Z2×Z2 \mathbb{Z}_2 \times \mathbb{Z}_2 generalizations of N=1{\cal N} = 1 superconformal Galilei algebras and their representations

We introduce two classes of novel color superalgebras of $\mathbb{Z}_2 \times \mathbb{Z}_2$ grading. This is done by realizing members of each in the universal enveloping algebra of the ${\cal N}=1$ supersymmetric extension of the conformal Galilei algebra. This allows us to upgrade any representation of the super conformal Galilei algebras to a representation of the $\mathbb{Z}_2 \times \mathbb{Z}_2$ graded algebra. As an example, boson-fermion Fock space representation of one class is given. We also provide a vector field realization of members of the other class by using a generalization of the Grassmann calculus to $\mathbb{Z}_2 \times \mathbb{Z}_2$ graded setting.Comment: 17 pages, no figur

Z2×Z2\mathbb{Z}_2 \times \mathbb{Z}_2 generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions

We introduce a class of novel $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal enveloping algebra of a Lie superalgebra which is a module extension of the Virasoro algebra. Then the complete classification of central extensions of the $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded color superalgebras is presented. It turns out that infinitely many members of the class have non-trivial extensions. We also demonstrate that the color superalgebras (with and without central extensions) have adjoint and superadjoint operations.Comment: 19 pages, no figure, Revision in Section 2 and 3. Some new reference

Accessible and inaccessible quantum coherence in relativistic quantum systems

The quantum coherence of a multipartite system is investigated when some of the parties are moving with constant acceleration. Due to relativistic motion the quantum coherence is divided into two parts as accessible and inaccessible coherence. First we investigate tripartite systems, considering both GHZ and W-states. We find that the quantum coherence of these states does not vanish in the limit of infinite acceleration, rather asymptoting to a non-zero value. These results hold for both single- and two-qubit relativistic motion. In the GHZ and W states the coherence is distributed as correlations between the qubits and is known as global coherence. But quantum coherence can also exist due to the superposition within a qubit, the local coherence. To study the properties of local coherence we investigate separable state. The GHZ state, W-state and separable states contain only one type of coherence. Next we consider the $W \bar{W}$ and star states in which both local and global coherences coexist. We find that under relativistic motion both local and global coherence show similar qualitative behaviour. Finally we derive analytic expressions for the quantum coherence of $N$-partite GHZ and W states where $n<N$ qubits are subject to relativistic motion. We find that the quantum coherence of a multipartite GHZ state falls exponentially with the number of accelerated qubits, whereas for multipartite W-states the quantum coherence decreases only polynomially. We conclude that W-states are more robust to Unruh decoherence and discuss some potential applications in satellite-based quantum communication and black hole physics.Comment: 18 page

Self Management and Telehealth: Lessons Learnt from the Evaluation of a Dorset Telehealth Program

Dorset Clinical Commissioning Group

New connection formulae for the q-orthogonal polynomials via a series expansion of the q-exponential

Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and q-Gegenbauer polynomials in terms of their respective classical analogs.Comment: 14 page

Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]

Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be expressed in terms of the $Q$-Hahn polynomials. We next investigate representations of the quantum supergroup OSp_q(1/2) which are not well-defined in the classical limit. Employing the universal T-matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in all cases. Using the Clebsch-Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even dimensional representations of the quantum supergroup OSp_q(1/2).Comment: 16 pages, no figure

A qualitative study of the experiences and perceptions of adults with chronic musculoskeletal conditions following a 12-week Pilates exercise programme

Introduction The aim of the present study was to explore the experiences and perceptions of adult patients with chronic musculoskeletal conditions following a Pilates exercise programme. A qualitative approach was taken to both data collection and analysis, with alignment to the philosophy of interpretive phenomenology. Participants included 15 women and seven men with a range of chronic musculoskeletal conditions, including nonspecific low back pain, peripheral joint osteoarthritis and a range of postsurgical conditions. The age range was from 36 years to 83 years, and the mean age was 57 years (standard deviation 14.1 years). Methods Data were collected via digital recordings of four focus groups in three North‐West of England physiotherapy clinics. The data were transcribed verbatim and then analysed using a thematic framework. Data were verified by a researcher and randomly selected participants, and agreement was achieved between all parties. Results The results were organized into five main themes: physical improvements; Pilates promotes an active lifestyle: improved performance at work and hobbies; psychosocial benefits and improved confidence; increased autonomy in managing their own condition; and motivation to continue with exercise. Conclusion The study was the first to investigate individual perceptions of the impact of Pilates on the daily lives of people with chronic conditions. The Pilates‐based exercise programme enabled the participants to function better and manage their condition more effectively and independently. Further to previous work, the study revealed psychological and social benefits which increase motivation to adhere to the programme and promote a healthier lifestyle

Evolution of defences in large tropical plant genera: perspectives for exploring insect diversity in a tri-trophic context

Divergence and escalation in defences promote chemical diversity in plants, and consequently the diversity of insect herbivores. This diversification cascades to insect parasitoids through direct effects on host herbivore susceptibility, changes in herbivore community composition, or disparity in plant volatiles. Large tropical plant genera represent an ideal model for studying these trends due to the high diversity of sympatric species and their insects. Novel measures of chemical structural similarity should be used to analyse evolutionary trends in both direct and indirect defences. Host chemical data need to be combined with detailed herbivore and parasitoid data. This will help to identify truly active compounds. Furthermore, resolved genomic phylogenies for plants and insects should be included to assign directionality in the processes

Generalized boson algebra and its entangled bipartite coherent states

Starting with a given generalized boson algebra U_(h(1)) known as the bosonized version of the quantum super-Hopf U_q[osp(1/2)] algebra, we employ the Hopf duality arguments to provide the dually conjugate function algebra Fun_(H(1)). Both the Hopf algebras being finitely generated, we produce a closed form expression of the universal T matrix that caps the duality and generalizes the familiar exponential map relating a Lie algebra with its corresponding group. Subsequently, using an inverse Mellin transform approach, the coherent states of single-node systems subject to the U_(h(1)) symmetry are found to be complete with a positive-definite integration measure. Nonclassical coalgebraic structure of the U_(h(1)) algebra is found to generate naturally entangled coherent states in bipartite composite systems.Comment: 15pages, no figur