scholarly journals Fuzzy cosets in AG-groups

2021 ◽  
Vol 7 (3) ◽  
pp. 3321-3344
Author(s):  
Aman Ullah ◽  
◽  
Muhammad Ibrahim ◽  
Tareq Saeed ◽  
◽  
...  
Keyword(s):  
Group Theory ◽  
Index Number ◽  
Left Coset ◽  
Lagrange's Theorem

<abstract><p>In this paper, the notion of fuzzy AG-subgroups is further extended to introduce fuzzy cosets in AG-groups. It is worth mentioning that if $ A $ is any fuzzy AG-subgroup of $ G $, then $ \mu_{A}(xy) = \mu_{A}(yx) $ for all $ x, \, y\in G $, i.e. in AG-groups each fuzzy left coset is a fuzzy right coset and vice versa. Also, fuzzy coset in AG-groups could be empty contrary to fuzzy coset in group theory. However, the order of the nonempty fuzzy coset is the same as the index number $ [G:A] $. Moreover, the notions of fuzzy quotient AG-subgroup, fuzzy AG-subgroup of the quotient (factor) AG-subgroup, fuzzy homomorphism of AG-group and fuzzy Lagrange's theorem of finite AG-group is also introduced.</p></abstract>

Group Theory

2009 ◽  
Author(s):  
Pierre Ramond
Keyword(s):  
Group Theory

High Antibody Levels to Prothrombin Imply a Risk of Deep Venous Thrombosis and Pulmonary Embolism in Middle-aged Men

1997 ◽  
Vol 78 (04) ◽  
pp. 1178-1182 ◽  
Author(s):  
Timo Palosuo ◽  
Jarmo Virtamo ◽  
Jari Haukka ◽  
Philip R Taylor ◽  
Kimmo Aho ◽  
...  
Keyword(s):  
Pulmonary Embolism ◽  
Venous Thrombosis ◽  
Deep Venous Thrombosis ◽  
Plasma Proteins ◽  
Alpha Tocopherol ◽  
Index Number ◽  
Thromboembolic Events ◽  
Middle Aged ◽  
Phospholipid Binding ◽  
Antiprothrombin Antibodies

SummaryAntibodies against phospholipid-binding plasma proteins, such as β2-glycoprotein I (β2-GPI) and prothrombin, are associated with thromboembolic events in patients with systemic lupus erythematosus and also in subjects with no evident underlying diseases. We wanted to examine whether increased levels of antibodies to negatively-charged phospholipids (cardiolipin), to phospholipid-binding plasma proteins β2-GPI and prothrombin and to oxidised low-density lipoprotein (LDL) were associated with risk of deep venous thrombosis or pulmonary embolism in subjects with no previous thrombosis. The antibodies were measured in stored serum samples from 265 cases of deep venous thrombosis of the lower extremity or pulmonary embolism occurring during a median follow-up of about 7 years and from 265 individually matched controls. The study subjects were middle-aged men participating in a cancer prevention trial of alpha-tocopherol and beta-carotene and the cases of thromboembolic events were identified from nationwide Hospital Discharge Register.The risk for thrombotic events was significantly increased only in relation to antiprothrombin antibodies. As adjusted for body mass index, number of daily cigarettes and history of chronic bronchitis, myocardial infarction and heart failure at baseline, the odds ratio per one unit of antibody was 6.56 (95% confidence interval 1.73-25.0). The seven highest individual optical density-unit values of antiprothrombin antibodies were all confined to subjects with thromboembolic episodes.In conclusion, the present nested case-control study showed that high autoantibody levels against prothrombin implied a risk of deep venous thrombosis and pulmonary embolism and could be involved in the development of the thrombotic processes.

Group Theory for Chemists

2011 ◽  
Author(s):  
Kieran C. Molloy
Keyword(s):  
Group Theory
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