Let $(G,\tau )$ be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If $(G,\tau )$ has the $A$(iii)-property, then its completion $(\widehat{G},\hat{\tau })$ is an order-complete locally solid lattice group. (2) If $G$ is order-complete and $\tau $ has the Fatou property, then the order intervals of $G$ are $\tau $-complete. (3) If $(G,\tau )$ has the Fatou property, then $G$ is order-dense in $\widehat{G}$ and $(\widehat{G},\hat{\tau })$ has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on it. As an application, a version of the Nikodym boundedness theorem for set functions with values in a class of locally solid topological groups is established.
A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. We characterize magic line graphs of general graphs and describe some class of supermagic line graphs of bipartite graphs.
A graph is called magic (supermagic) if it admits a labeling of the edges by pairwise different (and consecutive) integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we characterize magic joins of graphs and we establish some conditions for magic joins of graphs to be supermagic.
In the article finite-buffer queueing systems of the <span class="tex">M/M/1/N</span> type with queue size controlled by AQM algorithms are considered, separately for single and batch arrivals. In the latter case two different acceptance strategies: WBAS (Whole Batch Acceptance Strategy) and PBAS (Partial Batch Acceptance Strategy) are distinguished. Three essential characteristics of the system are investigated: the stationary queue-size distribution, the number of consecutively dropped packets (batches of packets) and the time between two successive accepted packets (batches of packets). For these characteristics the formulae which can be easily numerically treated are derived. Numerical results obtained for three sample dropping functions are attached as well.
It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator $T$ can be approximated by a sequence of maximal monotone operators of type NI, which converge to $T$ in a reasonable sense (in the sense of Kuratowski-Painleve convergence).
Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in Rn is given.
The system of zero-pressure gas dynamics conservation laws describes the dynamics of free particles sticking under collision while mass and momentum are conserved. The existence of such solutions was established some time ago. Here we report a uniqueness result that uses the Oleinik entropy condition and a cohesion condition. Both of these conditions are automatically satisfied by solutions obtained in previous existence results. Important tools in the proof of uniqueness are regularizations, generalized characteristics and flow maps. The solutions may contain vacuum states as well as singular measures.
Standard properties of ϕ-divergences of probability measures are widely applied in various areas of information processing. Among the desirable supplementary properties facilitating employment of mathematical methods is the metricity of ϕ-divergences, or the metricity of their powers. This paper extends the previously known family of ϕ-divergences with these properties. The extension consists of a continuum of ϕ-divergences which are squared metric distances and which are mostly new but include also some classical cases like e. g. the Le Cam squared distance. The paper establishes also basic properties of the ϕ-divergences from the extended class including the range of values and the upper and lower bounds attained under fixed total variation.