We define algebras of triple semigroup and DeMorgan triple semigroup and by defining three Mann’s compositions and one unary operation on the set of 3-place(ternary) functions over some set, we construct a DeMorgan triple semigroup of 3-place (ternary) functions and so find an abstract characterization of this algebras.

We show a connection between the deMorgan formula size of a Boolean function and the noise stability of the function. Using this connection, we show that the Fourier spectrum of any balanced Boolean function computed by a deMorgan formula of size s is concentrated on coefficients of degree up to O( √ s). These results have several applications that apply to any function f that can be computed b...

In this paper we establish that the causal order determined by an Ol’shanski semigroup on the corresponding homogeneous space is globally hyperbolic. Using this fact, we present sufficient conditions for a special class of Lie semigroups to admit a canonical “triple decomposition,” namely those for which the Lie algebra is of Cayley type. This theory applies in particular to semigroups which ar...

The concepts of P-compactness, countable P-compactness, the P-Lindelöf property are introduced in L-topological spaces by means of preopen L-sets and their inequalities when L is a complete DeMorgan algebra. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required. They can also be characterized by means of preclosed L-sets and their inequalit...

In this paper, we consider the norm-trace curves which are defined by the equation y r−1 + y r−2 + · · ·+ y = x qr−1 q−1 over IFqr where q is a power of a prime number and r ≥ 2 is an integer. We determine the Weierstrass semigroup of the triple of points (P∞, P00, P0b) on this curve.

We make preliminary investigations into the model theory of DeMorgan logics, attempting to make a case for the worth of such investigations before tackling the plight of particular mathematical theorems in these logics. We demonstrate that Loś’ Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case ...

We will discuss the concepts of interlaced, modular, distributive , Boolean (DeMorgan) and Ginsberg bilattices with their characterizations by hyperidentities and superproducts.

We prove lower bounds for a proof system having exponential speed-up over both polynomial calculus and constant-depth Frege systems in DeMorgan language.