Characterization of LiM-doped (M = V, Nb, Ta, or Zr) piezoelectric aluminum nitride ((LiyM1−y)xAl1−xN) was performed by first-principles calculations and experimental approaches. The calculation results show that for all (LiyM1−y)xAl1−xN, coefficient d33,f is increased increasing the LiM doping concentration x up to 0.25. In comparison results, reveal only (LiyNb1−y)xAl1−xN has d33. absolute va...

Polycrystalline silver(I) deca-calcium heptakis(orthophos-phate), AgCa10(PO4)7, was obtained by solid-state reaction. It is isotopic with members of the series MCa10(PO4)7 (M = Li, Na, K and Cs), and is closely related to the structure of β-Ca3(PO4)2. The crystal structure of the title compound is built up from a framework of [CaO9] and two [CaO8] polyhedra, one [CaO6] octa-hedron (site symmetr...

The monoclinic form of trilithium dichromium(III) tris-(ortho-phosphate), Li3Cr2(PO4)3, was prepared by the reactive halide flux method. The structure of the title compound is composed of a three-dimensional anionic framework with composition ∞ (3)[Cr2(PO4)3](3-) and Li(+) ions situated in the empty channels. The rigid framework built up from CrO6 octa-hedra and PO4 tetra-hedra is the same as t...

Let F be a field and let F(X1,…,Xn) the of rational functions in n variables X1,…,Xn over F. T=X1+⋯+Xn∈F(X1,…,Xn) m positive integer such that charF∤m. Is it possible to express each Xi as function X1m…,Xnm T F? It is not difficult prove this can done but another matter show how done. We answer above question affirmatively with nonconstructive proof constructive proof.

Zinc phosphate (Zn3(PO4)2) nanoparticles were successfully prepared by precipitation method using zinc acetate and Phosphoric acid as the zinc and phosphate sources. The synthesized Zn3(PO4)2 nanoparticles were characterized by X-ray diffraction, Scanning electron microscope and Transmission electron microscope in order to confirm the phase purity and morphology of the sample. Zn3(PO4)2 nanopar...

and Applied Analysis 3 In the sequel, let q > 1 4p and . . . , φ, ψ, φ, ψ, . . . the unique prime period-two solution of 1.1 with φ < ψ. Define f ∈ C φ, ψ × φ, ψ , φ, ψ by f ( x, y ) p y qx y 2.2 for any x, y ∈ φ, ψ and g ∈ C φ, ψ , φ, ψ by y∗ g ( y ) p y − y2 qy 2.3 for any y ∈ φ, ψ . Then

We mainly study the global behavior of the nonlinear difference equation in the title, that is, the global asymptotical stability of zero equilibrium, the existence of unbounded solutions, the existence of period two solutions, the existence of oscillatory solutions, the existence, and asymptotic behavior of non-oscillatory solutions of the equation. Our results extend and generalize the known ...