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We study here $T_{0}$-$Q$-bitopological spaces and sober $Q$-bitopological spaces and their relationship with two particular Sierpinski objects in the category of $Q$-bitopological spaces. The epireflective hulls of both these Sierpinski objects in the category of $Q$-bitopological spaces turn out to be the category of $T_0$-$Q$-bitopological spaces. We show that only one of these Sierpinski ob...
introduction: trichophyton rubrum is one of the most common species of dermatophytes which affects superficial keratinous tissue. it is not especially virulent but it can be responsible for considerable morbidity. although there are different therapeutic modalities to treat fungal infections, clinicians are searching for alternative treatment because of the various side effects of the present t...
We consider the half-wave equation with mass critical in two dimensions {iut=Du?|u|u, u(t0,x)=u0(x), First, we prove existence of a family traveling solitary waves. then show finite-time blowup solutions ground state ?u0?2=?Q?2, where Q is solution DQ+Q=Q2.
heuristics are often used to provide solutions for flow shop scheduling problems.the performance of a heuristic is usually judged by comparing solutions and run times on test cases.this investigation proposes an analytical alternative ,called asymptotic convergence ,which tests the convergence of the heuristic to a lower bound as problem size grows. the test is a stronger variation of worst cas...
We construct quantum MDS codes with parameters $$ [\![ q^2+1,q^2+3-2d,d ]\!] _q$$ for all $$d \leqslant q+1$$ , \ne q$$ . These are shown to exist by proving that there classical generalised Reed–Solomon which contain their Hermitian dual. constructions include many were previously known but in some cases these new. go on prove if $$d\geqslant q+2$$ then is no $$[n,n-d+1,d]_{q^2}$$ code contain...
The Padmakar-Ivan (PI) index of a graph G is the sum over all edges uv of G of the number of edges which are not equidistant from u and v. In this paper, the notion of vertex PI index of a graph is introduced. We apply this notion to compute an exact expression for the PI index of Cartesian product of graphs. This extends a result by Klavzar [On the PI index: PI-partitions and Cartesian product...
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