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For finite groups X, G and the right G-action on X by group automorphisms, the non-balanced quantum double D(X; G) is defined as the crossed product (ℂXop)* ⋊ ℂG. We firstly prove that D(X; G) is a finite-dimensional Hopf C*-algebra. For any subgroup H of G, D(X; H) can be defined as a Hopf C*-subalgebra of D(X; G) in the natural way. Then there is a conditonal expectation from D(X; G) onto D(X; H) and the index is [G; H]. Moreover, we prove that an associated natural inclusion of non-balanced quantum doubles is the crossed product by the group algebra. [ABSTRACT FROM AUTHOR]

Two classes of optimal quaternary sequences have been constructed by applying the sign alternation transform and Gray mapping to Legendre sequence pair, twin-prime sequence pair and GMW sequence pair. In this paper, a new method for investigating the linear complexity over finite field is proposed, and the exact values of the linear complexity over finite field F 4 and Galois ring Z 4 of the quaternary sequences are determined. The results show that their linear complexity are quite good. [ABSTRACT FROM AUTHOR]

The geological formation immediately surrounding a nuclear waste disposal facility has the potential to undergo a complex set of physical and chemical processes starting from construction and continuing many years after closure. The DECOVALEX project (DEvelopment of COupled models and their VALidation against EXperiments) was established and maintained by a variety of waste management organisations, regulators and research organisations to help improve capabilities in experimental interpretation, numerical modelling and blind prediction of complex coupled systems. In the present round of DECOVALEX (D-2015), one component of Task C1 has considered the detailed experimental work of Yasuhara et al. (Earth Planet Sci Lett 244:186-200, 2006), wherein a single artificial fracture in novaculite (micro- or crypto-crystalline quartz) is subject to variable fluid flows, mechanical confining pressure and different applied temperatures. This paper presents a synthesis of the completed work of six separate research teams. A range of approaches are presented including 2D and 3D high-resolution coupled thermo-hydro-mechanical-chemical models. The results of the work show that while good, physically plausible representations of the experiment can be obtained using a range of approaches, there is considerable uncertainty in the relative importance of the various processes, and that the parameterisation of these processes can be closely linked to the interpretation of the fracture surface topography at different spatial scales. [ABSTRACT FROM AUTHOR]

It has been shown that for two different multipartite unitary operations U and U , when tr( U U ) = 0, they can always be perfectly distinguished by local operations and classical communication in the single-run scenario. However, how to find the detailed scheme to complete the local discrimination is still a fascinating problem. In this paper, aiming at some U and U acting on the bipartite and tripartite space respectively, especially for U U locally unitary equivalent to the high dimensional X-type hermitian unitary matrix V with tr V = 0, we put forward the explicit local distinguishing schemes in the single-run scenario. [ABSTRACT FROM AUTHOR]

Arbitrated quantum signature (AQS) is a cryptographic scenario in which the sender (signer), Alice, generates the signature of a message and then a receiver (verifier), Bob, can verify the signature with the help of a trusted arbitrator, Trent. In this paper, we point out there exist some security weaknesses in two AQS protocols. Our analysis shows Alice can successfully disavow any of her signatures by a simple attack in the first protocol. Furthermore, we study the security weaknesses of the second protocol from the aspects of forgery and disavowal. Some potential improvements of this kind of protocols are given. We also design a new method to authenticate a signature or a message, which makes AQS protocols immune to Alice's disavowal attack and Bob's forgery attack effectively. [ABSTRACT FROM AUTHOR]