Nonlinear and
Noncommutative Mathematics: New Developments and Applications in Quantum
Physics" of Advances in Mathematical Physic
Archivists and Historians: A View from the United States
Considers the debate about the relationship of history and archives and archivists by examining the mission of the archival profession, the nature of archival theory and knowledge, and, as a case study, the career of Lester J. Cappon (1900-1981) as both historian and archivist
Gruenhage compacta and strictly convex dual norms
We prove that if K is a Gruenhage compact space then C(K)* admits an
equivalent, strictly convex dual norm. As a corollary, we show that if X is a
Banach space and X* is the |.|-closed linear span of K, where K is a Gruenhage
compact in the w*-topology and |.| is equivalent to a coarser, w*-lower
semicontinuous norm on X*, then X* admits an equivalent, strictly convex dual
norm. We give a partial converse to the first result by showing that if T is a
tree, then C(T)* admits an equivalent, strictly convex dual norm if and only if
T is a Gruenhage space. Finally, we present some stability properties satisfied
by Gruenhage spaces; in particular, Gruenhage spaces are stable under perfect
images
Trees, linear orders and G\^ateaux smooth norms
We introduce a linearly ordered set Z and use it to prove a necessity
condition for the existence of a G\^ateaux smooth norm on C(T), where T is a
tree. This criterion is directly analogous to the corresponding equivalent
condition for Fr\'echet smooth norms. In addition, we prove that if C(T) admits
a G\^ateaux smooth lattice norm then it also admits a lattice norm with
strictly convex dual norm.Comment: A different version of this paper is to appear in J. London Math. So
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