Aspects of Cosmological Relativity

In this paper we review cosmological relativity,a new special theory of relativity that was recentlydeveloped for cosmology, and discuss in detail some ofits aspects. We recall that in this theory it is assumed that gravitation is negligible.Under this assumption, the receding velocities ofgalaxies and the distances between them in the Hubbleexpansion are united into a four-dimensionalpseudo-Euclidean manifold, similarly to space and time inordinary special relativity. The Hubble law is assumedand is written in an invariant way that enables one toderive a four-dimensional transformation which issimilar to the Lorentz transformation. The parameter inthe new transformation is the ratio between the cosmictime to the Hubble time (in which the cosmic time ismeasured backward with respect to the present time). Accordingly, the new transformationrelates physical quantities at different cosmic times inthe limit of weak or negligible gravitation. Thetransformation is then applied to the problem of the expansion of the universe at the very earlystage when gravity was negligible and thus thetransformation is applicable. We calculate the ratio ofthe volumes of the universe at two different timesT₁ and T₂ after the big bang. Under theassumptions that T₂ – T₁ 10^-32 sec and T₂ 1 sec,we find that V₂/V₁ =10^-16/T₁. For T₁ 10^-132 sec we obtainV₂/V₁ 10⁵⁰. Thisresult conforms with the standard inflationary universe theory, but now it isobtained without assuming that the universe is propelledby antigravity. New applications of the theory arepresented. This includes a new law for the decay of radioactive materials that was recentlydeveloped by Carmeli and Malin. The new law is amodification of the standard exponential formula whencosmic times are considered instead of the ordinarylocal times. We also show that there is no need to assumethe existence of galaxy dark matter; the Tully-Fisherlaw is derived from our theory. A significant extensionof the theory to cosmology that was recently made by Krori, Pathak, Das, and Purkayastha isgiven. In this way cosmological relativity becomes ageneral theory of relativity in seven dimensions ofcurved space-time-velocity. The solutions of the field equations in seven dimensions obtained by Kroriet al. are given and compared to those of the standardFriedmann-Robertson-Walker result. A completely newpicture of the expanding universe is thus obtained and compared to the FRW one.     

Catalytic coupling of terminal alkynes with isonitriles promoted by organoactinide complexes

The coupling reaction of terminal alkynes and tert-butylisonitrile to yield substituted alpha,beta-acetylenic aldimines is catalyzed by the organoactinide neutral complexes Cp*2AnMe2 (Cp* = C5Me5, An = Th, U) and the cationic complex [(Et2N)3U][BPh4]. The reaction proceeds by a 1,1-insertion of the isonitrile into the metal-acetylide bond. Additional insertion products can be obtained by altering the catalyst and the reactant ratios. A plausible mechanism for the catalytic reaction is presented, in addition to the crystal structure of Cp*2UMe2     

Isotropic Gauss-Markov currents

Summary A natural definition of the Markov property for multi-parameter random processes (random fields) is the following. Let {X _t,t ^N } be a multiparameter process. For any set D in ^N let _D denote the -field generated by {X _t , tD}. The field {X _t,tD} is said to be Markov (or Markov of degree 1 [6], or sharp Markov) if, for any bounded open set D with smooth boundary, _D and _D ^c are conditionally independent given _D . It has been known for some time that to find interesting examples of Markov processes under this definition; it is necessary to consider generalized random functions. In this paper we show that a natural framework for the Markov property of multiparameter processes is a class of generalized random differential forms (i.e., random currents). Our principal objective is to relate the Markovian nature of an isotropic gaussian current to its spectral properties.Work supported by the Army Research Office, Grant No. DAAG 29-85-K-0233Work done while at the University of California at Berkeley     

Generalized stochastic integrals and the malliavin calculus

Summary The paper first reviews the Skorohod generalized stochastic integral with respect to the Wiener process over some general parameter space T and it's relation to the Malliavin calculus as the adjoint of the Malliavin derivative. Some new results are derived and it is shown that every sufficiently smooth process {u_t, tT} can be decomposed into the sum of a Malliavin derivative of a Wiener functional, and a process whose generalized integral over T vanishes. Using the results on the generalized integral, the Bismut approach to the Malliavin calculus is generalized by allowing non adapted variations of the Wiener process yielding sufficient conditions for the existence of a density which is considerably weaker than the previously known conditions.Let e _i be a non-random complete orthonormal system on T, the Ogawa integral u W is defined as _i (e _i u) e _i dW where the integrals are Wiener integrals. Conditions are given for the existence of an intrinsic Ogawa integral i.e. independent of the choice of the orthonormal system and results on it's relation to the Skorohod integral are derived.The transformation of measures induced by (W + u d u non adapted is discussed and a Girsanov-type theorem under certain regularity conditions is derived.The work of M.Z. was supported by the Fund for Promotion of Research at the Technion     

Propellanes. Part LXXX. Baeyer-Villiger Oxidation of [4.3.3]Propellane-8,11-dione

Oxidation of the title compound with m-chloroperbenzoic acid affords a keto-lactone, two bis-lactones and a bis-spirolactone, in varying amounts depending upon the reaction conditions. The structures were established by means of X-ray diffraction, ¹H- and ¹³C-NMR spectroscopy.     

Moving waves and spatiotemporal patterns due to weak thermal effects in models of catalytic oxidation

We analyze the behavior of a microkinetic model of a catalytic reaction coupled with weak enthalpy effects to show that under fixed gas-phase concentrations it can produce moving waves with an intrinsic length scale, when the underlying kinetics is oscillatory. The kinetic model incorporates dissociative oxygen adsorption, reactant adsorption and desorption, and surface reaction. Three typical patterns may emerge in a one-dimensional system (a long wire or a ring): homogeneous oscillations, a family of moving waves propagating with constant velocities, and patterns with multiple source/sink points. Pattern selection depends on the ratio of the system length to the intrinsic wave length and the governing parameters. We complement these analysis with simulations that revealed a plethora of patterned states on one- and two-dimensional systems (a disk or a cylinder). This work shows that weak long-range coupling due to high feed rates maintains such patterns, while low feed rates or strong long-range interaction can gradually suppress the emerging patterns.     

The chemistry of polycyclic arene imines. II. Photochemistry of phenanthrene 9,10-imine and of its N-butyl derivative

The uv irradiation of phenanthrene 9, 10-imine has been shown to give 9H-tetrabenzo[a, c, g, i]carbazole as the major photo-product both in argon purged acetone and in dichloromethane. Phenanthrazine, N-9-phenanthrenyl-9-phenanthrenamine and phenanthrene were formed in smaller quantities. 9-Phenanthrenamine was found to be a minor by-product. N-Butylphenanthrene 9, 10-imine yielded under similar conditions phenanthrene and N-butyl-9-phenanthrenamine as the only isolable polycyclic compounds. In the presence of air the substituted imine gave mainly 2-propylphenanthro[9, 10-d]oxazole.     

Dynamic in situ characterization of organic monolayer formation via a Novel substrate-mediated mechanism

Ultrahigh vacuum scanning tunneling microscopy data investigating octylsilane (C8H17SiH3) monolayer pattern formation on Au(111) are presented. The irregular monolayer pattern exhibits a 60 A length scale. Formation of the octylsilane monolayer relaxes the Au(111) 23 x square root3 surface reconstruction and ejects surface Au atoms. Au adatom diffusion epitaxially extends the Au(111) crystal lattice via step edge growth and island formation. The chemisorbed monolayer covers the entire Au surface at saturation exposure. Theoretical and experimental data suggest the presence of two octylsilane molecular adsorption phases: an atop site yielding a pentacoordinate Si atom and a surface vacancy site yielding a tetracoordinate Si atom. Theoretical simulations investigating two-phase monolayer self-assembly dynamics on a solid surface suggest pattern formation results from strain-induced spinodal decomposition of the two adsorption phases. Collectively, the theoretical and experimental data indicate octylsilane monolayer pattern formation is a result of interfacial Au-Si interactions and the alkyl chains play a negligible role in the monolayer pattern formation mechanism.     

Intervalence charge transfer in the stereoisomers of a dinuclear ruthenium complex containing the bridging ligand dibenzoeilatin

The dinuclear species [{Ru(bpy)2}2(micro-dbneil)]4+(bpy = 2,2'-bipyridine; dbneil = dibenzoeilatin) was separated into its three stereoisomeric forms by cation-exchange chromatographic techniques. The NMR characteristics of the two diastereoisomers (meso and rac) are very similar, consistent with the decreased anisotropic interactions between the terminal bpy ligands located on different ruthenium centres because of their large spatial separation. Spectroelectrochemical measurements of the IVCT transitions in the mixed valence (5+) species show the system to be in the class II-III regime with substantial electronic communication between the metal centres. There is no significant difference in IVCT behaviour between the two diastereoisomers.