There are no magnetically charged particle-like solutions of the Einstein Yang-Mills equations for Abelian models

We prove that there are no magnetically charged particle-like solutions for Abelian models in Einstein Yang-Mills, but for non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.Comment: 48 pages, 1 figur

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

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

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

Visual function in Norwegian children aged 5–13 years with prenatal exposure to opioid maintenance therapy: A case–control study

Purpose: To assess various aspects of visual function in school children prenatally exposed to opioid maintenance therapy (OMT) and to explore possible outcome differences between prenatal methadone and buprenorphine exposure. Methods: In a cross-sectional case–control study, 63 children aged 5–13 years with prenatal OMT exposure were compared with 63 age- and gender-matched, non-exposed controls regarding important visual parameters, such as visual acuity, orthoptic status, refractive state, colour vision, and visual field. Results: The OMT-exposed children had significantly poorer visual acuity, both for the best eye, the worst eye and binocularly. Two children had mild visual impairment. Manifest strabismus was more frequent in the OMT group, 30%, vs. 4.8% in the control group. The most frequent types of strabismus were accommodative esotropia and intermittent exotropia. Manifest nystagmus was present in 10 (16%) of the exposed children compared to one among the non-exposed children. The accommodative amplitude was decreased in the OMT group compared to the controls. After adjusting for polydrug exposure and SGA (small-for-gestational-age), the between-group differences in visual acuity, strabismus, and nystagmus remained. The methadone-exposed children had poorer visual acuity, increased frequency of strabismus and a higher percentage of nystagmus, hypermetropia and astigmatism compared to the buprenorphine-exposed children. Conclusions: School-age children exposed to methadone or buprenorphine in utero had a higher prevalence of strabismus and nystagmus, and a lower visual acuity and accommodation amplitude. Buprenorphine exposure was associated with more favourable results than methadone exposure on most visual outcome measures and should be the preferred substance in OMT.publishedVersio

Certified Computer Algebra on top of an Interactive Theorem Prover

Contains fulltext : 35027.pdf (publisher's version ) (Open Access

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

Diagnostic accuracy of ultrasonography compared to unenhanced CT for stone and obstruction in patients with renal failure

BACKGROUND: To determine accuracy of ultrasound (US) kidney, ureter and bladder (KUB) compared to un-enhanced helical CT (UHCT) in patients with renal failure in the diagnosis of stone and obstruction. METHODS: This is a case controlled study conducted in the period from June 2000 to July 2003 at a university hospital. All patients had both US and UHCT scan. Patients with serum creatinine ≥ 1.8 mg/dl were included in the study. Only direct visualization of stone was considered as confirmatory. In both the studies, UHCT and US, presence of stone and obstruction were noted. The relevant biochemicals, radiological and clinical records of all the patients were analyzed. Data was analyzed using commercially available software. RESULTS: During the period of study 864 patients had UHCT for evaluation of the urinary tract in patients presenting with flank pain. Out of these 34 patients had both UHCT and US done within a span of one day and had serum creatinine of ≥1.8 mg/dl. Mean age was 48 ±15.8 years and 59% of patients were males. UHCT identified renal stones in 21 (62%), whereas 17 of these were identified on US, with a sensitivity of 81%. Of the four patients with renal stones missed on US, three were identified on plain x-ray; the mean size of stones missed was 6.3 mm. Of the 22 (65%) patients with ureteric stone on UHCT, US could only identify 10; a further 7 were identified on x-ray KUB, giving a sensitivity of 45% (US alone) and 77% (US with x-ray KUB). CONCLUSIONS: US is sensitive and specific for renal stones, 81% and 100% and for hydronephrosis, 93% and 100%, respectively. Its sensitivity to pick ureteric stone (46%) and to identify hydroureter (50%) is low. Addition of x-ray KUB abdomen increases the sensitivity for ureteric stones to 77%

Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te