The KMO Method for Solving Non-homogenous, mth Order Differential Equations

This paper shows a simple tabular procedure \added{derived from the method of undetermined coefficients} for finding a particular solution to differential equations of the form \sum_{j=0}^m a_j\frac{d^j y}{dx^j} = P(x)e^{\alpha{}x}. This procedure reduces the derivatives of the product of an arbitrary polynomial and an exponential to rows of constants representing the coefficients of the terms. The rows are each multiplied by aj and summed to produce a mth order differential equation such that its solution is the polynomial part of the particular solution of the above equation. Solving this corresponding differential equation determines the coefficients of the polynomial. The underlying algebra of this conversion and its formulaic implication are then discussed. Using the formula derived, the particular solution is found. This procedure is based on but different than the method of undetermined coefficients because while the method of undetermined coefficients requires substitution of a product of a polynomial, Q, and an exponential into the differential equation immediately, this procedure is derived from the examination of the substitution of the product of any function and an exponential. This allows for a richer understanding of the relationship between the differential equation for y and the differential equation for Q. Ultimately this method is better than the method of undetermined coefficients because it is more straightforward. In any case, both methods solve the same problem but KMO is faster

AN ACCURATE DESCRIPTION OF WATER USING THE MANY-BODY EXPANSION AND PERTURBATION THEORY

Ph.DDOCTOR OF PHILOSOPH

Seismic Analysis and Retrofitting Priorities for Highway Bridges on Earthquake Priority Route System in Western Kentucky

Concern has grown in recent years over the seismic activity of the New Madrid seismic zone in Western Kentucky. Bridges, as the vital links of the priority route system, need to be prevented from sever earthquake damages in order to keep the routes passible after an earthquake has occurred. In this report, seismic rating and seismic analysis were performed for each of 276 bridges on the priority route system. A priority order of retrofitting for the bridges was listed according to their vulnerability to the earthquake. At least 111 bridges need retrofitting based on the results of seismic analyses. The numbers of bridges needing to be retrofitted were determined for different confidence levels. The methods of estimating spanloss type of bridge collapse due to earthquake induced abutment sliding and evaluating bridge damages related to earthquake induced vibration of pier or bent were developed. ATC analysis was also conducted for each bridge

Exploring germ granule function in small RNA biology

P granules protect RNA interference genes from silencing by piRNAs Abstract P granules are perinuclear condensates in C. elegans germ cells proposed to serve as hubs for self/non-self RNA discrimination by Argonautes. We report that a mutant (meg-3 meg-4) that does not assemble P granules in primordial germ cells loses competence for RNA-interference over several generations and accumulates silencing small RNAs against hundreds of endogenous genes, including the RNA-interference genes rde-11 and sid-1. In wild-type, rde-11 and sid-1 transcripts are heavily targeted by piRNAs, accumulate in P granules, but maintain expression. In the primordial germ cells of meg-3 meg-4 mutants, rde-11 and sid-1 transcripts disperse in the cytoplasm with the small RNA biogenesis machinery, become hyper-targeted by secondary sRNAs, and are eventually silenced. Silencing requires the PIWI-class Argonaute PRG-1 and the nuclear Argonaute HRDE-1 that maintains trans-generational silencing of piRNA targets. These observations support a “safe harbor” model for P granules in protecting germline transcripts from piRNA-initiated silencing. Two parallel sRNA amplification cycles contribute to transgenerational RNAi in C. elegans Abstract: RNA-mediated interference (RNAi) is a conserved mechanism that uses small RNAs (sRNAs) to tune gene expression. In C. elegans, exposure to dsRNA induces the production of gene-specific sRNAs that are propagated to progeny not exposed to the dsRNA trigger. We present evidence that RNAi inheritance is mediated by two parallel sRNA amplification loops. The first loop, dependent on the nuclear Argonaute HRDE-1, targets nascent transcripts, and reduces but does not eliminate productive transcription at the locus. The second loop, dependent on the conserved helicase ZNFX-1, targets mature transcripts and concentrates them in perinuclear condensates (nuage). Each amplification loop generates a distinct class of sRNAs that perpetuate silencing into the next generation, with the ZNFX-1 loop responsible for the bulk of sRNA production. We speculate that nuage is a germline adaptation that allows for cytoplasmic transcripts to be used as templates for robust sRNA amplification in the absence of the original trigger

Developing a Relative Humidity Correction for Low-Cost Sensors Measuring Ambient Particulate Matter.

There is increasing concern about the health impacts of ambient Particulate Matter (PM) exposure. Traditional monitoring networks, because of their sparseness, cannot provide sufficient spatial-temporal measurements characteristic of ambient PM. Recent studies have shown portable low-cost devices (e.g., optical particle counters, OPCs) can help address this issue; however, their application under ambient conditions can be affected by high relative humidity (RH) conditions. Here, we show how, by exploiting the measured particle size distribution information rather than PM as has been suggested elsewhere, a correction can be derived which not only significantly improves sensor performance but which also retains fundamental information on particle composition. A particle size distribution⁻based correction algorithm, founded on κ -Köhler theory, was developed to account for the influence of RH on sensor measurements. The application of the correction algorithm, which assumed physically reasonable κ values, resulted in a significant improvement, with the overestimation of PM measurements reduced from a factor of ~5 before correction to 1.05 after correction. We conclude that a correction based on particle size distribution, rather than PM mass, is required to properly account for RH effects and enable low cost optical PM sensors to provide reliable ambient PM measurements

Status of FAA Studies in Thermal Acoustics

As with many aerospace applications, commercial jet engine components are operated in demanding environments, often at extreme temperature and stress conditions. The predominant used surface inspection method used on these components is fluorescent penetrant inspection. Research has been ongoing for a number of years on a new technology using a short burst of low frequency ( ∼ 20 KHz) ultrasound to “heat up” cracks and make them visible in the infrared range. The basic premise of the Thermal Acoustic method is to use an energy source with recent efforts using an ultrasonic horn originally intended for use in ultrasonic welding to excite the component. The energy source causes an increase in local heating, which is detectable with infrared cameras typically used in Thermographic inspection. While considerable research is underway, additional information on the sensitivity and applicability of this technique to engine components and alloys is needed prior to widespread use in the aviation industry. The purpose of this program is to provide additional data to determine applicability of this method to engine components

Premature polyadenylation-mediated loss of stathmin-2 is a hallmark of TDP-43-dependent neurodegeneration.

Amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) are associated with loss of nuclear transactive response DNA-binding protein 43 (TDP-43). Here we identify that TDP-43 regulates expression of the neuronal growth-associated factor stathmin-2. Lowered TDP-43 levels, which reduce its binding to sites within the first intron of stathmin-2 pre-messenger RNA, uncover a cryptic polyadenylation site whose utilization produces a truncated, non-functional mRNA. Reduced stathmin-2 expression is found in neurons trans-differentiated from patient fibroblasts expressing an ALS-causing TDP-43 mutation, in motor cortex and spinal motor neurons from patients with sporadic ALS and familial ALS with GGGGCC repeat expansion in the C9orf72 gene, and in induced pluripotent stem cell (iPSC)-derived motor neurons depleted of TDP-43. Remarkably, while reduction in TDP-43 is shown to inhibit axonal regeneration of iPSC-derived motor neurons, rescue of stathmin-2 expression restores axonal regenerative capacity. Thus, premature polyadenylation-mediated reduction in stathmin-2 is a hallmark of ALS-FTD that functionally links reduced nuclear TDP-43 function to enhanced neuronal vulnerability