Salem numbers and arithmetic hyperbolic groups

In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic hyperbolic n-orbifold for each dimension n. We also discuss a "short geodesic conjecture", and prove its equivalence with "Lehmer's conjecture" for Salem numbers.Comment: The exposition in version 3 is more compact; this shortens the paper: 26 pages now instead of 37. A discussion on Lehmer's problem has been added in Section 1.2. Final version, to appear is Trans. AM

Bulletin No. 16: A Guided Tour of the Connecticut Arboretum

Reprinted 1974. Illustrated guide to the woody plant collections and dynamics of plant communities. 32 pp

Larval trematode populations and host-parasite interactions in Cerithidea Californica

Cerithidea california is examined to determine the fecundity of the parasitic trematode species in its gonad. Five species of trematodes are studied (Cloacitrema michiganensis, Euhaplorchis californiensis, Parorchis acanthus, Himasthia rhigedana, and Acanthoraryphium sp.). Their fecundity is determined by direct counts of rediae and estimation of the cercarial population. Correlations are shown for trematode numbers and snail size. Incidences of infection are given with regard to site, snail size, and trematode species. Comparison is made between infection ratios of C. californica and another marsh snail, Batillaria zonalis

Geology of the Crystal Mine, Hardin County, Illinois

The study of the geology and mineralization of the Crystal Mine was undertaken at the suggestion of Mr. Dodson G. Gibson of the Crystal Fluorspar Company, who allowed access to the mine and its records for this purpose. The problem was to develop a system of prospecting the so-called bedded-replacement fluorspar deposits of Hardin County, Illinois. It is believed that an economically feasible method has been developed. This method involves not only the actual finding of fluorspar, but also serves as a guide in revealing structural trends suggestive of mineralization. The fluorspar deposits of the Crystal Mine are representative of the mineralized areas in the Cave In Rock district. They are composed, principally, of crustified, “coontail” and disseminated fluorspar which is associated with very small amounts of calcite, barite, sphalerite, galena, chalcopyrite, pyrite and hydrocarbons. The fluorspar occurs in horizontal bladed* [*Refers to geologic structures having dimensions approximately 100:10:1] deposits along definite stratigraphic horizons. The principal mineralized zones are at the base of the Bethel sandstone and at the bases of the Rosiclare and Sub-Rosiclare members of the Ste. Genevieve limestone. These zones occur in fossiliferous limestone and are associated with trough-like structures which are superimposed upon a regional structure having a strike of N. 73° W. and a dip of about 4° N. 17° E. The trends of the fluorspar deposits are N. 50° E. and from N. 40° W. to N. 70° W. They are, in general, parallel and normal to the Peters Creek fault which marks the northern boundary of the district. The principal mineralization is parallel to the fault. As the trough-like structures which accompany the mineralization are readily evident, their careful delineation should aid in locating the fluorspar deposits. Because they are minor structures, superimposed upon the regional dip and somewhat obscured by it, the writer conceived the idea that they might best be shown by drawing structure contour maps at various well defined horizons, using as a datum, not sea level, but an inclined plane parallel to the regional dip. The delineation of these trough-like structures is based upon well logs of approximately 400 diamond and churn drill holes. Although these trough-like structures are indicative of mineralization, other features considered important in localization of the fluorspar are: suitable lithology, high permeability, fracturing, faulting and the presence of preexisting solution channels. Because of heavy flooding by rains, only about 25 percent of the mine workings were accessible. For these workings, the geology was mapped in detail and correlated with the data obtained from the well logs. It is believed that enough of the mine was mapped and compared to the structure to predict the geology throughout the rest of the mine --Introduction, pages 1-2

A Microscopic Model for D-Wave Pairing in the Cuprates: What Happens when Electrons Somersault?

We present a microscopic model for a strongly repulsive electron gas on a 2D square lattice. We suggest that nearest neighbor Coulomb repulsion stabilizes a state in which electrons undergo a "somersault" in their internal spin-space (spin-flux). When this spin-1/2 antiferromagnetic (AFM) insulator is doped, the charge carriers nucleate mobile, charged, bosonic vortex solitons accompanied by unoccupied states deep inside the Mott-Hubbard charge-transfer gap. This model provides a unified microscopic basis for (i) non-Fermi-liquid transport properties, (ii) mid-infrared optical absorption, (iii) destruction of AFM long range order with doping, (iv) angled resolved spectroscopy (ARPES), and (v) d-wave preformed charged carrier pairs. We use the Configuration Interaction (CI) method to study the quantum translational and rotational properties of such pairs. The CI method systematically describes fluctuation and quantum tunneling corrections to the Hartree-Fock approximation and recaptures essential features of the (Bethe ansatz) exact solution of the Hubbard model in 1D. For a single hole in the 2D AFM plane, we find a precursor to spin-charge separation. The CI ground state consists of a bound vortex-antivortex pair, one vortex carrying the charge and the other one carrying the spin of the doping hole.Comment: 10 pages, 8 figure

Neutron isotope reactions

The field of low temperature nuclear reactions has made slow but steady progress. Evidence has accumulated for production of energy at the level of a few watts, for production of helium in proportion to energy, for energetic particles, and for transmutations of elements. But there is no generally accepted theory for these phenomena. Progress requires a body of experimental evidence and a candidate theory through which theory and experiment can gain mutual support and acceptance. We explore the possibility that transfer of neutrons from neutron isotopes to ordinary nuclei, followed by beta decay of the neutron-enriched nuclei, facilitates a class of low-temperature transmutations. We have tested this possibility by comparing the implications of neutron isotope theory with the transmutations reported by Iwamura and associates. We find that experiment quantifies and supports the theory, and that theory clarifies and supports the experimental observations

Effect of Tunnel Configuration and Testing Technique on Cascade Performance

An investigation has been conducted to determine the influence of aspect ratio, boundary-layer control by means of slots and porous surfaces, Reynolds number, and tunnel end-wall condition upon the performance of airfoils in cascades. A representative compressor-blade section (the NACA 65-(12)(10) of aspect ratios of 1, 2, and 4 has been tested at low speeds in cascades with solid and with porous side walls. Two-dimensional flow was established in porous-wall cascades of each of the three aspect ratios tested; the flow was not two-dimensional in any of the solid-wall cascades. Turbine-blade sections of aspect ratio 0.83 were tested in cascades with solid and porous side walls and blade sections of aspect ratio 3.33 were tested in cascades with solid wall. No particular advantage was observed in the use of porous walls for the turbine cascades tested