Verallgemeinerungen der Wielandt-Untergruppe

The Wielandt subgroup and the Norm of a group are group theoretic concepts which have been introduced as generalisations of the center of a group. The first aim of this Thesis is to generalise Wielandt's idea further. For this we first investigate the structural properties of the existing generalisation introduced in my MPhil Thesis. Given a group G this generalisation is a subgroup defined relative to a normal subgroup in G. We investigate the structural behaviour of the generalised Wielandt subgroup and its generalised Wielandt length. We also correct a mistake in my MPhil Thesis. We introduce a new generalisation of the Wielandt subgroup which we call the "relative Wielandt subgroup". It is noted that the relative Wielandt subgroup satisfies some properties which do not hold in case of the ordinary Wielandt subgroup and an example is given which shows that the relative Wielandt subgroup is non-trivial in a wider class of groups than the Wielandt subgroup. Further, we developed algorithms to compute the Norm of a finite or a polycyclic group. We also introduced methods to determine the ordinary, generalised or relative Wielandt subgroup of a finite group. By using these algorithms and the available classification of groups of order dividing p^6, we classify the groups of order dividing p^4 (up to isomorphism) with maximal Wielandt subgroup for all primes and those of order dividing p^6 for a variety of primes.Die Wielandt-Untergruppe und die Norm einer Gruppe sind gruppentheoretische Konzepte, die als Verallgemeinerungen des Zentrums einer Gruppe eingeführt wurden. Das erste Ziel dieser Arbeit ist es die Ideen von Wielandt weiter zu verallgemeinern. Zu diesem Zweck untersuchen wir die strukturellen Eigenschaften der bereits in meiner MPhil-Arbeit eingeführten Verallgemeinerung. Zu einer gegebenen Gruppe G wird diese Verallgemeinerung relativ zu einem Normalteiler in G definiert. Wir untersuchen die strukturellen Eigenschaften dieser verallgemeinerten Wielandt-Untergruppe und die Länge der verallgemeinerten Wielandt-Reihe. Außerdem verbessern wir einen Fehler in der MPhil-Arbeit. Wir führen eine neue Verallgemeinerung der Wielandt-Untergruppe ein, die wir "relative Wielandt-Untergruppe" nennen. Wir bemerken, dass diese relative Wielandt-Untergruppe einige Eigenschaften hat, die für die gewöhnliche Wielandt-Untergruppe nicht gelten. Zusätzlich geben wir ein Beispiel, welches zeigt, dass die relative Wielandt-Untergruppe in einer größeren Klasse von Gruppen nichttrivial ist als w(G). Weiterhin haben wir Algorithmen entwickelt, um die Norm einer endlichen oder polyzyklischen Gruppe G zu berechnen. Wir haben außerdem Methoden entwickelt, um die gewöhnliche, die verallgemeinerte und die relative Wielandt-Untergruppe für eine endliche Gruppe G zu bestimmen. Unter Verwendung dieser Algorithmen und der Klassifikation der Gruppen, deren Ordnung p^6 teilt, klassifizieren wir (bis auf Isomorphie) für alle Primzahlen, die Gruppen mit maximaler Wielandt-Untergruppe, deren Ordnung p^4 teilt. Für die Gruppen, deren Ordnung p^6 teilt, klassifizieren wir diese Gruppen für einige Primzahlen

Satisfaction on Online Learning during Covid-19 Pandemic: Perspective of Malaysian students

This study investigated the determinants of students’ satisfaction with their online learning experience during the COVID-19 pandemic. The data was collected among 241 undergraduates enrolled in information management from a selected universities in Malaysia. The Structural Equation Modelling (SEM) results revealed that the independent variables, namely course design and digital resources, influenced students’ satisfaction with their new online learning experience. The findings have several implications for developing and maintaining practical and student-friendly online learning spaces in higher education. Keywords: Online learning; digital resources; Malaysian students; Higher education eISSN: 2398-4287 © 2022. The Authors. Published for AMER ABRA cE-Bs by E-International Publishing House, Ltd., UK. This is an open-access article under the CC  BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of AMER (Association of Malaysian Environment-Behavior Researchers), ABRA (Association of Behavioral Researchers on Asians), and cE-Bs (Centre for Environment-Behavior Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia

Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator and Its Application to Decision Making

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach

Isolation and preliminary evaluation of Mulva Neglecta mucilage: a novel tablet binder

O objetivo deste estudo foi avaliar o potencial de ligação de mucilagem de Mulva neglecta (MNM), com posterior comparação ao PVP K30. Oito lotes de comprimidos de diclofenaco de sódio foram preparados pela técnica de granulação úmida, mantendo diferentes concentrações (4, 6, 8 e 10% w/w) de mucilagem de Mulva neglecta (extraída de folhas de Mulva neglecta) e PVP K30 como ligante padrão. Os grânulos de lotes formulados mostraram densidade aparente (g/mL) 0.49 ± 0.00-0.57 ± 0.00, densidade compactada (g/mL) 0.59 ± 0.01-0.70 ± 0.01, índice de Carr 09.27 ± 0.95-19.65 ± 0.59, a relação de Hausner 1.12 ± 0.00-1.24 ± 0.01 e ângulo de repouso 30.37 ± 2.90 °C a 36.86 ± 0.94 °C. Os comprimidos foram prensados à dureza de 7.50-7.95 kg/cm2. Os comprimidos apresentaram 0.39 ± 0.02-0.39 ± 0.01% friabilidade e 7:20-14:00 min de tempo de desintegração. A avaliação de grânulos e pós-compressão revelou que todos os parâmetros estavam dentro dos limites da farmacopeia. Os resultados (dureza, desintegração e dissolução) provaram que a mucilagem de Mulva neglecta tem maior capacidade de ligação na preparação da forma de dosagem de comprimido não revestido em relação à PVP K30. Entre todas as formulações, MN-1 e MN-4 mostraram liberação lenta em comparação com PV-1 e PV-4 e, assim, a mucilagem de Mulva neglecta exibiu liberação do fármaco satisfatória para os comprimidos de diclofenaco de sódio.The aim of this study was to evaluate binding potential of Mulva neglecta mucilage (MNM) with subsequent comparison to PVP K30. Eight batches of Diclofenac sodium tablets were prepared by wet granulation technique keeping different concentrations (4, 6, 8 & 10% w/w) of Mulva neglecta mucilage (extracted from leaves of Mulva neglecta) and PVP K30 as standard binder. The granules of formulated batches showed bulk density (g/mL) 0.49 ± 0.00 to 0.57 ± 0.00, tapped density (g/mL) 0.59 ± 0.01 to 0.70 ± 0.01, Carr's index 09.27 ± 0.95 to 19.65 ± 0.59, Hausner's ratio 1.12 ± 0.00 to 1.24 ± 0.01 and angle of repose 30.37 ± 2.90 °C to 36.86 ± 0.94 °C. Tablets were compressed to hardness 7.50 to 7.95 kg/cm2. The tablets showed 0.39 ± 0.02 to 0.39 ± 0.01% friability and 7:20 to 14:00 min disintegration time. Granules and post-compression evaluation revealed that parameters assessed were all found to be within the pharmacopoeial limits. The results (hardness, disintegration and dissolution) proved that Mulva neglecta mucilage has better binding capacity for preparation of uncoated tablet dosage form as compared to PVP K30. Among all the formulations, MN-1 to MN-4 showed slow release as compared to PV-1 to PV-4 and thereby Mulva neglecta mucilage exhibited satisfactory drug release phenomenon tablets of diclofenac sodium

BINARY SOFT PRE-SEPARATION AXIOMS IN BINARY SOFT TOPOLOGICAL SPACES

In this article, we introduce binary soft pre-separation axioms in binary soft Topological space along with several properties of binary soft pre τ△i , i = 0; 1; 2, binary soft pre-regular, binary soft pre τ△3 , binary soft pre-normal and binary soft τ△4 axioms using binary soft points. We also mention some binary soft invariance properties namely binary soft topological property and binary soft hereditary property. We hope that these results will be useful for the future study on binary soft topology to carry out general background for the practical applications and to solve the thorny problems containing doubts in different grounds

Multiple attribute decision-making based on Fermatean fuzzy number

Multiple attribute decision-making concerns with production significant in our everyday life. To resolve the problems that decision makers might feel uncertain to choose the suitable assessment values among several conceivable ideals in the procedure. Fuzzy model, and its extensions are extensively applied to MADM problems. In this study, we proposed an innovative Schweizer-Sklar t-norm and t-conorm operation of FFNs, Fermatean fuzzy Schweizer-Sklar operators. They were used as a framework for the development of an MCDM method, which was illustrated by an example to demonstrate its effectiveness and applicability. Finally, a complete limitation study, rational examination, and comparative analysis of the presented approaches has been exhibited, we originate that our technique is superior in offering DMs a better decision-making choice and reducing the restrictions on stating individual partialities

In vitro evaluation of scavenging and anti-adipogenic activity of Momordica cochinchinensis (Lour). Spreng fruit extracts on 3T3-L1 adipocytes

Gac fruit, scientifically known as Momordica cochinchinensis (Lour) Spreng, is rich in potent bioactive compounds, particularly carotenoids such as β-carotene, lycopene, and lutein. This study investigated the effects of gac fruit extract fractions (peel, pulp, and aril) on the scavenging, cytotoxic, and anti-adipogenic activities in 3T3-L1 adipocytes. The study assessed the DPPH radical scavenging activity of gac extracts through serial dilution at a concentration of 1000 μg/mL. The viability of 3T3-L1 preadipocytes was measured using the MTT assay. Differentiated adipocytes were treated with gac extracts at concentrations of 75, 150, and 300 μg/mL for 7 days. The impact on lipid accumulation and adipogenesis inhibition was determined through Oil Red O staining and triglyceride content analysis. The IC50 values for DPPH radical scavenging were 573.40 μg/mL for peel, 525.46 μg/mL for pulp, and 817.33 μg/mL for aril extracts. No toxicity was observed in 3T3-L1 cells at concentrations up to 200 μg/mL. At 200 μg/mL, gac extracts reduced 3T3-L1 cell viability while promoting growth and proliferation. Treatment with gac extracts significantly reduced lipid accumulation and inhibited 3T3-L1 cell differentiation in a dose-dependent manner. Among the gac extract fractions, pulp notably decreased intracellular triglyceride content in adipocytes, surpassing aril and peel extracts. In conclusion, gac fruit extract fractions (peel, pulp, and aril) effectively inhibited adipogenesis in 3T3-L1 adipocytes, as evidenced by reduced lipid accumulation, triglyceride content, and cell viability. These findings unveil valuable insights into bioactive compounds from Momordica cochinchinensis and their potential for addressing obesity prevention and treatment

Antioxidant and Anti-Adipogenic Activities of Momordica cochinchinensis (Lour). Spreng Fruit Extracts

Momordica cochinchinensis (Lour) Spreng, known as gac fruit, is rich in bioactive compounds like carotenoids (β-carotene, lycopene, and lutein). This study assessed the antioxidant, cytotoxic, and anti-adipogenic properties of gac fruit extracts (GFE) from different fractions (peel, pulp, aril), using 3T3-L1 adipocytes. Method: Gac extracts’ DPPH radical scavenging was tested with 1000µg/mL dilutions. 3T3-L1 pre-adipocyte viability was measured via MTT assay. Differentiated adipocytes were treated (75, 150, 300 µg/mL) with GFE for 7 days. Inhibitory effects on adipogenesis and lipid accumulation were studied through Oil Red O staining. Triglyceride content was quantified and compared to controls. Results: IC50 values against DPPH radicals were 660µg/mL (peel), 560µg/ mL (pulp), and 820µg/mL (aril). 3T3-L1 cell viability was unaffected up to 200µg/mL. However, 200µg/mL GFE decreased viability, inhibiting growth. Gac extracts effectively reduced lipid accumulation and hindered cell differentiation dose-dependently. Pulp extract notably reduced intracellular triglycerides, surpassing aril and peel effects. Conclusion: Gac fruit extract fractions (peel, pulp, and aril) efficiently inhibited adipogenesis in 3T3-L1 cells, evidenced by lowered lipid accumulation, triglyceride content, and cell viability. This study highlights gac fruit extracts’ potential therapeutic use against obesity

Proximate composition, sugar profiles, minerals and carotenoids content and antioxidant capacity of momordica cochinchinensis L. Spreng or Gac (Vietnam) or Teruah (Malaysia) fruit fractions (peel, pulp, and aril)

The proximates, sugar profiles, minerals, carotenoids, and antioxidant capacity of Momordica cochinchinensis L. Spreng or Gac (Vietnam) or Teruah (Malaysia) fruits fractions (peel, pulp, and aril); were evaluated. Results showed Gac aril to contain the significant highest carbohydrate (55.6g/100g); compared to the pulp (30.9g/100g) and peel (19.3g/100g). Meanwhile, Gac peel contained the highest protein (6.2g/100g) and dietary fibre (56.9g to 58.1g/100g). Glucose and fructose are present in Gac fruit. Glucose was the main type of sugar in both Gac pulp and aril, with a significant value of 6.66 g/100 g and 7.55 g/100 g, respectively. Meanwhile, fructose also detected in Gac pulp and aril amounted to 5.84 g/100 g and 6.45 g/100 g, respectively. Potassium was the most abundant mineral in the Gac peel (817.59 mg/100g), followed by pulp (658.20 mg/100g) and aril (228.79 mg/100g). Lycopene was the main carotenoid found in Gac aril (31.7 – 103.7 mg/g) followed by β-carotene (2.9 – 9.6 mg/g); astaxanthin, (1.54 – 4.91 mg/g); lutein, (0.16 – 1.35 mg/g) and zeaxanthin (0.35 – 1.49 mg/g) in the pulp. Antioxidant activities of Gac were found between 22.61% – 58.76%, 37.63% – 41.64% and 2.46% –19.66% in the gac peel, pulp, and aril, respectively, using the DPPH assay. In conclusion, Gac pulp and aril contained good sources of carbohydrates, minerals, lycopene, and β-carotene