We show that for any regular matroid on m elements and $\alpha \geq 1$, the number of $\alpha$-minimum circuits, or circuits whose size is at most an $\alpha$-multiple minimum a circ...

Abstract Asymptotically safe gravity is based on the idea that main contribution to Schwarzschild-like black hole spacetime due value of gravitational coupling which depends distance from origin and approaches its classical in far zone. However, at some stage this approach has an arbitrariness choice identification parameter. The two cases are considered here: first, by modified proper length (...

The point estimate of sample coefficient alpha may provide a misleading impression of the reliability of the test score. Because sample coefficient alpha is consistently biased downward, it is more likely to yield a misleading impression of poor reliability. The magnitude of the bias is greatest precisely when the variability of sample alpha is greatest (small population reliability and small s...

Abstract We define an attractive gravity probe surface (AGPS) as a compact 2-surface $S_\alpha$ with positive mean curvature $k$ satisfying $r^a D_a k / k^2 \ge \alpha$ (for constant $\alpha>-1/2$) in the local inverse flow, where k$ is derivative of outward unit normal direction. For asymptotically flat spaces, any AGPS proved to satisfy areal inequality $A_\alpha \le 4\pi [ ( 3+4\alpha...

We give bounds for optimal coverings of finite sets by elements of regular families of subsets, and show that both upper and lower bounds are asymptotically sharp for some families of examples.

We study the phase space of the spherically symmetric solutions of Einstein-Gauss-Bonnet system nonmin-imally coupled to a scalar field and show that in four dimensions the only regular black hole solutions are asymptotically flat.

We study properties of eigenvalues a matrix associated with randomly chosen partial automorphism regular rooted tree. show that asymptotically, as the level number goes to infinity, fraction non-zero converges zero in probability.