Moon [J. Combin. Inform. System Sci. 19 (1994), 207–214] showed that every strong tournament contains a Hamiltonian cycle through at least three pancyclic arcs. In this paper, we extend the result of Moon and prove that if D is a strong c-partite tournament with c ≥ 3, then D contains a cycle C containing vertices from exactly c partite sets such that C contains at least three arcs, each of whi...

We consider a singular Schrödinger operator in L(R) written formally as −∆ − βδ(x − γ) where γ is a C smooth open arc in R of length L with regular ends. It is shown that the jth negative eigenvalue of this operator behaves in the strong-coupling limit, β → +∞, asymptotically as Ej(β) = − β 4 + μj +O ( log β β ) , where μj is the jth Dirichlet eigenvalue of the operator − d 2 ds2 − κ(s) 2 4 on ...

During the 17 March 2015 geomagnetic storm, citizen scientist observations from Dunedin (45.95°S, 170.32°E), New Zealand, revealed a bright wide red arc known as stable auroral (SAR) evolving into thin white-mauve arc, Strong Thermal Emission Velocity Enhancement (STEVE). An all-sky imager at Mount John Observatory (43.99°S, 170.46°E), 200 km north of Dunedin, detected an extremely in 630.0 nm,...

Let D = (V,A) be a digraph of order n, S a subset of V of size k and 2 ≤ k ≤ n. Strong subgraphs D1, . . . , Dp containing S are said to be internally disjoint if V (Di)∩V (Dj) = S and A(Di)∩A(Dj) = ∅ for all 1 ≤ i < j ≤ p. Let κS(D) be the maximum number of internally disjoint strong digraphs containing S in D. The strong subgraph kconnectivity is defined as κk(D) = min{κS(D) | S ⊆ V, |S| = k}...

In 1963, Tibor Gallai [9] asked whether every strongly connected directed graph D is spanned by α directed circuits, where α is the stability of D. We give a proof of this conjecture. 1 Coherent cyclic orders. In this paper, circuits of length two are allowed. Since loops and multiple arcs play no role in this topic, we will simply assume that our digraphs are loopless and simple. A directed gr...

Background: Malnutrition is a great challenge for the public health system. Therefore, this study aimed to study the spatial pattern malnutrition using GIS in the world's countries. Materials and Methods: In this cross-sectional study, secondar...

A dicycle cover of a digraphD is a familyF of dicycles ofD such that each arc ofD lies in at least one dicycle inF. We investigate the problem of determining the upper bounds for the minimum number of dicycles which cover all arcs in a strong digraph. Best possible upper bounds of dicycle covers are obtained in a number of classes of digraphs including strong tournaments, Hamiltonian oriented g...

We present a combined analysis of mass estimates in the central cores of galaxy clusters from the strong lensing, the X-ray measurements and the universal density profile (NFW). Special attention is paid to the questions (1)whether the previously claimed mass discrepancy between the strong lensing and X-ray measurements is associated with the presence of cooling/non-cooling flows, (2)whether th...