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Efficient machining using wire electrical discharge machining (WEDM) technology is a compromise between cutting speed and resulting surface quality. Typical morphology of the surface machined by WEDM shows a plenty of craters caused by electrospark discharges produced during the cutting process. This work is focused on assessing the impact of machine setting parameters on quantitative and qualitative evaluation of the workpiece surface of aluminium alloy AlZn6Mg2Cu. Using metallography, the surface effects arisen during the process of wire spark erosion on cross-sections of preparations were studied. Using local spot EDX microanalysis, the chemical composition of the surfaces of the samples was studied. The attention was also paid to the highest height of profile of the craters, which were studied using 3D filtered images.

We establish nonoscillation criteria for the even order half-linear difference equation of Euler type n X lD0. 1/ n lˇn l n l k .˛ lp/˚ n l x kCl ÁÁ D 0;ˇn WD 1; where˚.t/ WD jt j p 1 sgn t, p 2 .1; 1/, n 2 N, k .ˇ/ denotes the falling factorial power (foř 2 R) and˛;ˇ0;ˇ1; : : : ;ˇn 1 are real constants. For the two-term equation. 1/ n n k .˛/˚ n x k Á Cˇ0k .˛ np/˚. x kCn / D 0 we establish the constant n;p;˛s uch that the two-term equation is nonoscillatory if 0 > n;p;˛. The criteria are derived using the variational technique and they are further extended via the theory of regularly varying sequences.

We establish nonoscillation criterion for the even order half-linear differential equation (−1)nfn(t)Φx(n)(n)+∑l=1n(−1)n−lβn−lfn−l(t)Φx(n−l)(n−l)=0, where β0,β1,…,βn−1 are real numbers, n∈N, Φ(s)=sp−1sgns for s∈R, p∈(1,∞) and fn−l is a regularly varying (at infinity) function of the index α−lp for l=0,1,…,n and α∈R. This equation can be understood as a generalization of the even order Euler type half-linear differential equation. We obtain this Euler type equation by rewriting the equation above as follows: the terms fn(t) and fn−l(t) are replaced by the tα and tα−lp, respectively. Unlike in other texts dealing with the Euler type equation, in this article an approach based on the theory of regularly varying functions is used. We establish a nonoscillation criterion by utilizing the variational technique.