In [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.Also, we exhibited the topic of limit summability of real functions in [2,3]. Inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. Finally, we pose an unsolved problem aboutthem.

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...

Operads (or at least An and En operads, which is what we’ll focus on) are a formalism for discussing various degrees to which associativity and commutativity can fail. Suppose I have a space X with a multiplication μ : X ×X → X that is not associative. In particular, μ(−, μ(−,−)) and μ(μ(−,−),−) are two different ternary operations. One approach is to consider a space O(3) of ternary operations...

The ternary Quantum-dot Cellular Automata (tQCA) were demonstrated to be a possible candidate for the implementation of a future multi-valued processing platform. Recent papers show that the application of the adiabatic pipelining can be used to solve the issues of the tQCA logic primitives. The architectures of the resulting tQCAs become similar to their binary counterparts and the physical de...

Ternary exclusive or is the (two valued) truth function that is true just in case exactly one of its three arguments is true. This is an interesting truth function, not definable in terms of the binary exclusive or alone, although the binary case is definable in terms of the ternary case. This article investigates the types of truth functions that can be defined by ternary exclusive or, and rel...

For simplicity, we adopt the following convention: D is a set, x, x0, y, y0, z, z0, r, s, t are real numbers, p, a, u, u0 are elements of R3, f , f1, f2, f3, g are partial functions from R3 to R, R is a rest, and L is a linear function. We now state three propositions: (1) dom proj(1, 3) = R3 and rng proj(1, 3) = R and for all elements x, y, z of R holds (proj(1, 3))(〈x, y, z〉) = x. (2) dom pro...

A new theoretical model based on the local composition concept (TNRF-mNRTL model) was proposed to express the short-range contribution of the excess Gibbs energy for the solutions containing polymer and electrolyte. This contribution of interaction along with the long-range contribution of interaction (Pitzer-Debye-Hückel equation), configurational entropy of mixing (Flory-Huggins relation)...

Let $A$ be a Banach ternary algebra over a scalar field $Bbb R$ or $Bbb C$ and $X$ be a ternary Banach $A$--module. Let $sigma,tau$ and $xi$ be linear mappings on $A$, a linear mapping $D:(A,[~]_A)to (X,[~]_X)$ is called a Lie ternary $(sigma,tau,xi)$--derivation, if $$D([a,b,c])=[[D(a)bc]_X]_{(sigma,tau,xi)}-[[D(c)ba]_X]_{(sigma,tau,xi)}$$ for all $a,b,cin A$, where $[abc]_{(sigma,tau,xi)}=ata...