Constructing the polynomlal identities and central identities of degree <9 of 3 × 3 matrices

AbstractWe present an algorithm for computing an independent generating set for the multilinear identities and the multilinear central identities of the m × m matrices over a field ø of characteristic zero or a large enough prime. Then we use it to construct all the multilinear identities and all the multilinear central identities of degree < 9 for M3(ø)

Constructing the identities and the central identities of degree \u3c 9 of the n x n matrices

In this paper, we present an algorithm that can be used to compute an independent generating set for the multilinear identities or multilinear central identities of the nx n matrices M[subscript]n([phi]) over a field [phi], where [phi] is of characteristic zero or a large enough prime. Furthermore, we prove that every identity or central identity is implied by the set of multilinear identities or central identities which the algorithm produces. Therefore, the procedure creates all the identities and central identities of degree n. Then we use this algorithm to construct all the multilinear identities and multilinear central identities of degree n\u3c9 for M[subscript]3([phi]). The results of the procedure are given in chapter 3. There are no identities or central identities of degree n\u3c6. The only multilinear identity of degree 6 is the standard identity of degree 6 which is given by (3.3). The multilinear identities (3.4)-(3.9) form an independent generating set for all the multilinear identities of degree 7. All of these identities are consequences of the standard identity of degree 6. Finally, the identities (3.10)-(3.11) together with the central identities (3.12)-(3.15) form an independent generating set for all of the multilinear central identities of degree 8

Effectiveness Of Economic Sanctions: Empirical Research Revisited

This paper reexamines economic sanctions research and identifies explanatory variables used by many previous theoretical and empirical research studies on the effectiveness of voluntary and non-voluntary economic sanctions since World War I. A normative legal, political, and economic methodology is used to measure effectiveness of economic sanctions as a random walk process.  The paper concludes that choosing a target and imposing economic sanctions is a random process that occurs when a sender is faced with a real or perceived threat.  Sanctions are imposed as an alternative to inaction or going to war.  The theory and research on effectiveness of sanctions has been a mere exercise in running regressions on a series of random numbers and do not shed any light to guide policymaking

Developmental Relationship Programs: An Empirical Study Of The Impact Of Peer-Mentoring Programs

This paper provides an empirical analysis of the impact and effectiveness of developmental relationships provided through academic intervention programs at a medium-size master’s level public university in the Northeastern United States.  The programs’ curriculum follows the Model of Strategic Learning’s four pillars of learning and is administered to students with diverse interventional needs. This paper presents a brief review of the literature about effective developmental relationship programs (mentoring and coaching) in higher education.  Then, Ordinary Least Squares regressions, as well as paired samples t-tests, are used to test the impact of programs offered through developmental relationships to students with varying academic deficiencies.  The immediate, as well as longer-term, impact and sustainability of students’ enhanced performance is statistically examined.  The paper concludes that students who fully take advantage of developmental relationships benefit the most and sustain their higher level of performance beyond the immediate post one-time intervention period.  However, in the absence of additional intervention, the academic performance gains seem to subside and flatten out

Sol-Gel Deposition and Characterization of 1 Vanadium Pentoxide Thin Films with High TCR

Vanadium pentoxide thin films have been deposited on quartz substrates via sol-gel synthesis and dip coating. The process was developed to establish a reliable and inexpensive method to produce thin films with a high temperature coefficient of resistance (TCR)for sensing applications. Sol-gel precursor concentration and post-deposition annealing conditions were varied to address their effects on film composition, morphology, structure, resistivity, and TCR response. The resulting thin films were structurally characterized by thin film profilometry, x-ray diffraction, scanning electron microscopy, and Raman spectroscopy. Resistivity and TCR measurements were carried out to determine their efficacy as sensor materials. Both low and high concentration alkoxide sol-gel precursors led to films of pure -V2O5 composition but with characteristically different structural and electrical properties. Low concentration films showed a modest decrease in resistivity and TCR with increasing annealing temperature, consistent with the formation of increasing grain size and the coalescence of largely planar grains with common crystalline orientation. In contrast, films fabricated from higher alkoxide precursor concentration are characterized by a higher density of grains with a larger dispersion in orientation and better-developed grain boundaries, leading to a general increase in resistivity and TCR with annealing temperature. The TCR of the films lied in the range of -3%◦C−1 to -4%◦C−1, comparing favorably with films produced through conventional techniques such as DC magnetron sputtering, chemical vapor deposition, or pulsed laser deposition. Further, their TCR and resistivity characteristics can be controlled through sol gel precursor concentration and post-deposition annealing temperature, indicating that sol-gel deposited vanadium pentoxide films are promising candidates for infrared sensor applications

Effects of applying a stochastic rebound model in erosion prediction of elbows and plugged tee

ABSTRACT Solid particle erosion is a complex phenomenon that depends on many factors such as particle and fluid characteristics, type of material being eroded, and flow geometry. Fittings used in the oil and gas industry such as elbows are susceptible to erosion when solid particles are present in the flow. The momentum of particles carries them across streamlines and the particles impinge the outer wall of the elbow resulting in erosion damage. In an erosive environment, plugged tees are commonly used instead of elbows to reduce the erosion especially where space considerations are important and long-radius elbows can not be used. However, it is unclear how much of a reduction in erosion occurs by replacing an elbow with a plugged tee. In order to compare the erosion in an elbow and a plugged tee exposed to the same flow conditions, a CFD-based erosion prediction model is applied. The model has three primary steps: flow modeling, particle tracking, and applying erosion equations. The results from the model agree with experimental findings for the elbow geometry. However, the simulation results for erosion rate generated for the plugged tee requires a stochastic approach. Results obtained with the erosion prediction model before and after this modification are shown

Effect of Temperature on Abrasion Erosion in Particle Based Concentrating Solar Powerplants

The use of solid particles as a heat transfer medium is being explored for concentrated solar power plants (CSP) to increase their efficiency by achieving operating temperature \u3e700 °C. During operation, these hot particles are expected to move along the various components within the collector system, resulting in material degradation from a combination of high-temperature oxidation and erosion. In the present study, the performance of candidate materials was evaluated through a series of abrasion erosion experiments at room temperature as well as at 800 °C. Wear in metallic and refractory type materials was investigated using CarboBead® HSP 40/70 particles inside a resistance heated kiln. Cross-sectional scanning electron microscopy (SEM) and energy dispersive x-ray spectroscopy (EDS) analysis on the specimens tested at 800 °C determined that the specific wear rate in Inconel 740H and stainless steel 316 metallic specimens was influenced by the thermally grown oxide morphology. High chromium Inconel 740H specimens exhibited greater resistance to wear with a steady state specific wear rate of 1.92E-4 mm3N-1m−1 compared to 5.7E-3 mm3N-1m−1 for Stainless Steel 316

Process Compensated Resonance Testing Modeling for Damage Evolution and Uncertainty Quantification

Process Compensated Resonance Testing (PCRT) is a nondestructive evaluation method that measures and analyzes the resonance frequencies of a component for material state characterization, defect detection and process monitoring. PCRT inspections of gas turbine engine components have demonstrated the sensitivity of resonance frequencies to manufacturing defects and in-service thermal and mechanical damage. Prior work on PCRT modeling has developed forward modeling and model inversion techniques that simulate the effects of geometry variation, material property variation, and damage on Mar-M-247 nickel-based superalloy samples. Finite element method (FEM) forward model simulations predicted the effects of variation in geometry, material properties and damage on resonance frequencies. Model inversion used measured resonance frequencies to characterize the material state of components. Parallel work developed a process for uncertainty quantification (UQ) in PCRT models and measurements. The UQ process evaluated the propagation of uncertainty from various sources, identified the most significant uncertainty sources, and enabled uncertainty mitigation to improve model and measurement accuracy. Current efforts have expanded on those developments in several areas. One-factor-at-a-time (OFAT) forward model simulations were conducted on cylindrical dog bone coupons made from Mar-M-247. The simulations predicted the resonance frequency response to variation in geometry, elastic properties, crystallographic orientation, creep strain and cracking. The OFAT studies were followed by forward model Monte Carlo simulations that predicted the effects of multiple, concurrent sources of variation and damage on resonance frequencies, allowing characterization of virtual populations and quantification of uncertainty propagation. The Monte Carlo simulation design points were used to demonstrate the generation of a virtual database of components for training PCRT inspection applications, or “sorting modules.” Virtual database training sets can potentially overcome the limitations imposed by the availability of components and material states for training sets based on physical examples. Forward modeling tools and techniques were applied to titanium to simulate the effects of material variation, damage, and crystallographic texture. Forward modeling was also applied to more complex geometries, including a notional turbine blade, to demonstrate the application of modeling tools to shapes representative of gas turbine engine components. Model inversion tools and techniques have also advanced under the current effort. Prior inversion methods relied on iterative fitting to polynomial expressions for simple geometries and bulk material properties. Current efforts have demonstrated FEM-based model inversion which allows characterization of complex shapes and material states. FEM-based design spaces were generated, model inversion was carried out for surrogate modeled resonance spectra, and inversion performance was evaluated. Analysis of PCRT modeling results led to the development of automated resonance mode matching tools based on the calculation of modal assurance criteria (MAC) values, mode shape displacement metrics and Hungarian Algorithm sorting methods

Model-based Probe State Estimation and Crack Inverse Methods Addressing Eddy Current Probe Variability

Recent work on model-based inverse methods with eddy current inspections of surface breaking discontinuities has shown some sizing error due to variability in probes with the same design specifications [1]. This is an important challenge for model-based inversion crack sizing techniques, to be robust to the varying characteristics of eddy current probes found in the field [1-2]. In this paper, a model-based calibration process is introduced that estimates the state of the probe. First, a carefully designed surrogate model was built using VIC-3D® simulations covering the critical range of probe rotation angles, tilt in two directions, and probe offset (liftoff) for both tangential and longitudinal flaw orientations. Some approximations and numerical compromises in the model were made to represent tilt in two directions and reduce simulation time; however, this surrogate model was found to represent the key trends in the eddy current response for each of the four probe properties in experimental verification studies well. Next, this model was incorporated into an iterative inversion scheme during the calibration process, to estimate the probe state while also addressing the gain/phase fit and centering the calibration notch indication. Results are presented showing several examples of the blind estimation of tilt and rotation angle for known experimental cases with good agreement within +/- 2.5 degrees. The RMS error was found to be significantly reduced by fitting the probe state and, in many instances, probe state estimation addresses the previously un-modelled characteristics (model error) with real probe inversion studies. Additional studies are presented comparing the size of the calibration notch and the quality of the calibration fit, where calibrating with too small or too large a notch can produce poorer inversion results. Once the probe state is estimated, the final step is to transform the base crack inversion surrogate model and apply it for crack characterization. Because of the dimensionality of this problem, simulations were made at a limited set of select flaw sizes with varying length, depth and width, and an interpolation scheme was used to address the effect of the probe state at intermediate solution points. Using this process, results are presented demonstrating improved crack inversion performance for extreme probe states

Detection and localization of early- and late-stage cancers using platelet RNA

Cancer patients benefit from early tumor detection since treatment outcomes are more favorable for less advanced cancers. Platelets are involved in cancer progression and are considered a promising biosource for cancer detection, as they alter their RNA content upon local and systemic cues. We show that tumor-educated platelet (TEP) RNA-based blood tests enable the detection of 18 cancer types. With 99% specificity in asymptomatic controls, thromboSeq correctly detected the presence of cancer in two-thirds of 1,096 blood samples from stage I–IV cancer patients and in half of 352 stage I–III tumors. Symptomatic controls, including inflammatory and cardiovascular diseases, and benign tumors had increased false-positive test results with an average specificity of 78%. Moreover, thromboSeq determined the tumor site of origin in five different tumor types correctly in over 80% of the cancer patients. These results highlight the potential properties of TEP-derived RNA panels to supplement current approaches for blood-based cancer screening