A weak form of the constructively important notion of locatedness is lifted from the context of a metric space to that of a uniform space. Certain fundamental results about almost located and totally bounded sets are then proved.
We consider a non-consuming agent investing in a stock and a money market interested in the portfolio market price far in the future. We derive a strategy which is almost log-optimal in the long run in the presence of small proportional transaction costs for the case when the rate of return and the volatility of the stock market price are bounded It\^o processes with bounded coefficients and when the volatility is bounded away from zero.
We prove that the interval topology of an Archimedean atomic lattice effect algebra E is Hausdorff whenever the set of all atoms of E is almost orthogonal. In such a case E is order continuous. If moreover E is complete then order convergence of nets of elements of E is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on E corresponding to compact and cocompact elements. For block-finite Archimedean atomic lattice effect algebras the equivalence of almost orthogonality and s-compact generation is shown. As the main application we obtain a state smearing theorem for these effect algebras, as well as the continuity of ⊕-operation in the order and interval topologies on them.
Let $N$ and $K$ be groups and let $G$ be an extension of $N$ by $K$. Given a property $\mathcal P$ of group compactifications, one can ask whether there exist compactifications $N^{\prime }$ and $K^{\prime }$ of $N$ and $K$ such that the universal $\mathcal P$-compactification of $G$ is canonically isomorphic to an extension of $N^{\prime }$ by $K^{\prime }$. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties $\mathcal P$ and then apply this result to the almost periodic and weakly almost periodic compactifications of $G$.
The paper is the extension of the author's previous papers and solves more complicated problems. Almost periodic solutions of a certain type of almost periodic linear or quasilinear systems of neutral differential equations are dealt with.
This paper is a continuation of my previous paper in Mathematica Bohemica and solves the same problem but by means of another method. It deals with almost periodic solutions of a certain type of almost periodic systems of differential equations.
We show that whenever the $q$-dimensional Minkowski content of a subset $A\subset \mathbb R^d$ exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in $\mathbb R^d$, $d\geq 3$.
We present general properties for almost-flat modules and we prove that a self-small right module is almost flat as a left module over its endomorphism ring if and only if the class of $g$-static modules is closed under the kernels.
Alogenní transplantace kmenových buněk krvetvorby je léčebnou metodou u celé řady maligních či nemaligních onemocnění. Zdravé buňky vhodného dárce nahradí chybějící, maligní či nefunkční buňky příjemce. Imunitní systém dárce zajistí protiinfekční ochranu a současně sníží riziko recidivy onemocnění. Může však způsobit poškození zdravých tkání příjemce (reakce štěpu proti hostiteli). Zdrojem zárodečných buněk může být kostní dřeň, stimulované periferní kmenové buňky nebo pupečníková krev od vhodného rodinného či anonymního dárce z registru., Allogeneic haematopoietic stem cell transplantation is a therapeutic method in a wide range of malignant or non-malignant diseases. Healthy cells of a suitable donor replace missing, malignant, or non-functional recipient's cells. The donor's immune system ensures protection from infections while reducing the risk of disease recurrence. However, it can cause damage to the recipient's healthy tissue (graft-versus-host disease). The sources of stem cells can include the bone marrow, stimulated peripheral blood stem cells, or umbilical- -cord blood from a suitable related or anonymous donor from a registry., Petr Sedláček, Petr Říha, and Literatura