Cartilage matrix is a promising material for cartilage regeneration given the evidence supporting its chondroinductive character. The "raw materials" of cartilage matrix can serve as building blocks and signals for tissue regeneration. These matrices can be created by chemical or physical processing: physical methods disrupt cellular membranes and nuclei but may not fully remove all cell components and DNA, whereas chemical methods combined with physical methods are effective in fully decellularizing such materials. It is important to delineate between the sources of the cartilage matrix, that is, derived from matrix in vitro or from native tissue, and then to further characterize the cartilage matrix based on the processing method, decellularization or devitalization. With these distinctions, four types of cartilage matrices exist: decellularized native cartilage (DCC), devitalized native cartilage (DVC), decellularized cell-derived matrix (DCCM), and devitalized cell-derived matrix (DVCM). One currently marketed cartilage matrix device is decellularized, although trends in patents suggest additional decellularized products may be available in the future. To identify the most relevant source and processing for cartilage matrix, testing needs to include targeting the desired application, optimizing delivery of the material, identify relevant FDA regulations, assess availability of materials, and immunogenic properties of the product.

The Bioactivity of Cartilage Extracellular Matrix in Articular Cartilage Regeneration

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On Commutative Matrices

/pdf/28-zur-geschlechtertheorie-in-quadratischen-zahlkorpern-s9dtnnuy03.pdf

28. Zur Geschlechtertheorie in quadratischen Zahlkörpern

Let $F$ be a finite extension of $Bbb Q$‎, ‎${Bbb Q}_p$ or a global‎ ‎field of positive characteristic‎, ‎and let $E/F$ be a Galois extension‎. ‎We study the realization fields of‎ ‎finite subgroups $G$ of $GL_n(E)$ stable under the natural‎ ‎operation of the Galois group of $E/F$‎. ‎Though for sufficiently large $n$ and a fixed‎ ‎algebraic number field $F$ every its finite extension $E$ is‎ ‎realizable via adjoining to $F$ the entries of all‎ ‎matrices $gin G$ for some finite Galois stable subgroup $G$ of $GL_n(Bbb C)$‎, ‎there is only a‎ ‎finite number of possible realization field extensions of $F$ if $Gsubset GL_n(O_E)$ over the‎ ‎ring $O_E$ of integers of $E$‎. ‎After an exposition of earlier results we give their refinements‎ ‎for the‎ ‎realization fields $E/F$‎. ‎We consider some applications to quadratic lattices‎, ‎arithmetic algebraic geometry and Galois cohomology of related arithmetic groups‎.

https://journals.ui.ac.ir/article_2865_15eedcf8206252b2004de346b12153d2.pdf

On finite arithmetic groups

On unramified Galois extensions over maximum abelian extensions of algebraic number fields = 代数体の最大アーベル拡大体上の不分岐ガロア拡大体について

Given the ring of integers OK of an algebraic number field K, for which natural numbers n there exists a finite group G ⊂ GL(n, OK) such that OKG, the OK-span of G, coincides with M(n, OK), the ring of (n × n)-matrices over OK? The answer is known if n is an odd prime In this paper we study the case n = 2; in the cases when the answer is positive for n = 2, for n = 2m there is also a finite group G ⊂ GL(2m, OK) such that OKG = M(2m, OK)

Realizability of Two-dimensional Linear Groups over Rings of Integers of Algebraic Number Fields

On the existence of finite galois stable groups over integers in unramified extensions of number fields

Galois stability for integral representations of finite groups

We consider the arithmetic background of integral representations of finite groups over p-adic and algebraic number rings. Some infinite series of integral pairwise inequivalent absolutely irreducible representations of finite p-groups with the extra congruence conditions are constructed, and some applications are given. Certain problems concerning integral irreducible two-dimensional representations over number rings are discussed.

Dmitry Malinin

Papers

Realizability of Two-dimensional Linear Groups over Rings of Integers of Algebraic Number Fields

On the existence of finite galois stable groups over integers in unramified extensions of number fields

Galois stability for integral representations of finite groups

On finite arithmetic groups

On integral absolutely irreducible representations of finite groups