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[en] This paper is devoted to the classical Knotting Problem: for a given manifold N and number m describe the set of isotopy classes of embeddings N→Sm. We study the specific case of knotted tori, that is, the embeddings Sp×Sq→Sm. The classification of knotted tori up to isotopy in the metastable dimension range m ≥ p + 3/2q + 2, p≤q, was given by Haefliger, Zeeman and A. Skopenkov. We consider the dimensions below the metastable range and give an explicit criterion for the finiteness of this set of isotopy classes in the 2-metastable dimension. Bibliography: 35 titles.
[en] We have measured the circular polarization of sunspots with a sensitivity of less than 3 x 10-6, over the range from 3700 A to 4.5 μm. Through all of our passbands of widths > or =0.1 μm, V has a single sign for a given spot, namely: if H is toward the observer, V is negative, i.e., the E vector rotates clockwise in a stationary plane over the spot. The rough magnitude, sign, and to some extent the spectral shape of V(lambda) for lambda> or =1.5 μm agree with a continuum magneto-opacity model. But the UV-visible polarization is anomalously large, e.g., > or approx. =0.05% in the B band, seemingly correlated with line blanketing. A new mechanism for this is proposed, magneto-emission by atoms oriented by anisotropic radiation
[en] A new high precision measurement of the muonium hyperfine structure interval Δν and its Zeeman effect in the n = 1 ground state is being undertaken at LAMPF. Aiming for a precision of 50 ppb for the muon to proton magnetic ratio μμ/μp and of 10 ppb for Δν, the present experimental uncertainties can be reduced by a factor of about 5 using line-narrowing techniques. It is emphasized that still more precise measurements would be possible in the future with the realization of a more intense pulsed muon source
[en] An approximately relativistic theory of bound states which ensures the Poincare invariance of atomic systems to relative order (v/c)2 is used to derive the Zeeman interaction Hamiltonians correct to order α3 and to all orders in me/mN for arbitrary two body systems and three body systems. Previously neglected radiative corrections of order α3 and recoil corrections of order α3m3/mN are also included. For neutral systems, the linear Zeeman Hamiltonians are unitarily equivalent to the linear Zeeman Hamiltonians obtained by other authors in the past. Explicit analytic expressions for the gJ and gI factors of hydrogen-like atoms are given and verify the results of Grotch and Kashuba. The positronium ground state g factor calculated here agrees exactly with previous calculations. The terms of order me/mN, α2, α3, and α2me/MN of the three-body linear Zeeman Hamiltonian are used to calculate the g factors for n=2 4He and 3He. The effect of the finite mass of the nucleus on the wavefunction is accounted for the work presented here. The 23S1 gJ factor is in excellent agreement with the results of Grotch and Hegstrom and experimental results. It is the first time that corrections of order α3 and α2me/mN have been used to calculate the 23PJ and 21P1 helium g factors. Three different wavefunctions are used to derive the 23J and 21P1 g factors for 4He and 3He. The most accurate is a 125 term configuration interaction wavefunction utilizing 12 nonlinear parameters. The resulting g's factor agrees exactly with the results of Lewis and Hughes (to order α2). The g'L factor obtained is a significant improvement over the results of Lewis and Hughes
[en] We calculate the vortex gyration in a nanodisk with existence of Dzyaloshinskii–Moriya interactions (DMI), including bulk DMI (BDMI) and interfacial DMI (IDMI). By analyzing the system energies, we establish quantitative relations between the gyration frequency and the magnetostatic, DMI, exchange, and Zeeman energies. Accordingly, we explain how the BDMI and IDMI alter the vortex gyration frequency in a nanodisk. - Highlights: • We study the vortex gyration frequency in a nanodisk with DMI. • Interfacial DMI decreases the gyration frequency obviously. • We explain how the DMI alter the vortex gyration frequency by analyzing the energies.