A new ternary intermetallic compound Al3GaCu9 was synthesized experimentally. A high-quality powder diffraction pattern of the compound was collected by an X-ray diffractometer, and its crystal structure was determined using the Rietveld refinement method. Results show that the compound has a cubic cell with the Al4Cu9 structure type (space group $P\bar{4}3m$ and Pearson symbol cP52). The lattice parameter a = 8.7132(3) Å, unit-cell volume V = 661.52 Å3, calculated density Dcalc = 7.26 g/cm3, and Z = 4. The residual factors converge to Rp = 2.96%, Rwp = 4.06%, and Rexp = 2.57%. The experimentally obtained reference intensity ratio value is 7.04.

A ternary compound Al3CoNd2 was synthesized and its crystal structure parameters were determined by the Rietveld refinement method based on powder X-ray diffraction data. Results show that the compound crystallizes in the MgCu2-type structure (cubic Laves C15 phase, space group $Fd\bar{3}m$), with the lattice parameter of a = 7.8424(2) Ǻ, unit-cell volume of V = 482.33 Å3, and calculated density of Dcalc = 5.90 g.cm−3. The residual factors converge to Rp = 0.1024 and Rwp = 0.1287. The reference intensity ratio value obtained experimentally is 3.03. Magnetic susceptibility measurements indicate an agreement with the Curie–Weiss law in the temperature range of 385–450 K, and paramagnetic Curie temperature of θp = 379.9 K. Both rare-earth elements and cobalt ions contribute to the paramagnetic moment. The saturation magnetic moment and magnetic hysteresis loop were measured for the Al3CoNd2 compound at various temperatures. Results show that the saturation magnetic moment value decreases with an increase in temperature and the compound becomes a ferromagnet below the Curie temperature Tc.

A new ternary compound Al5NdNi2 was prepared by melting a stoichiometric mixture of aluminum, neodymium, and nickel in an arc furnace and annealing in vacuum. The crystal structure of Al5NdNi2 was studied by X-ray powder diffraction technique and Rietveld analysis. All diffraction lines of Al5NdNi2 were indexed, and the lattice parameters were refined with an orthorhombic structure type of space group Immm (No.71) using Rietveld analysis program DBWS-9807. The lattice parameters are presented, a = 7.0508(1) Å, b = 9.5690(1) Å, c = 3.9792(1) Å, V = 268.47 Å3, Z = 2, ρ = 4.91 g cm−3, and RIR = 1.23.

The new ternary compound of Al2Cu3Gd was prepared by melting with stoichiometric composition in an electric arc furnace. The X-ray powder diffraction data of Al2Cu3Gd have been collected by the Rigaku Smart Lab X-ray powder diffractometer. The Rietveld refinement method had been used to study the crystal structure of Al2Cu3Gd. The results showed that the Al2Cu3Gd, new compound have the hexagonal structure, space group P6/mmm (No. 191) with a = 5.1822 (1) Å, c = 4.1566 (1) Å, V = 96.67 Å3, Z = 1, and the density is 6.62 g cm−3, and the intensity ratio reference intensity ratio is 1.29.

A new quaternary compound AlCeCo2Ni2 was synthesized and studied by means of X-ray powder diffraction technique. The powder pattern of AlCeCo2Ni2 was indexed and refined, giving a hexagonal structure, space group P6/mmm (No. 191) with the CaCu5 structure type. a = 4.9242(2) Å, c = 4.0524(1) Å, V = 85.1 Å3, Z = 1, ρx = 7.85 g cm−3, F30 = 130.2(0.010, 30), and RIR = 0.71(2).

The ternary compound of AlCu4Y was synthesized by melting under argon atmosphere in the arc furnace. High-quality X-ray powder diffraction data of AlCu4Y have been collected using a Rigaku SmartLab X-ray powder diffractometer. The Rietveld refinement results of the X-ray diffraction pattern for the AlCu4Y compound showed that the AlCu4Y is the hexagonal structure, space-group P6/mmm (No. 191) with a = 5.0658(1) Å, c = 4.1569(1) Å, V = 92.38 Å3, Z = 1, and the density is 6.66 g cm−3, and the intensity ratio RIR is 1.96.

We obtain uniform consistency results for kernel-weighted sample covariances in a nonstationary multiple regression framework that allows for both fixed design and random design coefficient variation. In the fixed design case these nonparametric sample covariances have different uniform asymptotic rates depending on direction, a result that differs fundamentally from the random design and stationary cases. The uniform asymptotic rates derived exceed the corresponding rates in the stationary case and confirm the existence of uniform super-consistency. The modelling framework and convergence rates allow for endogeneity and thus broaden the practical econometric import of these results. As a specific application, we establish uniform consistency of nonparametric kernel estimators of the coefficient functions in nonlinear cointegration models with time varying coefficients or functional coefficients, and provide sharp convergence rates. For the fixed design models, in particular, there are two uniform convergence rates that apply in two different directions, both rates exceeding the usual rate in the stationary case.

This paper establishes uniform consistency results for nonparametric kernel density and regression estimators when time series regressors concerned are nonstationary null recurrent Markov chains. Under suitable regularity conditions, we derive uniform convergence rates of the estimators. Our results can be viewed as a nonstationary extension of some well-known uniform consistency results for stationary time series.

A new quaternary compound PrAlFeNi3 was synthesized and studied by means of X-ray powder diffraction technique. The powder pattern of PrAlFeNi3 was indexed and refined, giving a hexagonal structure, space group P6/mmm (No. 191) with the CaCu5 structure type, a = 5.1132(2) Å, c = 4.0737(1) Å, V = 92.19 Å3, Z = 1, ρx = 7.20 g cm−3, F30 = 173.61 (0.0054, 32) and RIR = 0.77.

The CeCo3Ni2 compound was synthesized by arc melting under argon atmosphere. High-quality powder X-ray diffraction (XRD) data of CeCo3Ni2 have been collected using a Rigaku SmartLab X-ray powder diffractometer. The refinement of the XRD pattern for the CeCo3Ni2 compound shows that the CeCo3Ni2 is a hexagonal structure, space group P6/mmm (No.191) with a = b = 4.9081(2) Å, c = 4.0034(2) Å, V = 83.52 Å3, Z = 1, and ρx = 8.6347 g cm−3. The Smith–Snyder FOM F30 = 112.7(0.0089, 30) and the intensity ratio RIR = 0.48.

A new ternary compound Ho2AlGe3 was synthesized and studied by means of X-ray powder diffraction technique. The powder pattern of Ho2AlGe3 was indexed and refined, giving an orthorhombic structure, space group Pnma (No. 62) with the Y2AlGe3 structure type: a = 6.743 98(8) Å, b = 4.163 73(5) Å, c = 17.5834(2) Å, V = 493.74 Å3, Z = 4, ρx = 7.73 g cm−3, F30 = 202.7 (0.004, 37), and RIR = 1.21.

In this paper, we propose a new diagnostic test for residual cross-section uncorrelatedness (CU) in a nonparametric panel data model. The proposed nonparametric CU test is a nonparametric counterpart of an existing parametric cross-section dependence test proposed in Pesaran (2004, Cambridge Working paper in Economics 0435). Without assuming cross-section independence, we establish asymptotic distribution for the proposed test statistic for the case where both the cross-section dimension and the time dimension go to infinity simultaneously, and then analyze the power function of the proposed test under a sequence of local alternatives that involve a nonlinear multifactor model. The simulation results and real data analysis show that the nonparametric CU test associated with an asymptotic critical value works well.

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.