“Judges Become Leery of Expert Witnesses,” ran a headline in the Wall Street Journal a couple of years ago; they are “Skeptical of Unproven Science”—the “Testimony of Dilettantes” (Schmitt 1997). Intrigued, I began to struggle through thickets of details of exploding tires, allegedly poisonous perfumes, leaking and bursting breast implants, contaminated insulating oil, etc., etc., and through l...

let f, g and h be all entire functions of several complex variables. in this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

When I started interacting with logicians, I was surprised to learn that fuzzy logic is still a big and active field of basic research. This surprise stemmed from my experience with fuzzy logic in my own field, linguistic semantics: In semantics, fuzzy logic was explored in the analysis of vagueness in the early seventies by Lakoff [10], but has been regarded as unsuitable for the analysis of l...

1 Drawing borders Logic arose in Antiquity from two sources: the study of real argumentation in the dialectical tradition, and that of axiom-based proof patterns organizing scientific inquiry. Over the centuries that followed, the discipline turned abstract and eventually, profoundly mathematical. Is logic still about human reasoning? Or is it, as Kant and Bolzano said, about an abstraction in ...

Let f, g and h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

views must be simpler but true Nobody doubts the value of abstraction, but it is essential to remember that everything that we can derive from an abstraction must be true of the real thing. If we can derive something that is not actually true, what we have is not an abstraction but a lie. Our role model should be engineers, not philosophers or logicians Engineers use mathematics in very differe...

This paper is concerned with Euler diagrammatic reasoning. Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by many logicians. Euler diagrams were introduced in the 18th century by Leonhard Euler [1768]. But it is quite rece...

a semi-batch crystallization system is used to determine growth kinetics and morphology of barium carbonate crystals, under a constant ph value and constant temperature in the various relative supersaturations. results show that crystal growth rate satisfies a first-order kinetic expression at high relative supersaturation, while at relative supersaturation values lower than 3,  the kinetic exp...