An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove th...

In this study, the maximum error-free transmission rate of an additive white Gaussian noise channel with a symmetric analog-to-digital converter (ADC) was derived as composite function binary entropy function, Q-function, and square root assuming that convex on set all non-negative real numbers. However, because mathematically proving convexity near zero is difficult, studies in field have only...

a {em 2-rainbow dominating function} (2rdf) of a graph $g$ is a function $f$ from the vertex set $v(g)$ to the set of all subsets of the set ${1,2}$ such that for any vertex $vin v(g)$ with $f(v)=emptyset$ the condition $bigcup_{uin n(v)}f(u)={1,2}$ is fulfilled, where $n(v)$ is the open neighborhood of $v$. the {em weight} of a 2rdf $f$ is the value $omega(f)=sum_{vin v}|f (v)|$. the {em $2$-r...

Stochastic nonlinear elliptic partial differential equations with white noise disturbances are studied in the countably additive measure set up. Introducing the Onsager-Machlup function to the system model, the smoothing problem for maximizing the modified likelihood functional is solved and the explicit form of nonlinear smoother is presented in the finitely additive observation noise set up. ...

The set functions associated with Schrr odinger's equation are known to be unbounded on the algebra of cylinder sets. However, there do exist examples of scalar values set functions which are unbounded, yet-additive on the underlying algebra of sets. The purpose of this note is to show that the set functions associated with Schrr odinger's equation and not-additive on cylinder sets. In the cour...

A simulation study was conducted to address the issue of how purely additive (simple) genetic architecture might impact on the efficacy of parametric and non-parametric genomic prediction methods. For this purpose, we simulated a trait with narrow sense heritability h2= 0.3, with only additive genetic effects for 300 loci in order to compare the predictive ability of 14 more practically used ge...