Basil Gordon

A Simple Non-Euclidean Geometry and Its Physical Basis

1. What is geometry?.- 2. What is mechanics?.- I. Distance and Angle Triangles and Quadrilaterals.- 3. Distance between points and angle between lines.- 4. The triangle.- 5. Principle of duality coparallelograms and cotrapezoids.- 6. Proof s of the principle of duality.- II. Circles and Cycles.- 7. Definition of a cycle radius and curvature.- 8. Cyclic rotation diameters of a cycle.- 9. The circumcycle and incycle of a triangle.- 10. Power of a point with respect to a circle or cycle inversion.- Conclusion.- 11. Einsteins principle of relativity and Lorentz transformations.- 12. Minkowskian geometry.- 13. Galilean geometry as a limiting case of Euclidean and Minkowskian geometry.- Supplement A. Nine plane geometries.- Supplement B. Axiomatic characterization of the nine plane geometries.- Supplement C. Analytic models of the nine plane geometries.- Answers and Hints to Problems and Exercises.- Index of Names.- Index of Subjects.

Codes with bounded synchronization delay

In this paper we study “bounded delay codes,≓ which have the property that every message can be uniquely decoded by examining a segment of bounded length, from any starting point. This class is shown to attain the upper bound on codebook size previously encountered (but not always attained) for the familiar subclass of “comma-free codes.≓ The problem of determining the smallest message length s0 which guarantees unique decipherability for such codes is discussed. The bounded delay codes are classified according to the value of s0. An extension is made to the case of variable length codes, in which the upper bound formula of the uniform word-length case is replaced by a system of inequalities.

Divisibility of Certain Partition Functions by Powers of Primes

AbstractLet

A Survey of Classical Mock Theta Functions

k = p_1^{a_1 } p_2^{a_2 } \cdot \cdot \cdot p_m^{a_m }

Generalizations of Schur's partition theorem

be the prime factorization of a positive integer k and let bk(n) denote the number of partitions of a non-negative integer n into parts none of which are multiples of k. If M is a positive integer, let Sk(N; M) be the number of positive integers ≤ N for which bk(n)≡ 0(modM). If

Modular Transformations of Ramanujan’s Fifth and Seventh Order Mock Theta Functions

p_i^{a_i } \geqslant \sqrt k