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Articles 9631 - 9660 of 302419

Full-Text Articles in Physical Sciences and Mathematics

Residential Metals Abatement Program Investigation Summary Report (Non-Residential Parcels – Indoor Dust) - Hillcrest Elementary School, Environmental Resource Management (Erm) Oct 2023

Residential Metals Abatement Program Investigation Summary Report (Non-Residential Parcels – Indoor Dust) - Hillcrest Elementary School, Environmental Resource Management (Erm)

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.


Key Technology And Application Of Digital Twin Modeling For Mri, Shanshan Chen, Hongzhi Wang, Tian Xia Oct 2023

Key Technology And Application Of Digital Twin Modeling For Mri, Shanshan Chen, Hongzhi Wang, Tian Xia

Journal of System Simulation

Abstract: With the accelerating digitalization in education, the construction of digital resources and application platforms has caught increasing attention. The framework of MRI equipment digital twin fivedimensional model is constructed to solve the problems in teaching and training for magnetic resonance imaging (MRI). A modeling and simulation method based on the mechanism model is proposed. The multi-dimensional physical data are obtained to perform digital human modeling, and the virtual acquisition and image reconstruction method is proposed to generate images. The digital twin data are adopted for iterative optimization to implement the whole process of the three-dimensional visual operation including preparation …


A Hybrid Empirical Method For Fast Modeling Of Ship Manoeuvring Motion, Peng Wu, Zongmo Yang, Qianfeng Jing, Yulin Li Oct 2023

A Hybrid Empirical Method For Fast Modeling Of Ship Manoeuvring Motion, Peng Wu, Zongmo Yang, Qianfeng Jing, Yulin Li

Journal of System Simulation

Abstract: Simulation testing is an important means to verify the functions of intelligent ships. Ship maneuvering motion modeling and simulation is the key theoretical basis for the intelligent collision avoidance of multiple vessels in complex sea areas. To address the problem that the calculation of the hydrodynamic coefficients required for ship maneuvering modeling is complex and difficult to obtain, a hybrid empirical method is proposed, a combination method of the existing regression methods is established, the comprehensive performance indicators are constructed, the optimal hydrodynamic coefficients groups are selected by simulated maneuvering experiments, and a rapid modeling program code is developed …


Learning And Analysis Of Dynamic Models For Grid Discrete Events Based On Log Information, Danlong Zhu, Yunqi Yan, Ying Chen, Jiaqi Zhang, Longxing Jin, Wei Fu Oct 2023

Learning And Analysis Of Dynamic Models For Grid Discrete Events Based On Log Information, Danlong Zhu, Yunqi Yan, Ying Chen, Jiaqi Zhang, Longxing Jin, Wei Fu

Journal of System Simulation

Abstract: With the increasing scale of power grid, the massive amount of log information generated bydevices in the power grid poses a challenge to the manual analysis of abnormal grid conditions. The log information generated during the operation of the power grid has the typical discrete sequential characteristics. By analyzing the log information of grid alarm messages, a station event transition probability model and an event sequence risk calculation method are proposed to effectively model and analyze the abnormal operation level of primary and secondary systems in substations. The proposed method not only successfully identifies the event sequences corresponding to …


A Fuzzy Group Decision-Making-Based Method For Green Supplier Selection And Order Allocation, Lu Liu, Wenxin Li, Xiao Song, Bingli Sun, Guanghong Gong Oct 2023

A Fuzzy Group Decision-Making-Based Method For Green Supplier Selection And Order Allocation, Lu Liu, Wenxin Li, Xiao Song, Bingli Sun, Guanghong Gong

Journal of System Simulation

Abstract: With the intensity of market competitiveness, the worsening of the global environment, and the improvement of public concern about environmental protection, the issue of green purchasing has received considerable attention. The vast majority of existing studies on green purchasing have concentrated on supplier selection with green criteria, so as to realize sustainable operations, whereas it is more feasible and economical for businesses to obtain the proper products from adaptable and suitable suppliers at the right times, rates, and volumes, which is referred to as supplier selection and order allocation. To resolve the aforementioned two crucial challenges, we propose a …


Broadband Quantum Enhancement Of The Ligo Detectors With Frequency-Dependent Squeezing, D. Ganapathy, W. Jia, M. Nakano, V. Xu, N. Aritomi, T. Cullen, N. Kijbunchoo, S. E. Dwyer, Francisco Llamas, Volker Quetschke Oct 2023

Broadband Quantum Enhancement Of The Ligo Detectors With Frequency-Dependent Squeezing, D. Ganapathy, W. Jia, M. Nakano, V. Xu, N. Aritomi, T. Cullen, N. Kijbunchoo, S. E. Dwyer, Francisco Llamas, Volker Quetschke

Physics and Astronomy Faculty Publications and Presentations

Quantum noise imposes a fundamental limitation on the sensitivity of interferometric gravitational-wave detectors like LIGO, manifesting as shot noise and quantum radiation pressure noise. Here, we present the first realization of frequency-dependent squeezing in full-scale gravitational-wave detectors, resulting in the reduction of both shot noise and quantum radiation pressure noise, with broadband detector enhancement from tens of hertz to several kilohertz. In the LIGO Hanford detector, squeezing reduced the detector noise amplitude by a factor of 1.6 (4.0 dB) near 1 kHz; in the Livingston detector, the noise reduction was a factor of 1.9 (5.8 dB). These improvements directly impact …


Search-Based Fairness Testing: An Overview, Hussaini Mamman, Shuib Basri, Abdullateef Balogun, Abdullahi Abubakar Imam, Ganesh Kumar, Luiz Fernando Capretz Oct 2023

Search-Based Fairness Testing: An Overview, Hussaini Mamman, Shuib Basri, Abdullateef Balogun, Abdullahi Abubakar Imam, Ganesh Kumar, Luiz Fernando Capretz

Electrical and Computer Engineering Publications

Artificial Intelligence (AI) has demonstrated remarkable capabilities in domains such as recruitment, finance, healthcare, and the judiciary. However, biases in AI systems raise ethical and societal concerns, emphasizing the need for effective fairness testing methods. This paper reviews current research on fairness testing, particularly its application through search-based testing. Our analysis highlights progress and identifies areas of improvement in addressing AI systems’ biases. Future research should focus on leveraging established search-based testing methodologies for fairness testing.


Using Post-Season Tissue Nitrogen Concentrations To Predict Adequacy Of In-Season Nitrogen Management, Kyle Hoegenauer, Trenton Roberts, Carrie Ortel, Jarrod Hardke, Mike Richardson, Mike Daniels Oct 2023

Using Post-Season Tissue Nitrogen Concentrations To Predict Adequacy Of In-Season Nitrogen Management, Kyle Hoegenauer, Trenton Roberts, Carrie Ortel, Jarrod Hardke, Mike Richardson, Mike Daniels

Crop, Soil and Environmental Sciences Faculty Publications and Presentations

High-yielding mechanized rice production requires large amounts of nitrogen (N) fertilizer, which can be particularly costly to producers when applied in excess. The development of a tissue test to detect overapplication of N to rice is needed. Nitrogen response trials arranged in a randomized complete block design were established to identify a critical concentration threshold for a tissue test to detect excess N availability. Rice stalk samples were collected from 0 to 20 cm above the soil within 5 days of harvest and analyzed for NO3 −-N concentration. Two models were fit to the data to represent rice grain …


Integrated Scheduling Simulation Based On Improved Moth Flame Optimizer, Tianrui Zhang, Huiyuan Niu, Wei Xie Oct 2023

Integrated Scheduling Simulation Based On Improved Moth Flame Optimizer, Tianrui Zhang, Huiyuan Niu, Wei Xie

Journal of System Simulation

Abstract: Aiming at the rising cost of manufacturing enterprises, a mathematical programming model of integrated scheduling of production and transportation is established, and a double adaptive weights for moth flame optimizer(DAWMFO) is proposed. A double adaptive weight mechanism is proposed. The spiral function is used to update the population, which improves the convergence speed and accuracy of the algorithm. The benchmark function is tested by the improved algorithm. The results show that the improved algorithm can converge quickly and not easily fall into local optimum. Compared with other algorithms, the optimization ability is also improved. Through the simulation experiment on …


Terrain Surface Texture Generation Networks For User Semantics Customization, Yan Gao, Jimeng Li, Jianzhong Xu, Hongyan Quan Oct 2023

Terrain Surface Texture Generation Networks For User Semantics Customization, Yan Gao, Jimeng Li, Jianzhong Xu, Hongyan Quan

Journal of System Simulation

Abstract: Customizing terrain based on user semantics has practical value in the virtual terrain modeling of military simulation applications. This study provides a terrain surface texture generation network (TSTG-Net) that can synthesize realistic terrain based on user input semantics. TSTG-Net is designed as a Pix2pix structure and is based on CGAN. It learns the topology of customized terrain by encoding and parsing user semantics and regards the semantics feature as the constraint of CGAN. In the generator-discriminator structure, user-customized semantics are used as the input, and the real terrain with semantics is employed as the ground truth in network optimization. …


A Precise Attention Tracking System Based On Computer Vision, Jiyuan Liu, Hanwen Qi, Zhicheng Liu, Minrui Fei, Kun Zhang Oct 2023

A Precise Attention Tracking System Based On Computer Vision, Jiyuan Liu, Hanwen Qi, Zhicheng Liu, Minrui Fei, Kun Zhang

Journal of System Simulation

Abstract: A precise attention tracking system based on machine vision is designed to address the difficulty in studying students' attention allocation. The system includes an image capture device and an accurate attention tracking algorithm. The image capture device can capture the clearer ocular images. The pupil center localization algorithm replaces VGG16 with lightweight MobileNetv3 and uses twostage feature fusion and center keypoint prediction techniques to improve the speed and accuracy. The algorithm achieves a speed of up to 36 frames/s and 97.42% accuracy. The gaze tracking algorithm compensates for the head movements to achieve the meticulous gaze tracking. An interactive …


Simulation And Research Of Manipulator Motion Strategy Based On Adaptive Dynamic Programming, Ming Li, Qun Xu, Yan Wang, Zhicheng Ji Oct 2023

Simulation And Research Of Manipulator Motion Strategy Based On Adaptive Dynamic Programming, Ming Li, Qun Xu, Yan Wang, Zhicheng Ji

Journal of System Simulation

Abstract: Aiming at the difficulty of manipulator to realize high-precision motion tracking in complex and harsh environment, a strategy method based on the combination of adaptive dynamic programming (ADP) and sliding mode admittance control is proposed. The unknown environment is modeled as a linear model and based on quasi, a sliding mode admittance controller is derived to resist disturbance interference. An optimal control method that combines ADP with sliding mode admittance controller is proposed, in which the definition of R-matrix in value function is optimized and improved to further improve the tracking accuracy. The neural network based on ADP is …


Time-Varying Rbf Neural Network-Based Controller Design For A Class Of Time-Varying Nonlinear Systems, Jing Li, Taotao Zhang, Kai Jin, Shengzhi Yuan, Zilong Zha Oct 2023

Time-Varying Rbf Neural Network-Based Controller Design For A Class Of Time-Varying Nonlinear Systems, Jing Li, Taotao Zhang, Kai Jin, Shengzhi Yuan, Zilong Zha

Journal of System Simulation

Abstract: A time-varying RBF neural network with time-varying properties is firstly proposed, and its approximation theorem is obtained. For a class of nonlinear systems with non-parametric time-varying uncertainties, the proposed time-varying RBF neural network is used to approximate the time-varying uncertainties, and the controller is designed by making use of Lyapunov stability theory and adaptive iterative learning control techniques. We obtain the stability theorem of the designed controller. The simulation results verify the effectiveness of the time-varying neural network and the correctness of the controller design scheme.


Air Distribution Simulation And Comfort Evaluation Of Large Space Building Based On Rans And Les, Shen Zhang, Ming Cheng, Yifan Wang, Fankai Meng, Ting Li, Han Chen, Zhifeng Ji Oct 2023

Air Distribution Simulation And Comfort Evaluation Of Large Space Building Based On Rans And Les, Shen Zhang, Ming Cheng, Yifan Wang, Fankai Meng, Ting Li, Han Chen, Zhifeng Ji

Journal of System Simulation

Abstract: Air distribution simulation and thermal comfort evaluation for heating, ventilation and air conditioning (HVAC) design of large space buildings is of great significance for the human thermal comfort improvement and the energy consumption reduction. By combining the steady analysis based on RANS and the transient analysis of large eddy simulation (LES), an air distribution simulation and thermal comfort evaluation process in large space buildings is established. Due to the low calculation consumption, the steady analysis based on RANS is conducted to efficiently evaluate the thermal comfort and the air quality under multiple working conditions. Considering the high computational consumption …


Design And Simulation Of A Location Privacy Protection Scheme Based On Zero-Knowledge Proof For Military Iot, Mingjie Shi, Chengyu Xie, Chuanfu Zhang Oct 2023

Design And Simulation Of A Location Privacy Protection Scheme Based On Zero-Knowledge Proof For Military Iot, Mingjie Shi, Chengyu Xie, Chuanfu Zhang

Journal of System Simulation

Abstract: In the military Internet of Things (IoT) combat environment, the location privacy issue becomes a key challenge. An innovative location privacy protection scheme based on zero-knowledge proof is proposed to ensure that in unreliable communication channels, the location information of combat units can be verified without revealing their specific coordinates, so as to achieve the goal of protecting sensitive location information. Based on the idea of cryptography, by using zero-knowledge proof, through algebraic circuit, rank-1 constraint system(R1CS), quadratic arithmetic programs(QAP), and other steps, the position coordinate information proof problem is transformed into a point verification problem on a polynomial …


A Developed Framework For Studying Cyberethical Behaviour In North Central Nigeria, Aderinola Ololade Dunmade, Adeyinka Tella, Uloma Doris Onuoha Oct 2023

A Developed Framework For Studying Cyberethical Behaviour In North Central Nigeria, Aderinola Ololade Dunmade, Adeyinka Tella, Uloma Doris Onuoha

Journal of Cybersecurity Education, Research and Practice

ICT advancements have enabled more online activities, resulting in several cyberethical behaviours. Literature documents prevalence of plagiarism, and online fraud, among other misbehaviours. While behaviour has been explained by several theories, as scholarship and research advances, frameworks are modified to include more constructs. The researchers modified Fishbein and Ajzen (2011)'s Reasoned Action Approach to study female postgraduate students' perspectives toward cyberethical behaviour in North Central Nigerian universities.

The study focused on four variables, which were adequately captured by the model: perception, awareness, and attitude.

An adapted questionnaire collected quantitative data. This study used multistage sampling. A sample size of 989 …


Pleistocene Bats (Late Irvingtonian And Late Rancholabrean) From Nuckolls And Sherman Counties, Nebraska, Nicholas J. Czaplewski, Richard George Corner Oct 2023

Pleistocene Bats (Late Irvingtonian And Late Rancholabrean) From Nuckolls And Sherman Counties, Nebraska, Nicholas J. Czaplewski, Richard George Corner

Transactions of the Nebraska Academy of Sciences and Affiliated Societies

We document rare finds of fossil bats from two localities representing the Pleistocene epoch in southern and central Nebraska, Albert Ahrens locality (No-104, late Irvingtonian age, Middle Pleistocene), Nuckolls County, and Litchfield (Sm-102, late Rancholabrean age, latest Pleistocene), Sherman County. The Albert Ahrens local fauna with strong boreal influence has produced two bats, Lasiurus cf. borealis and Cf. Myotis sp. The Litchfield local fauna, also showing a strong boreal influence, has yielded two bats, Eptesicus fuscus and Cf. Myotis, among a diverse Pleistocene fauna of small vertebrates and a pollen record indicating a boreal mixed conifer and deciduous woodland, …


Executive Order On The Safe, Secure, And Trustworthy Development And Use Of Artificial Intelligence, Joseph R. Biden Oct 2023

Executive Order On The Safe, Secure, And Trustworthy Development And Use Of Artificial Intelligence, Joseph R. Biden

Copyright, Fair Use, Scholarly Communication, etc.

Section 1. Purpose. Artificial intelligence (AI) holds extraordinary potential for both promise and peril. Responsible AI use has the potential to help solve urgent challenges while making our world more prosperous, productive, innovative, and secure. At the same time, irresponsible use could exacerbate societal harms such as fraud, discrimination, bias, and disinformation; displace and disempower workers; stifle competition; and pose risks to national security. Harnessing AI for good and realizing its myriad benefits requires mitigating its substantial risks. This endeavor demands a society-wide effort that includes government, the private sector, academia, and civil society.

My Administration places the highest urgency …


Short History Of The Unl Digital Commons, Paul Royster Oct 2023

Short History Of The Unl Digital Commons, Paul Royster

University of Nebraska-Lincoln Libraries: Conference Presentations and Speeches

From 2005 through 2023, the UNL Digital Commons grew to be a leading example of an institutional repository. This presentation reports on personnel, history, strategy, and outstanding examples of series or contributors.

Announcement about the session:

UNL Digital Commons began in 2005 and grew into America’s 3rd-largest and most-trafficked institutional repository. Approaching 100 million downloads and spreading UNL scholarship and branding across the globe, the UNL Digital Commons boasts works from a wide variety of affiliated faculty, researchers, and students. Their participation is opening the dissemination of scholarship in radical and fundamental ways. In this session, Paul Royster traces this …


Run From The Chatbots Or Embrace Them? There Is A Middle Way, Kenneth Worthy Oct 2023

Run From The Chatbots Or Embrace Them? There Is A Middle Way, Kenneth Worthy

School of Science Faculty Works

No abstract provided.


Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli Oct 2023

Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli

CODEE Journal

The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.


Roadway Floods And Their Associated Weather-Related Conditions: New Insights Using Cars 511 Data For State And Federal Highways In Nebraska, Usa, Logan R. Bundy, Mark Anderson, Clinton M. Rowe, Rezaul Mamood Oct 2023

Roadway Floods And Their Associated Weather-Related Conditions: New Insights Using Cars 511 Data For State And Federal Highways In Nebraska, Usa, Logan R. Bundy, Mark Anderson, Clinton M. Rowe, Rezaul Mamood

Department of Earth and Atmospheric Sciences: Faculty Publications

This study examined roadway flooding event data provided by the Nebraska Department of Transportation via the Condition Acquisition Reporting System (CARS) 511 archive (2016–2021). With these data, a novel analysis was completed to further the understanding of where, when, and why (meteorologically) roadway flooding occurs on Nebraska state and federal highways. In the study period, 298 roadway floods occurred, with an annual median of 16 per year. There was a greater risk for roadway floods to transpire more frequently in eastern Nebraska, which was attributed to the spatial climatology of heavy rainfall and the higher density of roadways and rivers. …


12th International Conference On Business, Technology And Innovation 2023, University For Business And Technology - Ubt Oct 2023

12th International Conference On Business, Technology And Innovation 2023, University For Business And Technology - Ubt

UBT International Conference

Welcome to IC – UBT 2023

UBT Annual International Conference is the 12th international interdisciplinary peer reviewed conference which publishes works of the scientists as well as practitioners in the area where UBT is active in Education, Research and Development. The UBT aims to implement an integrated strategy to establish itself as an internationally competitive, research-intensive university, committed to the transfer of knowledge and the provision of a world-class education to the most talented students from all background. The main perspective of the conference is to connect the scientists and practitioners from different disciplines in the same place and make …


International Conference On Mechatronic, University For Business And Technology - Ubt Oct 2023

International Conference On Mechatronic, University For Business And Technology - Ubt

UBT International Conference

UBT Annual International Conference is the 12th international interdisciplinary peer reviewed conference which publishes works of the scientists as well as practitioners in the area where UBT is active in Education, Research and Development. The UBT aims to implement an integrated strategy to establish itself as an internationally competitive, research-intensive university, committed to the transfer of knowledge and the provision of a world-class education to the most talented students from all background. The main perspective of the conference is to connect the scientists and practitioners from different disciplines in the same place and make them be aware of the recent …


Preparation And Electrocatalytic Performance Of Feni-Cop/Nc Bifunctional Catalyst, Si-Miao Liu, Jing-Jiao Zhou, Shi-Jun Ji, Zhong-Sheng Wen Oct 2023

Preparation And Electrocatalytic Performance Of Feni-Cop/Nc Bifunctional Catalyst, Si-Miao Liu, Jing-Jiao Zhou, Shi-Jun Ji, Zhong-Sheng Wen

Journal of Electrochemistry

Rechargeable zinc-air batteries have gradually attracted much attention worldwide due to their high capacity, high energy density and low price. Oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) correspond to the charging and discharging processes in rechargeable zinc-air battery, respectively. At present, commercial Pt/C and IrO2 catalysts hinder the large-scale application of zinc-air batteries due to low reserves, high prices and poor stability. Therefore, exploring high performance, low cost and high stability with dual functional catalysts is important for the development of rechargeable zinc-Air batteries. The metal-organic frameworks (MOFs) have high specific surface area, structural stability, good catalytic …


Charge-Dependence Of Dissolution/Deposition Energy Barrier On Cu(111) Electrode Surface By Multiscale Simulations, Hang Qiao, Yong Zhu, Sheng Sun, Tong-Yi Zhang Oct 2023

Charge-Dependence Of Dissolution/Deposition Energy Barrier On Cu(111) Electrode Surface By Multiscale Simulations, Hang Qiao, Yong Zhu, Sheng Sun, Tong-Yi Zhang

Journal of Electrochemistry

Behaviors of electrified interface under different applied potentials/charges play the central role in electroplating process and electrochemical corrosion. The mechanism, however, is unclear yet for a surface atom dissolving/depositing from/on an electrode surface under an applied potential. The energy barrier along the reaction path is the key variable. The present work conductes hybrid first-principle/hybrid calculations to study the direct and indirect dissolution/deposition of a Cu atom on perfect/stepped Cu(111) planar electrodes in an electrolyte under different excess charges. Energy profiles present a linear relationship between the energies of the initial/final state and the activation state of different reaction paths under …


Ship Registry And Flag State Obligations For The Plurinational State Of Bolivia: A Case Study For A Landlocked State, Marco Antonio Lucano Uzquiano Oct 2023

Ship Registry And Flag State Obligations For The Plurinational State Of Bolivia: A Case Study For A Landlocked State, Marco Antonio Lucano Uzquiano

World Maritime University Dissertations

No abstract provided.


Research Progress And Performance Improvement Strategies Of Hard Carbon Anode Materials For Sodium-Ion Batteries, Xiu-Ping Yin, Yu-Feng Zhao, Jiu-Jun Zhang Oct 2023

Research Progress And Performance Improvement Strategies Of Hard Carbon Anode Materials For Sodium-Ion Batteries, Xiu-Ping Yin, Yu-Feng Zhao, Jiu-Jun Zhang

Journal of Electrochemistry

This paper systematically summarizes the research progress of hard carbon anode materials in sodium ion batteries(SIBs) and the development of the corresponding sodium storage mechanism in recent years, and reviews the performance improvement strategies of hard carbon materials from the aspects of structural design and electrolyte regulation. The effects of the selection of precursors, carbonization temperature, pretreatment, pore formers, heteroatom doping, material compounding, electrolyte regulation and pre-sodiumization on the sodium storage performance of hard carbon anode materials are briefly described. This paper provides new insights into the design, synthesis and electrolyte
matching of high-performance and low-cost hard carbon materials, and …


Surface Modifications Of Lini0.96Co0.02Mn0.02O2 With Tungsten Oxide And Phosphotungstic Acid, Gang Zhao, Zheng-Liang Gong, Yi-Xiao Li, Yong Yang Oct 2023

Surface Modifications Of Lini0.96Co0.02Mn0.02O2 With Tungsten Oxide And Phosphotungstic Acid, Gang Zhao, Zheng-Liang Gong, Yi-Xiao Li, Yong Yang

Journal of Electrochemistry

With the rapid development of electric vehicles, enormous demands are made for higher energy density, better cycling performance and lower cost of lithium-ion batteries (LIBs). As an important high capacity cathode material for LIBs, the high nickel layered oxide material LiNi0.8Co0.1Mn0.1O2(NCM811) can reach an energy density of 760 Wh·kg-1. The ultra-high nickel ternary positive electrode material (LiNi1-x-yCoxMnyO2, x ≥ 0.90) has a specific capacity of more than 210 mAh·g-1, and can realize higher energy density. Besides, an ultra-high nickel material …


Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine Oct 2023

Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine

Rose-Hulman Undergraduate Mathematics Journal

We find a formula for the probability that the product of n positive integers, chosen at random, is divisible by some integer d. We do this via an inductive application of the Chinese Remainder Theorem, generating functions, and several other combinatorial arguments. Additionally, we apply this formula to find a unique, but slow, probabilistic primality test.