ON s-CRITICAL GROUPS

Bryant, R. M.

doi:10.1093/qmath/22.1.91

Cited by 8 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…52 In addition, the positively charged molecules may facilitate cell differentiation by electrostatically binding cell membrane and negatively charged GAGs. 53,54 In fact, it has been observed that increasing CTS content within dense Coll gels has a stimulatory effect towards the chondrocytic lineage, revealing that CTS plays an important role in stimulating ECM production. 27 Moreover, this in vitro model may also be used as a simple tool to measure the interaction of connective tissue GAGs with collagen, as well as with cell surfaces through a receptor-like mechanism.…”

Section: Discussionmentioning

confidence: 99%

Effect of chitosan incorporation on the consolidation process of highly hydrated collagen hydrogel scaffolds

et al. 2013

View full text Add to dashboard Cite

Collagenous body tissues exhibit diverse physicochemical and biomechanical properties depending upon their compositions (e.g. proteins, polysaccharides, minerals and water). These factors influence cell function and can contribute to tissue dysfunction and disease when they are either deficient or present in excess.Similarly, the constituents of tissue engineering hydrogel scaffolds must be carefully considered for the optimal design of engineered constructs for therapeutic applications. As a natural polysaccharide glycosaminoglycan-analog, chitosan (CTS) holds potential for generating highly hydrated collagen type I hydrogel (Coll) based scaffolds that mimic the native extracellular matrix. Analysis of fluid loss in Coll-CTS hydrogels undergoing either a gravity-driven consolidation process (self-compression; SC) or plasticcompression (PC) offers the potential for the controlled production of tissue-equivalent dense hydrogels with tailored physical and mechanical properties. Herein, the effect of CTS on Coll gels microstructural evolution involved in SC and PC was investigated by detecting the spatiotemporal distribution of fluorescent beads within Coll-CTS hydrogels using confocal microscopy. The hydraulic permeability (k), pre-and post-consolidation, as a function of CTS content, was estimated by the Happel model. The effect of CTS fixed charge on dense Coll-CTS hydrogels was investigated through structural, mechanical and swelling characterizations under isotonic and hypertonic conditions. Image analysis revealed a temporal increase in bead density, with both rate and extent of consolidation, correlating strongly with increasing CTS content. k decreased from 1.4 Â 10 À12 to 1.8 Â 10 À13 m 2 and from 2.9 Â 10 À14 to 6.8 Â 10 À15 m 2 for highly hydrated and dense hydrogels, respectively, with higher amount of CTS, resulting in a concomitant increase in the scaffold compressive modulus (from 7.65 to 14.89 kPa). In summary, understanding the effect of CTS on Coll hydrogel properties enables the development of tailored scaffolds for use as tissue models for various biomedical applications.

show abstract

Section: Discussionmentioning

confidence: 99%

Effect of chitosan incorporation on the consolidation process of highly hydrated collagen hydrogel scaffolds

et al. 2013

View full text Add to dashboard Cite

show abstract

“…Let P x , P 2 ,...,P, be the projective covers of X x , X 2 ,...,X t in varX. Since {P} is the s-critical basis for var ^([2; page 172, paragraph 2]) it follows from Theorem 3.3 of [1] that every X t is a homomorphic image of P. Since P is projective, therefore, Pj is also a homomorphic image of P. But since an s-critical refinement of {P x , P 2 ,...,P,} is also the s-critical basis for varX([2; loc. cit.])…”

Section: X T ) (B)mentioning

confidence: 99%

“…Then a and a" 1 are not conjugate in K. For if a k = a" 1 for some k E K we should have that k 2 centralizes a, then that k centralizes a since k has odd order, whence a = a~l or a 2 = 1, and finally a = 1. It follows that the conjugacy classes [a] of A, other than that consisting of the identity element alone, may be paired off Consequently, representatives of the conjugacy classes other than [1] may be chosen in the form a,, af 1 But ^ has odd multiplicative order so 6 is also an isometry. This completes the induction and the proof of (4.9).…”

Section: {B) Since (K) < B [A/a'k] = A/a' By (21)(d) It Follows mentioning

confidence: 99%

See 1 more Smart Citation

On certain varieties of groups which are central extensions

Bryce

1984

J Aust Math Soc A

View full text Add to dashboard Cite

show abstract

“…His construction of equations works the same way for A or B when V = var (A) = var (B), so the result follows. Using properties of the Frattini subgroup, Bryant gave an affirmative answer to Neumann's question for arbitrary finite groups in [1]. The same question for other types of algebras is considered in the papers [9,7,10] and [5].…”

Section: Introductionmentioning

confidence: 99%