AN ANALYSIS OF OPTIMAL FARM CAPITAL STRUCTURE

Agricultural Finance,

A MATHEMATICAL ANALYSIS OF THE GAME OF CHESS

This paper analyzes chess through the lens of mathematics. Chess is a complex yet easy to understand game. Can mathematics be used to perfect a player’s skills? The work of Ernst Zermelo shows that one player should be able to force a win or force a draw. The work of Shannon and Hardy demonstrates the complexities of the game. Combinatorics, probability, and some chess puzzles are used to better understand the game. A computer program is used to test a hypothesis regarding chess strategy. Through the use of this program, we see that it is detrimental to be the first player to lose the queen. Ultimately, it is shown that mathematics exists inherently in chess. Therefore math can be used to improve, but not perfect, chess skills

Frequency control in synchronized networks of inhibitory neurons

We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically-based synaptic influence. We argue that such a reduced model can quantitatively capture the frequency behavior of a larger class of neuronal models. We show that in different parameter regimes, the network frequency depends in different ways on the intrinsic and synaptic time constants. Only in one portion of the parameter space, called `phasic', is the network period proportional to the synaptic decay time. These results are discussed in connection with previous work of the authors, which showed that for mildly heterogeneous networks, the synchrony breaks down, but coherence is preserved much more for systems in the phasic regime than in the other regimes. These results imply that for mildly heterogeneous networks, the existence of a coherent rhythm implies a linear dependence of the network period on synaptic decay time, and a much weaker dependence on the drive to the cells. We give experimental evidence for this conclusion.Comment: 18 pages, 3 figures, Kluwer.sty. J. Comp. Neurosci. (in press). Originally submitted to the neuro-sys archive which was never publicly announced (was 9803001

Small-Scale structure in the Galactic ISM: Implications for Galaxy Cluster Studies

Observations of extragalactic objects need to be corrected for Galactic absorption and this is often accomplished by using the measured 21 cm HI column. However, within the beam of the radio telescope there are variations in the HI column that can have important effects in interpreting absorption line studies and X-ray spectra at the softest energies. We examine the HI and DIRBE/IRAS data for lines of sight out of the Galaxy, which show evidence for HI variations in of up to a factor of three in 1 degree fields. Column density enhancements would preferentially absorb soft X-rays in spatially extended objects and we find evidence for this effect in the ROSAT PSPC observations of two bright clusters of galaxies, Abell 119 and Abell 2142. For clusters of galaxies, the failure to include column density fluctuations will lead to systematically incorrect fits to the X-ray data in the sense that there will appear to be a very soft X-ray excess. This may be one cause of the soft X-ray excess in clusters, since the magnitude of the effect is comparable to the observed values.Comment: 16 pages, 9 figures, to appear in the Astrophysical Journal, vol. 597 (1 Nov 2003

Variations in mineralogy, temperature, and oxygen fugacity in a suite of strongly peralkaline lavas and tuffs, Pantelleria, Italy.

Eight samples of pantelleritic lava and tuff and a lithic inclusion of trachyte from Pantelleria, Italy, have been thoroughly analyzed with an electron microprobe. These samples reveal fi ve different mineral assemblages if classifi ed by the presence of fayalite, aenigmatite, ilmenite, and magnetite: (1) augite + fayalite + ilmenite + magnetite, (2) augite + fayalite + ilmenite, (3) hedenbergite or sodian hedenbergite + fayalite + ilmenite + aenigmatite + quartz, (4) sodian hedenbergite or aegirine-augite + ilmenite + aenigmatite + quartz ± ferrorichterite, and (5) aegirine-augite + aenigmatite + quartz. Alkali feldspar (Or35–37) is present as the dominant phyric phase in each assemblage. Whole-rock silica and peralkalinity correlate strongly with the mineral assemblage: assemblage 1 is found in the sample with the lowest agpaitic index [A.I. = molar (Na + K)/Al] and silica concentration (A.I. \u3c 1.31, SiO2 \u3c 64.8 wt%) and equilibrated at 991–888°C at an oxygen fugacity between 0.7 and 1.1 log units below the FMQ buffer (FMQ – 0.7 to FMQ – 1.1). Assemblage 2 is associated with a higher agpaitic index and silica concentration (A.I. = 1.42, SiO2 = 67.1%) and equilibrated at ~794°C at FMQ – 0.5. Assemblage 3 is associated with a still higher agpaitic index and silica concentration (A.I. in the range 1.55 – 1.63, 66.8 \u3c SiO2 \u3c 67.8%) and equilibrated at 764–756°C at FMQ – 0.5 to FMQ – 0.2. Assemblage 4 is associated with a slightly higher agpaitic index and yet higher silica concentration (1.61 \u3c A.I \u3c 1.75, 67.6 \u3c SiO2 \u3c 72.0%) and equilibrated between 740–700°C at oxygen fugacities at or just below the FMQ buffer. Assemblage 5 is associated with the highest agpaitic index and highest concentration of silica (A.I. = 1.97, SiO2 = 69.7%) and equilibrated at \u3c700°C at an oxygen fugacity just above the FMQ buffer in a “no-oxide” fi eld. Despite the paucity of two-oxide, two-pyroxene, or two-feldspar pairs, it may be possible to accurately constrain temperature and oxygen fugacity in peralkaline rocks with QUIlF equilibria given an equilibrium assemblage of fayalite, ilmenite, and clinopyroxene

G2-structures for N=1 supersymmetric AdS4 solutions of M-theory

We study the N=1 supersymmetric solutions of D=11 supergravity obtained as a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold M. Using the octonion bundle structure on M we reformulate the Killing spinor equations in terms of sections of the octonion bundle on M. The solutions then define a single complexified G2-structure on M or equivalently two real G2-structures. We then study the torsion of these G2-structures and the relationships between them.Comment: 48 pages, updated references, corrected minor errors and typos, Class. Quantum Grav. (2018

Volcanic Mound Fields on the East Pacific Rise, 16˚-19˚S: Low Effusion Rate Eruptions at Overlapping Spreading Centers for the Past 1 Myr

Volcanic mound fields identified on SeaMARC II and HMR1 12 kHz side-scan data from the southern East Pacific Rise (SEPR) occur near overlapping spreading centers (OSCs) and migration traces of OSCs. The volcanic mound fields appear as a distinctive hummocky seafloor fabric due to side-scan backscatter reflections from clusters of moundshaped reflectors. The lack of growth of the mound fields away from the ridge axis, and their occurrence in association with OSC traces, suggests that mound fields form along the ridge crest near OSCs. Volcanic mound fields are found where 120 kHz side-scan and visual observations find fields of pillow mounds. Since pillow mounds are constructed by low effusion rate eruptions, the volcanic mound fields found near the OSCs and in their migration traces indicate that volcanic effusion rates tend to be lower near ridge discontinuities than midsegment regions. This tendency for low effusion rate eruptions at OSCs is documented for the past _1 Myr. Three independent measurements of ridge segmentation, (1) volcanic segment boundaries marked by the low effusion rate eruptions, (2) tectonic segments defined by OSCs, and (3) magmatic segment boundaries based on continuity of parental magma composition, all coincide in the study area. High backscatter off-axis lava fields not associated with seamounts are found on seafloor younger than _0.2 Ma. The _0.2 Ma corridor corroborates previous results from the distribution of small isolated volcanoes that indicates randomly distributed off-axis eruptions mainly occur on crust younger than _0.2 Ma