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This paper solves the problem of a sliding ladder for the cases with and without friction at the wall and at the floor. Solutions for arbitrary initial conditions are obtained by strict application of the fundamental principles of mechanics. The validity of these solutions is discussed in context with the loss of contact of the ladder with the wall. A phase space representation is used to visualize for which initial conditions the ladder stays in contact with the wall and at which angle it would lose contact. [ABSTRACT FROM AUTHOR]

Static dipole polarizability functions (α|| and α⊥) and thermally averaged isotropic polarizabilities (α) of Li2, Na2, and K2 in their electronic ground states have been obtained from all-electron SCF+valence CI calculations which include core polarization effects by use of an effective potential. As a function of internuclear separation, α⊥ shows a monotonic increase in all three cases while α|| exhibits a pronounced maximum at about 1.5 Re. For T=300 K, we find α(Li2)=214, α(Na2)=262, and α(K2)=477 a.u. Our results, to which we attribute an uncertainty of 2%, support the measured value for the average polarizability of Li2 [R. W. Molof et al., J. Chem. Phys. 61, 1816 (1974)] but disagree with their results for Na2 and K2. For these dimers, Molof ’s mean experimental values appear to be in error by 33% and 18%, respectively. [ABSTRACT FROM AUTHOR]

Preliminary theoretical results, cited by Meloni and Gingerich in the title paper, are supplemented by new information (a) on the structure of the SnBi[sub 2] molecule, and (b) on computed atomization energies for SnBi[sub n] (n=1–3). © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The paper considers endospectral trees, a special class of graphs associated with the production of numerous isospectral graphs. Endospectral graphs have been considered in the literature sporadically (the name was suggested very recently [M. Randic, SIAM J. Algebraic Discrete Meth. 6, 145 (1985)]). They are characterized by the presence of a pair of special vertices that, if replaced by any fragment, produce an isospectral pair of graphs. Recently Jiang [Y. Jiang, Sci. Sin. 27, 236 (1984)] and Randic and Kleiner (M. Randic and A. F. Kleiner, ‘‘On the construction of endospectral trees,’’ submitted to Ann. NY Acad. Sci.) considered alternative constructive approaches to endospectral trees and listed numerous such graphs. The listing of all such trees having n=16 or fewer vertices has been undertaken here. It has been found that relatively few endospectral trees have novel structural features and cannot be reduced to some already known endospectral tree. These few have been named ‘‘irreducible endospectral trees.’’ They are responsible for the occurrence of a large number of isospectral trees, leading to, when one considers trees of increasing size, the situation that led Schwenk [A. J. Schwenk, in New Directions in the Theory of Graphs, edited by F. Harary (Academic, New York, 1973), pp. 275–307] to conclude that ‘‘almost all trees are isospectral.’’ [ABSTRACT FROM AUTHOR]