The Abel-Zeilberger Algorithm

We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger algorithm to prove the Paule-Schneider identities, the Apery-Schmidt-Strehl identity, Calkin's identity and some identities involving Fibonacci numbers.Comment: 18 page

Distinct behaviors of suppression to superconductivity in LaRu3Si2LaRu_3Si_2 induced by Fe and Co dopants

In the superconductor LaRu$_3$Si$_2$ with the Kagome lattice of Ru, we have successfully doped the Ru with Fe and Co atoms. Contrasting behaviors of suppression to superconductivity is discovered between the Fe and the Co dopants: Fe-impurities can suppress the superconductivity completely at a doping level of only 3%, while the superconductivity is suppressed slowly with the Co dopants. A systematic magnetization measurements indicate that the doped Fe impurities lead to spin-polarized electrons yielding magnetic moments with the magnitude of 1.6 $\mu_B$\ per Fe, while the electrons given by the Co dopants have the same density of states for spin-up and spin-down leading to much weaker magnetic moments. It is the strong local magnetic moments given by the Fe-dopants that suppress the superconductivity. The band structure calculation further supports this conclusion.Comment: 6 pages, 7 figure

Cooperative Label-Free Moving Target Fencing for Second-Order Multi-Agent Systems with Rigid Formation

This paper proposes a label-free controller for a second-order multi-agent system to cooperatively fence a moving target of variational velocity into a convex hull formed by the agents whereas maintaining a rigid formation. Therein, no label is predetermined for a specified agent. To attain a rigid formation with guaranteed collision avoidance, each controller consists of two terms: a dynamic regulator with an internal model to drive agents towards the moving target merely by position information feedback, and a repulsive force between each pair of adjacent agents. Significantly, sufficient conditions are derived to guarantee the asymptotic stability of the closed-loop systems governed by the proposed fencing controller. Rigorous analysis is provided to eliminate the strong nonlinear couplings induced by the label-free property. Finally, the effectiveness of the controller is substantiated by numerical simulations

Minimal-time Deadbeat Consensus and Individual Disagreement Degree Prediction for High-order Linear Multi-agent Systems

In this paper, a Hankel matrix-based fully distributed algorithm is proposed to address a minimal-time deadbeat consensus prediction problem for discrete-time high-order multi-agent systems (MASs). Therein, each agent can predict the consensus value with the minimum number of observable historical outputs of its own. Accordingly, compared to most existing algorithms only yielding asymptotic convergence, the present method can attain deadbeat consensus instead. Moreover, based on the consensus value prediction, instant individual disagreement degree value of MASs can be calculated in advance as well. Sufficient conditions are derived to guarantee both the minimal-time deadbeat consensus and the instant individual disagreement degree prediction. Finally, both the effectiveness and superiority of the proposed deadbeat consensus algorithm are substantiated by numerical simulations.Comment: 12 pages, 3 figure

Investigating Ds+→π0ℓ+νℓD_s^+ \to \pi^0 \ell^+ \nu_\ell decay process within QCD sum rule approach

In this paper, the semileptonic decays $D_s^+ \to \pi^0\ell^+ \nu_\ell$ with $\ell=(e,\mu)$ are investigated by using the light-cone sum rule approach. Firstly, the neutral meson mixing scheme between $\pi^0$, $\eta$, $\eta^\prime$ and pseudoscalar gluonium $G$ is discussed in a unified way, which leads to the direct connection between two different channels for $D_s^+\to \pi^0\ell^+\nu_\ell$ and $D_s^+ \to \eta\ell^+\nu_\ell$ by the $\pi^0-\eta$ mixing angle. Then we calculated the $D_s\to \pi^0$ transition form factors (TFFs) within QCD light-cone sum rule approach up to next-to-leading order correction. At the large recoil point, we have $f_+^{D_s^+\pi^0}(0)=0.0113_{-0.0019}^{+0.0024}$ and $f_-^{D_s^+\pi^0}(0)=0.0020_{-0.0009}^{+0.0008}$. Furthermore, the TFFs are extrapolated to the whole physical $q^2$-region by using the simplified $z(q^2)$-series expansion. The behaviors of TFFs and related three angular coefficient functions $a_{\theta_\ell}(q^2)$, $b_{\theta_\ell}(q^2)$ and $c_{\theta_\ell}(q^2)$ are given. The differential decay widths for $D_s^+ \to \pi^0\ell^+ \nu_\ell$ with respect to $q^2$ and $\cos\theta_\ell$ are displayed, and also lead to the branching fractions ${\cal B}(D_s^+\to \pi ^0e^+\nu_e) =2.60_{-0.51}^{+0.57}\times 10^{-5}$ and ${\cal B}(D_s^+\to \pi ^0\mu^+\nu _\mu )= 2.58_{-0.51}^{+0.56}\times 10^{-5}$. These results show well agreement with the recent BESIII measurements and theoretical predictions. Then the differential distributions and integrated predictions for three angular observables, {\it i.e.} forward-backward asymmetries, $q^2$-differential flat terms and lepton polarization asymmetry are given separately. Lastly, we estimate the ratio for different decay channels ${\cal R}_{\pi ^0/\eta}^{\ell}=1.108_{-0.071}^{+0.039}\times 10^{-3}$.Comment: 10 pages, 5 figure

Cleaner production of wheat straw pulp with potash

A pulping method using KOH-K2SO3-AQ system as cooking liquor on wheat straw was studied in this paper. Digestion quantities on pulp yield and hardness during cooking was discussed and determined. It looks promising to use effluents of cooking into fertilizer because it contains rich nutrition such as potassium and lignin. A new pattern of ecological cycling may be set up between paper industry and farming

Ethyl 2-diethyl­amino-4-oxo-3,5-diphenyl-4,5-dihydro-3H-pyrrolo­[3,2-d]pyrimidine-7-carboxyl­ate

In the title compound, C25H26N4O3, the two fused pyrrolo­[3,2-d]pyrimidine rings form a dihedral angle of 3.7 (2)°. The two substituent phenyl rings are twisted with respect to the pyrrole and pyrimidine rings, making dihedral angles of 57.2 (2) and 69.0 (2)°, respectively. The ethyl and eth­oxy groups are disordered over two positions; the site occupancies are 0.53 (1) and 0.47 (1) for ethyl, and 0.63 (1) and 0.37 (1) for eth­oxy. The crystal packing features C—H⋯O hydrogen bonds