The operator e−tA and the heat trace Tr e−tA, for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0+. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A...

We establish an exact differential equation for the operator describing time-dependent measurements continuous in time and obtain a series solution. Suppose the projection operator E(t) = U(t)EU (t) is measured continuously from t = 0 to T , where E is a projector leaving the initial state unchanged and U(t) a unitary operator obeying U(0) = 1 and some smoothness conditions in t. We prove that ...

According to the Maupertuis principle, the movement of a classical particle in an external potential V (x) can be understood as the movement in a curved space with the metric gμν(x) = 2M [V (x) − E]δμν . We show that the principle can be extended to the quantum regime, i.e., we show that the wave function of the particle follows a Schrödinger equation in curved space where the kinetic operator ...

The main purpose of this paper is to use a new way to extend fuzzy implications $I$ from a generalized sublattice $M$ to a bounded lattice $L$, such that the extended implications preserve many of the considered properties of fuzzy implications on $M$.Furthermore, as a special case, we investigate the extension of $(S,N)-$implications. Results indicate that the extended implications preserve ma...

The operator e−tA and the heat trace Tr e−tA, for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0+. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A...

The quantum deformation of the oscillator algebra and its implications on the phase operator are studied from a view point of an index theorem by using an explicit matrix representation. For a positive deformation parameter q or q = exp(2πiθ) with an irrational θ, one obtains an index condition dim ker a − dim ker a † = 1 which allows only a non-hermitian phase operator with dim ker e iϕ − dim ...

ions apply to concretions more or less exactly as in the π-calculus. Definition 6.3. The application G@C of a φ-abstraction and concretion is defined as follows: ((~ w)P )@ν~z〈 ~y 〉.Q =def ν~z( {~y/~ w}P ‖ Q ) where ~ y and ~ w have the same length, and where names in N must be substituted for names in N , and names in X for names in X . Applications can of course be carried out in the context ...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

This paper proposes a coroutine operator for E-Lotos. The syntax, the static semantics, and the dynamic semantics of the operator are provided. We show by several examples that the coroutine operator is adequate to express suspension and resuming. Moreover, it is more general and simpler than the suspend-resume operator.