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A classification of semi-equivelar gems of PL d-manifolds on the surface with Euler characteristic -1
No full textA semi-equivelar gem of a PL -manifold is a regular colored graph that represents the PL -manifold and regularly embeds on a surface, with the property that the cyclic sequence of lengths of faces in the embedding around each vertex is identical.
In \cite{bb24}, the authors classified semi-equivelar gems of PL -manifolds embedded on surfaces with Euler characteristics greater than or equal to zero.
In this article, we focus on classifying semi-equivelar gems of PL -manifolds embedded on the surface with Euler characteristic .
We prove that if a semi-equivelar gem embeds regularly on the surface with Euler characteristic , then it belongs to one of the following types: ,
, , , , , ,
, , , and . Furthermore, we provide constructions that demonstrate the existence of such
gems for each of the aforementioned types
Characterizing Lipschitz images of injective metric spaces
No full textA metric space is {\em injective} if every non-expanding map defined on a subspace of a metric space can be extended to a non-expanding map .
We prove that a metric space is a Lipschitz image of an injective metric space if and only if is {\em Lipschitz connected} in the sense that for every points , there exists a Lipschitz map such that
and . In this case the metric space carries a well-defined intrinsic metric.
A metric space is a Lipschitz image of a compact injective metric space if and only if is compact, Lipschitz connected and its intrinsic metric is totally bounded.
A metric space is a Lipschitz image of a separable injective metric space if and only if is a Lipschitz image of the Urysohn universal metric space if and only
if is analytic, Lipschitz connected and its intrinsic metric is separable
Paweł Kaźmierczak (1970–2024) – badacz i nauczyciel akademicki (W pierwszą rocznicę śmierci)
Get PDFThis article is devoted to the research and teaching activities of Dr. habil. Paweł Kaźmierczak, Prof. UIK, who worked as a scholar at Ignatianum University in Krakow for 18 years. August 10, 2025 will mark the first anniversary of his death. He passed away due to illness at the height of his intellectual activity, having consistently carried out his planned work and developing further research projects until the very end. The purpose of this article is to show the Professor’s contributions in various fields. The first part outlines his academic career, drawing attention to the most important areas of his research, which led not only to successive academic degrees but, above all, to numerous books, articles, and translations—as indicated in the list of selected works provided at the end of the article. The second part of the article describes his work as an academic teacher at the present-day Ignatianum University in Krakow, with particular attention to the topics and objectives of his teaching. These resulted from his research interests and were correlated with his organizational role within the University structure. The authors present him as a respected colleague and collaborator, as well as a dedicated academic teacher who was valued and liked by students.Artykuł został poświęcony działalności naukowo-badawczej i dydaktycznej dr. hab. Pawła Kaźmierczaka, prof. UIK, przez 18 lat nauczyciela akademickiego Uniwersytetu Ignatianum w Krakowie. W dniu 10 sierpnia 2025 roku minie pierwsza rocznica jego śmierci. Odszedł w pełni sił twórczych, przegrywając z chorobą, do końca konsekwentnie realizując zaplanowane prace i planując kolejne projekty badawcze. Celem artykułu jest przedstawienie działalności Profesora w różnych wymiarach. W pierwszej części została ukazana jego droga naukowa uwzględniająca najważniejsze obszary poszukiwań badawczych, które zaowocowały kolejnymi stopniami naukowymi, ale przede wszystkim wieloma książkami, artykułami i tłumaczeniami, co dokumentuje przedstawiony na końcu tego artykułu wykaz jego najważniejszych prac. W części drugiej artykułu opisane zostały obszary jego działalności jako nauczyciela akademickiego Uniwersytetu Ignatianum w Krakowie, widoczne w tematyce i celach realizowanych zajęć dydaktycznych. Wynikały one zarówno z zainteresowań badawczych, jak i skorelowane były z przynależnością organizacyjną w strukturach Uczelni. Autorzy przybliżają jego postać jako cenionego kolegę i współpracownika oraz oddanego i lubianego przez studentów nauczyciela akademickiego
Memoriał dr. Emila Sommersteina i opinia prawna dr. Michała Szuldenfreia – krytyczna edycja źródeł o statusie prawnym ludności polskiej w ZSRR (1944 r.)
Get PDFThe article presents early concepts for regulating the citizenship of the Polish population in the USSR, primarily focusing on those who were victims of Soviet repressions between 1939 and 1941. Their authors were active members of the Union of Polish Patriots and of the administration of Poland staff subordinated to the Soviets (the Polish Committee of National Liberation, National Council). The study focuses on the two documents created in 1944 – during the period when the Kremlin issued important legal acts concerning the Polish population (decisions of the Presidium of the Supreme Soviet of the USSR on the restoration of Polish citizenship and amnesty), and when the Polish Committee of National Liberation concluded agreements on resettlement with the neighbouring Soviet republics.Celem artykułu jest przybliżenie wczesnych koncepcji właściwego uregulowania kwestii obywatelstwa ludności polskiej w ZSRR – w większości ofiar radzieckich represji z lat 1939–1941. Ich autorami były osoby działające w Związku Patriotów Polskich oraz zaangażowane w podporządkowaną Sowietom administrację Polski (Polski Komitet Wyzwolenia Narodowego, Krajowa Rada Narodowa). Omówione zostały dwa dokumenty powstałe w 1944 r. – w okresie wydawania przez Kreml istotnych aktów prawnych dotyczących ludności polskiej (decyzje Prezydium Rady Najwyższej ZSRR o odzyskiwaniu obywatelstwa polskiego oraz o amnestii), a także zawierania przez PKWN umów o przesiedleniach z ościennymi republikami radzieckimi
Penetration of heavy metals into breast milk and their impact on infant health - research analysis and literature review
Get PDFIntroduction and Purpose:Breast milk is considered the best food for infants due to its nutritional and protective properties. However, in the era of increasing environmental pollution, there is a problem of heavy metals penetrating breast milk, which may pose a threat to infants' health. The aim of the study was to review studies on the presence of heavy metals in mothers' milk, their sources, mechanisms of penetration, and the impact on infants' health.
Materials and Methods:
The work is based on a review of the scientific literature on the content of heavy metals in human milk and their impact on infant development. Publications from peer-reviewed scientific journals, reports from public health institutions and guidelines from organizations such as WHO, EFSA and FDA were used. Data on the levels of lead, mercury, cadmium and arsenic in human milk from different regions of the world were analyzed, taking into account environmental, dietary and lifestyle factors.
Results:Research results clearly indicate a significant impact of environmental factors and lifestyle on the content of heavy metals in breast milk, which emphasizes the need for preventive measures and educating women on how to minimize exposure to these substances.
Conclusion:The presence of heavy metals in breast milk poses a serious threat to the health of infants. Therefore, it is necessary to implement preventive measures, such as educating mothers about their diet and limiting their exposure to toxic substances. It is also important to conduct biomonitoring and develop effective strategies to reduce environmental pollution. The work emphasizes the importance of further research on the mechanisms of heavy metal transfer to breast milk and their long-term effects on infant health
Exploring the Role of Magnetotherapy, Laser Therapy, Electrotherapy, and Cryotherapy in Rheumatoid Arthritis Treatment: A Review
Get PDFRheumatoid arthritis (RA) is a chronic systemic autoimmune connective tissue disorder that leads to disability, impairment and premature mortality. As non-pharmacological approaches that do not interfere with existing treatments, magnetotherapy, laser therapy, electrotherapy and cryotherapy present promising supplemental options. Although they are employed in the treatment of RA patients,their mechanisms of action and advantages are not fully understood and remain an area of ongoing research.
Aim of the Study: This review explores the mechanisms of magnetotherapy, laser therapy, electrotherapy andcryotherapy and evaluates their effects on inflammation, oxidative stress, pain, and functional outcomes in RA, providing insights into their potential as a complementary treatment and identifying potential risks.
Materials and Methods: A review of research literature was conducted through databases such as PubMed, Google Scholar, ResearchGate, and the Cochrane Library
Results: The studied methods effectively reduced pain and disease activity in RA patients.
Conclusions: These methods can complement conventional treatments, but further research is needed to standardize protocols and assess risks
The importance of biochemical and ultrasound markers in prenatal diagnosis: current methods and development perspectives
Get PDFThis paper explores the role of biochemical and ultrasound markers in prenatal diagnosis, emphasizing their importance in early detection of chromosomal and structural abnormalities in the fetus. It aims to characterize the most relevant diagnostic markers, evaluate the sensitivity and specificity of current methods, and discuss modern advancements such as non-invasive prenatal testing (NIPT). Biochemical and ultrasound markers remain fundamental tools in prenatal screening, providing crucial information for risk stratification and early intervention. The integration of traditional methods with advanced technologies such as NIPT offers a comprehensive approach to fetal health assessment. Continuous refinement of diagnostic algorithms and broader access to non-invasive testing are key directions for future development, aiming to improve both prenatal care quality and patient safety
Current Perspectives on Anorexia Nervosa in Health and Therapy - a review
Get PDFIntroduction and purpose: Anorexia nervosa is a serious mental disorder characterized by persistent food restriction, intense fear of gaining weight, and distorted body image. Despite decades of research, anorexia remains challenging to diagnose and treat due to its complex psychological, social, and biological roots. This review aims to summarize current knowledge on anorexia nervosa, focusing on updated diagnostic criteria, risk factors, treatment strategies, and emerging trends in therapy and healthcare.
Material and method: A narrative literature review was conducted using publications from 2010 to 2024, sourced from databases such as PubMed, Scopus, and Web of Science. Inclusion criteria covered peer-reviewed articles on the epidemiology, diagnosis, treatment, and neurobiological or psychosocial aspects of anorexia nervosa. Studies were selected based on relevance, methodological quality, and applicability to adolescent and adult populations.
Results: The review highlights significant developments in understanding anorexia nervosa. Diagnostic updates in DSM-5 and ICD-11 have influenced prevalence estimates. Risk factors include genetic predisposition, personality traits, and sociocultural pressures. Contemporary treatments integrate psychotherapies (CBT-E, FBT, ACT), digital interventions, and pharmacotherapy. Barriers such as stigma, late diagnosis, and insufficient specialist care persist. Emerging research explores neurobiology, executive functioning, and circadian rhythms.
Conclusions: Anorexia nervosa is a multifactorial disorder requiring interdisciplinary approaches. Advances in diagnosis and treatment must be supported by greater public awareness, early intervention, and integration of educational and therapeutic strategies. Further research is needed to personalize care and improve long-term outcomes
The Gluten-free diet and oncological prevention – the importance of a conscious lifestyle for physically active people – A Literature Review
Get PDFIntroduction:Celiac disease is a chronic autoimmune disorder triggered by gluten ingestion in genetically predisposed individuals. If untreated, it leads to villous atrophy, chronic inflammation, and immune dysfunction. Studies show that active, untreated celiac disease increases cancer risk, particularly for lymphomas and gastrointestinal malignancies. The only effective treatment is a gluten-free diet. Recent research also suggests that regular physical activity may help modulate inflammation and boost immunity, potentially lowering cancer risk in autoimmune conditions like celiac disease. Aim of the Study: This review examines whether celiac patients are more prone to cancer and how a gluten-free diet modifies this risk. It focuses on cancers commonly linked to celiac disease—lymphomas, small intestine, esophageal, and hormone-related cancers—based on epidemiological, clinical, and pathophysiological studies. Materials and Methods: This review analyzes recent scientific literature, including cohort studies and meta-analyses, on the link between celiac disease and cancer. Increased risks are most evident for enteropathy-associated T-cell lymphoma, small intestine adenocarcinoma, and esophageal squamous cell carcinoma. Risk factors include chronic mucosal inflammation and immune dysregulation, especially before diagnosis or in those not adhering to dietary guidelines. Conclusions:A gluten-free diet is crucial for symptom control and cancer prevention, promoting mucosal healing and immune normalization. Long-term adherence significantly lowers cancer risk, often to general population levels. While data on stomach and colon cancer remain mixed, no elevated risk is seen in compliant patients. Interestingly, hormone-related cancers (e.g., breast, ovarian) may be less common, possibly due to altered hormone levels. Importantly, regular physical activity offers added protection by reducing inflammation and improving immune function
Platelet-rich plasma in the treatment of osteoarthritis – a systematic review
Get PDFIntroduction: Platelet-rich plasma (PRP) is an autologous preparation gaining popularity in regenerative medicine. It is prepared from a patient's blood by centrifugation, which results in a much higher concentration of platelets than in a standard sample. The rich content of growth factors and signaling molecules provides proliferative and regenerative effects on other cells. These properties are generating considerable interest in plasma for the treatment of degenerative diseases.
Purpose: This systematic review analyzes the evidence from different studies evaluating the validity of platelet-rich plasma in the treatment of degenerative diseases.
Materials and Methods: The article was written based on scientific papers available on PubMed and Google Scholar.
Results: Platelet-rich plasma has demonstrated beneficial effects on joint health in patients with osteoarthritis (OA). Most studies report pain reduction and improved joint function following PRP treatment. When combined with other agents, such as hyaluronic acid, PRP may have synergistic effects. The most favorable outcomes are observed in younger patients with early-stage OA.
Conclusions: PRP injections may represent a significant component of osteoarthritis (OA) treatment. However, this approach requires standardization in terms of preparation methods, concentration of individual components, as well as the volume and frequency of administration.
Keywords: osteoarthritis, platelet-rich plasma, cartilage, intra-articular treatment, hyaluronic acid, LP-PRP, LR-PR