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We introduce families of two-parameter multivariate polynomials indexed by pairs of partitions $v,w$ -- {\it biaxial double} $(\beta,q)$-{\it Grothendieck polynomials} -- which specialize at $q=0$ and $v=1$ to double $\beta$-Grothendieck polynomials from torus-equivariant connective K-theory. Initially defined recursively via divided difference operators, our main result is that these new polynomials arise as partition functions of solvable lattice models. Moreover, the associated quantum group of the solvable model for polynomials in $n$ pairs of variables is a Drinfeld twist of the $U_q(\widehat{\mathfrak{sl}}_{n+1})$ $R$-matrix. By leveraging the resulting Yang-Baxter equations of the lattice model, we show that these polynomials simultaneously generalize double $\beta$-Grothendieck polynomials and dual double $\beta$-Grothendieck polynomials for arbitrary permutations. We then use properties of the model and Yang-Baxter equations to reprove Fomin-Kirillov's Cauchy identity for $\beta$-Grothendieck polynomials, generalize it to a new Cauchy identity for biaxial double $\beta$-Grothendieck polynomials, and prove a new branching rule for double $\beta$-Grothendieck polynomials. 

The DECam Ecliptic Exploration Project (DEEP) is a deep survey of the trans-Neptunian solar system being carried out on the 4 m Blanco telescope at the Cerro Tololo Inter-American Observatory in Chile using the Dark Energy Camera (DECam). By using a shift-and-stack technique to achieve a mean limiting magnitude ofr∼ 26.2, DEEP achieves an unprecedented combination of survey area and depth, enabling quantitative leaps forward in our understanding of the Kuiper Belt populations. This work reports results from an analysis of 20, 3 deg²DECam fields along the invariable plane. We characterize the efficiency and false-positive rates for our moving-object detection pipeline, and use this information to construct a Bayesian signal probability for each detected source. This procedure allows us to treat all of our Kuiper Belt object (KBO) detections statistically, simultaneously accounting for efficiency and false positives. We detect approximately 2300 candidate sources with KBO-like motion with signal-to-noise ratios > 6.5. We use a subset of these objects to compute the luminosity function of the Kuiper Belt as a whole, as well as the cold classical (CC) population. We also investigate the absolute magnitude (H) distribution of the CCs, and find consistency with both an exponentially tapered power law, which is predicted by streaming instability models of planetesimal formation, and a rolling power law. Finally, we provide an updated mass estimate for the CC Kuiper Belt of$M_{\mathit{CC}}(H_r<12)={0.0017}_{-0.0004}^{+0.0010}{M}_{\oplus }$, assuming albedop= 0.15 and densityρ= 1 g cm⁻³.

 

The citizen Continental-America Telescopic Eclipse (CATE) Experiment was a new type of citizen science experiment designed to capture a time sequence of white-light coronal observations during totality from 17:16 to 18:48 UT on 2017 August 21. Using identical instruments the CATE group imaged the inner corona from 1 to 2.1 RSun with 1.″43 pixels at a cadence of 2.1 s. A slow coronal mass ejection (CME) started on the SW limb of the Sun before the total eclipse began. An analysis of CATE data from 17:22 to 17:39 UT maps the spatial distribution of coronal flow velocities from about 1.2 to 2.1 RSun, and shows the CME material accelerates from about 0 to 200 km s⁻¹across this part of the corona. This CME is observed by LASCO C2 at 3.1–13 RSun with a constant speed of 254 km s⁻¹. The CATE and LASCO observations are not fit by either constant acceleration nor spatially uniform velocity change, and so the CME acceleration mechanism must produce variable acceleration in this region of the corona.