We give an integral identity which was conjectured and proved by using the continuous version of the multi-WZ method. Submitted: May 25, 1999; Accepted: October 20, 1999. Mathematical Reviews Subject Numbers: 05, 33.

Complex numbers are a fundamental aspect of the mathematical formalism of quantum physics. Quantum-like models developed outside physics often overlooked the role of complex numbers. Specifically, previous models in Information Retrieval (IR) ignored complex numbers. We argue that to advance the use of quantum models of IR, one has to lift the constraint of real-valued representations of the in...

Motivated by the desire to visualize large mathematical data sets, especially in number theory, we offer various tools for representing floating point numbers as planar (or three dimensional) walks and for quantitatively measuring their “randomness.”

The notion of exponents of convergence has many applications in different mathematical disciplines. In this paper we consider exponents of convergence of sequences of positive real numbers in connection with games and selection principles. AMS Subject Classifications: 40A05, 91A05.

Motivated by the desire to visualize large mathematical data sets, especially in number theory, we offer various tools for representing floating point numbers as planar (or three dimensional) walks and for quantitatively measuring their “randomness.”

Mathematical cognition researchers have studied the mental representations of natural numbers, integers, and fractions extensively. We investigated the representations of irrational and perfect square numbers in a laboratory setting. Eighty participants performed (1) a magnitude comparison task (MC) by indicating which of two numbers is greater or lesser, (2) a number line estimation task (NLE)...

The mechanisation of the real numbers within theorem provers is of practical bene t for the veri cation of real-time systems. The real numbers provide a foundation within the theorem prover for classical mathematical analysis such as di erentiation and integration. The approach we have taken makes extensive use of theory interpretation to maximise theory reuse and hence minimise theorem redunda...

The widely studied benchmark problem, 2-D driven cavity flow problem is discussed in details in terms of physical and mathematical and also numerical aspects. A very brief literature survey on studies on the driven cavity flow is given. Based on the several numerical and experimental studies, the fact of the matter is, above moderate Reynolds numbers physically the flow in a driven cavity is no...

Winding numbers are fundamental objects arising in algebraic topology, with many applications in non-constructive complex analysis. We present a formalization in Coq of the winding numbers and their main properties. As an application of this development, we also give non-constructive proofs of the following theorems: the Fundamental Theorem of Algebra, the 2-dimensional Brouwer Fixed-Point theo...