Twisted linear periods and a new relative trace formula

We study the linear periods on $GL_{2n}$ twisted by a character using a new relative trace formula. We establish the relative fundamental lemma and the transfer of orbital integrals. Together with the spectral isolation technique of Beuzart-Plessis--Liu--Zhang--Zhu, we are able to compare the elliptic part of the relative trace formulae and to obtain new results generalizing Waldspurger's theorem in the $n=1$ case

Robust Intrinsic Ferromagnetism and Half Semiconductivity in Stable Two-Dimensional Single-Layer Chromium Trihalides

Two-dimensional (2D) intrinsic ferromagnetic (FM) semiconductors are crucial to develop low-dimensional spintronic devices. Using density functional theory, we show that single-layer chromium trihalides (SLCTs) (CrX$_3$,X=F, Cl, Br and I) constitute a series of stable 2D intrinsic FM semiconductors. A free-standing SLCT can be easily exfoliated from the bulk crystal, due to a low cleavage energy and a high in-plane stiffness. Electronic structure calculations using the HSE06 functional indicate that both bulk and single-layer CrX$_3$ are half semiconductors with indirect gaps and their valence bands and conduction bands are fully spin-polarized in the same spin direction. The energy gaps and absorption edges of CrBr$_3$ and CrI$_3$ are found to be in the visible frequency range, which implies possible opt-electronic applications. Furthermore, SLCTs are found to possess a large magnetic moment of 3$\mu_B$ per formula unit and a sizable magnetic anisotropy energy. The magnetic exchange constants of SLCTs are then extracted using the Heisenberg spin Hamiltonian and the microscopic origins of the various exchange interactions are analyzed. A competition between a near 90$^\circ$ FM superexchange and a direct antiferromagnetic (AFM) exchange results in a FM nearest-neighbour exchange interaction. The next and third nearest-neighbour exchange interactions are found to be FM and AFM respectively and this can be understood by the angle-dependent extended Cr-X-X-Cr superexchange interaction. Moreover, the Curie temperatures of SLCTs are also predicted using Monte Carlo simulations and the values can further increase by applying a biaxial tensile strain. The unique combination of robust intrinsic ferromagnetism, half semiconductivity and large magnetic anisotropy energies renders the SLCTs as promising candidates for next-generation semiconductor spintronic applications.Comment: 12 pages, 14 figures. published in J. Mater. Chem.

Hierarchical control for the semilinear parabolic equations with interior degeneracy

This paper concerns with the hierarchical control of the semilinear parabolic equations with interior degeneracy. By a Stackelberg-Nash strategy, we consider the linear and semilinear system with one leader and two followers. First, for any given leader, we analyze a Nash equilibrium corresponding to a bi-objective optimal control problem. The existence and uniqueness of the Nash equilibrium is proved, and its characterization is given. Then, we find a leader satisfying the null controllability problem. The key is to establish a new Carleman estimate for a coupled degenerate parabolic system with interior degeneracy

Carbonate-superstructured solid fuel cells with hydrocarbon fuels

A basic requirement for solid oxide fuel cells (SOFCs) is the sintering of electrolyte into a dense impermeable membrane to prevent the mixing of fuel and oxygen for a sufficiently high open-circuit voltage (OCV). However, herein, we demonstrate a different type of fuel cell, a carbonate-superstructured solid fuel cell (CSSFC), in which in situ generation of superstructured carbonate in the porous samarium-doped ceria layer creates a unique electrolyte with ultrahigh ionic conductivity of 0.17 S.cm21 at 550 °C. The CSSFC achieves unprecedented high OCVs (1.051 V at 500 °C and 1.041 V at 550 °C) with methane fuel. Furthermore, the CSSFC exhibits a high peak power density of 215 mW.cm22 with dry methane fuel at 550 °C, which is higher than all reported values of electrolyte-supported SOFCs. This provides a different approach for the development of efficient solid fuel cells

An improved method to determine the Ξc−Ξc′\Xi_c-\Xi_c' mixing

We develop an improved method to explore the $\Xi_c- \Xi_c'$ mixing which arises from the flavor SU(3) and heavy quark symmetry breaking. In this method, the flavor eigenstates under the SU(3) symmetry are at first constructed and the corresponding masses can be nonperturbatively determined. Matrix elements of the mass operators which break the flavor SU(3) symmetry sandwiched by the flavor eigenstates are then calculated. Diagonalizing the corresponding matrix of Hamiltonian gives the mass eigenstates of the full Hamiltonian and determines the mixing. Following the previous lattice QCD calculation of $\Xi_c$ and $\Xi_c'$, and estimating an off-diagonal matrix element, we extract the mixing angle between the $\Xi_c$ and $\Xi_c'$. Preliminary numerical results for the mixing angle confirm the previous observation that such mixing is incapable to explain the large SU(3) symmetry breaking in semileptonic decays of charmed baryons.Comment: 7 pages, 3 figure

Planning multiple movements within a fixed time limit: The cost of constrained time allocation in a visuo-motor task

S.-W. Wu, M. F. Dal Martello, and L. T. Maloney (2009) evaluated subjects' performance in a visuo-motor task where subjects were asked to hit two targets in sequence within a fixed time limit. Hitting targets earned rewards and Wu et al. varied rewards associated with targets. They found that subjects failed to maximize expected gain; they failed to invest more time in the movement to the more valuable target. What could explain this lack of response to reward? We first considered the possibility that subjects require training in allocating time between two movements. In Experiment 1, we found that, after extensive training, subjects still failed: They did not vary time allocation with changes in payoff. However, their actual gains equaled or exceeded the expected gain of an ideal time allocator, indicating that constraining time itself has a cost for motor accuracy. In a second experiment, we found that movements made under externally imposed time limits were less accurate than movements made with the same timing freely selected by the mover. Constrained time allocation cost about 17% in expected gain. These results suggest that there is no single speed–accuracy tradeoff for movement in our task and that subjects pursued different motor strategies with distinct speed–accuracy tradeoffs in different conditions

Octa: Omissions and Conflicts in Target-Aspect Sentiment Analysis

Sentiments in opinionated text are often determined by both aspects and target words (or targets). We observe that targets and aspects interrelate in subtle ways, often yielding conflicting sentiments. Thus, a naive aggregation of sentiments from aspects and targets treated separately, as in existing sentiment analysis models, impairs performance. We propose Octa, an approach that jointly considers aspects and targets when inferring sentiments. To capture and quantify relationships between targets and context words, Octa uses a selective self-attention mechanism that handles implicit or missing targets. Specifically, Octa involves two layers of attention mechanisms for, respectively, selective attention between targets and context words and attention over words based on aspects. On benchmark datasets, Octa outperforms leading models by a large margin, yielding (absolute) gains in accuracy of 1.6% to 4.3%.Comment: Accepted by Findings of EMNLP 202