Abstract Self-interaction in the active neutrinos is studied literature to alleviate H_0 tension. Similar self-interaction can also explain observed dips flux of coming from distant astro-physical sources IceCube detectors. In contrast flavour universal neutrino interaction considered for solving H 0 tension, which ruled out particle physics experiments, we consider specific interactions. We sh...

In this article, semi-ring and semi-algebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semi-ring of sets has already been formalized in [12], that is, strictly speaking, a definition of a quasi semi-ring of sets suggested in the last few decades [14]. We adopt a classical definition of a semi-ring of sets here to avoid such a confusion. Ring ...

We prove several dichotomy theorems which extend some known results on σ -bounded and σ -compactpointsets. In particular we show that, given a finite number of Δ1 equivalence relations F1 , . . . , Fn , any Σ1 set A of the Baire space either is covered by compact Δ1 sets and lightface Δ1 equivalence classes of the relations Fi , or A contains a superperfect subset which is pairwise Fi -inequiva...

The essentially Σ1 formulae of ΣL are exactly those which are provably equivalent to a disjunction of conjunctions of 2 and Σ1 formulae.

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions 1 2 σ < d < 3 2 σ , where 0 < σ ≤ 2 is a parameter controlling the decay of the long-range interaction,...