The problem of adequately defining numbers

Includes bibliographical references.Natural numbers, although they pervade much of mathematics, are among the most difficult entities for which to provide definitions. Although it is often overlooked, as the efforts of pure mathematics are directed toward the maximization of rigor, the development of sound definitions for numbers can be viewed as one of the most critical objectives of the discipline. This paper is an examination and a support for the efforts in this area of the German logician Gottlob Frege, and in particular of his landmark treatise die Grundlagen der Arithmetik. This work marked the first successful attempt to define numbers through appeal to pure logic alone, and stands as a significant achievement in the history of mathematical philosophy

Sensorimotor Integration an a Small Motor Circuit

Rhythmic motor patterns, which underlie behaviors such as mastication, respiration and locomotion, are generated by specialized neural circuits called central pattern generators (CPGs). Although CPGs can generate their rhythmic motor output in the absence of rhythmic input, these motor patterns are modified by rhythmic sensory feedback in vivo. Furthermore, although the importance of sensory feedback in shaping CPG output is well known, most systems lack the experimental access needed to elucidate the mechanisms underlying sensorimotor integration at the cellular and synaptic level. I am therefore examining this issue using the gastric mill CPG, a circuit which generates the rhythmic retraction and protraction motor activity that drives chewing by the teeth in the gastric mill compartment of the crustacean stomach. The gastric mill CPG is well defined and very accessible at the cellular level. Specifically, I am examining the mechanism by which the gastropyloric receptor (GPR), a phasically active proprioceptor, selectively prolongs one phase (retraction) of the gastric mill rhythm in the isolated nervous system when it is activated in a pattern that mimics its in vivo activity. I first demonstrate that GPR regulation of the gastric mill rhythm relies on its presynaptic inhibition of modulatory commissural neuron 1 (MCN1), a projection neuron that activates and drives this rhythm. I also demonstrate that the GPR inhibition of MCN1 regulates the gastric mill rhythm by selectively regulating peptidergic cotransmission by MCN1. Lastly, I demonstrate that a peptide hormone (crustacean cardioactive peptide) that only modestly modifies the gastric mill rhythm, strongly gates the GPR regulation of this rhythm. Mechanistically, it acts not by influencing GPR or MCN1, but by activating the same excitatory current in the CPG neuron LG (lateral gastric) that is activated by MCN1-released peptide. This novel gating mechanism reduces GPR control over the amplitude of this excitatory current in LG. Thus, I have identified specific cellular mechanisms by which (a) phase-specific regulation of an ongoing motor pattern by a sensory input is accomplished, and (b) hormonal modulation gates that sensory input. These events are likely to reflect comparable ones occurring in the larger and less accessible vertebrate CNS

Quantifying Resiliency Risk Metrics through Facility Dispersion

During the last century, airbases were attacked at least 26 times in an effort to destroy the enemy at its base. Attacks on military airbases impose prohibitive losses to critical infrastructure, which in turn impacts the maintenance of air power projection. The primary enemy threat facing critical infrastructure today is the use of ballistic and land-attack cruise missiles to disrupt an airbase’s ability to launch and recover aircraft. Over the last decade, ballistic and cruise missile technology has grown to allow the world’s most powerful countries to achieve a nascent threat to forward operating bases used in theater security campaigns worldwide. Planners can reduce the impact of ballistic and cruise missile attacks on aircraft projection platforms by incorporating a number of resiliency measures, including dispersal of critical infrastructure assets, such as aircraft fuel containment and conveyance equipment. The integration of resiliency measures increases construction costs; therefore, planners need to identify an optimum balance between maximizing airbase resiliency and minimizing site costs. This research presents an airbase resiliency assessment capable of quantifying facility dispersal and risk tolerance levels in an environment threatened by missile attack. Model performance was evaluated using a case study from Osan AB, Republic of Korea. The model’s distinctive capabilities are expected to support planners in the critical task of analyzing and selecting the design strategy that maximizes airbase resiliency against the threat of ballistic and cruise missile attack

Mollusc shell periostracum as an alternative to tissue in isotopic studies

Recent studies have used carbon and nitrogen stable isotope ratios of preserved soft tissues to examine historical changes in trophic patterns of aquatic ecosystems. A limitation in this application is the difficulty in finding specimens for primary consumers, which can act as a surrogate for basal food sources in determining the trophic status of higher consumers. The availability of preserved soft tissues of invertebrate primary consumers is often limited in museum and archival collections; hard parts such as mollusc shells, however, are often abundant because of their ease of storage. We used stable isotope ratios of carbon and nitrogen to determine if there was a relationship between the isotopic composition of the periostracum of the shell and soft body tissue of freshwater molluscs. We found a significant correlation between (1) periostracum and tissue of freshly collected freshwater mussels, (2) ethanol-preserved adductor muscle tissue and dry-preserved mussels from museum collections, and (3) ethanol-preserved tissue and periostracum of gastropods from museum collections. The predictability of these relationships enhances the capacity to track changes in trophic complexity over time and responses of food webs to natural and anthropogenic environmental perturbations

Space Station evolution study oxygen loop closure

In the current Space Station Freedom (SSF) Permanently Manned Configuration (PMC), physical scars for closing the oxygen loop by the addition of oxygen generation and carbon dioxide reduction hardware are not included. During station restructuring, the capability for oxygen loop closure was deferred to the B-modules. As such, the ability to close the oxygen loop in the U.S. Laboratory module (LAB A) and the Habitation A module (HAB A) is contingent on the presence of the B modules. To base oxygen loop closure of SSF on the funding of the B-modules may not be desirable. Therefore, this study was requested to evaluate the necessary hooks and scars in the A-modules to facilitate closure of the oxygen loop at or subsequent to PMC. The study defines the scars for oxygen loop closure with impacts to cost, weight and volume and assesses the effects of byproduct venting. In addition, the recommended scenarios for closure with regard to topology and packaging are presented

Non-Fermi-liquid behavior in nearly ferromagnetic metallic SrIrO3 single crystals

We report transport and thermodynamic properties of single-crystal SrIrO3 as a function of temperature T and applied magnetic field H. We find that SrIrO3 is a non-Fermi-liquid metal near a ferromagnetic instability, as characterized by the following properties: (1) small ordered moment but no evidence for long-range order down to 1.7 K; (2) strongly enhanced magnetic susceptibility that diverges as T or T1/2 at low temperatures, depending on the applied field; (3) heat capacity C(T,H) ~ -Tlog T that is readily amplified by low applied fields; (4) a strikingly large Wilson ratio at T< 4K; and (5) a T3/2-dependence of electrical resistivity over the range 1.7 < T < 120 K. A phase diagram based on the data implies SrIrO3 is a rare example of a stoichiometric oxide compound that exhibits non-Fermi-liquid behavior near a quantum critical point (T = 0 and H = 0.23 T)

Low DC power, high gain-bandwidth product, coplanar Darlingtonfeedback amplifiers using InAlAs/InGaAs heterojunction bipolartransistors

[[abstract]]Broad band amplifiers with two Darlington feedback topologies, namely resistive biased and mirror biased, have been designed, fabricated and characterized. The HBT layers used for amplifiers were grown by MBE. To reduce the knee voltage and increase the breakdown voltage of the devices, graded base-emitter junction and low-doped, thick collector have been employed. The fabricated amplifiers have achieved 10.95 dB gain with 25.5 GHz bandwidth at DC power consumption of only 34.7 mW. State-of-art Gain-Bandwidth-Products per dc power were achieved for both amplifiers (⩾2.60 GHz/mW). The fabricated amplifiers also demonstrated moderate output power (8.3 dBm) at 10 GHz with a low DC power consumption of only 40 mW[[fileno]]2030121030001[[department]]電機工程學