In this paper the explicit form of the operator of transformation of the vacuum states for the general two-mode Bogolubov transformation is found † On leave of absence from VNIIFTRI, Mendeleevo, Moscow Region 141570, Russia 1

We provide a method of inserting and removing any finite number of prescribed eigenvalues into spectral gaps of a given one-dimensional Dirac operator. This is done in such a way that the original and deformed operator are unitarily equivalent when restricted to the complement of the subspace spanned by the newly inserted eigenvalue. Moreover, the unitary transformation operator which links the...

In this paper, we develop a solid theoretical foundation for a bottom up program transformation, capable of specialising a logic program with respect to a set of unit clauses. Extending a well-known operator , originally introduced for composing logic programs, we deene a bottom up partial deduction operator and prove correctness of the transformation with respect to the S-semantics. We also sh...

A bstract Recently, Gaiotto and Rapcak proposed a generalization of W N algebra by considering the symmetry at corner brane intersection (corner vertex operator algebra). The algebra, denoted as Y L,M,N , is characterized three non-negative integers L, M, . It has manifest triality automorphism which interchanges can be obtained reduction 1+∞ with “pit” in plane partition representation. Later,...

Time-dependent unitary transformations are used to study the Schrödinger equation for explicitly timedependent Hamiltonians of the form H(t) = ~ R(t) · ~ J , where ~ R is an arbitrary real vector-valued function of time and ~ J is the angular momentum operator. The solution of the Schrödinger equation for the most general Hamiltonian of this form is shown to be equivalent to the special case ~ ...