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This comparison of optical character recognition software includes: OCR engines , that do the .... "Asprise Java OCR Library Features". asprise.com. Retrieved ...

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Dear all, We are very new to Abby Fine Reader. We would need to do some customization to read the.

| h such that [T (H) (H)]n | = 0, for all H h and some n Then | is called a weight vector if n = 1, that is, T (H)| = (H)| , H h In particular, | is called a highest (or lowest) weight vector if T (E + )| = 0 , + + , (or T (E )| = 0 , ) , (B10)



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where + , or , is the set of the positive, or negative, roots The interest of this notion is the fundamental result obtained by Cartan which says that the irreducible, nite-dimensional, Hermitian representations of simple Lie algebras are in one-toone correspondence with highest-weight vectors for the geometrical construction of representations in those terms) We illustrate this with the simplest example, namely, su(2), with the familiar angular momentum basis { J o , J + , J } and = { } In the unitary spin-j irreducible representation D j of SU (2), of dimension 2 j + 1, with standard basis {| j, m | m = j, , j}, the highest (or lowest) weight vector | j , j (or | j, j ) satis es the relation J + | j, j = 0 (or J | j, j = 0) and has an isotropy subalgebra u(1) (by this, we mean the subalgebra that annihilates the given vector) Notice that here C 2 = J 2 + J + J + J J + is indeed diagonal in D j , with eigenvalue j ( j + 1) o





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(a) Was the way in which participants were selected appropriate and were there enough participants Justify your comments. (b) Why do you think participants were asked to read each new task aloud before starting it and to return to the home page

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A Lie group G may be de ned in several ways, for instance, as a smooth manifold with a group structure such that the group operations ( g 1 , g 2 ) g 1 g 2 , g g 1 are C k , for some k v 2 This actually implies that all group operations are in fact (real) analytical A Lie group is said to be simple, or semisimple, if it has no nontrivial invariant subgroup, or Abelian invariant subgroup Let G be a Lie group For g G consider the map Lg : G G with Lg ( g ) = g g The derivative of this map at g G, denoted T g (Lg ), sets up an isomorphism T g (Lg ) : T g G T g g G between the tangent spaces at g and g g For any vector X T e G (the tangent space at the identity), let us de ne a vector eld X on G by X g = T e (Lg )X Such a vector eld is said to be left-invariant It can be demonstrated that the usual Lie bracket [X , Y ] of two left-invariant vector elds is again a leftinvariant vector eld Using this fact, we see that if Y g = T e (Lg )Y , Y T e G, the relation [X , Y ] = [X , Y ] de nes a Lie bracket on the tangent space, T e G, at the identity of the Lie group G Thus, equipped with this bracket relation, T e G becomes a Lie algebra which we denote by g Next, it can be shown that for any X g, there exists a unique analytical homomorphism, t X (t) of R into G such that d X (0) = X (t)|t=0 = X , dt and for each X g we then write exp X = X (1) The map X exp X is called the exponential map and it de nes a homeomorphism between an open neighborhood.

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The shell passes the string value entered into the command line to the script. However, you ll have a problem if you try to do this with a text string that contains spaces:

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