We prove that, for every cardinal number ≥ , there exists a metrizable space with || = such that for every pair of quasiorders ≤, ≤ on a set with || ≤ satisfying the implicationthere exists a system {() : ∈ of non-homeomorphic clopen subsets of with the following properties:• ≤ ′...

The inverse scattering transform is applied to solve the nonlinear equations that govern the motion of two pendulums coupled by an elastic spring. The thetafunction representation of the solutions is describable as a linear superposition of Jacobean elliptic functions (cnoidal vibrations) and...

It is shown that each continuous transformation from Euclidean -space ( > 1) into Euclidean -space that preserves the equality of distances (that is, fulfils the implication is a similarity map. The case of equal dimensions already follows from the Beckman-Quarles Theorem

Since the 19th century, the Edgeworth-Pareto principle is an effective tool for solving numerous multicriteria problems. Nevertheless there is no an appropriate mathematical formulation of it. The main objective of the paper is to state and justify the Edgeworth-Pareto principle for a certain...

Two-hundred, fifty years have lapsed since Christian Goldbach proposed (in 1742) that every positive even Integer, not 2, can be expressed as the sum of two primes. This manuscript attempts to show that the proposition is correct as a consequence of Wilson's Theorem. Little effort will be...

A dominant factor is extracted from the Jacobian matrix. The semilinear system is transformed by a linear function and split into the dominant part and the residual part by using the dominant factor. The dominant part is exactly computed by evaluating only scalar functions exp, sin, and cos, and...

Two-hundred, fifty years have lapsed since Christian Goldbach proposed (in 1742) that every positive even Integer, not 2, can be expressed as the sum of two primes. This manuscript attempts to show that the proposition is correct as a consequence of Wilson's Theorem. Little effort will be...

This paper will provide some theoretical foundation for the computation of the order or index of the element ω + ω, called a period of degree n, in the (2n+1)th cyclotomic extension , where 1, 2, 3 mod 4, 2 + 1 is prime, the integer 2 has order ord2+1 % n or 2n modulo, 2 + 1, and ω is a...

In order to study maximally non-linear functions, we introduce a transform which is rather similar to a Fourier transform. We express the Hamming distance between a general function and a linear function using this transform. Then we study some properties of the maximal distance from a function...

Gouliang Yu has introduced a property of discrete metric spaces and groups called property A which implies the coarse Baum-Connes Conjecture and hence the Novikov Higher Signature Conjecture. In this paper we extend a result of Jean-Louis Tu to conclude that a group acting by isometries on a...