For a system strongly coupled to a heat bath, the quantum coherence of the system and the heat bath plays an important role in the system dynamics. This is particularly true in the case of non-Markovian noise. We rigorously investigate the influence of system-bath coherence by deriving the reduced hierarchal equations of motion (HEOM), not only in real time, but also in imaginary time, which re...

Although our proof is standard (essentially the same as presented by Serre [2], whose was the first account that I understood) we eschew complexvariable theory. Instead we use simple estimates from real-variable theory. Only one new difficulty is introduced: proving that L(1, χ) 6= 0 for nontrivial real-valued Dirichlet characters χ. We use an argument of Monsky [1] to prove this fact. Our argu...

Our remark concerns the structure of the pencil of conics containing three degenerate conics of which two represent conjugate imaginary line pairs, i.e. the pencil defined by Eq. (24) in [1]. In what follows we will demonstrate that Campbell’s claim that also the third singular conic ‘must be a conjugate imaginary line pair’ is false, because this conic is, in fact, a real line pair. The proof ...

Reaction-diffusion systems which include processes of the form A+A → A or A+A → ∅ are characterised by the appearance of ‘imaginary’ multiplicative noise terms in an effective Langevin-type description. However, if ‘real’ as well as ‘imaginary’ noise is present, then competition between the two could potentially lead to novel behaviour. We thus investigate the asymptotic properties of the follo...

In the two decades since the Supreme Court protected a crude rap spoof from copyright liability in Campbell v. Acuff-Rose Music, Inc., courts have grown to understand the great value of parodic expression in trademark cases as well. Today, plausible claims of parody almost always prevail over trademark rights in judicial rulings. This Article demonstrates that it is simply wrong to suggest, as ...

We apply the resolvent technique to the computation of the QED effective action in time dependent electric field backgrounds. The effective action has both real and imaginary parts, and the imaginary part is related to the pair production probability in such a background. The resolvent technique has been applied previously to spatially inhomogeneous magnetic backgrounds, for which the effective...

In this paper we introduce the notion of a discrete-time negative imaginary system and we investigate its relations with discrete-time positive real system theory. In the framework presented here, discrete-time negative imaginary systems are defined in terms of a sign condition that must be satisfied in a domain of analyticity of the transfer function, in analogy with the case of discrete-time ...

abstract: focusing on spiritual and mental needs of slow-pace people i.e. mentally retarded people has been always an integral part of designing spaces for them. according to lacan’s way of thinking, real, imaginary and symbolic orders are three ways of expression through human’s reality language and it usually considers reality as a combination of symbolic and imaginary orders. this research a...

A general approach to the problem of simultaneous computation of the discrete Fourier transform (DFT) of two sequences of length N , which may be real, imaginary, conjugated symmetric or conjugated anti-symmetric, using a single N -point DFT of a complex sequence is presented. The framework developed is applied to the simultaneous computation of two DFTs, one DFT and one inverse DFT (IDFT) or t...