A topological space X is said to be generated by an ideal I if for all A ⊆ X and all x ∈ A there is E ⊆ A in I such that x ∈ E, and is said to be weakly generated by I if whenever a subset A of X contains E for every E ⊆ A with E ∈ I, then A itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Haus...

It is proved that no region of a homogeneous locally compact, locally connected metric space can be cut by an Fσ-subset of a “smaller” dimension. The result applies to different finite or infinite topological dimensions of metrizable spaces. The classical Hurewicz-Menger-Tumarkin theorem in dimension theory says that connected topological n-manifolds (with or without boundary) are Cantor manifo...

The problem of splitting effects by vertex angles is discussed for nonintegrable rational polygonal billiards. A statistical analysis of the decay dynamics in weakly open polygons is given through the orbit survival probability. Two distinct channels for the late-time relaxation of type tδ are established. The primary channel, associated with the universal relaxation of ”regular” orbits, with δ...

A set D of vertices in a graph G = (V, E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdiv...

The government organizations in Africa, Asia and South America are adopting OSS solutions because of its low cost and availability of cheap skilled programmers in their countries to customize the software to their needs. In a study conducted to track the usage of OSS, it was found that OSS is extensively promoted in countries like India, China and Taiwan followed by South Korea, Malaysia, Singa...

We study row-finite Leavitt path algebras. We characterize the row-finite graphs E for which the Leavitt path algebra is weakly Noetherian. Our main result is that a Leavitt path algebra is weakly Noetherian if and only if there is ascending chain condition on the hereditary and saturated closures of the subsets of the vertices of the graph E.

The rules of a game dice are extended to ``hyper-die'' with \(n\in\mathbb{N}\) equally probable faces, numbered from 1 \(n\). We derive recursive and explicit expressions for the probability mass function cumulative distribution gain \(G_n\) arbitrary values A numerical study suggests conjecture that \(n \to \infty\) expectation scaled \(\mathbb{E}[{H_n}]=\mathbb{E} [{G_n/\sqrt{n}\,}]\) converg...

Given a graph $G=(V,E)$ and a vertex $v in V$, by $N(v)$ we represent the open neighbourhood of $v$. Let $f:Vrightarrow {0,1,2}$ be a function on $G$. The weight of $f$ is $omega(f)=sum_{vin V}f(v)$ and let $V_i={vin V colon f(v)=i}$, for $i=0,1,2$. The function $f$ is said to bebegin{itemize}item a Roman ${2}$-dominating function, if for every vertex $vin V_0$, $sum_{uin N(v)}f(u)geq 2$. The R...

Building computers able to answer questions on any subject is a long standing goal of artificial intelligence. Promising progress has recently been achieved by methods that learn to map questions to logical forms or database queries. Such approaches can be effective but at the cost of either large amounts of human-labeled data or by defining lexicons and grammars tailored by practitioners. In t...