Results 111 to 120 of about 321,441 (313)
THE THEOREM FOR ORDERED GROUPS
, 2017 Recently, Freiman et al. [‘Small doubling in ordered groups’, J. Aust. Math. Soc. 96(3) (2014), 316–325] proved two ‘structure theorems’ for ordered groups. We give elementary proofs of these two theorems.
PREM PRAKASH PANDEY
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Molecular Oncology, EarlyView.Tumors contain diverse cellular states whose behavior is shaped by context‐dependent gene coordination. By comparing gene–gene relationships across biological contexts, we identify adaptive transcriptional modules that reorganize into distinct vulnerability axes.
Brian Nelson +9 more
wiley +1 more source
, 1982 As a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study ...
A. M. W. Glass
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PALINDROMES AND ORDERINGS IN ARTIN GROUPS [PDF]
Journal of Knot Theory and Its Ramifications, 2010 The braid group Bn, endowed with Artin's presentation, admits two distinguished involutions. One is the anti-automorphism rev : Bn→Bn, [Formula: see text], defined by reading braids in the reverse order (from right to left instead of left to right).
openaire +4 more sources
Somatic mutational landscape in von Hippel–Lindau familial hemangioblastoma
Molecular Oncology, EarlyView.The causes of central nervous system (CNS) hemangioblastoma in Von Hippel–Lindau (vHL) disease are unclear. We used Whole Exome Sequencing (WES) on familial hemangioblastoma to investigate events that underlie tumor development. Our findings suggest that VHL loss creates a permissive environment for tumor formation, while additional alterations ...
Maja Dembic +5 more
wiley +1 more source
Wreath Products of Nonoverlapping Lattice Ordered Groups
, 1975 One of the fundamental tools in the theory of totally ordered groups is Hahn’s Theorem (a detailed discussion may be found in Fuchs [3]), which asserts, roughly, that every abelian totally ordered group can be embedded in a lexicographically ordered ...
John A. Read
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Molecular Oncology, EarlyView.We have established a humanized orthotopic patient‐derived xenograft (Hu‐oPDX) mouse model of high‐grade serous ovarian cancer (HGSOC) that recapitulates human tumor–immune interactions. Using combined anti‐PD‐L1/anti‐CD73 immunotherapy, we demonstrate the model's improved biological relevance and enhanced translational value for preclinical ...
Luka Tandaric +10 more
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The structure of transitive ordered permutation groups [PDF]
, 1999 summary:We give some necessary and sufficient conditions for transitive $l$-permutation groups to be $2$-transitive. We also discuss primitive components and give necessary and sufficient conditions for transitive $l$-permutation groups to be normal ...
Zhenyu, Huang, Zhu, Zuo-Tong,
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c-regular cyclically ordered groups
, 2013 20 pagesWe define and we characterize regular and c-regular cyclically ordered abelian groups. We prove that every dense c-regular cyclically ordered abelian group is elementarily equivalent to some cyclically ordered group of unimodular complex numbers,
Lucas, Francois, Leloup, Gérard
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Enumeration and Representation Theory of Spin Space Groups
Physical Review XFundamental physical properties, such as phase transitions, electronic structures, and spin excitations, in all magnetic ordered materials, were ultimately believed to rely on the symmetry theory of magnetic space groups.
Xiaobing Chen +9 more
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