in this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$  is orthogonality in the sense of ratz.

Verticillium wilt (VW) is one of the important yield-limiting diseases for potato production. To develop resistant clones, the potential for early generation selection was studied using three basic selection methods, individual, family, and within family selection, for two clonal generations. A total of 152 clones were derived from four cross types (2x · 2x, 2x · 4x, 4x · 2x and 4x · 4x). Clone...

In this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$  is orthogonality in the sense of Ratz.

When breeding diploid potatoes, tetraploid progeny can result from the union of 2n eggs and pollen in 2x-2x crosses. Thirty-three crosses were made to examine frequency All between S. tuberosum dihaploids self-compatible donors, M6 DRH S6-10-4P17. Using chloroplast counting for ploidy determination, was as high 45% one 33 Based upon single nucleotide polymorphism (SNP) genotyping, attributed bi...

In this paper, the authors investigate the generalized Hyers-UlamAoki-Rassias stability of a quartic functional equation g(2x+ y + z) + g(2x+ y − z) + g(2x− y + z) + g(−2x+ y + z) + 16g(y) + 16g(z) = 8[g(x+ y) + g(x− y) + g(x+ z) + g(x− z)] + 2[g(y + z) + g(y − z)] + 32g(x). (1) The above equation (1) is modified and its Hyers-Ulam-Aoki-Rassias stability for the following quartic functional equ...

A pair (X, ) of a finite set X and a closure operator : 2X → 2X is called a closure space. The class of closure spaces includes matroids as well as antimatroids. Associated with a closure space (X, ), the extreme point operator ex: 2X → 2X is defined as ex(A) = {p|p ∈ A,p / ∈ (A − {p})}. We give characterizations of extreme point operators of closure spaces, matroids and antimatroids, respectiv...

Biexciton photoluminescence (PL) quantum yields (Q(2X)) of individual CdSe/CdS core-shell nanocrystal quantum dots with various shell thicknesses are derived from independent PL saturation and two-photon correlation measurements. We observe a near-unity Q(2X) for some nanocrystals with an ultrathick 19-monolayer shell. High Q(2X)'s are, however, not universal and vary widely among nominally ide...