Variations on seven points: An introduction to the scope and methods of coding theory and finite geometries

We use a simple example (the projective plane on seven points) to give an introductory survey on the problems and methods in finite geometries — an area of mathematics related to geometry, combinatorial theory, algebra, group theory and number theory as well as to applied mathematics (e.g., coding theory, information theory, statistical design of experiments, tomography, cryptography, etc.). As this list already indicates, finite geometries is — both from the point of view of pure mathematics and from that of applications related to computer science and communication engineering — one of the most interesting and active fields of mathematics. It is the aim of this paper to introduce the nonspecialist to some of these aspects.To Professor Günter Pickert on the occasion of his 65th birthday     

Formulation of Zeeman modulation as a signal filter

The Bloch equation containing a Zeeman modulation field is solved analytically by treating the Zeeman modulation frequency as a perturbation. The absorption and dispersion signals at both 0 degrees and 90 degrees modulation phase are obtained. The solutions are valid to first order in the modulation frequency, but are otherwise valid for any value of modulation amplitude or microwave amplitude. A first order treatment of modulation frequency is shown to be a valid approximation over a wide range of typical experimental EPR conditions. The solutions derived from the Bloch equation suggest that the effect of over-modulation on first and second harmonic EPR spectra can be formulated as a mathematical filter that smoothes and broadens the under-modulated signal. The only adjustable filter parameter is a width that is equivalent to the applied peak-to-peak modulation amplitude. The true spin-spin and spin-lattice relaxation rates are completely determined from the under-modulated spectrum. The filters derived from the analytic solutions of the Bloch equation in the linear limit of modulation frequency are tested against numerical solutions of the Bloch equation that are valid for any modulation frequency to show their applicability. The filters are further tested using experimental EPR spectra. Experimental under-modulated spectra are mathematically filtered and compared with the experimental over-modulated spectra. The application of modulation filters to STEPR spectra is explored and limitations are discussed.     

The rank of the AG(2,n) incidence matrix over any prime field

The dimension of the F-row spaces of the incidence matrices of all affine planes AG(2,n) is determined. The proof presented here gives a unified method for the cases when charF is or is not a divisor of n.     

Co-transport of H+/Cl- by a synthetic prodigiosin mimic

An amidopyrrole with appended imidazole group can bind and co-transport H+/Cl- across vesicle membranes much more effectively than an analogue with an appended pyridyl group.     

The effect of CpG-ODN on antigen presenting cells of the foal

Background  

Cytosine-phosphate-guanosine oligodeoxynucleotide (CpG-ODN) has been used successfully to induce immune responses against viral and intracellular organisms in mammals. The main objective of this study was to test the effect of CpG-ODN on antigen presenting cells of young foals.     

Density functional approach to quantum lattice systems

For quantum lattice systems, we consider the problem of characterizing the set of single-particle densities,, which come from the ground-state eigenspace of someN-particle Hamiltonian of the form whereH ₀ is a fixed, bounded operator representing the kinetic and interaction energies. We show that the conditions on are that it be strictly positive, properly normalized, and consistent with the Pauli principle. Our results are valid for both finite and infinite lattices and for either bosons or fermions. The Coulomb interaction may be included inH ₀ if the lattice dimension is 2. We also characterize those single-particle densities which come from the Gibbs states of such Hamiltonians at finite temperature. In addition to the conditions stated above, must satisfy a finite entropy condition.Research supported by the National Science Foundation under grant No. PHY-82-03669.Research supported by Office of Naval Research under grant No. 0014-80-G-0084.On leave from Department of Mathematics, University of Lowell, Massachusetts 01854.     

Glaucolide-A and -B,new germacranolide-type sesquiterpene lactones from Vernonia (compositae)

The structures of two new germacranolides, glaucolide-A (1a) and -B (1b), isolated from more than 25 species of Vernonia from the Western Hemisphere, have been established by a series of chemical transformations, and spectral and X-ray crystallographic studies.     

Design machines: Algebraically well described interconnection networks

We present a method constructing efficient multiprocessor networks based on combinatorial designs and group theory. The principal idea is to combine 1-factorizations of complete graphs on each block of certain 2-designs, to obtain efficient networks with a short maximum distance between any pair of processors. Using a smart multiplexing technique derived from the 1-factorization of complete graphs we can circumvent the restrictive Moore bound for (, d)-graphs.