in this paper, we define the concepts of a complex fuzzy subset and a complex fuzzy finite state automaton. then we extend the notion of a complex fuzzy finite state automaton and introduce the notion of a general complex fuzzy automaton. after that we define the concept of a max- min general complex fuzzy automaton and construct some equivalence relations and some congruence relations in a max...

Example 1.1. A field homomorphism K → F is a character by restricting it to the nonzero elements of K (that is, using G = K×) and ignoring the additive aspect of a field homomorphism. In particular, when L/K is a field extension any element of Aut(L/K) is a field homomorphism L→ L and therefore is a character of L× with values in L×. Example 1.2. For any α ∈ F×, the map Z→ F× by k 7→ αk is a ch...

Let R be an oriented compact surface without boundary of genus exceeding one, and let θ : π1(R;O) → Γ ⊂ PSL(2,C) be a homomorphism of its fundamental group onto a nonelementary group Γ of Möbius transformations. We present a complete, self-contained proof of the following facts: (i) θ is induced by a complex projective structure for some complex structure on R if and only if θ lifts to a homomo...

From Rickard’s work, we know that two rings are derived equivalent if there is a tilting complex, constructed from projective modules over the first ring such that the second ring is the endomorphism ring of this tilting complex. In this work I describe, under some conditions, the homomorphism space in the derived category between two complexes as iterated pullback of homomorphism spaces betwee...

‎In wireless communication systems‎, ‎space-time codes are applied to encode data when multiple antennas are used in the receiver and transmitter‎. ‎The concept of diversity is very crucial in designing space-time codes‎. ‎In this paper‎, ‎using the equivalent definition of full diversity space-time codes‎, ‎we first characterize all real and complex $2times 2$ rate one linear dispersion space-...

We define two concordance invariants of knots using framed instanton homology. These $\nu^\sharp$ and $\tau^\sharp$ provide bounds on slice genus maximum self-linking number, the latter is a homomorphism which agrees in all known cases with $\tau$ invariant Heegaard Floer use to compute homology nonzero rational Dehn surgeries on: 20 35 nontrivial prime through 8 crossings, infinite families tw...

In this note a proof of a differential analog of Chevalley’s theorem [C] on homomorphism extensions is given. An immediate corollary is a condition of finitenes of extensions of differential algebras and several equivalent definitions of a differentially closed field, including Kolchin’s Nullstellensatz. In this note I give a proof of the following differential analog of Chevalley’s theorem [C]...

The biologically inspired framework of port-graphs has been successfully used to specify complex systems. It is the basis of the PORGY modelling tool. To facilitate the specification of proof normalisation procedures via graph rewriting, in this paper we add higher-order features to the original port-graph syntax, along with a generalised notion of graph morphism. We provide a matching algorith...