A hierarchy of approximate models for the Maxwell equations

Summary. In this paper we perform an asymptotic study of the Maxwell equations with respect to the small parameter where is the characteristic velocity associated with the physical problem and is the speed of light. This enables us to derive the quasistatic and Darwin models as respectively first and second order approximations of the Maxwell equations. Moreover, an interpretation of the obtained variational formulations gives us the appropriate boundary conditions for these models. Received May 18, 1995     

Gravitational contribution to the Casimir energy in Kaluza-Klein theories

The Casimir energy of the gravitational field in Kaluza-Klein theories is investigated. The mathematical techniques needed to compute the contribution of a single graviton loop to the quantum effective potential on a background manifold of (Minkowski space) ? (N-sphere) are developed. In these computations the cosmological constant plays a dynamical role, acting like a mass for the graviton. The numerical work for the case N = 1 is done explicitly, and a solution to the one-loop corrected equations of motion is found, although it is not stable. The possibility of an imaginary part to the effective potential for N > 1 is noted, and its existence is attributed to tachyonic terms in the mode sum.     

Safe disposal of diisopropyl fluorophosphate (DFP)

Diisopropyl fluorophosphate (DFP), a volatile highly toxic enzyme inhibitor, in buffer (pH 3, pH 5, pH 7, pH 9, pH 11, Hank’s, Dulbecco’s, PBS, TBE, and HEPES) or water (10 mM), in DMF solution (200 mM), and bulk quantities can be degraded by adding 1M NaOH. The DFP was completely degraded, as determined by enzymatic assay, and the final reaction mixtures were not mutagenic.     

Recent results on hyperpolarized<Superscript>3</Superscript>He−<Superscript>4</Superscript>He liquid mixtures

Laser optical pumping in low magnetic field provides very high nuclear polarizations in gaseous helium mixtures, and is used to prepare polarized liquid. Wall relaxation in glass cells is effiently reduced using cesium coatings, and bulk longitudinal relaxation times are measured. In highly magnetized samples, dipolar fields control the spin dynamics in anisotropic volumes and weak external magnetic field inhomogeneities. Long lived magnetostatic modes are observed by pulsed NMR. Detailed analysis of their frequency and damping gives information on magnetization density and spin diffusion coefficient in polarized mixtures. Experiments are performed above 0.2 K on mixtures with³He concentrations of order a few percents or larger. When phase separation occurs, the³He-rich phase retains a high polarization.     

Dimeric ruthenium complexes of dicyanopyrazines: complexes with an unstable mixed-valence state

Pentaammineruthenium complexes bridged by 2,3-dicyanopyrazine and 2,3-dicyano-5, 6-dimethylpyrazine have been prepared and characterized. The bridging ligand binds to the metal atoms through the cyano nitrogen. Complexes can be prepared in the +4 and +6 oxidation states but the mixed-valence, +5, state is not observed experimentally, unlike the previously prepared 1,2-dicyanobenzene dimer which does have a stable +5 state. A simple electronic model is constructed from the spectroscopic data and is used to show that the electronic perturbations caused by the uncomplexed nitrogen atoms in the pyrazine ring are sufficient to drive the disproportionation reaction of the +5 state.     

Spectrum (super-) symmetries of particles in a Coulomb potential

The Schrödinger equation for a spin-0 particle in the field of a dyon is obtained by dimensional reduction of the four-dimensional harmonic oscillator; the reduction is effected by imposing an equivariance condition on the wave functions of the latter system. This geometrical construction allows for a simple derivation of the SO(4, 2) spectrum symmetry of the dyon system. A supermultiplet of one $\text{spin}\text{-}\text{1}\text{2}$ and two spin-0 particles in a Coulomb potential is demonstrated to possess an N = 2 conformal supersymmetry through a generalization of the same method. The states and wave functions for these systems can be obtained from the representation theory of the corresponding symmetry algebras. A particular case for which this approach provides a complete group theoretical analysis is that of the Pauli equation for a $\text{spin}\text{-}\text{1}\text{2}$ particle in the field of a dyon.     

Shifting From Ziegler–Natta to Philips‐Type Catalyst? A Simple and Safe Access to Reduced Titanium Systems for Ethylene Polymerization

Silica‐supported titanium(IV) chloride is readily reduced by Mashima and co‐workers' reagent (1‐methyl‐3,6‐bis(trimethylsilyl)‐1,4‐cyclohexadiene) to afford materials active in ethylene polymerisation without need of aluminum alkyl cocatalyst.     

On the Intersection Problem for Steiner Triple Systems of Different Orders

A Steiner triple system of order v, or STS(v), is a pair (V, ) with V a set of v points and a set of 3-subsets of V called blocks or triples, such that every pair of distinct elements of V occurs in exactly one triple. The intersection problem for STS is to determine the possible numbers of blocks common to two Steiner triple systems STS(u), (U, ), and STS(v), (V, ), with U⊆V. The case where U=V was solved by Lindner and Rosa in 1975. Here, we let U⊂V and completely solve this question for v−u=2,4 and for v≥2u−3. supported by NSERC research grant #OGP0170220. supported by NSERC postdoctoral fellowship. supported by NSERC research grant #OGP007621.     

Reverse lexicographic and lexicographic shifting

A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, Δ_lex—an operation that transforms a monomial ideal of S = K[x_i: i ∈ ℕ] that is finitely generated in each degree into a squarefree strongly stable ideal—is defined and studied. It is proved that (in contrast to the reverse lexicographic case) a squarefree strongly stable ideal I ⊂ S is fixed by lexicographic shifting if and only if I is a universal squarefree lexsegment ideal (abbreviated USLI) of S. Moreover, in the case when I is finitely generated and is not a USLI, it is verified that all the ideals in the sequence } are distinct. The limit ideal is well defined and is a USLI that depends only on a certain analog of the Hilbert function of I. Research partially supported by NSF grants DMS 0070571 and DMS 0100141.