The rectilinear local crossing number of KnK_n

We determine ${\bar{\rm{lcr}}}(K_n)$, the rectilinear local crossing number of the complete graph $K_n$ for every $n$. More precisely, for every $n \notin \{8, 14 \},$ $${\bar{\rm{lcr}}}(K_n)=\left\lceil \frac{1}{2} \left( n-3-\left\lceil \frac{n-3}{3} \right\rceil \right) \left\lceil \frac{n-3}{3} \right\rceil \right\rceil,$$ ${\bar{\rm{lcr}}}(K_8)=4$, and ${\bar{\rm{lcr}}}(K_{14})=15$.Comment: 6 Figures. Changes from v1: Added keywords, MSC2010 codes, a single formula to consider all cases together, and the resolution of the case n=14 that remained as a conjecture on the previous version. Changes from v2: A minor error in Lemma 2 was corrected. Some typos were fixed. Figure 1 was eliminated and Figures 2 and 5 were improved slightly. The last section was split into two section

Current and Shot Noise Measurements in a Carbon Nanotube-Based Spin Diode

Low-temperature measurements of asymmetric carbon nanotube (CNT) quantum dots are reported. The CNTs are end-contacted with one ferromagnetic and one normal-metal electrode. The measurements show a spin-dependent rectification of the current caused by the asymmetry of the device. This rectification occurs for gate voltages for which the normal-metal lead is resonant with a level of the quantum dot. At the gate voltages at which the current is at the maximum current, a significant decrease in the current shot noise is observed

Effect of damping on excitability of high-order normal modes

The effect of localized structural damping on the excitability of higher-order large space telescope spacecraft modes is investigated. A preprocessor computer program is developed to incorporate Voigt structural joint damping models in a finite-element dynamic model. A postprocessor computer program is developed to select critical modes for low-frequency attitude control problems and for higher-frequency fine-stabilization problems. The selection is accomplished by ranking the flexible modes based on coefficients for rate gyro, position gyro, and optical sensor, and on image-plane motions due to sinusoidal or random PSD force and torque inputs

Correlations in nuclear energy recurrence relations

The excitation energies of states belonging to the ground state bands of heavy even-even nuclei are analysed using recurrence relations. Excellent agreement with experimental data at the 10 keV level is obtained by taking into account strong correlations which emerge in the analysis. This implies that the excitation energies can be written as a polynomial of maximum degree four in the angular momentum.Comment: 4 pages, 1 figure, 1 table, 9 reference

Book crossing numbers of the complete graph and small local convex crossing numbers

A $k$-page book drawing of a graph $G$ is a drawing of $G$ on $k$ halfplanes with common boundary $l$, a line, where the vertices are on $l$ and the edges cannot cross $l$. The $k$-page book crossing number of the graph $G$, denoted by $\nu_k(G)$, is the minimum number of edge-crossings over all $k$-page book drawings of $G$. Let $G=K_n$ be the complete graph on $n$ vertices. We improve the lower bounds on $\nu_k(K_n)$ for all $k\geq 14$ and determine $\nu_k(K_n)$ whenever $2 < n/k \leq 3$. Our proofs rely on bounding the number of edges in convex graphs with small local crossing numbers. In particular, we determine the maximum number of edges that a convex graph with local crossing number at most $\ell$ can have for $\ell\leq 4$.Comment: Version 2 extends our result on the maximum number of edges on a convex graph with local crossing number at most c for c=4. In This in turn improves most of the bounds in Version

The effects of localized damping on structural response

The effect of localized structural damping on the excitability of higher order normal modes of the large space telescope was investigated. A preprocessor computer program was developed to incorporate Voigt structural joint damping models in a NASTRAN finite-element dynamic model. A postprocessor computer program was developed to select critical modes for low-frequency attitude control problems and for higher frequency fine-stabilization problems. The mode selection is accomplished by ranking the flexible modes based on coefficients for rate gyro, position gyro, and optical sensors, and on image-plane motions due to sinusoidal or random power spectral density force and torque inputs