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Comparative Evaluation Of Selected Properties Of Tetrahedral Amorphous Carbon (Ta-C) Coated And Uncoated Beta Titanium (Β-Ti) Archwires - An In Vitro Study, Abhinaya Jotheswaran, Kurunji Kumaran Navaneethakrishnan Jul 2026

Comparative Evaluation Of Selected Properties Of Tetrahedral Amorphous Carbon (Ta-C) Coated And Uncoated Beta Titanium (Β-Ti) Archwires - An In Vitro Study, Abhinaya Jotheswaran, Kurunji Kumaran Navaneethakrishnan

Taiwanese Journal of Orthodontics

Objective: The development of newer archwires can be achieved either by discovering novel materials or by modifying existing ones. The objective of the present study was to coat beta-titanium (β-Ti) archwires with tetrahedral amorphous carbon (ta-C)/hard carbon and to evaluate selected physical and mechanical properties. Methods: Hard carbon–coated (n = 5) and uncoated (n = 5) β-Ti wires were assessed for surface roughness, wear resistance, load-deflection characteristics, and friction using appropriate testing apparatus under dry in vitro conditions. Results: Compared to uncoated β-Ti wires, ta-C–coated β-Ti wires demonstrated a statistically significant reduction in surface roughness, increased wear resistance, and lower …


A Holistic Perspective On (In)Formal English Learning Through Mobile Apps, Gamification, And Virtual And Augmented Reality, Ahmed Abdullah Ahmed Alshehri Jul 2026

A Holistic Perspective On (In)Formal English Learning Through Mobile Apps, Gamification, And Virtual And Augmented Reality, Ahmed Abdullah Ahmed Alshehri

UB Journal for Humanities

Using digital tools such as Computer-Assisted Language Learning (CALL), Mobile-Assisted Language Learning (MALL), Virtual Reality (VR), Augmented Reality (AR), and gamification has remodeled language learning. Despite their advances and integration into language programs, gaps remain in personalization, accessibility, and skill development. This study aims to explore the impact of such tools on language learning outcomes in formal and informal settings, with a focus on mobile Apps, VR/AR, and gamification. A mixed-method approach was employed, interconnecting quantitative surveys with 150 participants and qualitative interviews. The former was used to assess tool usage, motivation, and proficiency, and the latter (qualitative data dealt …


Blended Learning Development In Mongolian K-12 Education: A Systematic Review And Psychometric Study Of Teacher Readiness, Batbold Bukhchuluun Jul 2026

Blended Learning Development In Mongolian K-12 Education: A Systematic Review And Psychometric Study Of Teacher Readiness, Batbold Bukhchuluun

Theses and Dissertations

This dissertation examines blended learning (BL) in Asian K-12 education through a systematic review and an empirical validation study in Mongolia. The first study reviews peer-reviewed K-12 BL research published between 2000 and 2024 using PRISMA procedures. We analyzed 42 studies to identify publication trends, geographic representation, BL model adoption, articulation of physical and pedagogical design layers, implementation challenges, and reported outcomes. Findings indicate that BL research is concentrated in a limited number of countries, frequently employs flipped learning models, and often lacks detailed pedagogical specification. Common challenges include infrastructure limitations, teacher preparedness, and institutional support. The second study adapts …


Continuous 1:1 Sitter Observation Versus Standard Safety Interventions To Reduce Falls In Hospitalized Adults At Risk, Zainab Williams Jul 2026

Continuous 1:1 Sitter Observation Versus Standard Safety Interventions To Reduce Falls In Hospitalized Adults At Risk, Zainab Williams

Student Scholarly Projects

Practice Problem: Patient falls remain a significant patient safety concern among hospitalized adults, particularly those at high risk. Traditional fall-prevention strategies, including continuous 1:1 sitter observation, require evaluation to determine their effectiveness in reducing falls and fall-related injuries.

PICOT: In hospitalized adult patients at high risk for falls (P), does continuous 1:1 sitter observation (I), compared to standard safety interventions (C), reduce fall rates (O) as measured by reported falls per 1,000 patient days during hospitalization over 12 weeks (T)?

Evidence: Current evidence supports multifactorial fall-prevention programs that combine patient assessment, staff engagement, and proactive nursing interventions through intentional rounding. …


School And Community-Based Mentoring: How Christian Principals Facilitate Connections For Socially Isolated Adolescents, Kellee Murrell Jul 2026

School And Community-Based Mentoring: How Christian Principals Facilitate Connections For Socially Isolated Adolescents, Kellee Murrell

Doctor of Ministry Projects and Theses

The dissertation focuses on research on adolescent social isolation and on the practices of Christian principals in implementing mentoring programs. Existing Christian and secular mentoring programs are analyzed to assess their effectiveness. The design of a pilot mentoring program tailored to the unique responsibilities of Christian principals, incorporating spiritual and emotional development, is presented. Developing mentoring programs and responding to vulnerable students are clear ways Christian school principals embody Christ’s love, justice, and concern. A contribution of this dissertation is that adolescent social isolation not only affects developmental growth but is also a moral issue.


Biquandle Virtual Brackets And Virtual Knotoids, Nesli̇han Gügümcü, Hamdi̇ Kayaslan Jul 2026

Biquandle Virtual Brackets And Virtual Knotoids, Nesli̇han Gügümcü, Hamdi̇ Kayaslan

Turkish Journal of Mathematics

In this paper, we introduce invariants of virtual knotoids based on biquandles and biquandle virtual brackets. We show that one of these invariants, namely biquandle virtual bracket matrix, is a proper enhancement of the other invariants introduced in this paper.


Biharmonic Curves In Warped Product Manifolds I ×FMN(C), Şaban Güvenç, Ci̇han Özgür Jul 2026

Biharmonic Curves In Warped Product Manifolds I ×FMN(C), Şaban Güvenç, Ci̇han Özgür

Turkish Journal of Mathematics

We explore the geometric properties of biharmonic curves in warped product manifolds of the form I ×f Mn(c), where I is an open interval and Mn(c) is a space of constant curvature. By establishing a main theorem, we analyze four distinct cases to reveal deeper curvature-related characteristics of these curves, including situations where they are slant. Finally, we construct three examples in I ×f S2(1).


Generalized Submaximality And Paracompactness In Ideal Topological Spaces Via Δβ*-𝔍-Open Sets, Chawalit Boonpok, Areeyuth Sama-Ae Jul 2026

Generalized Submaximality And Paracompactness In Ideal Topological Spaces Via Δβ*-𝔍-Open Sets, Chawalit Boonpok, Areeyuth Sama-Ae

Turkish Journal of Mathematics

This paper explores the notions of δβ*-𝔍-submaximality and δβ*-𝔍-paracompactness within ideal topological spaces, viewing them as natural generalizations of the traditional concepts of submaximality and paracompactness. These concepts arise naturally in the context of ideal topology, where an ideal 𝔍 on a topological space provides additional structure for analyzing topological properties. It focuses on the study of submaximal spaces by employing δβ*-𝔍-open sets, which serve as fundamental building blocks for understanding the topological behavior in ideal spaces. Furthermore, the work provides multiple characterizations of δβ*-𝔍-paracompact spaces and examines how this property behaves …


Impulsive Hahn--Sturm--Liouville Equations, Bi̇lender Paşaoğlu Allahverdiev, Hüseyi̇n Tuna, Hati̇ce Bulut Demi̇ralay Jul 2026

Impulsive Hahn--Sturm--Liouville Equations, Bi̇lender Paşaoğlu Allahverdiev, Hüseyi̇n Tuna, Hati̇ce Bulut Demi̇ralay

Turkish Journal of Mathematics

In this study, we investigate the Hahn--Sturm--Liouville problems with impulsive boundary conditions. The basic spectral properties of this type of equations are investigated.


The Kinematic Relationship Between Plücker Coordinates,  Moments Of Ruled Surfaces, And Real Quaternion Algebra, Selahatti̇n Aslan Jul 2026

The Kinematic Relationship Between Plücker Coordinates,  Moments Of Ruled Surfaces, And Real Quaternion Algebra, Selahatti̇n Aslan

Turkish Journal of Mathematics

This paper introduces a new kinematic method for generating ruled surfaces in Euclidean 3-space. We demonstrate that the Plücker coordinate method for straight lines can be extended to ruled surfaces. We prove that the moment of a ruled surface is a unique curve, which is independent of the chosen base curve. Moreover, we introduce a novel and distinctive base curve that is defined as the set of points on the rulings of the ruled surface such that these points are closest to the origin. Thus, we prove that each ruled surface can be generated using a real quaternion and a …


Notes On The Geometry Of Electromagnetic Fields And Maxwell’S Equations Along A Nonnull Curves In Nonflat-3d Space Forms MQ3(C), Fatma Almaz, Cumali̇ Eki̇ci̇ Jul 2026

Notes On The Geometry Of Electromagnetic Fields And Maxwell’S Equations Along A Nonnull Curves In Nonflat-3d Space Forms MQ3(C), Fatma Almaz, Cumali̇ Eki̇ci̇

Turkish Journal of Mathematics

In this paper, the directional derivatives in accordance with the orthonormal frame {T→, N→, B→} are defined in Mq3(c), the extended Serret-Frenet relations by using Frenet formulas are expressed. Furthermore, we express the bending elastic energy function for the same particle in Mq3(c) according to curve γ(s, ξ, η) and we tried to interpret it from a geometric perspective of the energy for unit vector fields. Also, Maxwell’s equations are expressed for the electric and magnetic field vectors …


Analysis And Categorization Of Second-Order Linear Partial Dynamic Equations On Time Scales, Svetlin G. Georgiev, Jervin Zen Lobo, Sanket Tikare Jul 2026

Analysis And Categorization Of Second-Order Linear Partial Dynamic Equations On Time Scales, Svetlin G. Georgiev, Jervin Zen Lobo, Sanket Tikare

Turkish Journal of Mathematics

In this paper, we obtain the canonical form of second-order linear partial dynamic equations in two independent variables on time scales, together with the identity for the characteristic quadratic form. This is then used to classify these equations as hyperbolic, elliptic, or parabolic. We deduce the characteristic equations in each case, determine their roots, and provide the corresponding characteristic curves. In one case, we derive the generalized Beltrami equations on time scales. Suitable examples involving equations of interest are explored, and the developed theory is illustrated through these examples.


Numerical Simulation Of Centrifugal Pump Performance Under Impeller Blade And Suction Diameter Variations, Gunawan Budi Santoso, Susanto -, Akhmad Nuriyanis, Anang Budhi Nugroho, Rizka Noor Miftakhul Ulum, Suyono - Jul 2026

Numerical Simulation Of Centrifugal Pump Performance Under Impeller Blade And Suction Diameter Variations, Gunawan Budi Santoso, Susanto -, Akhmad Nuriyanis, Anang Budhi Nugroho, Rizka Noor Miftakhul Ulum, Suyono -

Journal of Mechanical Engineering Science and Technology (JMEST)

The objective of this study is to model variations in pump geometry to obtain optimal performance under the effects of cavitation. The resulting geometric variation models were then simulated using ANSYS Fluent software. The first geometric variation model used a standard 5-blade impeller with suction pipe diameter variations of 2, 2 ½, 2 ¾, 3, 3 ¼, 3 ½, and 4 inches. The second geometric variation model for simulation used a standard 3-inch suction pipe with impeller blade variations of 3, 4, 5, 6, 7, 8, and 9. The simulation results indicated that the number of blades without changes in …


Why Do Location-Based Preference Effects Occur Within Decision Making? Evidence From The Magician’S Force, Gustav Kuhn, Rachael Bulford-Forbes, Liliana Schirru, Meda Valecke, Geoff G. Cole Jul 2026

Why Do Location-Based Preference Effects Occur Within Decision Making? Evidence From The Magician’S Force, Gustav Kuhn, Rachael Bulford-Forbes, Liliana Schirru, Meda Valecke, Geoff G. Cole

School of Psychology

Preference research has shown that humans have a bias towards items located in the middle of the visual field and a number of theories have been suggested to explain the phenomenon. The conjuring trick known as the placement force not only exploits this central bias but also shows that the preference is subtly biased to the right of centre. We used the force, together with eye tracking, to test the different theories. In a single experiment, four face-down playing cards were presented on a table in a horizontal row. Participants (n = 137) were asked to select one by pushing …


Grit And Psychological Well-Being As Predictors Of Job Persistence Among K–12 Teachers In The United States, Tina Marie Sheppard Jul 2026

Grit And Psychological Well-Being As Predictors Of Job Persistence Among K–12 Teachers In The United States, Tina Marie Sheppard

Walden Dissertations and Doctoral Studies

Throughout the United States, K–12 public school teachers are leaving the profession, contributing to teacher shortages and instability in classrooms and schools. Teacher persistence is critical to student success, yet little was known about the nature of the predictive relationship between grit and psychological well-being on job persistence among K–12 public school teachers in the United States. Guided by the framework of positive psychology, the purpose of this quantitative nonexperimental correlational study was to investigate the nature of the predictive relationship between the independent variables grit, as measured by the 12-Item Grit Scale, and psychological well-being, as measured by the …


The Lived Experiences Of The Flint Water Crisis And Its Psychological Effects, Joe W. Glenn Jul 2026

The Lived Experiences Of The Flint Water Crisis And Its Psychological Effects, Joe W. Glenn

Walden Dissertations and Doctoral Studies

The Flint, Michigan, water crisis of 2014, with lead contamination of drinking water, adversely affected predominantly Black, socioeconomically disadvantaged residents. However, no research has investigated residents’ experiences, especially their trust in local and state government leaders. The purpose of this study was to explore the lived experiences of the Flint water crisis and its psychological effects. Rawls’s theory of justice provided the framework for the study. Three research questions guided this qualitative descriptive phenomenological study. Information from eight Flint residents was collected through semi-structured interviews. Data analysis followed Giorgi’s descriptive phenomenological steps. Five strong themes emerged: understanding individual perceptions, views …


Residual Effects Of Childhood Sexual Victimization On Black Caribbean Immigrants’ Adult Functionality, Sophia Elaine Profit Jul 2026

Residual Effects Of Childhood Sexual Victimization On Black Caribbean Immigrants’ Adult Functionality, Sophia Elaine Profit

Walden Dissertations and Doctoral Studies

Childhood sexual victimization is associated with long-term psychological, emotional, and functional challenges that may persist into adulthood. Despite a growing body of literature on childhood trauma, limited research has explored its residual effects on adult functionality among Black Caribbean immigrants. The purpose of this qualitative phenomenological study was to explore the residual effects of childhood sexual victimization on adult functionality among Black Caribbean immigrants. Purposive and snowball sampling were used to recruit 9 participants through social media platforms. Rational choice theory served as the conceptual framework to examine how trauma-related and sociocultural factors shaped participants' decision-making processes. Data were collected …


General And Special Education Teachers’ Experiences With The Implementation Of Inclusive Education, Katie Chardoussin Jul 2026

General And Special Education Teachers’ Experiences With The Implementation Of Inclusive Education, Katie Chardoussin

Walden Dissertations and Doctoral Studies

Some elementary special education and general education teachers in New Jersey struggle to implement inclusion programs. The purpose of this study was to explore special and general education teachers’ experiences with the challenges they encountered teaching in inclusion classrooms. The conceptual framework for this study was Anderson’s ecology of inclusive education, which highlighted the importance of students having meaningful relationships with their peers. For this basic qualitative design, semistructured interviews were conducted with 19 participants, of whom eight were special education teachers, and 11 were general education teachers. Through inductive coding, the following three themes emerged: Special education and general …


Administrative Discharge Strategies To Decrease Readmission Rates Of Black Patients In Acute Care Hospitals, Patricia Cummings Jul 2026

Administrative Discharge Strategies To Decrease Readmission Rates Of Black Patients In Acute Care Hospitals, Patricia Cummings

Walden Dissertations and Doctoral Studies

High 30-day hospital readmission rates among Black patients remain a healthcare administration problem associated with high costs and poor care quality. The purpose of this integrative review was to identify evidence-based discharge planning strategies to reduce hospital readmissions among Black patients. The review question was used to examine strategies healthcare administrators can implement to enhance discharge planning for Black patients. Donabedian’s structure-process-outcome model guided the review. A literature search yielded 87 relevant articles; 27 articles published from 2021 through 2026 were appraised using the Johns Hopkins evidence-based practice model, and 25 were used in this review. Thematic analysis resulted in …


In Re: Boy Scouts Of America And Delaware Bsa Llc Jul 2026

In Re: Boy Scouts Of America And Delaware Bsa Llc

2026 Decisions

USDC for the District of Delaware


Association Of New Jersey Rifle And Pistol Clubs I V. Attorney General New Jersey Jul 2026

Association Of New Jersey Rifle And Pistol Clubs I V. Attorney General New Jersey

2026 Decisions

USDC for the District of New Jersey


A Modest Proposal For Discourse Analysis In Nonbinary Communities: Method And Case Study, Nikoli Michael Daigneault Jul 2026

A Modest Proposal For Discourse Analysis In Nonbinary Communities: Method And Case Study, Nikoli Michael Daigneault

Electronic Theses and Dissertations

While linguists have long used discourse analysis to study language variation in binary and nonnormative gender groups, nonbinary people have often been excluded from analyses or treated without a nonbinary-informed framework. Nevertheless, nonbinary language use can provide key insights into the relationship between gender and language. In this thesis, I propose Nonbinary Discourse Analysis, a set of recommendations and best practices for conducting discourse analysis in nonbinary communities. These methods are informed by previous empirical research on nonnormative gender identities and theoretical work in trans linguistics (Zimman, 2020) and trans epistemologies (Nordmarken, 2019; Raclaw, in press). To demonstrate the methodology, …


Transcriptomic And Genomic Insights Into Nutrient Stress Responses And Subgenome Evolution In Chenopodium, Ashley Kathleen Marcheschi Jul 2026

Transcriptomic And Genomic Insights Into Nutrient Stress Responses And Subgenome Evolution In Chenopodium, Ashley Kathleen Marcheschi

Theses and Dissertations

Chenopodium is a diverse genus of nutritionally and ecologically important species in the Amaranthaceae family. This thesis investigates two outstanding questions in the genus: how Chenopodium quinoa responds transcriptionally to nutrient deficiency and how Australian Chenopodium species are related through their subgenomic ancestry and evolutionary history. First, we characterized transcriptomic responses of C. quinoa to deficiencies of twelve essential macro- and micronutrients across leaf and root tissues using RNA sequencing. Leaves showed the strongest responses under nitrogen, potassium, magnesium, and zinc deficiency, while roots responded more evenly across conditions. Recurring responses included suppression of photosynthesis, remodeling of translational machinery, reactive …


Association Between Occupational Stress, Sleep Quality, And Premature Ejaculation Among Indonesian Information Technology Workers, Muhammad Faisal Ratman, Suryo Wibowo, Muhammad Ilyas, Retno Asti Werdhani, Dewi Yunia Fitriani Jul 2026

Association Between Occupational Stress, Sleep Quality, And Premature Ejaculation Among Indonesian Information Technology Workers, Muhammad Faisal Ratman, Suryo Wibowo, Muhammad Ilyas, Retno Asti Werdhani, Dewi Yunia Fitriani

Occupational and Environmental Medicine Journal of Indonesia

Introduction Premature ejaculation (PE) is a common sexual dysfunction that significantly impacts quality of life. Occupational stress and poor sleep quality are hypothesized as risk factors, particularly among Information and Technology (IT) workers who experience unique occupational stressors. This study aimed to evaluate the proportion of PE, examine the influence of occupational stress and sleep quality on PE, and determine whether sleep quality mediates the relationship between occupational stress and PE among Indonesian IT workers.

Methods This cross-sectional study involved 89 married male IT workers who completed online questionnaires, including the Premature Ejaculation Diagnostic Tool (PEDT), Perceived Occupational Stress (POS) …


Depro: Understanding The Role Of Llms In Debugging Competitive Programming Code, Nabiha Parvez, Md Tanvin Sarkar Pallab, Mia Mohammad Imran, Tarannum Shaila Zaman Jul 2026

Depro: Understanding The Role Of Llms In Debugging Competitive Programming Code, Nabiha Parvez, Md Tanvin Sarkar Pallab, Mia Mohammad Imran, Tarannum Shaila Zaman

Computer Science Faculty Research & Creative Works

Debugging consumes a substantial portion of the software development lifecycle, yet researchers do not yet understand well the effectiveness of Large Language Models (LLMs) in this task. Competitive programming offers a rich benchmark for such evaluation, given its diverse problem domains and strict efficiency requirements. We present an empirical study of LLM-based debugging on competitive programming problems and introduce DePro, a test-case-driven approach that assists programmers by correcting existing code rather than generating new solutions. DePro combines brute-force reference generation, stress testing, and iterative LLM-guided refinement to efficiently identify and resolve errors. Experiments on 13 faulty user submissions from Codeforces …


Perceived Level Of Preparedness For A Terrorist Event Between State, Local And Tribal Law Enforcement Officers, Herbert Henderson Jul 2026

Perceived Level Of Preparedness For A Terrorist Event Between State, Local And Tribal Law Enforcement Officers, Herbert Henderson

Walden Dissertations and Doctoral Studies

In this quantitative cross-sectional study, differences in perceived preparedness among state, local, and tribal law upon Kingdon’s multiple streams approach and Baumgartner and Jones’ punctuated equilibrium theory to explain administrative changes in law enforcement following the September 11, 2001, attacks. Data were collected from 53 full-time police officers across state, local and tribal agencies using a web-based survey instrument measuring enforcement officers in a northern border region were examined. Officers’ perceived preparedness to identify, prevent, and respond to future terrorist threats were evaluated. Whether perceived preparedness differed by agency type and whether officers with military experience or advanced homeland security …


Llm-Enabled Open-Source Systems In The Wild: An Empirical Study Of Vulnerabilities In Github Security Advisories, Fariha Tanjim Shifat, Hariswar Baburaj, Ce Zhou, Jaydeb Sarker, Mia Mohammad Imran Jul 2026

Llm-Enabled Open-Source Systems In The Wild: An Empirical Study Of Vulnerabilities In Github Security Advisories, Fariha Tanjim Shifat, Hariswar Baburaj, Ce Zhou, Jaydeb Sarker, Mia Mohammad Imran

Computer Science Faculty Research & Creative Works

Large language models (LLMs) are increasingly embedded in open-source software (OSS) ecosystems, creating complex interactions among natural language prompts, probabilistic model outputs, and execution-capable components. However, it remains unclear whether traditional vulnerability disclosure frameworks adequately capture these model-mediated risks. To investigate this, we analyze 295 GitHub Security Advisories published between January 2025 and January 2026 that reference LLM-related components, and we manually annotate a sample of 100 advisories using the OWASP Top 10 for LLM Applications 2025.We find no evidence of new implementation-level weakness classes specific to LLM systems. Most advisories map to established CWEs, particularly injection and deserialization weaknesses. …


“Innocent” Electrolytes Can Influence Organic Electrosynthetic Selectivity, Zachary A. Nguyen, Nhu H. Quach, Mayank Tanwar, Joshua A. Beeler, Kevin Mcfadden, Dylan G. Boucher, Matthew Neurock, Shelley D. Minteer Jul 2026

“Innocent” Electrolytes Can Influence Organic Electrosynthetic Selectivity, Zachary A. Nguyen, Nhu H. Quach, Mayank Tanwar, Joshua A. Beeler, Kevin Mcfadden, Dylan G. Boucher, Matthew Neurock, Shelley D. Minteer

Chemistry Faculty Research & Creative Works

Organic electrosynthesis has emerged as a powerful strategy for leveraging electricity in organic synthesis. Despite its growing popularity, the fundamental molecular interactions governing electrochemical systems remain poorly understood. Many electrosynthetic reactions show strong dependence on the identity of the allegedly inert supporting electrolyte, which can significantly impact yields and selectivity, yet the physical origins of these effects are largely unexplored. A mechanistic understanding of electrolyte effects would enable more rational reaction design for applications. Here, we use cyclic voltammetry to investigate cobalt-based metal–carbon bond homolysis and elucidate how common supporting electrolytes influence reaction rates. Bulk electrolysis experiments further reveal how …


Marlin Lopez-Ramirez V. Attorney General United States Of America Jul 2026

Marlin Lopez-Ramirez V. Attorney General United States Of America

2026 Decisions

Agency


Warped Product Ptr-Submanifolds In A Kähler Manifold, Firat Yerli̇kaya, Bayram Şahi̇n Jul 2026

Warped Product Ptr-Submanifolds In A Kähler Manifold, Firat Yerli̇kaya, Bayram Şahi̇n

Turkish Journal of Mathematics

Recently, the PTR-submanifold of an almost Hermitian manifold has been defined and studied as a large class including CR-submanifolds, hemi-slant submanifolds, and pointwise hemi-slant submanifolds, which are well-known in the literature. This novel category of submanifolds comprises two distributions, one of which is antiinvariant while the complementary distribution is arbitrary. This paper discusses the case of a PTR-submanifold being a warped product. It is first shown that there are no such warped product submanifolds for the case where the first factor is antiinvariant. Therefore, warped product PTR-submanifolds whose second factor is antiinvariant are examined. A characterization is given for this …