Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Climate change and forests in India: adaptation opportunities and challenges

Climate change is projected to lead to shift of forest types leading to irreversible damage to forests by rendering several species extinct and potentially affecting the livelihoods of local communities and the economy. Approximately 47% and 42% of tropical dry deciduous grids are projected to undergo shifts under A2 and B2 SRES scenarios respectively, as opposed to less than 16% grids comprising of tropical wet evergreen forests. Similarly, the tropical thorny scrub forest is projected to undergo shifts in majority of forested grids under A2 (more than 80%) as well as B2 scenarios (50% of grids). Thus the forest managers and policymakers need to adapt to the ecological as well as the socio-economic impacts of climate change. This requires formulation of effective forest management policies and practices, incorporating climate concerns into long-term forest policy and management plans. India has formulated a large number of innovative and progressive forest policies but a mechanism to ensure effective implementation of these policies is needed. Additional policies and practices may be needed to address the impacts of climate change. This paper discusses an approach and steps involved in the development of an adaptation framework as well as policies, strategies and practices needed for mainstreaming adaptation to cope with projected climate change. Further, the existing barriers which may affect proactive adaptation planning given the scale, accuracy and uncertainty associated with assessing climate change impacts are presented.

E. C. G. Sudarshan and Symmetry in Classical Dynamics, Optics and Quantum Mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.

The Evolution of Animal Welfare and the 3Rs in Brazil, China, and India

Increasingly, scientific collaborations and contracts cross country borders. The need for assurance that the quality of animal welfare and the caliber of animal research conducted are equivalent among research partners around the globe is of concern to the scientific and laboratory animal medicine communities, the general public, and other key stakeholders. Therefore, global harmonization of animal care and use standards and practices, with the welfare of the animals as a cornerstone, is essential. In the evolving global landscape of enhanced attention to animal welfare, a widely accepted path to achieving this goal is the successful integration of the 3Rs in animal care and use programs. Currently, awareness of the 3Rs, their implementation, and the resulting animal care and use standards and practices vary across countries. This variability has direct effects on the animals used in research and potentially the data generated and may also have secondary effects on the country's ability to be viewed as a global research partner. Here we review the status of implementation of the 3Rs worldwide and focus on 3 countries-Brazil, China and India-with increasing economic influence and an increasing footprint in the biomedical research enterprise.

Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains

It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic group on finite-dimensional inner product spaces. The representations, and the induced bundles, have composition series with irreducible factors. We write down an equivariant constant coefficient differential operator that intertwines the bundle with the direct sum of its irreducible factors. As an application, we show that in the case of the closed unit ball in C-n all homogeneous n-tuples of Cowen-Douglas operators are similar to direct sums of certain basic n-tuples. (c) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.