Some basic algebraic features of quasiparticle transformations are reviewed. Special nonlinear quasiparticle transformations are introduced leading to the second quantized counterparts of gerninal-type (correlated) wave functions. Algebraic representa-' tions of strong and weak orthogonality are discussed, and these issues are generalized to the case of non-orthogonal basis sets leading to the ...

We discuss certain features of pseudo-Hermiticity and weak pseudo-Hermiticity conditions and point out that, contrary to a recent claim, there is no inconsistency if the correct orthogonality condition is used for the class of pseudo-Hermitian, PTsymmetric Hamiltonians of the type Hβ = [p + iβν(x)] 2/2m + V (x). PACS: 03.65.Ca

‎in this work we prove malliavin differentiability for the solution to an sde with locally lipschitz and semi-monotone drift‎. ‎to prove this formula‎, ‎we construct a sequence of sdes with globally lipschitz drifts and show that the $p$-moments of their malliavin derivatives are uniformly bounded‎.

We present some sufficient conditions for which a Banach space X has normal structure in term of the modulus of U -convexity, modulus of W ∗-convexity and the coefficient of weak orthogonality. Some known results are improved.

Two statements by von Neumann and a thought-experiment by Peres prompts a discussion on the notions of one-shot distinguishability, orthogonality, semi-permeable diaphragm, and their thermodynamic implications. In the first part of the paper, these concepts are defined and discussed, and it is explained that one-shot distinguishability and orthogonality are contradictory assumptions, from which...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...