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Articles 211 - 240 of 291657

Full-Text Articles in Physical Sciences and Mathematics

Gc-Ms Profiling And Antibacterial Activity Of Cold-Macerated Garlic Extracts Against Multidrug-Resistant Uropathogens, Fatima A. Khalaf, Saeed A. Fayadh Sep 2026

Gc-Ms Profiling And Antibacterial Activity Of Cold-Macerated Garlic Extracts Against Multidrug-Resistant Uropathogens, Fatima A. Khalaf, Saeed A. Fayadh

Karbala International Journal of Modern Science

The growing number of cases of multidrug-resistant (MDR) urinary tract infections has made the clinical management of urinary tract diseases a significant challenge; therefore, the need for effective adjunctive therapies cannot be overemphasized. This study evaluated the bioactive components and antibacterial efficacy of cold-macerated garlic extracts obtained using distilled water, 70% ethanol and hexane solvents against antimicrobial-resistant urinary isolates. Out of 250 urine samples that were analyzed, 124 (49.6%) showed significant microbial growth, with Escherichia coli being the most frequently isolated organism. The results of the phytochemical screening and Gas Chromatography-Mass Spectrometry (GC-MS) analysis showed that the ethanolic extract had …


Monitoring System In The Georeactor Area During The Underground Coal Gasification Process, Aleksandra Tokarz, Jacek Grabowski, Krzysztof Korczak Sep 2026

Monitoring System In The Georeactor Area During The Underground Coal Gasification Process, Aleksandra Tokarz, Jacek Grabowski, Krzysztof Korczak

Journal of Sustainable Mining

Safety control of the underground coal gasification (UCG) process involves ensuring that the process runs smoothly, monitoring changes occurring on the surface and in the rock mass, and counteracting the negative environmental impact of the process. The article presents the application of a monitoring system implemented in Poland, both in pilot tests conducted in shallow coal seams at the Barbara Experimental Mine and in deep coal seams at the Wieczorek mine, where a full-scale gasification process was tested. The analysis of the monitoring results carried out during the gasification experiment in an operating mine allowed for the identification of key …


Fast Computation And Model Order Reduction Of The Friction Stir Welding Process With Pod-Deim, Joshua Kay, Zilong Song Sep 2026

Fast Computation And Model Order Reduction Of The Friction Stir Welding Process With Pod-Deim, Joshua Kay, Zilong Song

Mathematics and Statistics Student Research and Class Projects

Friction stir welding (FSW) is a solid-state manufacturing process widely used in joining aluminum and other metal workpieces. The FSW process can be modeled by a coupled system of non-Newtonian Navier–Stokes and heat-transfer equations. However, solving this non-linear system with high accuracy requires significant computational power. This work refines the system by introducing corrected coefficients and new treatments for boundary conditions near the tool. Then, model order reduction, including the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), is applied to efficiently solve the FSW system in a low-dimensional space. To enhance accuracy and effectiveness, two novel treatments …


Fastest-Warming States And Cities In The Mountain West, 2025, Maisoon Faris, Kahlen Coss, Kevin Yang, Caitlin J. Saladino, William E. Brown Jr. Sep 2026

Fastest-Warming States And Cities In The Mountain West, 2025, Maisoon Faris, Kahlen Coss, Kevin Yang, Caitlin J. Saladino, William E. Brown Jr.

Environment

This fact sheet presents data published by Climate Central on the change in average annual temperatures for the five Mountain West states of Arizona, Colorado, Nevada, New Mexico, and Utah and 15 Mountain West cities from 1970 to 2025. City-level data are derived from Applied Climate Information System (ACIS) operated by National Oceanic and Atmospheric Administration (NOAA), state-level data are derived from NOAA’s National Centers for Environmental Information (NCEI).


Studying Electromagnetic Wave Scattering From Small Dielectric Particles Using Neural Networks, Bryan Taylan, Patrick Corzo, Chris Velissaris, Theodoros Panagiotakopoulos Sep 2026

Studying Electromagnetic Wave Scattering From Small Dielectric Particles Using Neural Networks, Bryan Taylan, Patrick Corzo, Chris Velissaris, Theodoros Panagiotakopoulos

Undergraduate Scholarship and Creative Works

Physics-informed neural networks solve the Helmholtz equation without labeled data, but a low residual alone does not confirm that a solution preserves the physical distinction a downstream task depends on. We trained a four-layer SIREN with physics-based residuals, a Sommerfeld condition, Adam, and L-BFGS, modeling a Gaussian source and a plane wave scattering from a small dielectric inclusion. Fine-tuning from four base models produced 600 complex fields spanning omega = 4 to 20. A compact CNN, three ResNet-18 variants, and a frozen OpenCLIP encoder classified these fields under five random seeds. The CNN achieved (95.65 +/- 0.77)% accuracy, outperforming OpenCLIP …


Fast Discovery Of Motivic Patterns In Symbolic Music Via Lossy Compression, Adam James Wilson Sep 2026

Fast Discovery Of Motivic Patterns In Symbolic Music Via Lossy Compression, Adam James Wilson

Publications and Research

Generative systems that react to live musicians require rapid analysis of musical data, which rules out deep learning models: they cannot be trained within the time constraints of live performance. But because analysis results are often transformed before use, we are free to reduce the parameters that undergo transformation to a small set of primitive states. We address this coincidence of constraint and opportunity with an algorithm for online discovery of maximal musical motives that achieves speed through lossy compression: the pitch and inter-onset-interval deltas for all pairs of events in a potential motive are reduced to two-bit values, conceptualized …


2026 September 3 - Tennessee Weekly Drought Summary, Tennessee Climate Office, East Tennessee State University Sep 2026

2026 September 3 - Tennessee Weekly Drought Summary, Tennessee Climate Office, East Tennessee State University

Tennessee Climate Office Weekly Drought Summaries

No abstract provided.


Microwave Thermal Pre-Treatment To Improve Nickel Extraction From Lateritic Ore, Johana Borda, Daniel Sosa, Robinson Torres Sep 2026

Microwave Thermal Pre-Treatment To Improve Nickel Extraction From Lateritic Ore, Johana Borda, Daniel Sosa, Robinson Torres

Journal of Sustainable Mining

Two heat treatment processes for a nickeliferous laterite sample are presented, one by the conventional muffle route and the other by microwave. The heating was carried out in order to improve the dissolution of nickel in an acid medium. The study describes the changes observed in the mineral for the increase in temperature as a consequence of radiation in the microwave and in the muffle. The changes in the mineral crystalline phases were analyzed by X-ray diffraction. The leaching media consisted of a 1 M sulfuric acid solution at ambient conditions for 7 h. The interaction between the reagent and …


On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci Sep 2026

On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci

Journal of Stochastic Analysis

We study a time-inhomogeneous nonlinear SDE with drift and diffusion governed by state-dependent variable exponents. This framework generalizes models like the geometric Brownian motion (GBM) and the constant elasticity of variance (CEV), offering flexibility to capture complex dynamics while posing analytical challenges. Using a fixed-point approach, we prove existence and uniqueness, analyze higher-order moments, derive asymptotic estimates, and assess stability. Finally, we illustrate an application where Poisson’s equation admits a probabilistic representation via a timehomogeneous nonlinear SDE with state-dependent variable exponents.


Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver Sep 2026

Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver

Journal of Stochastic Analysis

Starting with a stochastic matrix, we study the behavior of powers of an associated companion matrix, which has the same characteristic polynomial as the original matrix. In general the companion matrix will have negative entries while maintaining rowsums equal to 1. We will find the growth rate even if the Ces`aro limit of the sums of the companion matrix diverge. Surprisingly, in the irreducible aperiodic case the powers of the companion matrix will converge even though the norm of the matrix exceeds 1 and it has possibly negative entries.


Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar Sep 2026

Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar

Journal of Stochastic Analysis

The goal of this article is to study in depth the subclass of Z+- valued additive processes in law with nonnegative increments. We establish key distributional properties of these processes and obtain some existence results under a variety of conditions. We show that they form a subclass of the family of inhomogeneous Markov chains with spatial homogeneity. We extend the notion of factoring introduced by Sato (2004, [9]) for Rd-valued additive processes in law to their Z+-valued counterparts with nonnegative increments. We give a sufficient condition for the existence of a factoring for these processes. Lastly, we obtain their representation …


Chemistry In The City Module, Ji Kim Sep 2026

Chemistry In The City Module, Ji Kim

Open Educational Resources

This project integrates a historical environmental health report from the CUNY Digital History Archive into an online Introductory Chemistry course to connect core chemical concepts with real urban pollution issues. Students analyze perchloroethylene contamination in apartments above dry cleaners, apply concepts such as volatility, vapor pressure, and concentration units, and reflect on chemical principles underlying indoor air pollution.


Chemistry In The City Module, Ji Kim Sep 2026

Chemistry In The City Module, Ji Kim

Open Educational Resources

This project integrates a historical environmental health report from the CUNY Digital History Archive into an online Introductory Chemistry course to connect core chemical concepts with real urban pollution issues. Students analyze perchloroethylene contamination in apartments above dry cleaners, apply concepts such as volatility, vapor pressure, and concentration units, and reflect on chemical principles underlying indoor air pollution.


"Our Heritage From The People", William Lindsey Mcdonald Sep 2026

"Our Heritage From The People", William Lindsey Mcdonald

Writings

A lecture presented to a history seminar at the University of North Alabama in March of 1979. The lecture addresses the geography and geology of North Alabama, removal of indigenous people, cultural influence of settlers, and development of the Tennessee Valley into contemporary settlements.


Motivating Second-Order Differential Equation Models Beyond The Spring–Mass System, Katherine E. Rutherford, John C. Borger Sep 2026

Motivating Second-Order Differential Equation Models Beyond The Spring–Mass System, Katherine E. Rutherford, John C. Borger

CODEE Journal

Students in introductory differential equations courses often learn to associate specific equation types with familiar physical systems. While this approach supports procedural fluency, it can inhibit transfer learning: students recognize familiar forms rather than construct models from first principles. This paper presents a modeling-first instructional approach designed to help students recognize the shared structure of second-order differential equations across diverse contexts. Students derive governing equations from fundamental physical laws for multiple systems, including an Inductor, Resistor, and Capacitor (LRC) electrical circuit, a simple pendulum, and viscous pipe flow. Through guided comparison, students identify common components such as inertia, damping, restoring …


The Colorado River Water Supply Crisis In A Few Graphs: Part 2 Agricultural Water Use In The Lower Basin, Jack Schmidt, Anne Castle, Eric Kuhn, Kathryn Sorensen, Katherine Tara Sep 2026

The Colorado River Water Supply Crisis In A Few Graphs: Part 2 Agricultural Water Use In The Lower Basin, Jack Schmidt, Anne Castle, Eric Kuhn, Kathryn Sorensen, Katherine Tara

The Traveling Wilburys of the Colorado River

Reductions in Lower Basin water use during the last four years, including

forecast use in 2026, are similar to the initial targets for Lower Basin shortages

described in the Final Environmental Impact Statement for Post-2026

Operational Guidelines and Strategies for Lake Powell and Lake Mead (FEIS)

and the accompanying Record of Decision (ROD).

6 Lower Basin consumptive

use in 2023, 2024, and 2025, and forecast for 2026 has been the smallest for

the entire 2010-2026 period. These four years of smallest use are between 1.4

and 1.7 million acre feet/year (maf/yr) less than the 7.50 maf/yr amount

generally recognized as …


Geographical Pattern Analysis Of Gis Images With Deep Learning And Voronoi Network, Nidaa Kareem, Tawfiq A. Al-Assadi Sep 2026

Geographical Pattern Analysis Of Gis Images With Deep Learning And Voronoi Network, Nidaa Kareem, Tawfiq A. Al-Assadi

Journal of Intelligent Informatics, Networking, and Cybersecurity

Localization is not enough for the analysis of spatial patterns; a principled geometric and statistical framework is required. This paper proposes an integrated spatial intelligence system combining deep learning, computational geometry, and spatial statistics, which is a unified and interpretable system. It is based on segmentation localization that accurately localizes the centroid of each object without the disadvantages of the bounding box. These centroids form a natural Voronoi tessellation of regions of spatial influence intrinsic to the data instead of imposing any artificial restrictions. A geometry-based density formulation is used to improve representation, which includes Voronoi cell areas and neighborhood …


Individualized Bayesian Inference Identifies Novel Genetic Variants For Parkinson's Disease, Jin Ren, Yasaman J. Soofi, Md Asad Rahman, Qing Lu, Jinling Liu Sep 2026

Individualized Bayesian Inference Identifies Novel Genetic Variants For Parkinson's Disease, Jin Ren, Yasaman J. Soofi, Md Asad Rahman, Qing Lu, Jinling Liu

Engineering Management and Systems Engineering Faculty Research & Creative Works

Parkinson's disease (PD) is a complex neurodegenerative disorder with a significant genetic component. While genome-wide association studies (GWAS) have been instrumental in identifying genetic variants associated with PD, the reliance on large sample sizes and population-level analyses may overlook variants with lower minor allele frequencies or individual-specific relevance. Individualized Bayesian Inference (IBI) offers a promising method to complement GWAS by identifying and prioritizing candidate genetic markers at both the individual and patients-like-me subgroup levels. This study evaluates the application of IBI to PD genetics, using GWAS as a baseline for comparison. We analyzed genetic data from the Fox Insight online …


Waste Streams From Next Generation Molten Salt Reactors: The Challenge Of Creating An Insoluble Ceramic For Chloride Salt Waste, Alevtina A. Maksimova, Jake W. Amoroso, Matthew Page, Gregory Morrison, Hans Conrad Zur Loye Sep 2026

Waste Streams From Next Generation Molten Salt Reactors: The Challenge Of Creating An Insoluble Ceramic For Chloride Salt Waste, Alevtina A. Maksimova, Jake W. Amoroso, Matthew Page, Gregory Morrison, Hans Conrad Zur Loye

Faculty Publications

Molten salt reactors (MSRs) design development is of interest to many research groups and companies. Waste management for MSRs is one of the most important issues that needs to be resolved due to its impact on environmental safety, primarily via the dissolution of radionuclides in water. Furthermore, the waste treatment strategy will have a significant influence on the operating cost of MSRs, which is why a reliable process for the immobilization, transportation, storage and disposal of MSR waste must be addressed. This work presents a new approach for the immobilization of chloride salts from molten salt reactors in stable oxyhalide …


The Application Of Machine Learning And Deep Learning On Demand Forecasting Across Time-Critical Industries: A Systematic Review, Asmaa Seyam, Sujith Samuel Mathew, May El Barachi, Cheng Zhang, Jun Shen Sep 2026

The Application Of Machine Learning And Deep Learning On Demand Forecasting Across Time-Critical Industries: A Systematic Review, Asmaa Seyam, Sujith Samuel Mathew, May El Barachi, Cheng Zhang, Jun Shen

All Works

The applications of machine learning and deep learning in demand forecasting have attracted increasing attention, as they offer remarkable predictive capabilities that help automate forecasting processes and achieve higher accuracy. While numerous review studies have examined solutions within specific industries, there is a lack of comprehensive literature review investigating these solutions across different sectors. Therefore, this study overviews machine learning and deep learning applications in demand forecasting across time-critical industries, including power, tourism, water, transportation, and food. A two-tier classification framework is proposed to categorize demand forecasting studies by both application industry and methodological architecture. In addition, the most popular …


Potential Energy Landscape Formalism For Quantum Liquids, Yang Zhou Sep 2026

Potential Energy Landscape Formalism For Quantum Liquids, Yang Zhou

Dissertations, Theses, and Capstone Projects

Atomic delocalization due to nuclear quantum effects (NQE) remains poorly understood in low-temperature liquids near the glass state and during vitrification. Many liquids can be described accurately by treating their nuclei as classical particles, but this approximation fails for light elements such as He and H₂, small hydrogen-containing molecules such as water, and systems in which zero-point motion or isotope-substitution effects are important. Developing a general thermodynamic and statistical-mechanical description of such liquids has been challenging. This dissertation extends the potential energy landscape (PEL) formalism, originally developed for classical liquids and glasses, to liquids that obey quantum mechanics and exhibit …


Neural Symphony Of Flow Experience: Evidence For High-Dimensional Metastable Dynamics, Abdelrahman B. M. Eldaly, Kris Zhangguang Kang, Fiona Fui-Hoon Nah, Leanne Lai-Hang Chan, Keng Siau, Xiao Fan Liu, Richard Huskey, Langtao Chen, Tejaswini Yelamanchili, Rene Weber Sep 2026

Neural Symphony Of Flow Experience: Evidence For High-Dimensional Metastable Dynamics, Abdelrahman B. M. Eldaly, Kris Zhangguang Kang, Fiona Fui-Hoon Nah, Leanne Lai-Hang Chan, Keng Siau, Xiao Fan Liu, Richard Huskey, Langtao Chen, Tejaswini Yelamanchili, Rene Weber

Research Collection School Of Computing and Information Systems

Flow, an optimal experience characterized by deep immersion and engagement in an activity, has been extensively studied in behavioral research. However, its neural dynamic mechanism remains poorly understood. In a within-subject video gaming experiment, we captured neural activity underlying flow, boredom, and anxiety using a 64-channel electroencephalogram (EEG) system. Compared to boredom and anxiety, flow exhibits the highest global functional connectivity, metastability, and dimensionality of dynamic functional connectivity patterns, suggesting that flow is a highly adaptable process that is supported by high-dimensional neural dynamics. Unlike previous studies that focused on identifying static or localized brain activity, we examine the neural …


Prune: A Patching Based Repair Framework For Certifiable And Privacy-Robust Unlearning Of Neural Networks, Xuran Li, Jingyi Wang, Xiaohan Yuan, Peixin Zhang Sep 2026

Prune: A Patching Based Repair Framework For Certifiable And Privacy-Robust Unlearning Of Neural Networks, Xuran Li, Jingyi Wang, Xiaohan Yuan, Peixin Zhang

Research Collection School Of Computing and Information Systems

Machine unlearning has emerged as a key mechanism for enabling the “right to be forgotten” in neural network models, allowing the selective removal of specific training data upon request. Existing approaches typically rely on retraining models with the remaining data, which is computationally expensive and difficult to verify, especially when deployed models are distributed or resource-constrained. To address this challenge, our prior conference work introduced PRUNE, a patching-based framework that formulates unlearning as a neural network repair problem. PRUNE achieves targeted forgetting by learning lightweight patch networks that redirect model predictions on the data to be unlearned while preserving performance …


Building Wellbeing Through Nature And Adventure For Justice-Involved Youth, Lewis Kogan, Meagan Ricks, Janna Coulter, Miranda Margetts, Lori Butterfield, Ben Ukoh-Eke Sep 2026

Building Wellbeing Through Nature And Adventure For Justice-Involved Youth, Lewis Kogan, Meagan Ricks, Janna Coulter, Miranda Margetts, Lori Butterfield, Ben Ukoh-Eke

Outcomes and Impact Quarterly

Justice-involved youth often experience elevated levels of stress, mental health challenges, and reduced access to positive developmental opportunities. A nature- and adventure-based youth development program designed to strengthen resilience, self-efficacy, nature-connectedness, and well-being among justice-involved youth was piloted in 2025 to address these challenges. Pilot findings indicated improvements in resilience, self-efficacy, hopefulness, and connectedness to nature.


Enhancing Programming Productivity For Individuals With Adhd Through Generative Artificial Intelligence: An Inductive Analysis, Lionel Mew Sep 2026

Enhancing Programming Productivity For Individuals With Adhd Through Generative Artificial Intelligence: An Inductive Analysis, Lionel Mew

School of Professional and Continuing Studies Faculty Publications

Attention-deficit/hyperactivity disorder (ADHD) significantly impacts computer programmers through challenges in sustained attention, executive functioning, and organizational skills. While traditional intervention strategies have shown varying degrees of success, the emergence of generative artificial intelligence (AI) presents novel opportunities to address ADHD-related programming challenges. This paper presents an inductive analysis synthesizing current research on ADHD's effects on programming, traditional productivity enhancement techniques, and the potential of generative AI tools. Through examination of recent literature and field studies, we propose that generative AI can serve as a transformative intervention by providing personalized cognitive support, reducing executive function demands, and enhancing code generation efficiency. …


Readme Template For Geospatial Data, Alyssa Renteria Sep 2026

Readme Template For Geospatial Data, Alyssa Renteria

Library Faculty Research

A readme file provides descriptive information about a dataset, file(s), or software. The goal is to ensure that the files and data can be correctly interpreted by your future self or others when sharing or publishing data, code, or software.


Trustworthy And Explainable Malware Threat Intelligence Through Social Media Analytics And Nature-Inspired Optimization, Feras Al-Obeidat, Muhammad Saad Rashad, Muhammad Amin, Waqas Ali, Bilal Khan, Sajid Anwar Sep 2026

Trustworthy And Explainable Malware Threat Intelligence Through Social Media Analytics And Nature-Inspired Optimization, Feras Al-Obeidat, Muhammad Saad Rashad, Muhammad Amin, Waqas Ali, Bilal Khan, Sajid Anwar

All Works

The convergence of media analytics, Cyber threat Intelligence (CTI) and trustworthy artificial intelligence has become essential for modern cybersecurity systems operating over large-scale, heterogenous data sources. In particular, Social Media Intelligence (SOCMINT) and Open Source Intelligence (OSINT) provide high-volume, real-time signals that complement structured CTI frameworks for early-stage malware and adversarial threat detection. However, integrating these unstructured and dynamic sources with Structured Threat Information Expression (STIX) remains challenging due to its hierarchical complexity, semantic redundancy, and computational overhead in resource-constrained environments. This paper proposes an explainable and optimized intelligence pipeline (BERT-STIX) that unifies SOCMINT, OSINT, and STIX-based CTI using deep …


Restoring Linguistic Grounding In Vla Models Via Train-Free Attention Recalibration, Ninghao Zhang, Bin Zhu, Shijie Zhou, Jingjing Chen Sep 2026

Restoring Linguistic Grounding In Vla Models Via Train-Free Attention Recalibration, Ninghao Zhang, Bin Zhu, Shijie Zhou, Jingjing Chen

Research Collection School Of Computing and Information Systems

Vision-Language-Action (VLA) models enable robots to perform manipulation tasks directly from natural language instructions and are increasingly viewed as a foundation for generalist robotic policies. However, their reliability under Out-Of-Distribution (OOD) instructions remains underexplored. In this paper, we reveal a critical failure mode in which VLA policies continue executing visually plausible actions even when the language instruction contradicts the scene. We refer to this phenomenon as linguistic blindness, where VLA policies prioritize visual priors over instruction semantics during action generation. To systematically analyze this issue, we introduce ICBench, a diagnostic benchmark constructed from the LIBERO dataset that probes language–action coupling …


On Families Of Finsler Metrics, İsmai̇l Sağlam, Ken'ichi Ohshika, Athanase Papadopoulos Sep 2026

On Families Of Finsler Metrics, İsmai̇l Sağlam, Ken'ichi Ohshika, Athanase Papadopoulos

Turkish Journal of Mathematics

In this paper, we answer some natural questions concerning symmetrisation and more general combinations of Finsler metrics, with a view to applications to Funk and Hilbert geometries and metrics on Teichmüller spaces. The metrics on Teichmüller space that we consider are the Thurston metric and the earthquake metric, both introduced by Thurston. The first metric has been thoroughly studied over the last couple of decades, and the second over the last few years. The Funk metric and its symmetrisation, the Hilbert metric, are classical metrics that have been investigated in the contexts of hyperbolic geometry and geometric function theory and, …


On The Monoid Of Partial Order-Preserving Transformations Of A Finite Chain Whose Domains And Ranges Are Intervals, Hayrullah Ayik, Vítor H. Fernandes, Emrah H. Korkmaz Sep 2026

On The Monoid Of Partial Order-Preserving Transformations Of A Finite Chain Whose Domains And Ranges Are Intervals, Hayrullah Ayik, Vítor H. Fernandes, Emrah H. Korkmaz

Turkish Journal of Mathematics

In this paper, we consider the monoid PIOn of all partial order-preserving transformations on a chain with n elements whose domains and ranges are intervals, along with its submonoid PIOn of order-decreasing transformations. Our main aim is to give presentations for PIOn and PIOn. Moreover, for both monoids, we describe regular elements and determine their ranks, cardinalities and the numbers of idempotents and nilpotents.