A new family of heavy transition metal coordination compounds and its application,I. Design,synthesis and characterization of volatile organohafnium precursors

The first three representatives of a new family of volatile organohafnium compounds suitable as metallo-organic chemical vapour deposition precursors were synthesized. A combination of cyclopentadienyl and alkoxo-ligands with a bicyclo[2.2.1]heptanc framework was used. Volatility at relatively low temperatures for hafnium compounds was found and the precursors were characterized by elemental analysis and spectroscopic methods (IR, ¹H and ¹³C NMR, mass spectrometry and mass-analysed ion kinetic energy spectroscopy). The outlook for use in hafnium functional materials synthesis was derived from the fragmentation data.     

Comparison of Krylov subspace methods on the PageRank problem

PageRank algorithm plays a very important role in search engine technology and consists in the computation of the eigenvector corresponding to the eigenvalue one of a matrix whose size is now in the billions. The problem incorporates a parameter that determines the difficulty of the problem. In this paper, the effectiveness of stationary and nonstationary methods are compared on some portion of real web matrices for different choices of . We see that stationary methods are very reliable and more competitive when the problem is well conditioned, that is for small values of . However, for large values of the parameter the problem becomes more difficult and methods such as preconditioned BiCGStab or restarted preconditioned GMRES become competitive with stationary methods in terms of Mflops count as well as in number of iterations necessary to reach convergence.     

The crystal structure of 3-methyluracil from X-ray powder diffraction data

The crystal structure of 3-methyluracil has been determined ab initio by conventional monochromatic X-ray powder diffraction data. The crystal data are: orthorombic, a=6.6294(1), b=13.1816(3), c=6.53938(9) (Å), V=571.45(3) (ų), space group Pbnm, Z=8. The structure was solved by direct methods and the final Rietveld refinement converged to R_p=0.0398, R_wp=0.0528, R_Bragg=0.0294. The crystal structure exhibits endless chains of planar molecules, connected via head-to-tail N-H?O hydrogen bonds.     

Inhomogenous Model of Crossing Loops and Multidegrees of Some Algebraic Varieties

We consider a quantum integrable inhomogeneous model based on the Brauer algebra B(1) and discuss the properties of its ground state eigenvector. In particular we derive various sum rules, and show how some of its entries are related to multidegrees of algebraic varieties.     

Linear programming with variable matrix entries

We consider linear programming (continuous or integer) where some matrix entries are decision parameters. If the variables are nonnegative the problem can be easily solved in two phases. It is shown that direct costs on the matrix entries make the problem NP-hard. Finally, a strong duality result is provided.     

Some notes on graphs whose index is close to 2

We consider two classes of graphs: (i) trees of order n and diameter d =n − 3 and (ii) unicyclic graphs of order n and girth g = n − 2. Assuming that each graph within these classes has two vertices of degree 3 at distance k, we order by the index (i.e. spectral radius) the graphs from (i) for any fixed k (1 ? k ? d − 2), and the graphs from (ii) independently of k.     

On open-loop and feedback attainability of a closed set for nonlinear control systems

In this note, we investigate the existence of controls which allow to reach a given closed set K through trajectories of a nonlinear control system. In the case where the set is sufficiently regular we give a condition allowing to find a feedback control law which ensures the existence of trajectories to reach the set. We also consider the case where all the trajectories reach K. When K is not necessarily attainable but only viable, we build a set-valued feedback for which the set is invariant. Our approach concerns continuous dynamics, possibly not C¹, so our methods do not come from geometric control theory. Furthermore, we do not require any regularity of the set K in order to obtain our results, except when we want to establish the existence of a feedback control law to achieve our goals.     

Existence of nash equilibria for generalized games without upper semicontinuity

The present note extends Debreu's equilibrium existence theorem for a generalized game in the context of finite-dimensional strategy spaces, by weakening the upper Semicontinuity and closed-valuedness assumption on the feasible strategy multifunctions. This is made by establishing an inequality of Ky Fan's type, whose proof is based on a selection theorem by E. Michael. An extension to generalized games with unbounded strategy spaces is also presented.