A contraction proximal point algorithm with two monotone operators

It is a known fact that the method of alternating projections introduced long ago by von Neumann fails to converge strongly for two arbitrary nonempty, closed and convex subsets of a real Hilbert space. In this paper, a new iterative process for finding common zeros of two maximal monotone operators is introduced and strong convergence results associated with it are proved. If the two operators are subdifferentials of indicator functions, this new algorithm coincides with the old method of alternating projections. Several other important algorithms, such as the contraction proximal point algorithm, occur as special cases of our algorithm. Hence our main results generalize and unify many results that occur in the literature.     

The Fermi Golden Rule and its Form at Thresholds in Odd Dimensions

Let H be a Schrödinger operator on a Hilbert space , such that zero is a nondegenerate threshold eigenvalue of H with eigenfunction Ψ₀. Let W be a bounded selfadjoint operator satisfying 〈 Ψ₀, WΨ₀〈>0. Assume that the resolvent (H?z)^?1 has an asymptotic expansion around z=0 of the form typical for Schrödinger operators on odd-dimensional spaces. Let H(?) =H+?W for ?>0 and small. We show under some additional assumptions that the eigenvalue at zero becomes a resonance for H(?), in the time-dependent sense introduced by A. Orth. No analytic continuation is needed. We show that the imaginary part of the resonance has a dependence on ? of the form ?^2+(ν/2) with the integer ν≥?1 and odd. This shows how the Fermi Golden Rule has to be modified in the case of perturbation of a threshold eigenvalue. We give a number of explicit examples, where we compute the ``location'' of the resonance to leading order in ?. We also give results, in the case where the eigenvalue is embedded in the continuum, sharpening the existing ones.     

Synthesis and inclusion capability of a β-cyclodextrin-tetrathiafulvalene derivative

The synthesis of 4,5-ethylenedithio-4′-[6-deoxy-β-cyclodextrin-6-yl-aminocarbonyl]-tetrathiafulvalene 3 is reported. Dominantly, the structure of 3 has been established on the basis of mass spectrometry, ROESY and ¹H NMR spectra, combined with a theoretical MM3 study, indicating an ‘open-cavity structure’. The sensing ability of 3 and the formation constant of the complex [(3)-(1-adamantanol)] have been evaluated experimentally by UV-vis spectroscopy and theoretically by the MM3 docking procedure method.     

Comparative evaluation of critical operating conditions for a tubular catalytic reactor using thermal sensitivity and loss-of-stability criteria

Optimal operation of a chemical reactor according to various performance criteria often drives the system towards critical boundaries. Thus, precise evaluation of runaway limits in the parametric space becomes a crucial problem not only for the reactor’s safe operation, but also for over-designing the system. However, obtaining an accurate estimate for operating limits is a difficult task due to the limited validity of kinetic models describing complex processes, as well as the inherent fluctuations of the system’s properties (catalyst, raw-material quality). This paper presents a comparison of several effective methods of deriving critical conditions for the case of a tubular fixed-bed catalytic reactor used for aniline production in the vapour phase. Even though the methods being compared are related to one another, the generalised sensitivity criterion of Morbidelli-Varma (MV) seems to be more robust, not depending on a particular parameter being perturbed, when compared to the criteria that detect an incipient loss of system stability in the critical region (i.e., div-methods based on the system’s Jacobian and Green’s function matrix analysis). Combined application of div- and MV criteria allows for an accurate evaluation of the distance from the reactor’s nominal conditions to the safety limits.     

On the compatibility relation for the Föppl–von Kármán plate equations

By using a coordinate-free approach we propose a new derivation of the compatibility equation for the Föppl–von Kármán nonlinear plate theory.     

On projective invariants of the complex Finsler spaces

In this paper we extend the results on projective changes of complex Finsler metrics obtained in Aldea and Munteanu (2012) [3], by the study of projective curvature invariants of a complex Finsler space. By means of these invariants, the notion of complex Douglas space is then defined. A special approach is devoted to the obtaining of equivalence conditions for a complex Finsler space to be a Douglas one. It is shown that any weakly Kähler Douglas space is a complex Berwald space. A projective curvature invariant of Weyl type characterizes complex Berwald spaces. These must be either purely Hermitian of constant holomorphic curvature, or non-purely Hermitian of vanishing holomorphic curvature. Locally projectively flat complex Finsler metrics are also studied.     

Enhancement of Mobile Phase Velocity in TLC by Means of an External Alternating Electric Field

JPC – Journal of Planar Chromatography – Modern TLC - In normal TLC practice, migration of the mobile phase through the layer is controlled by capillary forces. Under these conditions...     

Schwarzschild-de-Sitter Solution in Quantum Gauge Theory of Gravity

We use the theory based on the gravitational gauge group G to obtain a spherical symmetric solution of the field equations for the gravitational potentials on a Minkowski space-time. The gauge group G is defined and then we introduce the gauge-covariant derivative Dμ. The strength tensor of the gravitational gauge field is also obtained and a gauge-invariant Lagrangian including the cosmological constant is constructed. A model whose gravitational gauge potentials A^α μ （x） have spherical symmetry, depending only on the radial coordinate τ is considered and an analytical solution of these equations, which induces the Schwarzschild-de-Sitter metric on the gauge group space, is then determined. All the calculations have been performed by GR Tensor II computer algebra package, running on the Maple V platform, along with several routines that we have written for our model.     

Weak Laws of Large Numbers in Some Non-Commutative Spaces

We prove weak laws of large numbers for freely independent,uniformly bounded and non-identically distributed random variablesbelonging to non-commutative Ciach and, in particular, LorentzL^p-spaces. 2000 Mathematics Subject Classification 60B11, 60F25,46L54, 47N30.     

The coupling of hyperbolic and elliptic boundary value problems with variable coefficients

We consider a one‐dimensional coupled problem for elliptic second‐order ODEs with natural transmission conditions. In one subinterval, the coefficient ϵ>0 of the second derivative tends to zero. Then the equation becomes there hyperbolic and the natural transmission conditions are not fulfilled anymore. The solution of the degenerate coupled problem with a flux transmission condition is corrected by an internal boundary layer term taking into account the viscosity ϵ. By using singular perturbation techniques, we show that the remainders in our first‐order asymptotic expansion converge to zero uniformly. Our analysis provides an a posteriori correction procedure for the numerical treatment of exterior viscous compressible flow problems with coupled Navier–Stokes/Euler models. Copyright © 2000 John Wiley & Sons, Ltd.