Optimal Control in Heterogeneous Domain Decomposition Methods for Advection-Diffusion Equations

New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence results are proved for the coupled problem, and the convergence of iterative processes is analyzed. The work was supported by the Russian Foundation for Basic Research (04-01-00615) and it was partly carried out while the first author was visiting the IACS at EPFL.     

Resolvability properties via independent families

The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω<λ?κ, no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a space of the form (DI(λ)) is λ-resolvable.     

On the pivot structure for the weighing matrix W(12,11)

In the present article we concentrate our study on the growth problem for the weighing matrix W(12,11) and show that the unique W(12,11) has three pivot structures. An improved algorithm for extending a k × k (0,+,-) matrix to a W(n,n-1), if possible, has been developed to simplify the proof. For the implementation of the algorithm special emphasis is given to the notions of data structures and parallel processing.     

Chromatic polynomial, q-binomial counting and colored Jones function

We define a q-chromatic function and q-dichromate on graphs and compare it with existing graph functions. Then we study in more detail the class of general chordal graphs. This is partly motivated by the graph isomorphism problem. Finally we relate the q-chromatic function to the colored Jones function of knots. This leads to a curious expression of the colored Jones function of a knot diagram K as a chromatic operator applied to a power series whose coefficients are linear combinations of long chord diagrams. Chromatic operators are directly related to weight systems by the work of Chmutov, Duzhin, Lando and Noble, Welsh.     

Packing Non-Zero A-Paths In Group-Labelled Graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem. These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow.     

Über die abstandsverträglichen Abbildungen auf dem Kreis und auf der reellen Geraden

Zusammenfassung. Eine Abbildung zwischen metrischen R?umen hei?t abstandsvertr?glich, wenn der Abstand der Bilder zweier Punkte nur vom Abstand der Punkte selbst abh?ngt. Wir zeigen, dass eine Abbildung genau dann abstandsvertr?glich ist, wenn der Cauchyschen Funktionalgleichung genügt, also ein Endomorphismus der Gruppe ist. Ein entsprechendes Resultat gilt auch für die abstandsvertr?glichen Abbildungen des Kreises (mit der Multiplikation komplexer Zahlen als Gruppenverknüpfung). Damit kann man sowohl alle messbaren abstandsvertr?glichen Abbildungen von bzw. in sich angeben, als auch einen Nachweis für die Existenz nichtmessbarer abstandsvertr?glicher Abbildungen auf und erbringen. Eingegangen am 20. Juni 2001 / Angenommen am 13. September 2001     

B物理中的难题

讨论单举B介子衰变中的难题, 包括直接CP非对称性及纵向极化分支比, 这些难题可能皆归因于量子色动力学的不准确度, 并非新物理的讯号.     

The design of the main accelerator for a pulsed positron beam

The pulsed positron beam at the Helsinki University of Technology is designed for the end energy of 3-30 keV and grounded target. This is achieved with a constant voltage acceleration followed by an adjustable deceleration. In the design of this accelerator-decelerator the possibility for electrical breakdowns and partial discharges must be eliminated.For designing the electrode and insulator structures for accelerator-decelerator configuration electric field simulations were carried out with the finite element analysis program. In this paper we present the design of the accelerator-decelerator and the results of the electric field simulations. The results of high voltage tests will also be presented and compared with the simulations.     

Phase transformation of Ni-B, Ni-P diffusion barrier deposited electrolessly on Cu interconnect

In this paper, we report that the phase transformation of Ni-B, Ni-P diffusion barriers deposited electrolessly on Cu, for the reason that the Ni-P layer is a more effective diffusion barrier than the Ni-B layer. The Ni₃B crystallized was decomposed to Ni and B₂O₃ above 400 °C and the Ni₃P crystallized was decomposed to Ni and P₂O₅ above 600 °C respectively in Ar atmosphere. Also, the Ni₃B was decomposed to Ni and free B above 400 °C and the Ni₃P was decomposed to Ni and free P above 600 °C respectively in H₂ atmosphere. The decomposed Ni formed a solid solution with Cu. The Cu diffusion occurred above 400 °C for Ni-B layer and above 600 °C for Ni-P layer, respectively. Because the decomposition temperature of Ni-P layer is about 200 °C higher than that of Ni-B layer, the Ni-P layer is a more effective barrier for Cu than the Ni-B layer.