Distance-regular graph with large a1 or c2

In this paper, we study distance-regular graphs $\Gamma$ that have a pair of distinct vertices, say x and y, such that the number of common neighbors of x and y is about half the valency of $\Gamma$. We show that if the diameter is at least three, then such a graph, besides a finite number of exceptions, is a Taylor graph, bipartite with diameter three or a line graph.Comment: We submited this manuscript to JCT

Description of SAFIRE for ISES

The SAFIRE (Spectroscopy of the Atmosphere using Far Infrared Emission) is a limb emission experiment using a far-IR Fourier transform spectrometer (FTS) and a mid-IR broadband multispectral radiometer covering the range 80 to 1600/cm. The purpose of this experiment is to obtain vertical distributions of temperature and key constituents of O(y), HO(y), NO(y), ClO(y), and BrO(y) families in the stratosphere, mesosphere, and thermosphere. The spectral channels and gases within each channel are summarized. The instrument includes a 48 element (6 x 8) Ge:GA detector array operating at 4 K in the far-IR and a 105 element (7 x 15) HgCdTe array operating at 80 K in the mid-IR. The SAFIRE uses four different scan modes for vertical coverage and resolution to address various scientific requirements. The SAFIRE data reduction will start with the retrieval of temperature profile as a function of pressure using two CO2 channel data. Constituent distributions then are obtained from other channel data using the retrieved temperature profile. The SAFIRE measurements are limited to the region above the tropopause because of radiance saturation by H2O and clouds. The computational capability necessary to process at the instrument data rate is estimated to be 19 MFLOPS for FTS data and 0.02 MFLOPS for radiometer data. It seems, therefore, that the real-time applications of SAFIRE data using an onboard processing device is not feasible. Although a temperature anomaly may be detected from the two CO2 radiometer channels using an onboard processor for the stratosphere, it is not possible to distinguish between CO2 outflux and temperature anomaly. Temperature anomaly does not, therefore, offer tropospheric information useful for real-time application

Shilla distance-regular graphs

A Shilla distance-regular graph G (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divides k for a Shilla distance-regular graph G, and for G we define b=b(G):=k/a3. In this paper we will show that there are finitely many Shilla distance-regular graphs G with fixed b(G)>=2. Also, we will classify Shilla distance-regular graphs with b(G)=2 and b(G)=3. Furthermore, we will give a new existence condition for distance-regular graphs, in general.Comment: 14 page

Bilayer Graphene Interferometry : Phase Jump and Wave Collimation

We theoretically study the phase of the reflection amplitude of an electron (massive Dirac fermion) at a lateral potential step in Bernal-stacked bilayer graphene. The phase shows anomalous jump of $\pi$, as the electron incidence angle (relative to the normal direction to the step) varies to pass $\pm \pi/4$. The jump is attributed to the Berry phase associated with the pseudospin-1/2 of the electron. This Berry-phase effect is robust against the band gap opening due to the external electric gates generating the step. We propose an interferometry setup in which collimated waves can be generated and tuned. By using the setup, one can identify both the $\pi$ jump and the collimation angle.Comment: 4 pages, 6 figure