Perfect Fluids: Field-theoretical Description and Gauge Symmetry Issue

We show that combinations of (in general,non-linear) two- and threeform fields, analogous to theMaxwell (one-form) field, completely describe perfectfluids, including the rotating ones. In the non-rotating case, the two-form field is sufficient, and afree three-form field proves to be equivalent toappearance of the cosmological term in Einstein'sequations (the square-root non-linearity correspondingto = 0). The gauge degrees of freedombreak down when a rotation is included, but even whenthey exist, there fails to be realized an equivalence ofthe two-form field and the massless scalar one recently claimed by Weinberg.     

Spinless Matter in Transposed-Equi-Affine Theory of Gravity

We derive and discuss the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the model of gravity recently proposed by A. Saa with covariantly constant volume with respect to the transposed connection in Einstein-Cartan spaces. A new interpretation of this theory as a theory with variable Planck constant is suggested. We show that the consistency of the semiclassical limit of the wave equation and classical motion dictates a new definite universal interaction of torsion with massive fields.     

一个新型分子铁磁体: 氰根桥联的铜(II)-铁(III)配合物

合成和表征了一个新的分子磁体,氰根桥联的杂化型异金属配合物[Cu(en)]~3[Fe(CN)~6]~2.3H~O(en为乙二胺)。变温磁化率、零场冷却磁化强度(ZFCM)、场冷却磁化强度(FCM)和磁滞回线测量表明铜铁离子间存在着铁磁性相互作用,其铁磁相变温度为T~c=11.0K,矫顽力为20×10^-^4T,剩磁为1.70×10^-^1cm^3.mol^-^1.T。该化合物为杂化型铜(II)-铁(III)普鲁士蓝类中具有铁磁相变温度的首例。     

On group orders of rational points of elliptic curves

We consider elliptic curves without complex multiplication defined over the rationals or with complex multiplication defined over the Hilbert class field of the endomorphism ring. We examine the distribution of almost prime group orders of these curves when reduced modulo a prime ideal.     

Massive, Non-ghost Solutions for the Dirac Field Coupled Self-consistently to Gravity

We present new, massive, non-ghost solutions for the Dirac field coupled self-consistently to gravity. We employ a gauge-theoretic formulation of gravity which automatically identifies the spin of the Dirac field with the torsion of the gauge fields. Homogeneity of the field observables requires that the spatial sections be flat. Expanding and collapsing singular solutions are given, as well as a solution which expands from a singularity before recollapsing. Torsion effects are only important while the Compton wavelength of the Dirac field is larger than the Hubble radius. We study the motion of spinning point-particles in the background of the expanding solution. The anisotropy due to the torsion is manifest in the particle trajectories.     

ELECTRORHEOLOGICAL PROPERTIES OF TALC POWDER/SILICONE OIL SUSPENSIONS UNDER DC FIELDS

In this study, the electrorheological （ER） behavior of suspensions prepared from d50 = 2.4 lam talc powder, dispersed in insulating silicone oil （SO） medium was investigated. Sedimentation stabilities of suspensions （c = 5 wt%） prepared using these talc powder powders were determined to be 78 days. The ER activity of all the suspensions was observed to increase with increasing electric field strength, concentration and decreasing shear rate. The shear stress of talc powder suspensions increased linearly with increasing concentrations of the particles and with the applied electric field strength. Electric field viscosity of all the suspensions decreased sharply with increasing shear rate and showed a typical shear thinning non-Newtonian visco-elastic behavior. Effects of frequency on the ER activity of talc powder/SO system were also investigated.     

Debye Potentials for Self-Dual Fields

It is shown that in a space-time that admits ageodetic and shear-free null vector field which is aprincipal direction of the conformal curvature(therefore, in any algebraically special solution of the Einstein vacuum field equations), any self-dualelectromagnetic field is locally given by a scalar(Debye) potential which obeys a second-orderdifferential equation and, similarly, that any self-dualYang-Mills field is locally given by a matrix-valuedpotential governed by a nonlinear second-orderdifferential equation. Using the fact that any self-dualelectromagnetic field is the self-dual part of a realsolution of the source-free Maxwell equations, it isshown that in any space-time of this class, the solutionof the source-free Maxwell equations is locally given bya Debye potential.     

A Note on the Rarita-Schwinger Equations

Assuming that the background spacetime is a solution of the Einstein vacuum equations without cosmological constant, we analyze how the Rarita-Schwinger equations can be obtained via a particular generalization of the usual spin-3/2 massless free field equations. On the basis of this analysis we speculate on the possibility of finding other generalizations of the Rarita-Schwinger equations.     

Molecular Force Fields of XY6 Type Molecules

Octahedral molecules of XY₆ type belonging to O_h symmetry have six normal modes of vibrations. On group theoretical considerations, Λ_vib, = a^1g + e_g + 2t_1u + t_2g + t_2u     

On Hausdorff dimension of certain Riesz product in local fields

In this paper, we consider the Riesz product dμ =^∞∏j=1（1＋ajRexbjλj（x））dx in local fields, and we obtain the upper and lower bound of its Hausdorff dimension.