Arc Valuations on Smooth Varieties.

For a nonsingular $CC$-arc valuation $v$ on a nonsingular variety $X$ over a field $CC$, we describe the maximal irreducible subset $C(v)$ of the arc space of X such that $val_{C(v)}=v$. We describe $C(v)$ both algebraically, in terms of the sequence of valuation ideals of $v$, and geometrically, in terms of the sequence of infinitely near points associated to $v$. For a singular $CC$-arc valuation $v$, we show that after a finite number of blowups of centers, its becomes nonsingular. When $X$ is a surface, our construction also applies to any divisorial valuation $v$, and in this case $C(v)$ coincides with the construction of Ein, Lazarsfeld, and Mustata (cite[Example 2.5]{mustata}). We also investigate the situation for irrational valuations on surfaces. Our results suggest that a more natural place to look for these valuations are in spaces that generalize arc spaces. Also, we compute the motivic measure of $C(v)$ for some of the various types of valuations on surfaces.Ph.D.MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60710/1/ykm_1.pd

MAntRA: A framework for model agnostic reliability analysis

We propose a novel model agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach -- referred to as MAntRA -- combines interpretable machine learning, Bayesian statistics, and identifying stochastic dynamic equation to evaluate reliability of stochastically-excited dynamical systems for which the governing physics is \textit{apriori} unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data, and aleatoric uncertainty because of environmental effect and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme and the probability failure is computed. The efficacy of the proposed approach is illustrated on three numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements

Interpretable Machine Learning Approach for Reliability Analysis

The reliability assessment of stochastic dynamic systems is a crucial issue, specifically for complex engineering systems. Mathematically, reliability can be estimated as the probability of not failing while meeting particular objective functions and constraints. It is achieved by shrinking the area under the probability distribution function (PDF) while moving the average value. There are well-established techniques available in the literature for reliability estimation; however, the reliability analysis of existing systems, particularly complex interdependent and integral structures, is often overlooked despite being an equally significant problem. It is widely recognized that the behavior of structures can change over time due to degradation. Understanding, controlling, and mitigating component degradation are key priorities for complex engineering assets. As expensive engineering systems age beyond their design lifetimes, it is important to ensure reliability: detect and track degradation and changes in degradation rates; monitor system components for degradation; classify and characterize their degradation modes; and perform prognosis of their future state. Similarly, industrial systems that undergo multiple maintenance tasks and component replacements can also experience alterations in their governing physics, making it challenging to estimate their reliability using traditional methods that rely on a model based on the design blueprint of the system [1]. To address this issue, We propose and develop an innovative approach named "model-agnostic reliability analysis framework". This development has been published [2], and now we are extending this tool for trustworthy reliability analysis of complex nuclear systems with Missouri S&T. This method integrates Bayesian statistics, interpretable machine learning, and identification of stochastic dynamic equations (SDEs) to estimate the reliability of complex systems with unknown/approximate physics. In the conference presentation, we will demonstrate the effectiveness of our development for complex systems while extending the test cases for nuclear systems and structures through numerical examples, highlighting its potential application in reliability analysis in the domain of nuclear systems

Evanescent wave sensor for potassium ion detection with special reference to agricultural application

We are introducing 4 & PRIME;-aminodibenzo-18-crown-6 ether (A2BC) modification of gold nanoparticles coated optical fiber as a new sensor for evanescent wave trapping on the polymer optical fiber to detect low-level potassium ions. We characterized these gold nanoparticles by X-ray Diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), Nanoparticle tracking analysis (NTA), Field Emission scanning electron microscopes (FE-SEM), and UV-Visible spectroscopy. In the present study, we modified the gold nanoparticles with A2BC for selective sensing of potassium (K+) ions. The interaction between A2BC and K+ ions leads to the temporary formation of a sandwich structure as crown ethers form steady complexes with metal ions. This sandwich structure leads to potassium detection. In our implementation, related operational parameters such as cladding length, roughness, and concentration of A2BC and gold nanoparticles, were optimized to achieve a detection threshold of 1 ppm. Additionally, we optimized the optical fiber sensor to increase its detection sensitivity from the μV range to the mV range. The sensor demonstrates a fast response time (10 s) and high sensitivity, selectivity, and stability, which cause a wide linear range (1-100 ppm) and a low limit of detection (LOD = 0.14 ppm). Lastly, we tested the sensor for a soil-sensing application.Acknowledgments. The authors would like to thank Rajiv Gandhi Science and Technology Commission, Mumbai. Maharashtra for providing financial assistance and Director, The Institute of Science, Dr. Homi Bhabha State University, Mumbai, for providing laboratory access for carrying out experiments. The authors would also like to thank DST for providing instruments to the Institute of Science under their FIST scheme. The authors would like to thank the researchers supporting project number (RSP2023R370), King Saud University, Riyadh, Saudi Arabia, for financial support

Synthesis and biological activity of 7-(2-(1H-1,2,4-triazol-1-yl)ethoxy)-4-(styryl/4-substituted styryl)-2H-chromen-2-one

Incorporation of other hetero-compounds to parent coumarin increases its effectiveness towards its bioactivity. In view of this finding we have synthesized coumarin triazole derivatives. The key synthon used for this reaction pathway are 7-hydroxy-4-methyl-2H-chromen-2-one. This substituted coumarin has been refluxed with 1-bromo-2-chloroethane in presence of anhydrous K2CO3 to afford 7-(2-chloroethoxy)-4-methyl-2H-chromen-2-one, which has been condensed with triazole to yield 4-methyl coumarin triazole derivative by optimising solvent/base pair. 4-Methyl group of coumarin triazole derivative has been condensed with aromatic aldehydes to afford 7-(2-(1H-1,2,4-triazol-1-yl) ethoxy)-4-(styryl/4-substituted styryl)-2H-chromen-2-one 7a-e. All the synthesized products are characterized using IR and, 1H, 13C NMR, mass spectroscopy and elemental analysis. Final synthesized compounds 7a-e have been evaluated for their anti-bacterial and anti-fungal activity.

Synthesis and biological activity of 7-(2-(1H-1,2,4-triazol-1-yl)ethoxy)-4-(styryl/4-substituted styryl)-2H-chromen-2-one

1197-1102Incorporation of other hetero-compounds to parent coumarin increases its effectiveness towards its bioactivity. In view of this finding we have synthesized coumarin triazole derivatives. The key synthon used for this reaction pathway are 7-hydroxy-4-methyl-2H-chromen-2-one. This substituted coumarin has been refluxed with 1-bromo-2-chloroethane in presence ofanhydrous K2CO3 to afford 7-(2-chloroethoxy)-4-methyl-2H-chromen-2-one, which has been condensed with triazole to yield4-methyl coumarin triazole derivative by optimising solvent/base pair. 4-Methyl group of coumarin triazole derivative has beencondensed with aromatic aldehydes to afford 7-(2-(1H-1,2,4-triazol-1-yl) ethoxy)-4-(styryl/4-substituted styryl)-2H-chromen-2-one 7a-e. All the synthesized products are characterized using IR and, 1H, 13C NMR, mass spectroscopy and elemental analysis.Final synthesized compounds 7a-e have been evaluated for their anti-bacterial and anti-fungal activity