つくばリポジトリ SR 8 1 1285

combinatorial invariant, in particular, it does not depend on the field K , while the depth is homological invariant and in case of squarefree monomial ideal, a topological invariant

An integral inequality is deduced from the negation of the geometrical condition in the bounded mountain pass theorem of Schechter, in a situation where this theorem does not

Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A

In the case of the KdV equation, the τ -function is a matrix element for the action of the loop group of GL 2 on one-component fermionic Fock space, see for instance [10, 20, 26]..

The Cauchy problem for the Laplace equation and for other elliptic equations is in general ill-posed in the sense that the solution, if it exists, does not depend con- tinuously on

We study the classical invariant theory of the B´ ezoutiant R(A, B) of a pair of binary forms A, B.. We also describe a ‘generic reduc- tion formula’ which recovers B from R(A, B)

We mentioned in Section 1 that in our models, the birth and death rates of individuals depend on the population density in such a way that they induce an equilibrating

For X-valued vector functions the Dinculeanu integral with respect to a σ-additive scalar measure on P (see Note 1) is the same as the Bochner integral and hence the Dinculeanu