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     

硼砂与氯化铵合成hBN反应机理的研究

 研究了以硼砂、氯化铵为原料在氨气气氛下合成hBN 的反应机理。指出氯化铵在反应中的主要作用是与硼砂反应形成可阻止硼砂颗粒团聚的高熔点膜层；而氨气的主要作用就是提供大量参与反应的NH₃分子，增加了反应几率；新生成的hBN则进一步隔离高度熔融的硼砂团粒，防止玻璃相的生成。     

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.     

A nondifferentiable extension of a theorem of Pucci and Serrin and applications

We study the multiplicity of critical points for functionals which are only differentiable along some directions. We extend to this class of functionals the three critical point theorem of Pucci and Serrin and we apply it to a one-parameter family of functionals Jλ, λ∈I⊂R. Under suitable assumptions, we locate an open subinterval of values λ in I for which Jλ possesses at least three critical points. Applications to quasilinear boundary value problems are also given.     

Large Discrepancy In Homogenous Quasi-Arithmetic Progressions

We prove that the class of homogeneous quasi-arithmetic progressions has unbounded discrepancy. That is, we show that given any 2-coloring of the natural numbers and any positive integer D, one can find a real number α≥1 and a set of natural numbers of the form {0, [α], [2α], [3α], . . . , [kα]} so that one color appears at least D times more than the other color. This was already proved by Beck in 1983, but the proof given here is somewhat simpler and gives a better bound on the discrepancy.     

An Enumerative Geometry for Magic and Magilatin Labellings

A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without the diagonals). A magilatin labelling is like a magic labelling but the values need be distinct only within each set. We show that the number of n × n magic or magilatin labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in the square. Our results differ from previous ones because we require that the entries in the square all be different from each other, and because we derive our results not by ad hoc reasoning but from a general theory of counting lattice points in rational inside-out polytopes. We also generalize from set systems to rational linear forms. Dedicated to the memory of Claudia Zaslavsky, 1917–2006 Received August 10, 2005     

Application of Electron-Shelving Detection via 423 nm Transition in Calcium-Beam Optical Frequency Standard

A new scheme of small compact optical frequency standard based on thermal calcium beam with application of 423 nm shelving detection and sharp-angle velocity selection detection is proposed. Combining these presented techniques, we conclude that a small compact optical frequency standard based on thermal calcium beam will outperform the commercial caesium-beam microwave dock, like the 5071 Cs clock （from Hp to Agilent, now Symmetricom company）, both in accuracy and stability.     

Euler configurations and quasi-polynomial systems

Consider the problem of three point vortices (also called Helmholtz’ vortices) on a plane, with arbitrarily given vorticities. The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria. This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an interaction proportional to r ^b, for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = −2 of this last statement is the well-known theorem due to Euler: in the Newtonian 3-body problem, for any choice of the 3 masses, there are 3 Euler configurations (also known as the 3 Euler points). These small upper bounds strengthen the belief of Kushnirenko and Khovanskii [18]: real varieties defined by simple systems should have a simple topology. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.