We can see that caution is needed when dealing with local spectral multiplicities: the values of function \(N_{L_2}\) have no meaning on the set \(X_1\setminus X_2\) and can be changed arbitrarily there, the same for \(N_{L_1}\) on \(X_2\setminus X_1\). So the ...
The reader should be warned that the same term is used in =-=[1]-=- with a different meaning. We add some details to the statement and the proof of Theorem 4.17 when the characteristic of k is positive. Theorem 0.1 Let O, v0, w, Π be as in Theorem 4.4. If Hom(V (λ), ....
A negative \({\delta }_{{ij}}\) indicates unfavored pair, meaning \(i\) and \(j\) repel each other. Random solid solution has \({\delta }_{{ij}}=0\). B2 cluster analysis Mo and Ta tend to attract each other and form the B2 structure. The B2 unit cell has a simple bcc ...
There are numerous ways to specialize this statement by indi-cating the exact meaning of “dense”, “large”, and “long”, but in our presentcontext the following result of Sárközy is the origin of things.Theorem 1 (Sárközy [3, Theorem 1]). Let l ? n ? 2 be integers and...
Since track 2 can exit the detector, the meaning of L_{22} and \sin \Theta _{22} differ somewhat from L_{21} and \sin \Theta _{21}. Two other two-track correlated variables of interest, which are not independent, are the cosine of the opening angle, \begin{aligned} \cos \Omega...
The word multiplicity is a general term meaning "the number of values for which a given condition holds." For example, the term is used to refer to the value of the totient valence function or the number of times a given polynomial equation has a root at a given point. Let be a ...