A Coboundary Morphism For The Grothendieck Spectral Sequence

Given an abelian category $\mathcal{A}$ with enough injectives we show that a short exact sequence of chain complexes of objects in $\mathcal{A}$ gives rise to a short exact sequence of Cartan-Eilenberg resolutions. Using this we construct coboundary morphisms between Grothendieck spectral sequences associated to objects in a short exact sequence. We show that the coboundary preserves the filtrations associated with the spectral sequences and give an application of these result to filtrations in sheaf cohomology.Comment: 18 page

On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

Cauchyness and convergence in fuzzy metric spaces

[EN] In this paper we survey some concepts of convergence and Cauchyness appeared separately in the context of fuzzy metric spaces in the sense of George and Veeramani. For each convergence (Cauchyness) concept we find a compatible Cauchyness (convergence) concept. We also study the relationship among them and the relationship with compactness and completeness (defined in a natural sense for each one of the Cauchy concepts). In particular, we prove that compactness implies p-completeness.Almanzor Sapena acknowledges the support of Ministry of Economy and Competitiveness of Spain under grant TEC2013-45492-R. Valentín Gregori acknowledges the support of Ministry of Economy and Competitiveness of Spain under grant MTM 2012-37894-C02-01.Gregori Gregori, V.; Miñana, J.; Morillas, S.; Sapena Piera, A. (2017). Cauchyness and convergence in fuzzy metric spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 111(1):25-37. https://doi.org/10.1007/s13398-015-0272-0S25371111Alaca, C., Turkoglu, D., Yildiz, C.: Fixed points in intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 29, 1073–1078 (2006)Edalat, A., Heckmann, R.: A computational model for metric spaces. Theor. Comput. Sci. 193, 53–73 (1998)Engelking, R.: General topology. PWN-Polish Sci. Publ, Warsawa (1977)Fang, J.X.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 46(1), 107–113 (1992)George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395–399 (1994)George, A., Veeramani, P.: Some theorems in fuzzy metric spaces. J. Fuzzy Math. 3, 933–940 (1995)George, A., Veeramani, P.: On some results of analysis for fuzzy metric spaces. Fuzzy Sets Syst. 90, 365–368 (1997)Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1989)Gregori, V., Romaguera, S.: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115, 485–489 (2000)Gregori, V., Romaguera, S.: On completion of fuzzy metric spaces. Fuzzy Sets Syst. 130, 399–404 (2002)Gregori, V., Romaguera, S.: Characterizing completable fuzzy metric spaces. Fuzzy Sets Syst. 144, 411–420 (2004)Gregori, V., López-Crevillén, A., Morillas, S., Sapena, A.: On convergence in fuzzy metric spaces. Topol. Appl. 156, 3002–3006 (2009)Gregori, V., Miñana, J.J.: Some concepts realted to continuity in fuzzy metric spaces. In: Proceedings of the conference in applied topology WiAT’13, pp. 85–91 (2013)Gregori, V., Miñana, J.-J., Sapena, A.: On Banach contraction principles in fuzzy metric spaces (2015, submitted)Gregori, V., Miñana, J.-J.: std-Convergence in fuzzy metric spaces. Fuzzy Sets Syst. 267, 140–143 (2015)Gregori, V., Miñana, J.-J.: Strong convergence in fuzzy metric spaces Filomat (2015, accepted)Gregori, V., Miñana, J.-J., Morillas, S.: Some questions in fuzzy metric spaces. Fuzzy Sets Syst. 204, 71–85 (2012)Gregori, V., Miñana, J.-J., Morillas, S.: A note on convergence in fuzzy metric spaces. Iran. J. Fuzzy Syst. 11(4), 75–85 (2014)Gregori, V., Morillas, S., Sapena, A.: On a class of completable fuzzy metric spaces. Fuzzy Sets Syst. 161, 2193–2205 (2010)Gregori, V., Morillas, S., Sapena, A.: Examples of fuzzy metric spaces and applications. Fuzzy Sets Syst. 170, 95–111 (2011)Kramosil, I., Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetika 11, 326–334 (1975)Mihet, D.: On fuzzy contractive mappings in fuzzy metric spaces. Fuzzy Sets Syst. 158, 915–921 (2007)Mihet, D.: Fuzzy $$\varphi$$ φ -contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets Syst. 159, 739–744 (2008)Mihet, D.: A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets Syst. 144, 431–439 (2004)Mishra, S.N., Sharma, N., Singh, S.L.: Common fixed points of maps on fuzzy metric spaces Internat. J. Math. Math. Sci. 17(2), 253–258 (1994)Morillas, S., Sapena, A.: On Cauchy sequences in fuzzy metric spaces. In: Proceedings of the conference in applied topology (WiAT’13), pp. 101–108 (2013)Ricarte, L.A., Romaguera, S.: A domain-theoretic approach to fuzzy metric spaces. Topol. Appl. 163, 149–159 (2014)Sherwood, H.: On the completion of probabilistic metric spaces. Z.Wahrschein-lichkeitstheorie verw. Geb. 6, 62–64 (1966)Sherwood, H.: Complete Probabilistic Metric Spaces. Z. Wahrschein-lichkeitstheorie verw. Geb. 20, 117–128 (1971)Tirado, P.: On compactness and G-completeness in fuzzy metric spaces. Iran. J. Fuzzy Syst. 9(4), 151–158 (2012)Tirado, P.: Contraction mappings in fuzzy quasi-metric spaces and [0,1]-fuzzy posets. Fixed Point Theory 13(1), 273–283 (2012)Vasuki, R., Veeramani, P.: Fixed point theorems and Cauchy sequences in fuzzy metric spaces. Fuzzy Sets Syst. 135(3), 415–417 (2003)Veeramani, P.: Best approximation in fuzzy metric spaces. J. Fuzzy Math. 9, 75–80 (2001

Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proven, that they are finite dimensional Lie groups for compact manifolds. Their examples are given. Many charactersitic features are found in comparison with commutative geometry over $\bf R$ or $\bf C$.Comment: 55 pages, 53 reference

Bdellovibrio bacteriovorus Inhibits Staphylococcus aureus Biofilm Formation and Invasion into Human Epithelial Cells

Bdellovibrio bacteriovorus HD100 is a predatory bacterium that attacks many Gram-negative human pathogens. A serious drawback of this strain, however, is its ineffectiveness against Gram-positive strains, such as the human pathogen Staphylococcus aureus. Here we demonstrate that the extracellular proteases produced by a host-independent B. bacteriovorus (HIB) effectively degrade/inhibit the formation of S. aureus biofilms and reduce its virulence. A 10% addition of HIB supernatant caused a 75% or greater reduction in S. aureus biofilm formation as well as 75% dispersal of pre-formed biofilms. LC-MS-MS analyses identified various B. bacteriovorus proteases within the supernatant, including the serine proteases Bd2269 and Bd2321. Tests with AEBSF confirmed that serine proteases were active in the supernatant and that they impacted S. aureus biofilm formation. The supernatant also possessed a slight DNAse activity. Furthermore, treatment of planktonic S. aureus with the supernatant diminished its ability to invade MCF-10a epithelial cells by 5-fold but did not affect the MCF-10a viability. In conclusion, this study illustrates the hitherto unknown ability of B. bacteriovorus to disperse Gram-positive pathogenic biofilms and mitigate their virulence.open6

Liver-Specific Expression of Transcriptionally Active SREBP-1c Is Associated with Fatty Liver and Increased Visceral Fat Mass

The pathogenesis of fatty liver is not understood in detail, but lipid overflow as well as de novo lipogenesis (DNL) seem to be the key points of hepatocyte accumulation of lipids. One key transcription factor in DNL is sterol regulatory element-binding protein (SREBP)-1c. We generated mice with liver-specific over-expression of mature human SREBP-1c under control of the albumin promoter and a liver-specific enhancer (alb-SREBP-1c) to analyze systemic perturbations caused by this distinct alteration. SREBP-1c targets specific genes and causes key enzymes in DNL and lipid metabolism to be up-regulated. The alb-SREBP-1c mice developed hepatic lipid accumulation featuring a fatty liver by the age of 24 weeks under normocaloric nutrition. On a molecular level, clinical parameters and lipid-profiles varied according to the fatty liver phenotype. The desaturation index was increased compared to wild type mice. In liver, fatty acids (FA) were increased by 50% (p<0.01) and lipid composition was shifted to mono unsaturated FA, whereas lipid profile in adipose tissue or serum was not altered. Serum analyses revealed a ∼2-fold (p<0.01) increase in triglycerides and free fatty acids, and a ∼3-fold (p<0.01) increase in insulin levels, indicating insulin resistance; however, no significant cytokine profile alterations have been determined. Interestingly and unexpectedly, mice also developed adipositas with considerably increased visceral adipose tissue, although calorie intake was not different compared to control mice. In conclusion, the alb-SREBP-1c mouse model allowed the elucidation of the systemic impact of SREBP-1c as a central regulator of lipid metabolism in vivo and also demonstrated that the liver is a more active player in metabolic diseases such as visceral obesity and insulin resistance

Obesity resistant mechanisms in the Lean polygenic mouse model as indicated by liver transcriptome and expression of selected genes in skeletal muscle

<p>Abstract</p> <p>Background</p> <p>Divergently selected Lean and Fat mouse lines represent unique models for a polygenic form of resistance and susceptibility to obesity development. Previous research on these lines focused mainly on obesity-susceptible factors in the Fat line. This study aimed to examine the molecular basis of obesity-resistant mechanisms in the Lean line by analyzing various fat depots and organs, the liver transcriptome of selected metabolic pathways, plasma and lipid homeostasis and expression of selected skeletal muscle genes.</p> <p>Results</p> <p>Expression profiling using our custom Steroltalk v2 microarray demonstrated that Lean mice exhibit a higher hepatic expression of cholesterol biosynthesis genes compared to the Fat line, although this was not reflected in elevation of total plasma or liver cholesterol. However, FPLC analysis showed that protective HDL cholesterol was elevated in Lean mice. A significant difference between the strains was also found in bile acid metabolism. Lean mice had a higher expression of <it>Cyp8b1</it>, a regulatory enzyme of bile acid synthesis, and the <it>Abcb11 </it>bile acid transporter gene responsible for export of acids to the bile. Additionally, a higher content of blood circulating bile acids was observed in Lean mice. Elevated HDL and upregulation of some bile acids synthesis and transport genes suggests enhanced reverse cholesterol transport in the Lean line - the flux of cholesterol out of the body is higher which is compensated by upregulation of endogenous cholesterol biosynthesis. Increased skeletal muscle <it>Il6 </it>and <it>Dio2 </it>mRNA levels as well as increased activity of muscle succinic acid dehydrogenase (SDH) in the Lean mice demonstrates for the first time that changes in muscle energy metabolism play important role in the Lean line phenotype determination and corroborate our previous findings of increased physical activity and thermogenesis in this line. Finally, differential expression of <it>Abcb11 </it>and <it>Dio2 </it>identifies novel strong positional candidate genes as they map within the quantitative trait loci (QTL) regions detected previously in crosses between the Lean and Fat mice.</p> <p>Conclusion</p> <p>We identified novel candidate molecular targets and metabolic changes which can at least in part explain resistance to obesity development in the Lean line. The major difference between the Lean and Fat mice was in increased liver cholesterol biosynthesis gene mRNA expression, bile acid metabolism and changes in selected muscle genes' expression in the Lean line. The liver <it>Abcb11 </it>and muscle <it>Dio2 </it>were identified as novel positional candidate genes to explain part of the phenotypic difference between the Lean and Fat lines.</p