Results 241 to 250 of about 124,317 (285)

The Mathematical History Behind the Granger–Johansen Representation Theorem

open access: yesOxford Bulletin of Economics and Statistics, EarlyView.
ABSTRACT When can a vector time series that is integrated once (i.e., becomes stationary after taking first differences) be described in error correction form? The answer to this is provided by the Granger–Johansen representation theorem. From a mathematical point of view, the theorem can be viewed as essentially a statement concerning the geometry of ...
Johannes M. Schumacher
wiley   +1 more source

Modular geodesics and wedge domains in non-compactly causal symmetric spaces. [PDF]

open access: yesAnn Glob Anal Geom (Dordr)
Morinelli V, Neeb KH, Ólafsson G.
europepmc   +1 more source

Laws and Reasons Why

open access: yesAnalytic Philosophy, EarlyView.
ABSTRACT Laws play some role in explanations: at the very least, they somehow connect what is explained, or the explanandum, to what explains, or the explanans. Thus, thermodynamical laws connect the match's being struck and its lightning, so that the former causes the latter; and laws about set formation connect Socrates' existence with {Socrates}'s ...
Julio De Rizzo
wiley   +1 more source

Polynomial Lie Algebras

Functional Analysis and Its Applications, 2002
Let \(P\) be an algebra of complex polynomials in \(\lambda_0, \ldots, \lambda_n\) and \(L_P\) the free left \(P\)-module with a basis \(1, l_0, \ldots, l_n\). Define the structure of a Lie algebra \(\mathfrak a(C,V)\) on \(L_P\) by setting \[ [l_i,l_j]=\sum c_{i,j}^k(\lambda)l_k,\quad [l_i,\lambda_q]=v_{i,q}(\lambda), \quad [\lambda_i,\lambda_j]=0, \]
Bukhshtaber, V. M., Leĭkin, D. V.
openaire   +2 more sources

Antinilpotent Lie Algebras

Mathematical Notes, 2005
A Lie algebra is said to be antinilpotent if any of its nilpotent subalgebras is abelian. The main motivation to consider the class of antinilpotent Lie algebras is the relation (first mentioned in [\textit{E. Dalmer}, J. Math. Phys. 40, No. 8, 4151--4156 (1999; Zbl 0966.17003)]) between antinilpotent Lie algebras and the problem of constructing ...
openaire   +2 more sources

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