On the Iwasawa -invariants of real abelian fields

For a prime number and a number field , let denote the projective limit of the -parts of the ideal class groups of the intermediate fields of the cyclotomic -extension over . It is conjectured that is finite if is totally real. When is an odd prime and is a real abelian field, we give a criterion for the conjecture, which is a generalization of results of Ichimura and Sumida. Furthermore, in a special case where divides the degree of , we also obtain a rather simple criterion.

     

Some families of Mordell curves associated to cubic fields

We introduce some Mordell curves of two different natures both of which are associated to cubic fields. One set of them consists of those elliptic curves whose rational points over the rational number field are described by or closely related to cubic fields. The other is a one-parameter family of Mordell curves which gives all (cyclic) cubic twists and all quadratic twists of the Fermat curve X³+Y³+Z³=0.     

A Sato–Tate Law for Drinfeld Modules

We formulate and prove a Sato–Tate equidistribution law for Drinfeld modules.     

A thermochemical instability. II. Inhomogeneous fluctuations

The behavior of coupled stochastic fields near a cusp bifurcation is studied. The results are applied to a thermochemical model and the possibility of observing nonclassical critidal behavior is discussed.     

Fast Encoding Method for Image Vector Quantization Based on Multiple Appropriate Features to Estimate Euclidean Distance

The encoding process of finding the best-matched codeword (winner) for a certain input vector in image vector quantization (VQ) is computationally very expensive due to a lot of k-dimensional Euclidean distance computations. In order to speed up the VQ encoding process, it is beneficial to firstly estimate how large the Euclidean distance is between the input vector and a candidate codeword by using appropriate low dimensional features of a vector instead of an immediate Euclidean distance computation. If the estimated Euclidean distance is large enough, it implies that the current candidate codeword could not be a winner so that it can be rejected safely and thus avoid actual Euclidean distance computation. Sum (1-D), L₂ norm (1-D) and partial sums (2-D) of a vector are used together as the appropriate features in this paper because they are the first three simplest features. Then, four estimations of Euclidean distance between the input vector and a codeword are connected to each other by the Cauchy–Schwarz inequality to realize codeword rejection. For typical standard images with very different details (Lena, F-16, Pepper and Baboon), the final remaining must-do actual Euclidean distance computations can be eliminated obviously and the total computational cost including all overhead can also be reduced obviously compared to the state-of-the-art EEENNS method meanwhile keeping a full search (FS) equivalent PSNR.     

Pressure dependence of electronic transitions of Fe,Co and Ni ions in layered dihalides

Abstract

The near infra-red absorption peaks due to transition metal ions in four halides of Fe, Co and Ni have been studied as a function of pressure. The behaviors of these ions' absorption peaks under pressure are found to be quite different. While the energy of the absorption peak in Col₂ increases with pressure similar to the behavior of transition metal ions in cubic crystal fields, the absorption peaks in the Fe halides are found to be almost independent of pressure. In Nil₂ two absorption peaks exhibit level-crossing at about 2GPa. The results have been interpreted in terms of a theory proposed by da Silva and Falicov [Phys. Rev. B 45,11511 (1992)] in which pressure changes the trigonal component of the crystal field at the transition metal ions.     

Energy Spectrum and Its Pressure-Induced Shift and g Factor of ZnS:Mn2+

By using strong-field scheme, the complete d⁵ energy matrix with D_2d symmetry has been constructed. Then, by diagonalization of this matrix at normal and various pressures,the whole energy spectrum [including the ground-state zero-field-splitting (GSZFS)], its PS and the g factor of the ground state for zns:Mn²⁺ have uniformly been calculated. According to the eigenfunctions and PS, the new assignments of five absorption bands have been given.The variation of tetragonal field with pressure makes a main contribution to the pressureinduced shift (PS) of GSZFS of zns:Mn²⁺, which supports the existence of tetragonal Jahn-Teller distortion in zns:Mn²⁺. It is found that when P≥62 kbar, t₂⁴(³T₁)e⁴T₁ merges with t₂e^{4 2}T₂, which has to be taken into account in the calculation of PS of the fifth band in the range of 1 bar ~ 95 kbar. It is demonstrated that the Mn²⁺ ions in ZnS:Mn²⁺ have tetrahedral coordination, and the difference between ζ and ζ' caused by the covalency effect is very important for GSZFS. The physical essentials of typical levels, GSZFS and their PS have been revealed. By taking into account the influence of covalency on t₂³(⁴A₂)e²(³A₂)⁴A₁ and t₂³(²E)e²(³A₂)⁴E, the positon of the third absorption band at normal pressure has been estimated.     

Anisotropic hubble expansion of large scale structures

With the aim of understanding the cosmic velocity fields at large scale, we investigate the dynamics of a pressureless distribution of gravitational sources moving under an anisotropic generalization of Hubble expansion and according to Euler-Poisson equations system. As a result, it turns out that such a behavior requires the distribution to be homogenous, similarly to Hubble law. Among several solutions, we show a planar kinematics which admits a constant (eternal) and rotational distortion, where the velocity field is not potential. Within this class, the one with no rotational distortion identifies to a bulk flow. To apply this model within cosmic structures as the Local Super Cluster, the solutions are interpreted as approximations providing us with an hint on the behavior of the cosmic flow just after decoupling era up to present date. Such a result suggests that the observed bulk flow may not be due exclusively to tidal forces but has a primordial origin. UPRES EA 2596. Unité Mixte de Recherche (UMR 6207) du CNRS, et des universités Aix-Marseille I, Aix-Marseille II et du Sud Toulon-Var. Laboratoire affiliéà la FRUMAM (FR 2291).     

Ultrasound velocimetry of ferrofluid spin-up flow measurements using a spherical coil assembly to impose a uniform rotating magnetic field

Ferrofluid spin-up flow is studied within a sphere subjected to a uniform rotating magnetic field from two surrounding spherical coils carrying sinusoidally varying currents at right angles and 90° phase difference. Ultrasound velocimetry measurements in a full sphere of ferrofluid shows no measureable flow. There is significant bulk flow in a partially filled sphere (1-14 mm/s) of ferrofluid or a finite height cylinder of ferrofluid with no cover (1-4 mm/s) placed in the spherical coil apparatus. The flow is due to free surface effects and the non-uniform magnetic field associated with the shape demagnetizing effects. Flow is also observed in the fully filled ferrofluid sphere (1-20 mm/s) when the field is made non-uniform by adding a permanent magnet or a DC or AC excited small solenoidal coil. This confirms that a non-uniform magnetic field or a non-uniform distribution of magnetization due to a non-uniform magnetic field are causes of spin-up flow in ferrofluids with no free surface, while tangential magnetic surface stress contributes to flow in the presence of a free surface.Recent work has fitted velocity flow measurements of ferrofluid filled finite height cylinders with no free surface, subjected to uniform rotating magnetic fields, neglecting the container shape effects which cause non-uniform demagnetizing fields, and resulting in much larger non-physical effective values of spin viscosity η′∼10⁻⁸−10⁻¹² N s than those obtained from theoretical spin diffusion analysis where η′≤10⁻¹⁸ N s. COMSOL Multiphysics finite element computer simulations of spherical geometry in a uniform rotating magnetic field using non-physically large experimental fit values of spin viscosity η′∼10⁻⁸−10⁻¹² N s with a zero spin-velocity boundary condition at the outer wall predicts measureable flow, while simulations setting spin viscosity to zero (η′=0) results in negligible flow, in agreement with the ultrasound velocimetry measurements. COMSOL simulations also confirm that a non-uniform rotating magnetic field or a uniform rotating magnetic field with a non-uniform distribution of magnetization due to an external magnet or a current carrying coil can drive a measureable flow in an infinitely long ferrofluid cylinder with zero spin viscosity (η′=0).     

Image segmentation using adaptive loopy belief propagation

Loopy belief propagation (LBP) algorithm over pairwise-connected Markov random fields (MRFs) has become widely used for low-level vision problems. However, Pairwise MRF is often insufficient to capture the statistics of natural images well, and LBP is still extremely slow for application on an MRF with large discrete label space. To solve these problems, the present study proposes a new segmentation algorithm based on adaptive LBP. The proposed algorithm utilizes local region information to construct a local region model, as well as a local interaction region MRF model for image segmentation. The adaptive LBP algorithm maximizes the global probability of the proposed MRF model, which employs two very important strategies, namely, “message self-convergence” and “adaptive label pruning”. Message self-convergence can improve the reliability of a pixel in choosing a label in local region, and label pruning can dismiss impossible labels for every pixel. Thus, the most reliable information messages transfer through the LBP algorithm. The experimental results show that the proposed algorithm not only obtains more accurate segmentation results but also greater speed.