Recently, the problem of spin and orbital angular momentum (AM) separation has widely been discussed. Nowadays, all discussions about possibility to separate AM from in gauge invariant manner are based on ansatz that gluon field can be presented form decomposition where physical components additive pure components, i.e. Aμ = $$A_{\mu }^{{{\text{phys}}}}$$ + }^{{{\text{pure}}}}$$ . In present pa...

2 Discussion of Kneser’s Theorem 3 2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 First Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Proving Kneser’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3.1 Part 1: Existence of a Prime Decomposition . . . . . . . . . . . . . 5 2.3.2 Part 2: Uniquene...

We present a general decomposition theorem for a positive inner regular finitely additive measure on an orthoalgebra L with values in an ordered topological group G, not necessarily commutative. In the case where L is a Boolean algebra, we establish the uniqueness of such a decomposition. With mild extra hypotheses on G, we extend this Boolean decomposition, preserving the uniqueness, to the ca...

In this paper we present a decomposition theorem for generalised quadratic forms over a division algebra with involution in characteristic 2. This is a generalisation of a decomposition result on quadratic forms in characteristic 2 from [3] and extends a generalisation of the Witt decomposition theorem for nonsingular forms to cover forms that may be singular.

recently, mohiuddine and alghamdi introduced the notion of lacunary statistical convergence in a locally solid riesz space and established some results related to this concept. in this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a tauberian theorem to the l...

in this paper, a local approach to the concept of hudetz $g$-entropy is presented. the introduced concept is stated in terms of hudetz $g$-entropy. this representation is based on the concept of $g$-ergodic decomposition which is a result of the choquet's representation theorem for compact convex metrizable subsets of locally convex spaces.