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From Villi To Alveoli: Lung Involvement In Celiac Disease – A Narrative Review, Mateusz Marzec, Patrycja Cecha

Journal of Community Hospital Internal Medicine Perspectives

Background:

Celiac disease (CD) is a chronic, immune-mediated enteropathy triggered by gluten that affects about 1% of the population and may present with extraintestinal manifestations. Pulmonary complications are considered rare and are poorly characterized. Lane-Hamilton syndrome is the best described lung manifestation, but data suggests a broader spectrum of respiratory involvement.

Methods:

We performed a narrative review with structured search strategy of PubMed and Embase (January 1, 1970 – December 1, 2025) using the terms celiac/coeliac and lung, pulmonary, respiratory, hemoptysis, hemosiderosis, alveolar hemorrhage, interstitial lung disease, alveolitis, bronchiectasis …

Echocardiography In Stroke Management: Necessary Or Overused?, Nicole Ann Tesoro, Jasvin Kurundrayil Manha, Jerold Fleishman, Sumanth Bandaru

Journal of Community Hospital Internal Medicine Perspectives

Stroke remains a leading cause of morbidity and mortality worldwide, leading to the development of efficient and evidence-based management strategies. Echocardiography is a crucial diagnostic tool for identifying cardiac sources of embolism, particularly in cardioembolic and cryptogenic strokes, yet its routine use in all stroke patients remains controversial. While evidence-based guidelines recommend a patient-specific approach, rigid hospital quality metrics have incentivized widespread echocardiography, even in low-yield cases such as large artery atherosclerotic strokes. This disconnect raises concerns regarding cost-effectiveness, resource allocation, and potential over-testing, delaying discharges and prolonging hospital length of stay. A more tailored approach, focusing on guideline-driven indications, …

A Comparative Analysis Of Opioid Overdose Hospitalizations Pre- And Post-Pandemic: Insights From The National Inpatient Sample Database, Hassan Shakir, Niloy Ghosh, Mohammed A Quazi, Tom Limanovich, Abdul Rafel Awan, Humza Saeed, Adeel Nasrullah, Christopher R Smith, Abu Baker Sheikh

Journal of Community Hospital Internal Medicine Perspectives

Background: The COVID-19 pandemic disrupted healthcare systems, affecting opioid overdose–related hospitalizations. National data examining how demographic and clinical outcomes evolved during this period, particularly by overdose intent, remain limited.

Methods: Using the National Inpatient Sample (2018–2021), we identified adult hospitalizations for opioid overdose using ICD-10 codes and categorized cases as intentional, unintentional, or unspecified. Patients were grouped into pre-COVID (2018–2019) and post-COVID (2020–2021) cohorts. Multivariable logistic and linear regression models adjusted for patient- and hospital-level factors evaluated demographic differences, complications, and outcomes

Results: Among 293,810 hospitalizations, intentional overdoses decreased over time, while unintentional overdoses remained predominant. Post-COVID hospitalizations had higher …

The Effect Of Empiric Initiation Of Treatment On Outcomes Among Patients Presenting With Extrapulmonary Mycobacterium Tuberculosis Infection In A Community Hospital Setting, Talha Awwal, Faisal Raja Kh, Hanya Awaba, Waseem Anwar, Jinma Ren, Muhammad Aamir Safdar, Saqib Walayat, John J. Farrell

Journal of Community Hospital Internal Medicine Perspectives

Background: Extrapulmonary tuberculosis (EPTB) accounts for ~20% of Mycobacterium tuberculosis infections in Pakistan. Diagnostic delays are common and may worsen outcomes. We evaluated whether empiric treatment initiation improves outcomes among patients with EPTB at a large public hospital in Islamabad, Pakistan. Methods: Retrospective cohort of consecutive EPTB cases at Pakistan Institute of Medical Sciences (January–June 2016). Patients were categorized as clinically diagnosed (symptoms/radiology) or laboratory-supported (histology, microbiology, or biochemical tests). Standard Directly Observed Therapy Short-course (DOTS) based regimens were used. Outcomes were treatment success, failure, loss to follow-up, and mortality; groups were compared using chi-square testing. Results: Of 317 EPTB …

Prognostic Utility Of Delta -Procalcitonin And Modified Shock Index For Risk Stratification Of Sepsis In Acute Care Settings, Sanveer Singh, Neeraj Singla, Navneet Sharma, Mandip Bhatia, Saurabh C Sharda

Journal of Community Hospital Internal Medicine Perspectives

Background: Risk stratification in sepsis remains challenging, and while several scoring systems exist, there is a need for simple tools that can reliably predict outcomes.

Aims: To study the role of Delta -Procalcitonin and Modified Shock Index (MSI) in predicting the severity of Multiple Organ Dysfunction Syndrome (MODS)like acute kidney injury, vasopressor requirement, need for mechanical ventilation, coagulopathy and 28 day mortality in sepsis

Methods: This prospective observational study recruited 122 patients with suspected sepsis. Delta- Procalcitonin was calculated by measuring the difference in procalcitonin values at the time of admission and after 48 hours. Modified Shock Index (MSI) is …

Evolving Trends And Racial Disparities In Alcohol Associated Liver Disease (Ald), Metabolic Dysfunction Associated Steatohepatitis (Mash) And Hepatitis C Viral Infection (Hcv) As Etiology Of Liver Transplantation: Past, Present, And Future Projections, Boniface Mensah, Albert E. Orhin, Natalie A. Y. Akoto, Seunghee Han, Rachel A Boateng, Ramya Varesiddy, Joseph Atarere, Simardeep Singh, Terrylyna Baffoe-Bonnie, Haider Naqvi, Christopher J. Haas

Journal of Community Hospital Internal Medicine Perspectives

Background

Liver transplantation remains the definitive treatment for end-stage liver disease (ESLD) and hepatocellular carcinoma (HCC). While hepatitis C virus (HCV) was historically the leading indication for liver transplant, the introduction of direct-acting antivirals (DAAs) has drastically reduced HCV-related ESLD. In contrast, metabolic dysfunction-associated steatohepatitis (MASH) and alcohol-associated liver disease (ALD) have emerged as predominant causes of liver transplantation. This study evaluates racial and ethnic disparities in liver transplantation indications from 2004 to 2023 and projects future trends through to 2040.

Methods

De-identified data from the Standard Transplant Analysis and Research (STAR) files of the United Network for Organ Sharing …

Influence Of Pre-Treatment Ca 125 Levels On Survival Outcomes Across Ethnic Groups In Ovarian Cancer Patients, Ayrton Bangolo, Behzad Amoozgar, Lili Zhang, Budoor Alqinai, Lejla Hodzic, Prathyusha Nadella, Mudra Patel, Kaushik Roy, Veena Lakshmana, Nirdosh Sharma, Sabrina Sultana, Berhane Yohannes, Hadrian Hoang-Vu Tran, Gabriel Ingersoll, Phyu Min Thet, Roshini W. Senevirathne, Prajwal Chandak, Nicole Maharaj, Chloe Aloimonos, Mehwish Safdar, Chathurika Priyabhashinie, Betsy Samuel, Maheswari Bommepalli, Ye Tun, Steven Swarath, Naresh Kumar, Rishabh Goyal, Sami Ai. Salih, Isaac O. Wiredu, Elena Umanets, Lisette L. Kiadidi, Prasansa Dhakal, Timerjot Kaur, Dengyumei Du, Komaldeep Gill, Muhammad Ali Raza Khan, Camila Arteaga, Helena Barbosa, Simcha Weissman

Journal of Community Hospital Internal Medicine Perspectives

Aim This study evaluates demographics, clinicopathological features, and mortality influencers among 16,466 US patients with ovarian cancer diagnosed between 2010 and 2017, focusing on CA 125 levels and racial disparities affecting outcomes.

Methods We analyzed SEER data for 16,466 patients diagnosed from 2010 to 2017. Demographic, clinical, overall mortality (OM), and cancer-specific mortality (CSM) variables were assessed. Factors with P < 0.1 on univariate Cox regression were entered into multivariate Cox models to identify independent prognostic factors, with hazard ratios greater than one indicating adverse prognosis.

Results Among 16,466 patients with ovarian cancer diagnosed between 2010 and 2017, most were aged 40–79 years and presented with distant-stage disease. The majority of patients were non-Hispanic White, followed by Hispanic and non-Hispanic Black patients. Serous carcinoma was the …

Correlation Between Aortic Valve Area Measured By Cardiac Computed Tomography And Transthoracic Echocardiography In Patients With Aortic Stenosis, Shehroz Sultan, Neeraj Joshi, Ali Haider Awan, Shabana Kauser, Hafsa Malik Aulakh, Bilal Ghafoor, Muhammad Ammar Ajmal, Abida Perveen, Jahanzeb Malik

Journal of Community Hospital Internal Medicine Perspectives

Background: Accurate assessment of aortic valve area (AVA) is essential for determining the severity of aortic stenosis (AS) and guiding clinical management. Transthoracic echocardiography (TTE) is the standard first-line imaging modality, while cardiac computed tomography (CT) provides direct anatomical planimetry and may offer complementary information in selected patients.

Objective: To evaluate the correlation and agreement between CT-derived and TTE-derived AVA measurements and to examine their association with clinical outcomes in patients with AS.

Methods: This single-center retrospective cohort study included 1,857 consecutive adults with moderate to severe AS who underwent both TTE and cardiac CT at the Rawalpindi Institute of …

Improving Pneumococcal Vaccination Rates During Hospitalization Via Resident Education Intervention: A Hospital-Based Quality Improvement Project In A Teaching Community Hospital, Shun Nakahara, Takahiko Tsutsumi, Masaru Kurihara

Journal of Community Hospital Internal Medicine Perspectives

Background: Pneumococcal vaccination coverage among eligible adults in Japan remains suboptimal. This gap may be partly attributable to insufficient physician and patient education, as well as limited coordination in delivery of preventive care. Therefore, we conducted a hospital-based quality improvement project combining resident education with system-level workflow modifications to enhance pneumococcal vaccination rates.

Methods: A single-center quality improvement study was conducted at a teaching community hospital in Japan, comparing outcomes between pre-intervention and intervention periods. The intervention included resident education, patient educational materials, integration of vaccination status into admission documentation, discharge checklists, and weekly reminders. The primary outcome was the …

Systematic Review Of Randomized Clinical Trials For The Treatment Of Long Covid Syndrome, Leonardo Tamariz, Dariel Rodriguez, Elizabeth Bast, Nancy Klimas, Morgan Pyne, Maricarmen Cruz-Jimenez, Diana Gomez Manjarrez, Ana Palacio

Journal of Community Hospital Internal Medicine Perspectives

Background: There is a critical need for interventions for long COVID. Our aim was to conduct a systematic review on the efficacy and safety of different interventions in patients with long COVID.

Methods: We searched the MEDLINE 1965 until August 2024. We included randomized clinical trials that reported a primary outcome. We evaluated the GRADE certainty of the effect measures.

Results: Our initial search yielded 2,606 potentially relevant studies. We include 43 randomized clinical trials that ultimately included 2,878 participants with long COVID. The GRADE criteria found all but one study had low certainty. Eight studies reported on the use …

Cipropad Learning Model To Improve Elementary School Students’ Hots In Geometry, Ria J. Salman, Heris Hendriana, Masta Hutajulu

Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan

The latest digital technology developments demand innovative learning models that are able to integrate active learning approaches, problem-solving, and digital collaborative platforms. This study aims to develop a CIPROPAD (Circuit Learning, Problem-Based-Learning, Padlet) learning model designed to improve students' HOTS. This study uses the Borg and Gall R&D method which includes the stages of needs analysis, model design, initial product development, expert validation, limited trials, revisions, and field trials. The research subjects consisted of 74 elementary school students divided into experimental and control groups. The research instruments used included expert validation sheets, HOTS tests, student activity observation sheets, and student …

Three-Dimensional Surgical Orthodontic Management Of Pruzansky Iia Craniofacial Microsomia With Severe Facial Asymmetry And Obstructive Sleep Apnea, Hung-Wen Chiu, Cheng-Hui Lin, Yi-Hsuan Carol Chen

Taiwanese Journal of Orthodontics

Background: Craniofacial microsomia (CFM) is the second most common craniofacial anomaly with asymmetrical, congenital malformation. Treatment is challenging and requires interdisciplinary cooperation to restore function and facial esthetics. Objective: A CFM patient suffered from facial asymmetry, occlusal plane cant, malocclusion and severe obstructive sleep apnea, and a 3D surgical orthodontic treatment was planned. Case report: A 37-year-old male patient complained of small chin with deviation. Craniofacial microsomia grade IIa by Pruzansky system and S2A1T1 by SAT system was diagnosed. Clinical examination showed severe facial asymmetry, right microtia, chin deviation to right side 7.0 mm, occlusal plane cant, right Class …

Management Of Skeletal Class Iii Malocclusion With Deep Bite And Moderate Overjet Using Improved Super-Elastic Ti-Ni Alloy Wire (Isw), Wen-Hsuan Lin, Ching-Yu Yang, Yuan-Hou Chen, Jian-Hong Yu

Taiwanese Journal of Orthodontics

A 20-year-old female presented with concerns about poor dental alignment and a tendency to bite on her lip easily. Clinical examination revealed a concave and brachy facial profile, accompanied by a deep overbite and a moderate overjet. Radiographic examination showed skeletal Class III with a low mandibular plane angle. Correction of the deep bite was achieved by using the Improved Super-elastic Ti-Ni alloy Wire (ISW) and Intermaxillary elastics (IMEs). To correct the moderate overjet, interproximal reduction (IPR), the Multi-bend Edgewise Archwire (MEAW) technique, and arch lengthening of the lower arch were applied. The active treatment duration took approximately 54 months, …

Improved Super-Elastic Ti-Ni Alloy Wire For The Treatment Of Skeletal Class Iii Malocclusion With Anterior Crossbite And Missing Lower Molar, De-Lun Zhuang, Yuan-Hou Chen, Jian-Hong Yu

Taiwanese Journal of Orthodontics

This case report describes the use of Improved Super-elastic Ti-Ni alloy wire (ISW), developed by Tokyo Medical and Dental University, in managing a skeletal Class III malocclusion with anterior crossbite and a missing lower molar. A 26-year-old female presented with a chief complaint of poor dental alignment. Clinical and radiographic evaluation revealed Angle Class III malocclusion, anterior crossbite, a missing mandibular first molar (36), and a centric occlusion–centric relation (CO–CR) functional shift, consistent with a skeletal Class III pattern. Treatment involved the use of ISW for leveling and alignment of both arches and correction of the anterior crossbite, while maintaining …

Inferior Alveolar Nerve Proximity In Mandibular Molar Distalization: Implications For Orthodontic Treatment Planning, Samantha Hsien-Chu Mao, Chia-Hsuan Chan, Yu-Jen Chang, Shiu-Shiung Lin, Chen-Feng Cheng, Te-Ju Wu

Taiwanese Journal of Orthodontics

Purpose: This study aimed to clarify the anatomical boundaries of mandibular molar distalization, emphasizing the risk of inferior alveolar nerve (IAN) contact. Patients and Methods: In total, 30 skeletal Class III patients undergoing orthognathic surgery (59 mandibular hemi-arches) were analyzed using pretreatment three-dimensional (3D) computed tomography scans. The shortest horizontal distance between the mandibular second molar and the inferior alveolar canal (M2-IAC) was measured at multiple depths below the cementoenamel junction, along with the distance to the lingual cortical plate (M2-MLC). Samples were categorized by vertical facial pattern (low-, normal-, and high-angle case). Simulated distalization cases predicting IAN contact were …

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 …

The Significance Of Medical Terminology In The Arabic 111 Course At King Saud Bin Abdulaziz University For Health Sciences (Ksau-Hs): An Analytical Pragmatic Study, Nuwair Abdullah Khalaf Al-Anzi

UB Journal for Humanities

Medical terminology in the “Arab 111” curriculum varies in its use within the educational context, which may affect students’ comprehension and understanding. Therefore, this study seeks to examine the suitability of these terms from a pragmatic perspective and their relationship to the effectiveness of scientific communication. Medical terminology possesses multiple contextual dimensions and is not confined solely to the scientific context among physicians, patients, and society. Pragmatics thus focuses on the way these terms are employed in everyday communication, since their circulation requires simplification to suit non-specialists. Moreover, misunderstanding medical terminology may lead to errors in diagnosis or treatment, making …

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 …

Profiling Students’ Academic Language Readiness For English‑Medium Instruction In Saudi Higher Education, Hanan Sarhan Alsubaiai

UB Journal for Humanities

Saudi universities have been rolling out English‑Medium Instruction (EMI) at a fast pace. But no standardized and validated instrument currently exists to assess students’ readiness. The present study developed the Academic Language Readiness Test (ALRT), administered it to undergraduate students, and determined the score cut-offs distinguishing those who are Ready, Borderline, and those who are Not Ready. A crosssectional, multisite quantitative design was employed with 712 undergraduate students from seven colleges at Bisha University. The ALRT measured four subskills: academic listening, academic reading, academic vocabulary and grammar, and academic study skills (notetaking and visual data interpretation). Psychometric analysis combined Classical …

The Role Of E-Commerce Platforms In Increasing Donations For Charitable Organizations: A Case Study Of Bani Yazid Charitable Society For Holy Quran Memorization (2017–2025), Abdulrhman Mohmmad Said Alamoudi, Abdulrahman Ahmad M. Waly, Mohammed Salman S. Alyazidi, Saad Mohammed A. Alqarni, Atiah Saad A. Alghamdi

UB Journal for Humanities

This study aims to analyze the role of electronic stores in increasing donations and developing financial resources for charitable organizations, using the Charitable Society for the Memorization of the Holy Quran in Bani Yazid as a case study during the period 2017–2025. The study employed a descriptive-analytical approach alongside quantitative methods to analyze financial data, and relied for data collection on semi-structured interviews with the society’s key officials, as well as on the analysis of financial records, performance reports, and e-store data. Time series analysis, T-test procedures, and simple linear regression were used to measure the impact of activating the …

The Right To Worker’S Wages: A Comparative Study Between Saudi Labor Law And International Conventions In Light Of Islam, Anwar Bin Ali Al-Asiri

UB Journal for Humanities

This study addresses one of the fundamental rights of workers — the right to wages, which represents a cornerstone of the employment contract. This right has received significant attention and protection under Islamic law, as well as at the international level, where the International Labour Organization (ILO) has long worked through conventions and conferences to safeguard workers’ wage rights. It has also been emphasized by various governments in their legal systems, most notably the Kingdom of Saudi Arabia, which issued its Labor Law to ensure the protection of workers’ wages. This study highlights the legal dimension of this system in …

How Rude?: Prohibitions On Insults And Abuse In International Human Rights Complaint Proceedings, Lisa Reinsberg

Northwestern Journal of Human Rights

May international human rights mechanisms close their doors to individuals who insult their members or Member States? Several do so, but the basis, scope, and impact of such rejections remain mostly unexamined. This article maps the relevant practices of regional and United Nations human rights bodies and compares them to other courts’ responses to contempt of court or vexatious litigation, to understand whether this admissibility criterion is a proper application of the prohibition on abuse of the right of petition or a legitimate exercise of a human rights body’s inherent powers. Three approaches emerge: ignore, balance, and punish. While the …

Overcoming Igf1r-Mediated Resistance To Oncolytic Hsv1 And Radiotherapy Via Triple Combination Therapy, Alexandra A Miller, Min-Hye Noh, Jin Muk Kang, Jiyeon Kim, Lily Nguyen, Amanda S Kouaho, Grace Nguyen, Minxin Huang, Stephanie M Bean, Joshua Davis, Matthew P Mullarkey, Sunil Krishnan, Zhongming Zhao, E Antonio Chiocca, Tae Jin Lee, Ji Young Yoo

The Brown Foundation: Institute of Molecular Medicine

FDA-approved oncolytic herpes simplex virus-1 (oHSV) therapy has emerged as a promising viro-immunotherapy for solid tumors. However, tumor- and tumor microenvironment (TME)-associated adaptations following viral treatment, such as feedback immune suppression, neoangiogenesis, and enhanced tumor aggressiveness, often hinder complete tumor eradication. A deeper understanding of the molecular mechanisms underlying resistance to oHSV is crucial to enhancing its clinical impact. We recently discovered that oHSV induces Insulin-like growth factor 2 (IGF2) secretion, shaping an immunosuppressive TME. Similarly, radiotherapy (RTx) activates the IGF1/IGF1R and YAP1 signaling pathways, further promoting therapeutic resistance. In this study, we investigated how oHSV-induced Insulin-like growth factor 1 …

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 …

Comparison Of Methods For Defatted Human Milk And Nutrient Composition: An Experimental Study, Kristin Cheng, Gina O'Toole, Stephanie Chang, Richard Chang, John Miklavcic

Food Science Faculty Articles and Research

Background

Human milk is considered the gold standard for infant nutrition; however, it is often discontinued in chylothorax and severe very long-chain acyl-CoA dehydrogenase (VLCAD) deficiency. As an alternative to complete human milk restriction, defatted human milk may be fed, though it may not fully support optimal infant growth and development. This study aimed to assess the micronutrient profile of defatted human milk.

Methods

Human milk was obtained from UCSD Human Milk Research Biorepository (San Diego, CA). Thirty samples representing 10 independent expressions in the morning, afternoon, and evening were pooled for analysis. Fat removal was performed by centrifugation at …

Bull’S-Eye On Borrelia: A Commensal And Consequential Pathogen, Alan L. Gillen

Faculty Publications and Presentations

If Lyme disease causes such urgent and chronic disease issues, where do Borrelia bacteria and ticks fit into a very good creation (Genesis 1)? How did bacteria and ticks change to rely on different hosts and blood for survival? And how are these adaptations informing today’s research in bacteriology, immunology, entomology, and disease ecology? The purposeful placement of Borrelia (Fig. 1) is most likely in the gut of wild mice (Fig. 2), not domesticated mice nor man. The bacteria are communalistic in wild mice, where they may be probiotic for mutual good (Fig. 2)—the Creator made it for good at …

Agent Of The Wild Heart, Allison Whittenberg

The Sucarnochee Review

No abstract provided.

Cover And Contents

Turkish Journal of Mathematics

No abstract provided.

Generalized Splines Over ℤ-Modules On Arbitrary Graphs, Gökçen Di̇laver, Selma Altinok

Turkish Journal of Mathematics

Let [[EQUATION]] be a commutative ring with identity and [[EQUATION]] a graph.  Fix an [[EQUATION]]-module [[EQUATION]] for each vertex [[EQUATION]] of [[EQUATION]], an extending generalized spline on [[EQUATION]] is a vertex labeling [[EQUATION]], where for each edge [[EQUATION]] there exists an [[EQUATION]]-module [[EQUATION]] together with homomorphisms [[EQUATION]] and  [[EQUATION]] such that [[EQUATION]]. Extending generalized splines are further generalizations for generalized splines. They can also be considered as generalized splines over modules.In this paper, we prove that some of the results for splines can be extended to extending generalized splines when [[EQUATION]] for each vertex [[EQUATION]], and we define a method …

On Construction Of Mannheim Curves With Myller Configuration, Zehra İşbi̇li̇r, Bahar Doğan Yazici, Murat Tosun

Turkish Journal of Mathematics

In this study, our aim is to strengthen the results of the existing literature on the concept of Mannheim curves by using the natural and idiosyncratic structure of Myller configuration. For this purpose, we examine Mannheim curves with Frenet-type frame in Myller configuration for Euclidean 3-space E₃ and Euclidean 4-space E₄. Since the classical Frenet frames in E₃ and E₄ are special cases of Frenet-type frames with Myller configuration in E₃ and E₄, and because of the special and natural structure of the Myller configuration, the Mannheim curves with Frenet frames in …