Partitioning Boolean lattices into chains of subsets

We prove that the Boolean lattice of all subsets of an n-set can be partitioned into chains of size four if and only if n9.Research supported in part by N.S.F. grant DMS-8401281.Research supported in part by N.S.F. grant DMS-8406451.     

A mild and efficient process for detoxifying polychlorinated biphenyls

Polychlorinated biphenyls (PCBs) were effectively dechlorinated to biphenyl under mild conditions using an aqueous solution of sodium hypophosphite in the presence of a palladium catalyst.     

Chemistry and Biology of Cylindrols: Novel Inhibitors of Ras Farnesyl-Protein Transferase from Cylindrocarpon lucidum

Farnesyl-protein transferase (FPTase) is an enzyme responsible for the farnesylation of Ras protein. Farnesylation is required for cell-transforming activity in several tumor-types, and therefore, inhibition of FPTase activity may be a potential target for anticancer drugs. Our continued search for novel inhibitors led to the isolation of a number of bicyclic resorcinaldehyde cyclohexanone derivatives named here cylindrols A(1) to A(4), cylindrols B and B(1), and a number of known compounds, from Cylindrocarpon lucidum. The compounds were isolated by bioassay-guided separation using Sephadex LH-20, silica gel, and reverse phase HPLC. Structures were elucidated by extensive application of 2D NMR and X-ray crystallography. The determination of absolute stereochemistry was accomplished by CD measurements. Chemical transformations of the most abundant compound resulted in a number of key derivatives which were critical for the evaluation of structure activity relationship. These compounds are members of ascochlorin family and showed a wide range of inhibitory activity (0.7 &mgr;M to >140 &mgr;M) against FPTase. The FPTase activity was noncompetitive with respect to both substrates. Isolation, structures, chemical transformations, and FPTase activity are discussed in detail.     

Personal reflections on receiving the Roger Adams Award in organic chemistry

The author reflects on his early experiences as a chemist, and on the subsequent shift in emphasis that his research has undergone from mechanistic and synthetic organic chemistry to natural products chemistry. Finally, the extension of the field of natural products chemistry into the emerging discipline of chemical ecology is noted. This essay concludes with a consideration of the importance of including science in the curricula of all college and university students.     

The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system,I

A systematic presentation of the quasi-linear first order symmetric hyperbolic systems of Friedrichs is presented. A number of sharp regularity and smoothness properties of the solutions are obtained. The present paper is devoted to the case ofR ⁿ with suitable asymptotic conditions imposed. As an example, we apply this theory to give new proofs of the existence and uniqueness theorems for the Einstein equations in general relativity, due to Choquet-Bruhat and Lichnerowicz. These new proofs usingfirst order techniques are considerably simplier than the classical proofs based onsecond order techniques. Our existence results are as sharp as had been previously known, and our uniqueness results improve by one degree of differentiability those previously existing in the literature.Partially supported by AEC Contract AT(04-3)-34.Partially Supported by NSF Contract GP-8257.     

Test of amplitude signs in pion photoproduction predicted by the transformation from current to constituent quarks

The transformation from current to constituent quark basis states is discussed as it applies to relating amplitudes for photon-nucleon decays of baryon resonances. The predictions for the relative signs of pion photoproduction amplitudes through baryon resonances in the $\text{70}\text{L = 1}$ and $\text{56}\text{L = 2}$ multiplets are presented and compared with experiment. Theory and experiment are found to be completely, with the pion-nucleom decay amplitudes of resonances in the $\text{70}\text{L = 1}$ having the signs characteristic of the $\text{3,}\text{3}\text{)?(}\text{3}\text{, 3)}$ rather than (8, 1)?(1, 8) term in the transformation axial-vector charge.     

Scaling and non-scaling in a rest frame quark-parton model of the proton

Electron-proton deep inelastic scattering is treated as the incoherent scattering of electrons by bound Dirac partons in the proton rest frame. An approximate bound state wave function is used for the initial parton, while the final parton is considered free. A good fit is obtained to the structure function F₁(x,Q²) in the range x > 0.15, Q² > 2 GeV. The subsequent prediction for F₂(x,Q²) is not as good, indicating a small additional contribution by longitudinal photons for W < 2.5 GeV. The parton momentum distribution is found to contain transverse momentum of 400–600 MeV, increasing with x.