We propose two fixed-parameter tractable algorithms for the weighted Max-Cut problem on embedded 1-planar graphs parameterized by crossing number k of given embedding. A graph is called if it can be drawn in plane with at most one per edge. Our recursively reduce a to 3k planar graphs, using edge removal and node contraction. main algorithm then solves FCE-MaxCut introduced Liers Pardella [23]....

Let U be a random unitary matrix drawn from the Hua-Pickrell distribution $$\mu _{\textrm{U}(n+m)}^{(\delta )}$$ on group $$\textrm{U}(n+m)$$ . We show that eigenvalues of truncated $$[U_{i,j}]_{1\le i,j\le n}$$ form determinantal point process $$\mathscr {X}_n^{(m,\delta unit disc $$\mathbb {D}$$ for any $$\delta \in \mathbb {C}$$ satisfying $$\textrm{Re}\,\delta >-1/2$$ also prove limiting ta...

In their paper [1] Barabási and Albert proposed a certain random process of evolving graphs as a model of real-world networks, like the Internet. In their model vertices are added to the graph one by one, and edges connecting the new vertex to the old ones are drawn randomly, with probabilities proportional to the degree of the endpoint. In the particular case where only a single edge is allowe...

Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. Two linear-time algorithms are known for solvin...

The current exploration is conceded on VCR diesel engine. It run with cotton seed oil as alternative fuel. Initially operate the engine base fuel, later blends B10, B20, B30 at different loads. From obtained results observed higher Brake Thermal efficiency (BTE) than other of B10 and B30. pure releases high amount HC emissions all stages. fuel blend release lesser emissions. that combustion don...