Characterization of SU(1,1) coherent states in terms of affine group wavelets

The Perelomov coherent states of SU(1,1) are labeled by elements of the quotient of SU(1,1) by the compact subgroup. Taking advantage of the fact that this quotient is isomorphic to the affine group of the real line, we are able to parameterize the coherent states by elements of that group or equivalently by points in the half-plane. Such a formulation permits to find new properties of the SU(1,1) coherent states and to relate them to affine wavelets.Comment: 11 pages, latex, to be published in J. Phys. A : Math. Ge

Carbon sequestration potential and the multiple functions of Nordic grasslands

Grasslands are important carbon sinks, but the underlying processes for their soil carbon sequestration potential are still not well understood, despite much attention given to this topic. In Europe, grasslands, especially semi-natural grasslands, are also important for promoting biodiversity. Moreover, recent global reports have highlighted the importance of biodiversity in supporting climate actions. In boreal and alpine regions in the Nordic countries, grasslands also play an important role in milk and meat production and food security. Certain grassland features and management practices may enhance their soil carbon sequestration potential. Semi-natural grasslands maintained by optimized livestock grazing are vital for aboveground biodiversity and show promise for belowground biodiversity and carbon sequestration potential. It is essential to assess the multiple functions of grasslands, particularly semi-natural grasslands, to facilitate the optimization of policy measures across policy areas. Climate and biodiversity policies should not counteract each other, as some do today. This essay addresses the multiple functions of grasslands and calls for more knowledge about carbon sequestration in Nordic grasslands. This will enable the management of these ecosystems to align with climate mitigation, maintain biodiversity, and satisfy the global need for increased food supply.publishedVersio

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Solving simple quaternionic differential equations

The renewed interest in investigating quaternionic quantum mechanics, in particular tunneling effects, and the recent results on quaternionic differential operators motivate the study of resolution methods for quaternionic differential equations. In this paper, by using the real matrix representation of left/right acting quaternionic operators, we prove existence and uniqueness for quaternionic initial value problems, discuss the reduction of order for quaternionic homogeneous differential equations and extend to the non-commutative case the method of variation of parameters. We also show that the standard Wronskian cannot uniquely be extended to the quaternionic case. Nevertheless, the absolute value of the complex Wronskian admits a non-commutative extension for quaternionic functions of one real variable. Linear dependence and independence of solutions of homogeneous (right) H-linear differential equations is then related to this new functional. Our discussion is, for simplicity, presented for quaternionic second order differential equations. This involves no loss of generality. Definitions and results can be readily extended to the n-order case.Comment: 9 pages, AMS-Te

Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Strong Clonal Relatedness between Serum and Gut IgA despite Different Plasma Cell Origins

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Longitudinal development of a substorm brightening arc

We present simultaneous THEMIS-ground observations of longitudinal (eastward) extension of a substorm initial-brightening arc at Gillam (magnetic latitude: 65.6°) at 08:13 UT on 10 January 2008. The speed of the eastward arc extension was ~2.7 km/s. The extension took place very close to the footprints of the longitudinally separated THEMIS E and D satellites at ~12 <I>R<sub>E</sub></I>. The THEMIS satellites observed field dipolarization, weak earthward flow, and pressure increase, which propagated eastward from E to D at a speed of ~50 km/s. The THEMIS A satellite, located at 1.6 <I>R<sub>E</sub></I> earthward of THEMIS E, observed fluctuating magnetic field during and after the dipolarization. The THEMIS E/D observations suggest that the longitudinal extension of the brightening arc at substorm onset is caused by earthward flow braking processes which produce field dipolarization and pressure increase propagating in longitude in the near-earth plasma sheet

Subnormal operators regarded as generalized observables and compound-system-type normal extension related to su(1,1)

In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also a framework of their implementations, we introduce a new concept compound-system-type normal extension, and we derive the compound-system-type normal extension of a subnormal operator, which is defined from an irreducible unitary representation of the algebra su(1,1). The squeezed states are characterized as the eigenvectors of an operator from this viewpoint, and the squeezed states in multi-particle systems are shown to be the eigenvectors of the adjoints of these subnormal operators under a representation. The affine coherent states are discussed in the same context, as well.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.sty, The previous version has some mistake

Interaction between expectancies and drug effects: an experimental investigation of placebo analgesia with caffeine as an active placebo

In a randomised placebo-controlled clinical trial it is assumed that psychosocial effects of the treatment, regression to the mean and spontaneous remission are identical in the drug and placebo group. Consequently, any difference between the groups can be ascribed to the pharmacological effects. Previous studies suggest that side effects of drugs can enhance expectancies of treatment effects in the drug group compared to the placebo group, and thereby increase placebo responses in the drug group compared to the placebo group. The hypothesis that side effects of drugs can enhance expectancies and placebo responses was tested. Painful laser stimuli were delivered to 20 healthy subjects before and after administration of a drink with 0 or 4 mg/kg caffeine. The drink was administered either with information that it contained a painkiller or that it was a placebo. Laser-evoked potentials and reports of pain, expectancy, arousal and stress were measured. Results Four milligrammes per kilogramme of caffeine reduced pain. Information that a painkiller was administered increased the analgesic effect of caffeine compared to caffeine administered with no drug information. This effect was mediated by expectancies. Information and expectancies had no effect on pain intensity when 0 mg/kg was administered. The analgesic effect of caffeine was increased by information that a painkiller was administered. This was due to an interaction of the pharmacological action of the drug and expectancies. Hence, psychosocial effects accompanying a treatment can differ when an active drug is administered compared to a placebo