Game of two cars: Case of variable speed

A stochastic version of Isaacs's (Ref. 1) game of two cars is dealt with here. In this version, the pursuer, owing to thrust and drag forces, has a variable speed, whereas the evader's speed is constant. Also, the pursuer can maneuver as long as his speed is bounded by some lower and upper limits. The probability of interception, corresponding to optimal (saddle-point) feedback strategies, is computed and serves as a reference for evaluating the performance of four different versions of the proportional navigation pursuit law as well as two other strategies.     

On disjoint configurations in infinite graphs

For a graph A and a positive integer n, let nA denote the union of n disjoint copies of A; similarly, the union of ?₀ disjoint copies of A is referred to as ?₀A. It is shown that there exist (connected) graphs A and G such that nA is a minor of G for all n??, but ?₀A is not a minor of G. This supplements previous examples showing that analogous statements are true if, instead of minors, isomorphic embeddings or topological minors are considered. The construction of A and G is based on the fact that there exist (infinite) graphs G₁, G₂,… such that G_i is not a minor of G_j for all i ≠ j. In contrast to previous examples concerning isomorphic embeddings and topological minors, the graphs A and G presented here are not locally finite. The following conjecture is suggested: for each locally finite connected graph A and each graph G, if nA is a minor of G for all n ? ?, then ?₀A is a minor of G, too. If true, this would be a far‐reaching generalization of a classical result of R. Halin on families of disjoint one‐way infinite paths in graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 222–229, 2002; DOI 10.1002/jgt.10016     

双电荷交换反应与双重子共振态

提出了核双电荷交换反应的双重子共振态的反应机制,成功地解释了长期以来一直困惑着人们的共振区反应的角分布的实验结果.说明了共振区核双电荷交换反应是寻找双重子共振态的一个可能的途径.     

Intermixing during epitaxial growth and Mössbauer spectroscopy with probe layers

Mössbauer spectroscopy with ⁵⁷Fe (¹¹⁹Sn) probe layers is a useful method to study the local magnetic structures at buried interfaces. However interface alloying, which always exists in the real samples, have to be taken into account for accurate interpretation of experimental data. We developed an algorithm, which describes the interface intermixing in the multilayers. Substituting deposited atoms by atoms of substrate and floating of deposited atoms in the upper layers during epitaxial growth leads to the formation of asymmetric chemical and magnetic interfaces. This asymmetry in the M₁/M₂ superlattices can explain the difference between magnetic responses from M₁ on M₂ and M₂ on M₁ interfaces which were observed in experiments. Applying this intermixing model to the systems with probe layers located at different distances from the interfaces gives the natural explanation of hyperfine fields distributions on probe atoms and helps us clarify some discrepancies reported in the literature.     

Spherical dye-doped silica particles

Organic dyes such as water soluble porphyrins were incorporated into monodispersed SiO₂ particles using the sol-gel technique (the Stober synthesis) and their monomeric and dimeric properties were investigated by aiming at the microcavity effect. Doping efficiencies of dyes into SiO₂ particles depended on dye's hydrophilic properties. The doping efficiency of a porphyrin, TTMAPP, decreased with increasing the nominal content in the starting solution and the doping content showed the maximum value of 1.6×10^–5 mol/g SiO₂. With increasing the TTMAPP content, spectra of doped particles were changed from dimeric to monomeric nature; the absorption peak due to dimers disappeared and halfwidth of absorption at Soret band decreased. This unusual change was caused by the decrease of particle sizes by dye doping. The TTMAPP-doped sample having monomeric spectrum showed the fluorescence life time of 8.5 nsec and photochemical hole burning at about 5 K.     

Synthesis and crystal structure of 1,3,5-tris [4-(phenylethynyl)phenyl]benzene

The crystal structure of 1,3,5-tris[4-(phenylethynyl)phenyl]benzene (1) has been investigated. Compound1 represents a model of the repeating unit of the most typical polyphenylene, which contains 1,3,5-trisubstituted benzene rings (chain centers) and acetylenic groups (complex-forming and cross-linking centers) in the main chain. The acetylene groups of neighboring molecules have a tendency to close mutual arrangement, which is favorable for their topochemical interaction. However, the relative conformational rigidity of molecules1 restricts not only the possibility of the optimal adjustment of the reactive sites of neighboring molecules to one another, but also hampers the close packing of molecules in the crystal, which contains channels filled by the solvent molecules (chloroform).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1986–1992, November, 1994.The work was carried out with the financial support of the International Science Foundation and the American Crystallographic Association.     

Anharmonic effects in large-amplitude vibrations of metal clusters

Two types of extreme collective motion, large-amplitude many-phonon vibration of the ionic core and rotation of the cluster with high angular momenta, are considered. The interplay between vibration and collective motion towards fission is discussed. A new mechanism of formation and rupture of the neck is proposed which is based on the Franck-Condon principle, and accounts for the interplay between vibration and fission. Under rotation, the change of the shape of the cluster and a phase transition from axially symmetric to triaxial ellipsoid are predicted. For studying the effects, vibrational motion can be induced by laser radiation. Rotational motion may arise in collisions of clusters. Received 26 April 2001 and Received in final form 15 October 2001     

ON SOME INTERPRETATIONS OF CLASSICAL LOGIC

In distinction from the well-known double-negation embeddings of the classical logic we consider some variants of single-negation embeddings and describe some classes of superintuitionistic first-order predicate logics in which the classical first-order calculus is interpretable in such a way. Also we find the minimal extensions of Heyting's logic in which the classical predicate logic can be embedded by means of these translations.