61 research outputs found
Strong conciseness in profinite groups
A group word w is said to be strongly concise in a class C of profinite groups if, for every group G in C such that w takes less than continum many values in G, the verbal subgroup w(G) is finite. Detomi, Morigi and Shumyatsky established that multilinear commutator words have the property that the corresponding verbal subgroup is finite in a profinite group G whenever the word takes at most countably many values in G. They conjectured that, in fact, this should be true for every word. In particular, their conjecture included as open cases power words and Engel words. In the present paper, we take a new approach via parametrised words that leads to stronger results. First we prove that multilinear commutator words are strongly concise in the class of all profinite groups. Then we establish that every group word is strongly concise in the class of nilpotent profinite groups. From this we deduce, for instance, that, if w is one of the group words x^2, x^3, x^6, [x^3,y] or [x,y,y], then w is strongly concise in the class of all profinite groups
ΠΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΡ ΡΠ°Π±ΠΎΡ ΠΏΠΎ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ Π°Π²Π°ΡΠΈΠΉΠ½ΠΎΠ³ΠΎ ΡΠ°Π·Π»ΠΈΠ²Π° Π½Π΅ΡΡΠΈ ΠΈ Π½Π΅ΡΡΠ΅ΠΏΡΠΎΠ΄ΡΠΊΡΠΎΠ² Π½Π° Π²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ Π½ΠΎΡΡΠΈ
ΠΠ±ΡΠ΅ΠΊΡΠΎΠΌ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π»ΡΡΡΡΡ ΠΌΠ΅ΡΠΎΠ΄Ρ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²ΠΎΠ² Π½Π΅ΡΡΠΈ Π½Π° Π²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ. Π¦Π΅Π»Ρ ΡΠ°Π±ΠΎΡΡ β ΠΏΡΠΎΠ²Π΅ΡΡΠΈ Π°Π½Π°Π»ΠΈΠ· ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠΈΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΈ ΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠ΅ΡΠΎΠΏΡΠΈΡΡΠΈΠΉ ΠΏΠΎ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²ΠΎΠ² Π½Π΅ΡΡΠΈ Π½Π° Π²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ.
Π ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΠ»ΡΡ Π°Π½Π°Π»ΠΈΠ· ΠΈΠΌΠ΅ΡΡΠΈΡ
ΡΡ Π΄Π°Π½Π½ΡΡ
, Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠΎΡΠΎΡΡΡ
Π±ΡΠ»ΠΈ Π²ΡΠ΄Π΅Π»Π΅Π½ΠΈΠ΅ Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²ΠΎΠ² Π½Π΅ΡΡΠΈ Π½Π° Π²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ ΡΠ°ΡΡΠ΅Ρ ΠΎΠ±ΡΠ΅ΠΌΠ° Π²ΡΡΠ΅ΠΊΡΠ΅ΠΉ Π½Π΅ΡΡΠΈ ΠΈ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΡΠΎΡΠ±Π΅Π½ΡΠ°, ΡΡΠ΅Π±ΡΠ΅ΠΌΠΎΠ³ΠΎ Π΄Π»Ρ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²Π°. Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π±ΡΠ»ΠΎ Π²ΡΡΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠΌ ΡΠΏΠΎΡΠΎΠ±ΠΎΠΌ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²ΠΎΠ² Π½Π° Π²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ ΡΠ²Π»ΡΡΡΡΡ Π±ΠΎΠ½Ρ Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠΌΠΈ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ°ΠΌΠΈ ΠΈΡ
ΡΡΡΠ°Π½ΠΎΠ²ΠΊΠΈ, Π° Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠΌΠΈ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ β ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠΊΠΈΠΌΠΌΠ΅ΡΠΎΠ² ΠΈ ΡΠΎΡΠ±Π΅Π½ΡΠΎΠ².ΠΠ±ΡΠ΅ΠΊΡΠΎΠΌ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π»ΡΡΡΡΡ ΠΌΠ΅ΡΠΎΠ΄Ρ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²ΠΎΠ² Π½Π΅ΡΡΠΈ Π½Π° Π²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ. Π¦Π΅Π»Ρ ΡΠ°Π±ΠΎΡΡ β ΠΏΡΠΎΠ²Π΅ΡΡΠΈ Π°Π½Π°Π»ΠΈΠ· ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠΈΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΈ ΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠ΅ΡΠΎΠΏΡΠΈΡΡΠΈΠΉ ΠΏΠΎ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²ΠΎΠ² Π½Π΅ΡΡΠΈ Π½Π° Π²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ.
Π ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΈΠ»ΡΡ Π°Π½Π°Π»ΠΈΠ· ΠΈΠΌΠ΅ΡΡΠΈΡ
ΡΡ Π΄Π°Π½Π½ΡΡ
, Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠΎΡΠΎΡΡΡ
Π±ΡΠ»ΠΈ Π²ΡΠ΄Π΅Π»Π΅Π½ΠΈΠ΅ Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΈ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²ΠΎΠ² Π½Π΅ΡΡΠΈ Π½Π° Π²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½ ΡΠ°ΡΡΠ΅Ρ ΠΎΠ±ΡΠ΅ΠΌΠ° Π²ΡΡΠ΅ΠΊΡΠ΅ΠΉ Π½Π΅ΡΡΠΈ ΠΈ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° ΡΠΎΡΠ±Π΅Π½ΡΠ°, ΡΡΠ΅Π±ΡΠ΅ΠΌΠΎΠ³ΠΎ Π΄Π»Ρ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²Π°. Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π±ΡΠ»ΠΎ Π²ΡΡΠ²Π»Π΅Π½ΠΎ, ΡΡΠΎ Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠΌ ΡΠΏΠΎΡΠΎΠ±ΠΎΠΌ Π»ΠΎΠΊΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΡΠ°Π·Π»ΠΈΠ²ΠΎΠ² Π½Π° Π²ΠΎΠ΄Π½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ ΡΠ²Π»ΡΡΡΡΡ Π±ΠΎΠ½Ρ Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠΌΠΈ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ°ΠΌΠΈ ΠΈΡ
ΡΡΡΠ°Π½ΠΎΠ²ΠΊΠΈ, Π° Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΡΠΌΠΈ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌΠΈ Π»ΠΈΠΊΠ²ΠΈΠ΄Π°ΡΠΈΠΈ β ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠΊΠΈΠΌΠΌΠ΅ΡΠΎΠ² ΠΈ ΡΠΎΡΠ±Π΅Π½ΡΠΎΠ²
Local erythropoietin and endothelial progenitor cells improve regional cardiac function in acute myocardial infarction
<p>Abstract</p> <p>Background</p> <p>Expanded endothelial progenitor cells (eEPC) improve global left ventricular function in experimental myocardial infarction (MI). Erythropoietin beta (EPO) applied together with eEPC may improve regional myocardial function even further by anti-apoptotic and cardioprotective effects. Aim of this study was to evaluate intramyocardial application of eEPCs and EPO as compared to eEPCs or EPO alone in experimental MI.</p> <p>Methods and Results</p> <p>In vitro experiments revealed that EPO dosed-dependently decreased eEPC and leukocyte apoptosis. Moreover, in the presence of EPO mRNA expression in eEPC of proangiogenic and proinflammatory mediators measured by TaqMan PCR was enhanced. Experimental MI was induced by ligation and reperfusion of the left anterior descending coronary artery of nude rats (n = 8-9). After myocardial transplantation of eEPC and EPO CD68+ leukocyte count and vessel density were enhanced in the border zone of the infarct area. Moreover, apoptosis of transplanted CD31 + TUNEL + eEPC was decreased as compared to transplantation of eEPCs alone. Regional wall motion of the left ventricle was measured using Magnetic Resonance Imaging. After injection of eEPC in the presence of EPO regional wall motion significantly improved as compared to injection of eEPCs or EPO alone.</p> <p>Conclusion</p> <p>Intramyocardial transplantation of eEPC in the presence of EPO during experimental MI improves regional wall motion. This was associated with an increased local inflammation, vasculogenesis and survival of the transplanted cells. Local application of EPO in addition to cell therapy may prove beneficial in myocardial remodeling.</p
Cell Origin of Human Mesenchymal Stem Cells Determines a Different Healing Performance in Cardiac Regeneration
The possible different therapeutic efficacy of human mesenchymal stem cells (hMSC) derived from umbilical cord blood (CB), adipose tissue (AT) or bone marrow (BM) for the treatment of myocardial infarction (MI) remains unexplored. This study was to assess the regenerative potential of hMSC from different origins and to evaluate the role of CD105 in cardiac regeneration. Male SCID mice underwent LAD-ligation and received the respective cell type (400.000/per animal) intramyocardially. Six weeks post infarction, cardiac catheterization showed significant preservation of left ventricular functions in BM and CD105+-CB treated groups compared to CB and nontreated MI group (MI-C). Cell survival analyzed by quantitative real time PCR for human GAPDH and capillary density measured by immunostaining showed consistent results. Furthermore, cardiac remodeling can be significantly attenuated by BM-hMSC compared to MI-C. Under hypoxic conditions in vitro, remarkably increased extracellular acidification and apoptosis has been detected from CB-hMSC compared to BM and CD105 purified CB-derived hMSC. Our findings suggests that hMSC originating from different sources showed a different healing performance in cardiac regeneration and CD105+ hMSC exhibited a favorable survival pattern in infarcted hearts, which translates into a more robust preservation of cardiac function
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