THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Selective metal cation activation of a DNA alkylating agent: synthesis and evaluation of methyl 1,2,9, 9a-Tetrahydrocyclopropa[c]pyrido[3,2-e]indol-4-one-7-carboxylate (CPyI)

The synthesis of methyl 1,2,9,9a-tetrahydrocyclopropa[c]pyrido[3, 2-e]indol-4-one-7-carboxylate (CPyI) containing a one carbon expansion of the C ring pyrrole found in the duocarmycin SA alkylation subunit and its incorporation into analogues of the natural product are detailed. The unique 8-ketoquinoline structure of CPyI was expected to provide a tunable means to effect activation via selective metal cation complexation. The synthesis of CPyI was based on a modified Skraup quinoline synthesis followed by a 5-exo-trig aryl radical cyclization onto an unactivated alkene with subsequent TEMPO trap or 5-exo-trig aryl radical cyclization onto a vinyl chloride for synthesis of the immediate precursor. Closure of the activated cyclopropane, accomplished by an Ar-3' spirocyclization, provided the CPyI nucleus in 10 steps and excellent overall conversion (29%). The evaluation of the CPyI-based agents revealed an intrinsic stability comparable to that of CC-1065 and duocarmycin A but that it is more reactive than duocarmycin SA and the CBI-based agents (3-4x). A pH-rate profile of the addition of nucleophiles to CPyI demonstrated that an acid-catalyzed reaction is observed below pH 4 and that an uncatalyzed reaction predominates above pH 4. The expected predictable activation of CPyI by metal cations toward nucleophilic addition was found to directly correspond to established stabilities of the metal complexes with the addition product (Cu(2+) > Ni(2+) > Zn(2+) > Mn(2+) > Mg(2+)) and provides the opportunity to selectively activate the agents upon addition of the appropriate Lewis acid. This tunable metal cation activation of CPyI constitutes the first example of a new approach to in situ activation of a DNA binding agent complementary to the well-recognized methods of reductive, oxidative, or photochemical activation. Resolution and synthesis of a full set of natural product analogues and subsequent evaluation of their DNA alkylation properties revealed that the CPyI analogues retain identical DNA alkylation sequence selectivity and near-identical DNA alkylation efficiencies compared to the natural products. Consistent with past studies and even with the deep-seated structural change in the alkylation subunit, the agents were found to exhibit potent cytotoxic activity that directly correlates with their inherent reactivity.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.     

Thermal Characterizations of Inorganic and Organometallic Polymers

This review emphasizes the breadth of metallic and metallic-like polymers evaluated as to thermal properties. Techniques usefully applied to particular systems are noted with the aim of suggesting their application to other systems.     

Low-lying energy levels of the FeH molecule

Multireference configuration interaction (MRCI) and complete active space second-order perturbation theory (CASPT2) calculations are performed on Fe₂ and Fe^? ₂. Although it is not possible to definitively identify the ground states of Fe₂ and Fe^? ₂, the calculations suggest that the ground state of Fe^? ₂ in ⁸Σ^? _u derived from 3d¹³4σ² _g4σ² _u and that the states observed in photodetachment are the ⁹Σ^? _g and ⁷Σ^? _g states with a 3d¹³4σ² _g4σ¹ _u occupation, but that the ground state of Fe₂ is ⁷Δ_u(3d¹⁴4σ² _g) and is not observed in the photo-detachment spectra.