We classify the countable homogeneous coloured multipartite graphs with any finite number of parts. By Fräıssé’s Theorem this amounts to classifying the families F of pairwise non-embeddable finite coloured multipartite graphs for which the class Forb(F) of multipartite graphs which forbid these is an amalgamation class. We show that once we understand such families F in the quadripartite case,...

The family of regular closed subsets of a topological space is used to introduce two concepts concerning a function f from a space X to a space Y . The first of them is the notion of f being rc-continuous. One of the established results states that a space Y is extremally disconnected if and only if each continuous function from a space X to Y is rc-continuous. The second concept studied is the...

We complement the literature by proving that for a fixed-point free map f : X → X the statements (1) f admits a finite functionally closed cover A with f [A]∩A = ∅ for all A ∈ A (i.e., a coloring) and (2) βf is fixed-point free are equivalent. When functionally closed is weakened to closed, we show that normality is sufficient to prove equivalence, and give an example to show it cannot be omitt...

A partially ordered Abelian group M is algebraically (existentially) closed in a class C M of such structures just in case any finite system of weak inequalities (and negations of weak inequalities), defined over M, is solvable in M if solvable in some N ⊇ M in C. After characterizing existentially closed dimension groups this paper derives amalgamation properties for dimension groups, dimensio...

BACKGROUND Quantifying genetic diversity and metapopulation structure provides insights into the evolutionary history of a species and helps develop appropriate management strategies. We provide the first assessment of genetic structure in spinner sharks (Carcharhinus brevipinna), a large cosmopolitan carcharhinid, sampled from eastern and northern Australia and South Africa. METHODS AND FIND...

In this paper, we derive the exact pairwise error probabilities (PEPs) of various quasi-orthogonal space– time block codes (QO-STBCs) using the moment generating function. By classifying the exact PEPs of QO-STBCs into three types, we derive the closed-form expression for each type of PEP. Based on these closed-form expressions, we obtain the union bounds on the symbol error probability and bit...

introduction: solubility of mineral trioxide aggregate (mta) is an important characteristic that affects other properties such as microleakage and biocompatibility. distilled water (dw) has previously been used for solubility tests. this experimental study compared the solubility of mta in dw, synthetic tissue fluid (stf) and new simulated plasma (sp). methods and materials: in this study, 36 s...

Let f, g : X → G/K be maps from a closed connected orientable manifold X to an orientable coset space M = G/K where G is a compact connected Lie group, K a closed subgroup and dimX = dimM . In this paper, we show that if L(f, g) = 0 then N(f, g) = 0; if L(f, g) 6= 0 then N(f, g) = R(f, g) where L(f, g), N(f, g), and R(f, g) denote the Lefschetz, Nielsen, and Reidemeister coincidence numbers of ...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...