In this article, the author analyzes the cricket series match between England and Australia by applying the concept of probability. The author presents solutions for obtaining results of either team winning or both ending up in a draw in the situation of a five-match series. The author also analyzes the probability wherein the series is still…

This note further discusses the functional equation and discusses two generalizations of it.

In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.

A hexagon with each pair of opposite sides parallel to a side of a triangle will be called a hexaparagon for that triangle. One way to construct a hexaparagon for a given triangle ABC is to use as vertices the centroids P, Q, R, S, T, and U of the six non-overlapping sub-triangles formed by the three medians of triangle ABC. The perimeter of this…

The Mean Value Theorem for Integrals is a powerful tool, which can be used to prove the Fundamental Theorem of Calculus, and to obtain the average value of a function on an interval. On the other hand, its weighted version is very useful for evaluating inequalities for definite integrals. This article shows the solutions on applying the weighted…

This paper deals with a simple method of evaluation of certain multiple definite integrals. This is followed by two main theorems concerning multiple definite integrals. Some examples of applications are given.

This note discusses some set equations, using set matrices, i.e. matrices whose entries are sets.

This paper introduces a class of matrices, the rows and columns of which add up to identical constants (generally speaking, different for rows and columns). Some properties of these matrices, which will be called "magic rectangles" are discussed.

A previous note described how complex numbers can be used for elementary analytic geometry in the plane, describing lines, circles and their intersections using complex Cartesian equations. In the present note, a description of elementary plane transformations, namely homotheties and translations, their group structure and their operations on…

This paper considers the problem of approximating an integrable function by piecewise linear functions that keep the integral and positivity of the original function.

The standard reverse-order law for the Moore-Penrose inverse of a matrix product is (AB)[dagger] = B[dagger]A[dagger]. The purpose of this article is to give a set of equivalences of this reverse-order law and other mixed-type reverse-order laws for the Moore-Penrose inverse of matrix products.

In this note, we discuss a coin tossing experiment with a new stopping rule. The two random variables involved in the experiment have some interesting properties.

Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson…

This classroom note presents a final solution for the functional equation: f(xy)=xf(y) + yf(x). The functional equation if formally similar to the familiar product rule of elementary calculus and this similarity prompted its study by Ren et al., who derived some results concerning it. The purpose of this present note is to extend these results and…

An explicit formula is established for the general solution of the homogeneous non-autonomous linear difference equation. The formula developed is then used to characterize globally periodic linear difference equations with constant coefficients.