An infinite class of planar configurations is constructed with distinct prime-field characteristic sets (i.e., configurations represented over a finite set of prime fields but over fields of no other characteristic). It is shown that if p is sufficiently large, then every subset of k primes between p and f(p, k) forms such a set (where f(p, k) = 2[(f-Ak3//2)Bk3/21 for constants A and B). In par...

Assuming the existence of an eV scale sterile neutrino, we develop a 3 + 1 neutrino mass model using A4 × Z4 Z2 symmetry group. Three Higgs fields \(H, H^{\prime }\) and \(H^{\prime \prime are considered to give desired matrix which generates non-zero

In the thirties of last century, I.M. Vinogradov proved that inequality ||pα||≤p−1/5+ε has infinitely prime solutions p, where ||.|| denotes distance to a nearest integer. This result subsequently been improved by many authors. particular, Vaughan (1978) replaced exponent 1/5 1/4 using his celebrated identity for von Mangoldt function and refinement Fourier analytic arguments. The current recor...

We prove that a valued field of positive characteristic [Formula: see text] has only finitely many distinct Artin–Schreier extensions (which is property infinite NTP 2 fields) dense in its perfect hull. As consequence, it deeply ramified and text]-divisible value group residue field. Further, we partial analogue for fields mixed observe an open problem about 1-units this setting. Finally, fill ...