The product of quantum mechanics is defined as the ordinary multiplication followed by the application of superoperator that orders involved operators. The operator version of Poisson bracket is defined being the Lie bracket which substitutes commutator in the von Neumann equation. These result in obstruction free quantization, with the ordering rule which coincides with Weyl ordering rule. e-m...

<p style='text-indent:20px;'>In the following work, we consider Boltzmann equation that models a diatomic gas by representing microscopic internal energy continuous variable I. Under some convenient assumptions on collision cross-section <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{B} $\end{document}</tex-math></inline-formula>, prove linearized ope...

An essential primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one smaller bond dimension. This forms central bottleneck algorithms for time evolution and contracting projected entangled pair states. We formulate tangent-space based variational algorithm to achieve this goal uniform (infinite) The exhibits favourable scaling computationa...

We present a new type of differential that is particularly suited to analyzing ciphers that use modular multiplication as a primitive operation. These differentials are partially inspired by the differential used to break Nimbus, and we generalize that result. We use these differentials to break the MultiSwap cipher that is part of the Microsoft Digital Rights Management subsystem, to derive a ...

THEOREM 4. Let a be an arbitrarily often differentiable function on the real line having countably many isolated zeros s1, S2, . . . offinite orders ml, M2, ..., respectively. Denote by A the multiplication operator mapping x into Ax = ax and let E be any linear space satisfying X = E (3 R*. Then there is a unique continuous linear op rator A-l :X -X whose range is orthogonal to E and is such t...

Regular operators on L p-spaces are characterised in terms of an operator bound which is associated with certain generalisations of the Feynman-Kac formula. of multiplication by the characteristic functions of elements of the-algebra S, so that if f is a bounded S-measurable function, Q(f) = R f dQ is the operator of multiplication by f. When is it true that we can nd a positive number C such t...

Abstract In this article, all sequences u {\boldsymbol{u}} , mathvariant="bold-italic">v {\boldsymbol{v}} and mathvariant="bold-italic">w {\boldsymbol{w}} that define continuous compact tridiagonal operators T u ,...