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2100631 results in Journals

Page 369 of 105032

  • Solitons of the spacelike mean curvature flow in standard static spacetimes

  • Jogli Araújo, Márcio Batista, Eudes de Lima, Henrique de Lima
  • Journal:
    Proceedings of the Edinburgh Mathematical Society , First View
    Published online by Cambridge University Press:
    19 February 2026, pp. 1-14

  • We study complete noncompact spacelike mean curvature flow solitons (SMCFS) in a standard static spacetime obeying a suitable constraint on the sectional curvature. In this context, we prove a version of the Omori–Yau generalized maximum principle and apply it to deduce that such an SMCFS must be maximal in the sense that its mean curvature vanishes identically. Next, we use other maximum principles which deal with the notions of convergence to zero at infinity and polynomial volume growth to prove rigidity results for SMCFS. Furthermore, we apply our previous results to establish nonexistence results concerning entire Killing graphs constructed over the Riemannian base of a standard static spacetime. Finally, we also exhibit an example showing the relevance of key hypotheses in our results.

  • Construction After Construction and Its Theoretical Challenges

  • Ray Jackendoff
  • Journal:
    Language / Volume 84 / Issue 1 / March 2008
    Published online by Cambridge University Press:
    19 February 2026, pp. 8-28

  • The English NPN construction, exemplified by construction after construction, is productive with five prepositions—by, for, to, after, and upon—with a variety of meanings, including succession, juxtaposition, and comparison; it also has numerous idiomatic cases. This mixture of regularity and idiosyncrasy lends itself to an account in the spirit of construction grammar, in which the lexicon includes specified syntactic structures matched with meanings. The internal syntactic structure of NPN violates standard principles of phrase structure, and the required identity of the two nouns (in most cases) presents descriptive difficulties. Furthermore, when NPN appears in NP positions, it can take normal NP complements and modifiers, and it has quantificational semantics despite the absence of a lexical quantifier. These peculiarities collectively present interesting challenges to linguistic theory. The best hope lies in a theory of grammar that (i) recognizes meaningful constructions as theoretical entities; (ii) recognizes a continuum of regularity between words and rules; and (iii) recognizes the autonomy of syntax from semantics and vice versa.

Page 369 of 105032