Mathematica Journal

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  1. A method of generating minimally unsatisfiable conjunctive normal forms is introduced. A conjunctive normal form (CNF) is minimally unsatisfiable if it is unsatisfiable and such that removing any one of its clauses results in a satisfiable CNF. Introduction Ivor Spence [1] introduced a method for producing small unsatisfiable formulas of propositional logic that were […]
  2. Given a rationally parameterized curve in or , where the and are polynomials, we find the dimension of the smallest linear subset of containing the curve. If all the and are of degree or less, then it is known abstractly that this dimension is or less and rational normal curves play a key role […]
  3. The Wolfram Language has numerous knowledge-based built-in functions to support financial computations. This article introduces many built-in and other financial functions that are based on concepts and models covered in undergraduate-level finance courses. Examples are taken from a wide range of finance areas. They emphasize importing and visualization of data from many sources, valuation, […]
  4. The metric structure on a Riemannian or pseudo-Riemannian manifold is entirely determined by its metric tensor, which has a matrix representation in any given chart. Encoded in this metric is the sectional curvature, which is often of interest to mathematical physicists, differential geometers and geometric group theorists alike. In this article, we provide a […]
  5. We study the distribution of eigenspectra for operators of the form with self-adjoint boundary conditions on both bounded and unbounded interval domains. With integrable potentials , we explore computational methods for calculating spectral density functions involving cases of discrete and continuous spectra where discrete eigenvalue distributions approach a continuous limit as the domain becomes […]
  6. H. S. M. Coxeter wrote several geometry film scripts that were produced between 1965 and 1971 [1]. In 1992, Coxeter gave George Beck mimeographs of two scripts that had not been made. Beck wrote Mathematica code for the stills and animations. This material was added to the third edition of Coxeter’s The Real Projective […]
  7. A comprehensive discussion is presented of the closed-form solutions for the responses of single-degree-of-freedom systems subject to swept-frequency harmonic excitation. The closed-form solutions for linear and octave swept-frequency excitation are presented and these are compared to results obtained by direct numerical integration of the equations of motion. Included is an in-depth discussion of the […]
  8. This article presents a numerical pseudo-dynamic approach to solve a nonlinear stationary partial differential equation (PDE) with bifurcations by passing from to a pseudo-time-dependent PDE . The equation is constructed so that the desired nontrivial solution of represents a fixed point of . The numeric solution of is then obtained as the solution of […]
  9. This article is a summary of my book A Numerical Approach to Real Algebraic Curves with the Wolfram Language [1]. 1. Introduction The nineteenth century saw great progress in geometric (real) and analytic (complex) algebraic plane curves. In the absence of an ability to do the large number of computations for a concrete theory, […]
  10. An important problem in graph theory is to find the number of complete subgraphs of a given size in a graph. If the graph is very large, it is usually only possible to obtain upper bounds for these numbers based on the numbers of complete subgraphs of smaller sizes. The Kruskal–Katona bounds are often […]

© Jürgen 2019

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