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The formula in Lemma 3(i) below for counting the Jordan blocks of a given size in the Jordan canonical form of a nilpotent matrix is used in the proof of Theorem 1..
A completely similar argument can be used in the study of elliptic boundary value problems for families of elliptic operators to prove that every family of elliptic
To prove that every isotrivial family with this fibre has a rational section it suffices to prove this when the base is projective, i.e., the discriminant of the family is empty..
a) For all increasing (resp. By virtue of Lemma 4.7, Proposition 5.3 and Lemma 5.4, it is clear that the mapping ˜ J is a linear injection and a Banach lattice homomorphism. That
µ is connected with the square root taken of the d’Alembert’s operator ∂ 2 [3], we shall try to connect the square root of the phase operators with the fermionic
Proposition 3.1.. The following proof is similar to that of Lemma 10.1 of [9], extended to the general Gaussian martingales. This is an extension of the simple case given in
In this short paper we prove the equivalence between the Radon- Nikodym Theorem for reflexive Banach spaces and the representability of weakly compact operators with domain L 1 ( µ
On entering the pipe, the fluid with low viscosity (water) is adjacent to the pipe wall and it surrounds the fluid with high viscosity (heavy oil). It is assumed that the flow
