A balanced part ternary design (BPTD) is a balanced ternary design (BTD) with a specified number of blocks, say b2, each having repeated elements. We prove some necessary conditions on b2 and show the existence of some particular BPTDs. We also give constructions of infinite families of BPTDs with b1 = 0, including families of ternary t-designs with t ≥ 3.

Using the X-ray diffraction, internal friction, 4-point bending, and electron microscopy methods we have studied structural compatibility influence of Y2O3 HfO2 dopants addition on structure phase composition ZrO2 powders ceramics based them. The mechanical properties ZrO2–Y2O3-HfO2 (YSZ) system been investigated. It was determined that similarity yttrium hafnium oxides is not complete. individ...

The microstructure of a melt-spun Zr28Ni44Cu28 (at. %) alloy was characterized in order to determine the structures and compositions crystalline phases that compete with glass formation during rapid solidification. Two were identified, namely, face centered cubic (FCC) zirconium oxide phase primitive version big-cube phase, using combination scanning electron microscopy, energy dispersive X-ray...

Coatings consisting of cobalt, nickel and iron (Co-Ni-Fe) oxides were electrophoretically deposited on AISI 304-type stainless steel using aqueous suspensions without any binder. The synthesis Co-Ni-Fe was carried out by the thermal decomposition metal nitrates with various molar ratios at 673 K. Structural morphological analysis confirmed that coatings mainly composed spinel-type predominantly...

generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and   -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. some new results are obtained.

The blocks of a balanced ternary design, BTD(V,B; ρ1, ρ2, R;K,Λ), can be partitioned into two sets: the b1 blocks that each contain no repeated elements, and the b2 = B − b1 blocks containing repeated elements. In this note, we address, and answer in some particular cases, the following question. For which partitions of the integer B as b1 + b2 does there exist a BTD(V,B; ρ1, ρ2, R;K,Λ)?

Let (ωn)0<n be the sequence known as Integer Sequence A047749 In this paper, we show that the integer ωn enumerates various kinds of symmetric structures of order two. We first consider ternary trees having a reflexive symmetry and we relate all symmetric combinatorial objects by means of bijection. We then generalize the symmetric structures and correspondences to an infinite family of symmetr...