Let f and g be transcendental entire functions, each with a bounded set of singular values, and suppose that g ◦ φ = ψ ◦ f , where φ, ψ : C → C are affine. We show that the escaping sets of f and g have the same Hausdorff dimension. Using a result of the second author, we deduce that there exists a family of transcendental entire functions for which the escaping set has Hausdorff dimension equa...

This paper introduces the notion of a transcendental problem motivated by the needs to engineer the system which can evolve as the situation changes. The problem is generally called transcendental if it addresses the solution adequacy of the system that is implemented without any provision for subsequent requirement changes. Subsequently, the transcendental problem evident in Turing’s test is a...

Let K be a field and v a valuation on K. We discuss some properties of extensions w of v to the field K(X1, . . . , Xn) of rational functions in n variables over K, for which the residue field of w has transcendence degree n over the residue field of v. 2000 Mathematics Subject Classification: 12J20, 12F20. 1.Introduction LetK be a field and v a valuation onK. Residual transcendental extensions...

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

The thought that I will explore in this paper is that the Sartre of B&N and the earlier writings is in certain fundamental respects a transcendental thinker, and that viewing him in this light makes a positive, favourable difference to how we understand and assess his ideas, arguments, and position as a whole. The use of such plastic and open-textured categories in the history of philosophy is,...

A negotiation model consists of two functions: a negotiation function and a weakening function. A negotiation function is defined to choose the weakest sources and these sources will weaken their point of view using a weakening function. However, the currently available belief negotiation models are based on classical logic, which make it difficult to define weakening functions. In this paper, ...