Synthesis and Structure of One Novel Polyoxometalate Compound Connected via Cerium(Ⅲ) Cation with Three-dimensional Framework H2{[K(H2O)2]2[Ce(H2O)5]2(H2Mo1.16W10.84O42)}·8H2O

One novel polyoxometalate compound connected via trivalent cerium cation as bridge H2{[K(H2O)2]2[Ce(H2O)5]2(H2Mo1.16W10.84O42)}·8H2O 1 was designed and synthesized in aqueous solution. X-ray diffraction analysis reveals that the structure of 1 is a three-dimensional framework assembled from the arrangement of H2Mo1.16W10.84O42 (named paradodecmetalate-B) and Ce(H2O)53 containing two planes, which are constructed through the unification of H2Mo1.16W10.84O4210- and Ce(H2O)53 along the [100] and [001] directions. Crystal data: H96Ce4K4Mo2.32O128W21.68, Mr = 7074.89, monoclinic, P21/n, a = 12.5037(17), b = 17.002(2), c = 12.7473(17) (A), β = 105.966(2)°, V = 2605.4(6) (A)3, Z = 1, Dc = 4.509 g/cm3, F(000) = 3132, μ = 26.098 mm(1, R = 0.0377 and wR = 0.0789 (I ＞ 2σ(I)).     

潮汐现象的成因

讨论了引潮力的成因，太阳的引潮力与月亮的引潮力的相对大小，并对潮汐现象的一些规律和影响因素作了简要介绍。     

Structure Equations in the U 4 Theory of Gravitation

Cartan’s equations of structure and Bianchi identities in the U ₄ theory of gravitation are derived. The relativistic language we adopted is that of Newman-Penrose-Jogia and Griffiths (NPJG). A number of important properties which arise in the development of basic equations are also presented in the NPJG formalism. It is hoped that the essence of non-Riemannian geometry can be summarized by exploiting these equations.     

Duality in physical sciences and beyond

An extended meaning of duality is suggested in the context of development of major themes in physical sciences since Newton. In such a generalization,five distinct aspects of duality are sought to be identified and illustrated through concrete examples drawn from various physical concepts, old and new. These are (i) reciprocity, (ii) parallelism, (iii) alternative formulation, (iv) unification and (v) measurement incompatibility. Bohr’s view of duality and the Copenhagen Interpretation are discussed briefly in this context. Finally, duality aspects beyond physics are briefly touched upon, the philosophical link being provided by Bohr’s Complementarity Principle on the one hand, and recent attempts (notably by Capra) to draw suggestive parallels between modern science and Eastern mysticism on the other. “Be in truth eternal, beyond earthly opposites”—Bhagwat Gita. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Stability of proton and maximally symmetric minimal unification model for basic forces and building blocks of matter

With the hypothesis that all independent degrees of freedom of basic building blocks should be treated equally on the same footing and correlated by a possible maximal symmetry, we arrive at a 4-dimensional space-time unification model. In this model the basic building blocks are Majorana fermions in the spinor repre- sentation of 14-dimensional quantum space-time with a gauge symmetry GM4D = SO(1,3)×SU(32)×U(1)A×SU(3)F. The model leads to new physics including mirror particles of the standard model. It enables us to issue some fundamental questions that include: why our living space-time is 4-dimensional, why parity is not con- served in our world, how the stability of proton is, what the origin of CP violation is and what the dark matter can be.     

Quirino Majorana’s Experiments on the Speed of Light and Gravitational Absorption

Quirino Majorana (1871–1957) was an outstanding Italian experimental physicist who investigated a wide range of phenomena during his long career in Rome,Turin, and Bologna. We focus on his experiments in Turin during 1916–1921 and in Bologna during 1921–1934 to test the validity of Albert Einstein’s postulate on the constancy of the speed of light and to detect gravitational absorption. These experiments required extraordinary skill, patience, and dedication, and all of them confirmed Einstein’s postulate and Isaac Newton’s law of universal gravitation to high precision. Had they not done so, Majorana’s fame among historians and physicists no doubt would be much greater than it is today. Giorgio Dragoni is Professor of History of Physics at the University of Bologna. Giulio Maltese is a Roman member of the Italian Society for the History of Physics and Astronomy. Luisa Atti is a Bolognese member of the Association for the Teaching of Physics.     

Gravitational Faraday Effect Produced by a Ring Laser

Using the linearized Einstein gravitational field equations and the Maxwell field equations it is shown that the plane of polarization of an electromagnetic wave is rotated by the gravitational field created by the electromagnetic radiation of a ring laser. It is further shown that this gravitational Faraday effect shares many of the properties of the standard electromagnetic Faraday effect. An experimental arrangement is then suggested for the observation of this gravitational Faraday effect induced by the ring laser.     

Energy-Level Shifts of a One-Electron Atom in Higher-Derivative Gravitational Field Caused by High-Power Laser Pulse

The gravitational field produced by a high-power laser pulse traveling with a velocity < c is found in the framework of higher-derivative theory of gravitation. The gravitational perturbations of the energy levels of a freely falling one-electron atom in the higher-derivative gravitational field are studied. The energy-level shifts of highly excited hydrogen atom are considered, and the influence of the additional forces included in the linearized higher-derivative gravitation on the energe level shifts of the atom is investigated.     

Wesson’s Induced Matter Theory with a Weylian Bulk

The foundations of Wesson’s induced matter theory are analyzed. It is shown that the empty—without matter—5-dimensional bulk must be regarded as a Weylian space rather than as a Riemannian one. Revising the geometry of the bulk, we have assumed that a Weylian connection vector and a gauge function exist in addition to the metric tensor. The framework of a Weyl–Dirac version of Wesson’s theory is elaborated and discussed. In the 4-dimensional hypersurface (brane), one obtains equations describing both fields, the gravitational and the electromagnetic. The result is a geometrically based unified theory of gravitation and electromagnetism with mass and current induced by the bulk. In special cases on obtains on the brane the equations of Einstein–Maxwell, or these of the original induced matter theory.     

Letter: Cerenkov Radiation from a Charged Particle in a Weyl–Dirac Theory

A thin shell can separate an interior region of Riemannian geometry from an exterior spherically symmetric Weyl space. We explore the possibility that a charged particle propagating in the gravitational field outside this thin shell could emit Cerenkov radiation. Some astrophysical scenarios in which such effect could arise are discussed.