The Lorentz group and its finite field analogues: local isomorphism and approximation

Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real 4-dimensional space-time. Bounded subsets of the real Lorentz group are retractable with arbitrary accuracy to finite subsets of such rational subgroups. These finite retracts correspond, via local isomorphisms, to well-behaved subsets of Lorentz groups over finite fields. This establishes a relationship of approximation between the real Lorentz group and Lorentz groups over very large finite fields

Cosmological perturbations on local systems

We study the effect of cosmological expansion on orbits--galactic, planetary, or atomic--subject to an inverse-square force law. We obtain the laws of motion for gravitational or electrical interactions from general relativity--in particular, we find the gravitational field of a mass distribution in an expanding universe by applying perturbation theory to the Robertson-Walker metric. Cosmological expansion induces an ($\ddot a/a) \vec r$ force where $a(t)$ is the cosmological scale factor. In a locally Newtonian framework, we show that the $(\ddot a/a) \vec r$ term represents the effect of a continuous distribution of cosmological material in Hubble flow, and that the total force on an object, due to the cosmological material plus the matter perturbation, can be represented as the negative gradient of a gravitational potential whose source is the material actually present. We also consider the effect on local dynamics of the cosmological constant. We calculate the perihelion precession of elliptical orbits due to the cosmological constant induced force, and work out a generalized virial relation applicable to gravitationally bound clusters.Comment: 10 page

Effect of inhomogeneity of the Universe on a gravitationally bound local system: A no-go result for explaining the secular increase in the astronomical unit

We will investigate the influence of the inhomogeneity of the universe, especially that of the Lema{\^i}tre-Tolman-Bondi (LTB) model, on a gravitationally bound local system such as the solar system. We concentrate on the dynamical perturbation to the planetary motion and derive the leading order effect generated from the LTB model. It will be shown that there appear not only a well-known cosmological effect arisen from the homogeneous and isotropic model, such as the Robertson-Walker (RW) model, but also the additional terms due to the radial inhomogeneity of the LTB model. We will also apply the obtained results to the problem of secular increase in the astronomical unit, reported by Krasinsky and Brumberg (2004), and imply that the inhomogeneity of the universe cannot have a significant effect for explaining the observed $d{\rm AU}/dt = 15 \pm 4 ~{\rm [m/century]}$.Comment: 12 pages, no figure, accepted for publication in Journal of Astrophysics and Astronom

Application of Time Transfer Function to McVittie Spacetime: Gravitational Time Delay and Secular Increase in Astronomical Unit

We attempt to calculate the gravitational time delay in a time-dependent gravitational field, especially in McVittie spacetime, which can be considered as the spacetime around a gravitating body such as the Sun, embedded in the FLRW (Friedmann-Lema\^itre-Robertson-Walker) cosmological background metric. To this end, we adopt the time transfer function method proposed by Le Poncin-Lafitte {\it et al.} (Class. Quant. Grav. 21:4463, 2004) and Teyssandier and Le Poncin-Lafitte (Class. Quant. Grav. 25:145020, 2008), which is originally related to Synge's world function $\Omega(x_A, x_B)$ and enables to circumvent the integration of the null geodesic equation. We re-examine the global cosmological effect on light propagation in the solar system. The round-trip time of a light ray/signal is given by the functions of not only the spacial coordinates but also the emission time or reception time of light ray/signal, which characterize the time-dependency of solutions. We also apply the obtained results to the secular increase in the astronomical unit, reported by Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267, 2004), and we show that the leading order terms of the time-dependent component due to cosmological expansion is 9 orders of magnitude smaller than the observed value of $d{\rm AU}/dt$, i.e., $15 \pm 4$ ~[m/century]. Therefore, it is not possible to explain the secular increase in the astronomical unit in terms of cosmological expansion.Comment: 13 pages, 2 figures, accepted for publication in General Relativity and Gravitatio

The European Insomnia Guideline : An update on the diagnosis and treatment of insomnia 2023

Publisher Copyright: © 2023 The Authors. Journal of Sleep Research published by John Wiley & Sons Ltd on behalf of European Sleep Research Society.Progress in the field of insomnia since 2017 necessitated this update of the European Insomnia Guideline. Recommendations for the diagnostic procedure for insomnia and its comorbidities are: clinical interview (encompassing sleep and medical history); the use of sleep questionnaires and diaries (and physical examination and additional measures where indicated) (A). Actigraphy is not recommended for the routine evaluation of insomnia (C), but may be useful for differential-diagnostic purposes (A). Polysomnography should be used to evaluate other sleep disorders if suspected (i.e. periodic limb movement disorder, sleep-related breathing disorders, etc.), treatment-resistant insomnia (A) and for other indications (B). Cognitive-behavioural therapy for insomnia is recommended as the first-line treatment for chronic insomnia in adults of any age (including patients with comorbidities), either applied in-person or digitally (A). When cognitive-behavioural therapy for insomnia is not sufficiently effective, a pharmacological intervention can be offered (A). Benzodiazepines (A), benzodiazepine receptor agonists (A), daridorexant (A) and low-dose sedating antidepressants (B) can be used for the short-term treatment of insomnia (≤ 4 weeks). Longer-term treatment with these substances may be initiated in some cases, considering advantages and disadvantages (B). Orexin receptor antagonists can be used for periods of up to 3 months or longer in some cases (A). Prolonged-release melatonin can be used for up to 3 months in patients ≥ 55 years (B). Antihistaminergic drugs, antipsychotics, fast-release melatonin, ramelteon and phytotherapeutics are not recommended for insomnia treatment (A). Light therapy and exercise interventions may be useful as adjunct therapies to cognitive-behavioural therapy for insomnia (B).Peer reviewe

Suomalaisen eläin- ja kasvitieteellisen seuran Vanamon julkaisuja osa 2

Kielet saksa ja suomi