A graph is radially maximal if its radius decreases after the addition of any edge of its complement. It is proved that any graph can be an induced subgraph of a regular radially maximal graph with a prescribed radius T 2: 3. For T 2: 4, k 2: 1, radially maximal graphs with radius T containing k cut-nodes are constructed.

in this paper, direct numerical simulation of two-phase incompressible gas-liquid flow for simulation of bubble motion in a microtube is presented. microtube radius is 10 µm. the interface is tracked using volume of fluid (vof) method with continuous surface force (csf) model. the flow is solved using a finite volume scheme, based on piso algorithm. numerical simulation is performed on a axisym...

In this paper, we prove that each of the following functions is convex on R: f(t) = wN(AtXA1?t ? A1?tXAt), g(t) wN(AtXA1?t), and h(t) wN(AtXAt) where A > 0, X Mn N(.) a unitarily invariant norm onMn. Consequently, answer positively question concerning convexity function t w(AtXAt) proposed by in (2018). We provide some generalizations extensions wN(.) using Kwong functions. More precisely, w...

Let $$\mathcal {H}$$ be a complex Hilbert space with inner product $$\langle \cdot , \rangle $$ and let A non-zero bounded positive linear operator on {H}.$$ $$\mathbb {B}_A(\mathcal {H})$$ denote the algebra of all operators which admit A-adjoint, $$N_A(\cdot )$$ seminorm . The generalized A-numerical radius $$T\in \mathbb is defined as $$\begin{aligned} \omega _{N_A}(T)=\displaystyle {\sup _{...

This paper deals with the so-called A-numerical radius associated a positive (semi-definite) bounded linear operator A acting on complex Hilbert space H. Several new inequalities involving this concept are established. In particular, we prove several estimates for 2×2 matrices whose entries A-bounded operators. Some of obtained results cover and extend well-known recent due to Bani-Domi Kittane...

If A, B are bounded linear operators on a complex Hilbert space, then we prove that $$\begin{aligned} w(A)\le & {} \frac{1}{2}\left( \Vert A\Vert +\sqrt{r\left( |A||A^*|\right) }\right) ,\\ w(AB \pm BA)\le 2\sqrt{2}\Vert B\Vert \sqrt{ w^2(A)-\frac{c^2(\mathfrak {R}(A))+c^2(\mathfrak {I}(A))}{2} }, \end{aligned}$$ where $$w(\cdot ),\left\| \cdot \right\| $$ , and $$r(\cdot )$$ the numerical radi...