Forced two layer beta-plane quasigeostrophic flow. Part I: Long-time existence and uniqueness of weak solutions

We consider a model of quasigeostrophic turbulence that has proven useful in theoretical studies of large scale heat transport and coherent structure formation in planetary atmospheres and oceans. The model consists of a coupled pair of hyperbolic PDEs with a forcing which represents domain-scale thermal energy source. Although the use to which the model is typically put involves gathering information from very long numerical integrations, little of a rigorous nature is known about long-time properties of solutions to the equations. In this first paper we define a notion of weak solution, and show using Galerkin methods the long-time existence and uniqueness of such solutions.     

Perturbative construction and rigorous proof of locality of effective lattice actions for continuum theories

We construct an effective lattice action for a continuum theory, by fixing a set of collective coordinates which play the role of lattice variables. As opposed to Symanzik's improvement program our method involves no expansion in powers of the lattice spacing; in other words it simultaneously yields all “irrelevant” operators generated by the renormalization group to a given order in the continuum coupling constant. We are thus able to rigorously establish that the effective lattice action, for both smooth and singular collective coordinates, is local in the sense that long-range couplings decay exponentially over a distance independent of the mass gap of the theory; for asymtotically free theories this is interpreted as an existence proof of Wilson's infrared stable trajectories. Our methods are for convenience described in the context of dimensional φ⁴, but can be easily extended to any theory with a set of collective coordinates which (i) are renormalizable and (ii) provide an infrared cutoff. Application to the 2-dimensional O(N) σ-model is, in particular, discussed; the technical problems of renormalization posed by gauge invariance are, on the other hand, not dealt with in this paper, although our treatment of singular coordinates is meant as a prelude to them. A by-product of our proofs is the derivation of an interesting factorization property of Zimmermann-subtracted diagrams.     

Fine structure in the alpha-cluster radioactivity of the255Fm nucleus

Within the one level R-matrix approach several hindrance factors for the radioactive decay of the²⁵⁵Fm nucleus in which are emitted alpha-nuclei are calculated. The interior wave functions are supposed to be given by the shell model with effective residual interactions. The exterior wave functions are calculated from a cluster-nucleus double-folding model potential obtained with the Michigan 3-Yukawa (M3Y) interaction. As example of the cluster decay fine structure we analyzed the case of alpha-decay of²⁵⁵Fm nucleus. Good agreement with the experimental data is obtained.The author would like to thank Dr. O. Dumitrescu for fruitful discussions concerning different parts of this work and help in computing different quantities entering the expressions of the hindrance factors.     

Exact steady periodic water waves with vorticity

We consider the classical water wave problem described by the Euler equations with a free surface under the influence of gravity over a flat bottom. We construct two‐dimensional inviscid periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use bifurcation and degree theory to construct a global connected set of such solutions. © 2003 Wiley Periodicals, Inc.     

About the foundations of the special theory of relativity

The principle of the constancy of the velocity of light propagation is used to introduce a differentiable structure on the universe of events E. Namely, using a theorem proved in [2] and some axioms imposed toE it is shown howE can be endowed with an atlas s.t. the coordinate transformations between the charts of this atlas are given by conformal (or Weyl) transformations.     

A convex sets in general position

The notion of convex cones in general position has turned out to be useful in convex programming theory. In this paper we extend the notion to convex sets and give some characterizations which yield a better insight into this concept. We also consider the case of convex sets in S-general position.     

Global existence for fully parabolic boundary value problems

We present some results on the global existence of classical solutions for quasilinear parabolic equations with nonlinear dynamic boundary conditions in bounded domains with a smooth boundary.     

Lie algebra cohomology and the fusion rules

We prove a vanishing theorem for Lie algebra cohomology which constitutes a loop group analogue of Kostant's Lie algebra version of the Borel-Weil-Bott theorem. Consider a complex semi-simple Lie algebra and an integrable, irreducible, negative energy representation of. Givenn distinct pointsz _k in , with a finite-dimensional irreducible representationV _k of assigned to each, the Lie algebra of-valued polynomials acts on eachV _k , via evaluation atz _k . Then, the relative Lie algebra cohomologyH ^* is concentrated in one degree. As an application, based on an idea of G. Segal's, we prove that a certain homolorphic induction map from representations ofG to representations ofLG at a given level takes the ordinary tensor product into the fusion product. This result had been conjectured by R. Bott.     

A case of chain propagation: α-aminoalkyl radicals as initiators for aryl radical chemistry

The generation of aryl radicals from the corresponding halides by redox chemistry is generally considered a difficult task due to their highly negative reduction potentials. Here we demonstrate that α-aminoalkyl radicals can be used as both initiators and chain-carriers for the radical coupling of aryl halides with pyrrole derivatives, a transformation often employed to evaluate new highly reducing photocatalysts. This mode of reactivity obviates for the use of strong reducing species and was also competent in the formation of sp² C–P bonds. Mechanistic studies have delineated some of the key features operating that trigger aryl radical generation and also propagate the chain process.

Aminoalkyl radicals can be used as both initiators and chain-carriers for the conversion of aryl halides into the corresponding radicals. This approach by-passes the requirement for strongly reducing photocatalysts.     

Alkaline Metal Stannide‐Stannates: ‘Double Salts’ with Zintl Sn and Stannate SnO Anions

Using the reduction of tin oxides with the elemental alkaline metals rubidium and cesium, stannide stannates have been synthesized which contain Zintl anions [Sn₄]^4— (i.e. Sn^—I) and isolated oxostannate ions [SnO₃]^4— (i.e. Sn^+II) together with further oxide ions for charge compensation. The crystal structures of the three compounds A_23.6Sn_7.4O_13.2 = A_23.6[Sn₄][SnO₃]_3.4[O]₃ (A = Rb 1a : monoclinic, P2₁/c, a = 2174.2(6), b = 1137.0(6), c = 2373.6(6) pm, β = 116.11(2)°, Z = 4, R1 = 0.056; A = Cs 1b : monoclinic, P2₁/c, a = 2042.6(6), b = 1185.4(3), c = 2481.1(7) pm, β = 97.06(2)°, Z = 4, R1 = 0.075) and Cs₄₈Sn₂₀O₂₁ = Cs₄₈[Sn₄]₄[SnO₃]₄[O]₇[O₂] ( 2 monoclinic, P2/c, a = 1701.8(3), b = 877.4(2), c = 4556.9(7) pm, β= 101.47(1)°, R1 = 0.093) have been determined on the basis of single crystal data. The transparency of the compounds allowed the recording of raman spectra of the anion [Sn₄]^4—. The ¹¹⁹Sn Moessbauer spectrum of the rubidium compound shows a singulet in good agreement with RbSn, overlapping a doublet caused by Sn²⁺ in the asymmetrical environment of the strongly electronegative oxygen ligands of SnO.