A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube

We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $\lambda_s$ (the algebraic convergence) and $\lambda_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively. In particular we show that $\lambda_{ls}$ is a topological convergence iff forcing by B does not produce new reals and that $\lambda_{ls}$ is weakly topological if B satisfies condition $(\hbar)$ (implied by the ${\mathfrak t}$-cc). On the other hand, if $\lambda_{ls}$ is a weakly topological convergence, then B is a $2^{\mathfrak h}$-cc algebra or in some generic extension the distributivity number of the ground model is greater than or equal to the tower number of the extension. So, the statement "The convergence $\lambda_{ls}$ on the collapsing algebra B=\ro ((\omega_2)^{<\omega}) is weakly topological" is independent of ZFC

Functions of several Cayley-Dickson variables and manifolds over them

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are proved in the new generalized form for functions of Cayley-Dickson variables instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson graded algebras are defined and investigated

On two-dimensional surface attractors and repellers on 3-manifolds

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $M^2_ \mathcal B$ is a supporting surface for $\mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is $k\geq 1$ such that: 1) $M^2_{\mathcal B}$ is a union $M^2_1\cup...\cup M^2_k$ of disjoint tame surfaces such that every $M^2_i$ is homeomorphic to the 2-torus $T^2$. 2) the restriction of $f^k$ to $M^2_i$ $(i\in\{1,...,k\})$ is conjugate to Anosov automorphism of $T^2$

Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and diffeomorphisms relative to which they are generalized Lie groups or topological groups. Among such topologies pairwise incomparable are found as well. Topological perfectness of the diffeomorphism group relative to certain topologies is studied. There are proved theorems about projective limit decompositions of these groups and their compactifications for compact manifolds. Moreover, an existence of one-parameter local subgroups of diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad

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

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

A Sterol-Regulatory Element Binding Protein Is Required for Cell Polarity, Hypoxia Adaptation, Azole Drug Resistance, and Virulence in Aspergillus fumigatus

At the site of microbial infections, the significant influx of immune effector cells and the necrosis of tissue by the invading pathogen generate hypoxic microenvironments in which both the pathogen and host cells must survive. Currently, whether hypoxia adaptation is an important virulence attribute of opportunistic pathogenic molds is unknown. Here we report the characterization of a sterol-regulatory element binding protein, SrbA, in the opportunistic pathogenic mold, Aspergillus fumigatus. Loss of SrbA results in a mutant strain of the fungus that is incapable of growth in a hypoxic environment and consequently incapable of causing disease in two distinct murine models of invasive pulmonary aspergillosis (IPA). Transcriptional profiling revealed 87 genes that are affected by loss of SrbA function. Annotation of these genes implicated SrbA in maintaining sterol biosynthesis and hyphal morphology. Further examination of the SrbA null mutant consequently revealed that SrbA plays a critical role in ergosterol biosynthesis, resistance to the azole class of antifungal drugs, and in maintenance of cell polarity in A. fumigatus. Significantly, the SrbA null mutant was highly susceptible to fluconazole and voriconazole. Thus, these findings present a new function of SREBP proteins in filamentous fungi, and demonstrate for the first time that hypoxia adaptation is likely an important virulence attribute of pathogenic molds

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

On realcompact topological vector spaces

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