We presented a series of four lectures to the Department of Mathematics at Ohio State University, entitled “Adventures in the Foundations of Mathematics”. Lecture 1, “The Structure of Proofs”, April 28, 2003. Lecture 2, “The Axioms for Mathematics”, April 30, 2003. Lecture 3, “Do...

The immune system is a complex system of cells and molecules distributed throughout our bodies that can provide us with a basic defense against pathogenic organisms. It is argued that immune system is an adaptive complex system. It is shown that it has emergent properties. Its network structure...

The main result is lower estimation of remain term in the central limit theorem for a sum of the functions of disjoint uniform k-spacings. From this theorem the Lindeberg type condition of asymptotically normality and Berry-Esseen type result are obtained. The asymptotic properties of goodness...

A set of well-known and new rank equalities for orthogonal projectors are presented. A variety of consequences for orthogonal projectors, especially for the commutativity of two orthogonal projectors, are also derived

The new measurement concept of ‘supplementary' influence is defined within the set-up of descriptive multiple regression analysis. The supplementary coefficient describes the average change of the regressand that can additionally be attributed to one regressor when several other regressors are...

The Helmholtz equation is considered. The matrices decomposition algorithms for Legendre spectral collocation approximation, which nearly reduce a half of scale for original discrete system, are achieved by the centrosymmetry and positivity. Also, the di erence and finite element preconditioning...

Suppose that G is a connected semisimple algebraic group defined over a p-adic field which is algebraically closed. Suppose further that has a characteristic ≥ 7. In this paper we are going to pose a conjecture stating that the Shalika's formula also holds for the above mentioned field

Assume (1) asset returns follow a stochastic multi-factor process with time-varying conditional expectations; (2) investments are linear functions of factors. This paper calculates asymptotic joint moments of the logarithm of investor's wealth and the factors. These formulas enable fast...

In this paper we point out a converse result of the celebrated Jensen inequality for di erentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon's and Rényi's entropy mappings are also given