The prime number theorem

Thesis (M.A.)--Boston Universit

Bibliography of Sequential Sampling Plans in Insect Pest Management Based on Wald\u27s Sequential Probability Ratio Test

This paper contains 65 references dealing with the development of sequential sampling plans in insect pest management based on Wald\u27s Sequential Probability Ratio Test (SPRT), 25 in forest entomology and 40 in agriculture entomology. The insect(s) sampled, whether the decision procedure was based on one or two SPRTs, and the mathematical distribution and probabilities of Type I and Type II errors used to develop the SPRTs are also given for each sequential sampling plan

The Wister Mud Pot Lineament: Southeastward Extension or Abandoned Strand of the San Andreas Fault?

We present the results of a survey of mud pots in the Wister Unit of the Imperial Wildlife Area. Thirty-three mud pots, pot clusters, or related geothermal vents (hundreds of pots in all) were identified, and most were found to cluster along a northwest-trending line that is more or less coincident with the postulated Sand Hills fault. An extrapolation of the trace of the San Andreas fault southeastward from its accepted terminus north of Bombay Beach very nearly coincides with the mud pot lineament and may represent a surface manifestation of the San Andreas fault southeast of the Salton Sea. Additionally, a recent survey of vents near Mullet Island in the Salton Sea revealed eight areas along a northwest-striking line where gas was bubbling up through the water and in two cases hot mud and water were being violently ejected

Explaining the Magnitude of Liquidity Premia: The Roles of Return Predictability, Wealth Shocks and State-Dependent Transaction Costs

The seminal work of Constantinides (1986) documents how, when the risky return is calibrated to the U.S. market return, the impact of transaction costs on per-annum liquidity premia is an order of magnitude smaller than the cost rate itself. A number of recent papers have formed portfolios sorted on liquidity measures and found a spread in expected per-annum return that is definitely not an order of magnitude smaller than the transaction cost spread: the expected per-annum return spread is found to be around 6-7% per annum. Our paper bridges the gap between Constantinides' theoretical result and the empirical magnitude of the liquidity premium by examining dynamic portfolio choice with transaction costs in a variety of more elaborate settings that move the problem closer to the one solved by real-world investors. In particular, we allow returns to be predictable and transaction costs to be stochastic, and we introduce wealth shocks, both stationary multiplicative and labor income. With predictable returns, we also allow the wealth shocks and transaction costs to be state dependent. We find that adding these real world complications to the canonical problem can cause transactions costs to produce per-annum liquidity premia that are no longer an order of magnitude smaller than the rate, but are instead the same order of magnitude. For example, predictable returns and i.i.d. labor income growth causes the liquidity premium for an agent with a wealth to monthly labor income ratio of 0 or 10 to be 1.68\% and 1.20\% respectively; these are 21-fold and 15-fold increases, respectively, relative to that in the standard i.i.d. return case. We conclude that the effect of proportional transaction costs on the standard consumption and portfolio allocation problem with i.i.d. returns can be materially altered by reasonable perturbations that bring the problem closer to the one investors are actually solving.

Labor Income Dynamics at Business-Cycle Frequencies: Implications for Portfolio Choice

A large recent literature has focused on multiperiod portfolio choice with labor income, and while the models are elaborate along several dimensions, they all assume that the joint distribution of shocks to labor income and asset returns is i.i.d.. Calibrating this joint distribution to U.S. data, these papers obtain three results not found empirically for U.S. households: young agents choose a higher stock allocation than old agents; young agents choose a higher stock allocation when poor than when rich; and, young agents always hold some stock. This paper asks whether allowing the conditional joint distribution to depend on the business cycle can allow the model to generate equity holdings that better match those of U.S. households, while keeping the unconditional distribution the same as in the data. Calibrating the business-cycle variation in the first two moments of labor income growth to U.S. data leads to large reductions in stock holdings by young agents with low wealth-income ratios. The reductions are so large that young, poor agents now hold less stock than both young, rich agents and old agents, and also hold no stock a large fraction of the time. Our results suggest that the predictability of labor-income growth at a business-cycle frequency plays an important role in a young agent's decision-making about her portfolio's stock holding.

Determination of the Equation of State of Dense Matter

Nuclear collisions can compress nuclear matter to densities achieved within neutron stars and within core-collapse supernovae. These dense states of matter exist momentarily before expanding. We analyzed the flow of matter to extract pressures in excess of 10^34 pascals, the highest recorded under laboratory-controlled conditions. Using these analyses, we rule out strongly repulsive nuclear equations of state from relativistic mean field theory and weakly repulsive equations of state with phase transitions at densities less than three times that of stable nuclei, but not equations of state softened at higher densities because of a transformation to quark matter.Comment: 26 pages, 6 figures; final versio

Development of Empirical Models to Rate Spruce-Fir Stands in Michigan\u27s Upper Peninsula for Hazard From the Spruce Budworm (Lepidoptera: Tortricidae): A Case History

The procedure used to develop empirical models which estimate potential spruce budworm impact to spruce-fir stands in Michigan\u27s Upper Peninsula is reviewed. Criteria used to select independent variables, to select the best of alternative multiple linear regression models. and to validate final models are discussed. Preliminary, intermediate, and final results demonstrate a cyclic pattern to the development procedure. Validation is emphasized as an important step in the procedure. Implications of using the hazard-rating system as a pest management tool in the stand management process are discussed

Apparatus for precision focussing and positioning of a beam waist on a target

The invention relates to optical focussing apparatus and, more particularly, to optical apparatus for focussing a highly collimated Gaussian beam which provides independent and fine control over the focus waist diameter, the focus position both along the beam axis and transverse to the beam, and the focus angle. A beam focussing and positioning apparatus provides focussing and positioning for the waist of a waisted beam at a desired location on a target such as an optical fiber. The apparatus includes a first lens, having a focal plane f sub 1, disposed in the path of an incoming beam and a second lens, having a focal plane f sub 2 and being spaced downstream from the first lens by a distance at least equal to f sub 1 + 10 f sub 2, which cooperates with the first lens to focus the waist of the beam on the target. A rotatable optical device, disposed upstream of the first lens, adjusts the angular orientation of the beam waist. The transverse position of the first lens relative to the axis of the beam is varied to control the transverse position of the beam waist relative to the target (a fiber optic as shown) while the relative axial positions of the lenses are varied to control the diameter of the beam waist and to control the axial position of the beam waist. Mechanical controllers C sub 1, C sub 2, C sub 3, C sub 4, and C sub 5 control the elements of the optical system. How seven adjustments can be made to correctly couple a laser beam into an optical fiber is illustrated. Prior art systems employing optical techniques to couple a laser beam into an optical fiber or other target simply do not provide the seven necessary adjustments. The closest known prior art, a Newport coupler, provides only two of the seven required adjustments