Elementary Nuclear Theory

Elementary Number Theory

Elementary Hilbert Space Theory

A Hilbert Space is an inner product space that is complete. Let H be a Hilbert space and for f, g ∈ H, let 〈f, g〉 be the inner product and ‖f‖ = √ 〈f, f〉. (1.1) We will consider Hilbert spaces over C. Most arguments go through for Hilbert spaces over R, and the arguments are simpler. We assume that the reader is familiar with some of the basic facts about the inner product. Let us prove a few t...

THEORY of ELEMENTARY PARTICLES

The theory of elementary particles permitting to explain their constitution, sizes, bond energy, possible channels of decay, spectrum of weights and other properties is offered.

Elementary number theory

The division relation plays a prominent role throughout this note, and so, we start by presenting some of its basic properties and their relation to addition and multiplication. First, it is re exive because multiplication has a unit (i.e., m= 1×m) and it is transitive, since multiplication is associative. It is also (almost) preserved by linear combination because multiplication distributes ov...

Elementary Number Theory

Forward We start with the set of natural numbers, N = {1, 2, 3, . . .} equipped with the familiar addition and multiplication and assume that it satisfies the induction axiom. It allows us to establish division with a residue and the Euclid’s algorithm that computes the greatest commond divisor of two natural numbers. It also leads to a proof of the fundamental theorem of arithmetic: Every natu...