The Rate of Convergence of Lupas q

We discuss the rate of convergence of the Lupas q-analogues of the Bernstein operators Rn,q(f;x) which were given by Lupas in 1987. We obtain the estimates for the rate of convergence of Rn,q(f) by the modulus of continuity of f, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions

The Ramsey Numbers of Fans Versus a Complete Graph of Order Five

For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest integer $N$ such that for any graph $G$ of order $N$, either $G$ contains $F$ or the complement of $G$ contains $H$. Let $F_l$ denote a fan of order $2l+1$, which is $l$ triangles sharing exactly one vertex, and $K_n$ a complete graph of order $n$. Surahmat et al. conjectured that $R(F_l,K_n)=2l(n-1)+1$ for $l\geq n\geq 5$. In this paper, we show that the conjecture is true for n=5

Three results on cycle-wheel Ramsey numbers

Given two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. We consider the case that G1 is a cycle and G2 is a (generalized) wheel. We expand the knowledge on exact values of Ramsey numbers in three directions: large cycles versus wheels of odd order; large wheels versus cycles of even order; and large cycles versus generalized odd wheels

Navigation Accuracy Category-Position Models and Estimate Position Uncertainty Calculations for TIS-B System

AbstractNavigation accuracy category-position (NACp) is an important parameter for system accuracy of traffic information service-broadcast (TIS-B), which is determined by estimate position uncertainty (EPU). Centered about the problems that the existing EPU calculation based on noise measurement is low in accuracy and unfit for describing uncorrected biases in target reports, this article analyses the traditional NACp model, and uses the least square estimation (LSE) in EPU calculation. Furthermore, it proposes an extended NACp model, which considers both noise and biases and acquires EPU estimation with the help of approximate multiplex Taylor expression. Analysis and simulation show that the proposed method not only leads to significant improvement of the accuracy of EPU calculation, but is fit for EPU calculation with tracking biases in TIS-B system as well. As such it can find application in practice to depict different kinds of error models in TIS-B system

Ionic blockade in a charged single-file water channel

The classical continuum theories fail to describe the ionic transport in Angstrom channels, where conduction deviates from Ohm's law, as attributed to dehydration/self-energy barrier and dissociation of Bjerrum ion-pairs in previous work. Here we found that the cations are strongly bound to the surface charge that blockade the ionic transport in a single-file water channel, causing nonlinear current-voltage responses. The presence of free ions significantly increased the probability of bound ions being released, resulting in an ionic current. We found that ionic conduction gradually becomes Ohmic as surface charge density increases, but the conduction amplitude decreased due to increased friction from bound ions. We rationalized the ionic transport by 1D Kramers' escape theory framework, which well described nonlinear ionic current, and the impact of surface charge density on turning to Ohmic system. Our results possibly provide an alternative view of ionic blockade in Angstrom channels