Partial Differentiation of Real Ternary Functions

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions

($phi,rho$)-Representation of $Gamma$-So-Rings

A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-represen...

Second-Order Partial Differentiation of Real Ternary Functions

For simplicity, we adopt the following rules: x, x0, y, y0, z, z0, r denote real numbers, u, u0 denote elements of R3, f , f1, f2 denote partial functions from R3 to R, R denotes a rest, and L denotes a linear function. Let f be a partial function from R3 to R and let u be an element of R3. We say that f is partial differentiable on 1st-1st coordinate in u if and only if the condition (Def. 1) ...

Partial second-order subdifferentials of -prox-regular functions

Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2  functions. The class of prox-regular functions covers all convex functions, lower C2  functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...

Simultaneous Spectrophotometric Determination of Iron, Cobalt and Copper by Partial Least-Squares Calibration Method in Micellar Medium

Iron, cobalt and copper are metals, which appear together in many real samples, both natural and artificial. Recently a classical univariate micellar colorimetric method has been developed for determination of these metal ions. The organized molecular assemblies such as micelles are used in spectroscopic measurements due to their possible effects on the systems of interest. The ability of mi...