In this paper we study integers of the form cp + Tx, where p is either zero or a prime congruent to r mod d, and Tx = x(x + 1)/2 is a triangular number. We also investigate integers of the form (2ap− r)/m+ Tx with p a prime. Several conjectures are raised with related analysis and numerical data; our main conjecture asserts that each natural number n 6= 216 can be written in the form p + Tx wit...

In characteristic zero the algebras Mn(E)⊗E andMn,n(E) appear in the list of non-trivial verbally-prime algebras. Verbally-prime algebras play a proeminent role in Kemer’s results about structure of the varieties of associative algebras in characteristic zero (see [8] for a detailed account of it). Recently, some new results have been obtained about the behavior of polynomial identities satisfi...

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

We discuss the specificity of interactions electroweak gauge boson excitations in models with warped extra dimensions. In particular, we show that couplings $W^{\prime}$, $Z^{\prime}$, and $\gamma^\prime$ to SM bosons treated as zero modes 5D fields are either exactly equal or very much suppressed. former case, three-particle four-particle interaction Lagrangians their lowest found explicitly. ...

Let R be a commutative ring and let ? Z n the zero divisor graph of id="M2"> R , whose vertices are nonzero divisors id="M3"> such that two id="M4"> u , v adjacen...

We prove an explicit log-free zero density estimate and an explicit version of the zero-repulsion phenomenon of Deuring and Heilbronn for Hecke L-functions. In forthcoming work of the second author, these estimates will be used to establish explicit bounds on the least norm of a prime ideal in a congruence class group and improve upon existing explicit bounds for the least norm of a prime ideal...

We study whether sufficiently large integers can be written in the form cp+ Tx, where p is either zero or a prime congruent to r mod d, and Tx = x(x + 1)/2 is a triangular number. We also investigate whether there are infinitely many positive integers not of the form (2ap−r)/m+Tx with p a prime and x an integer. Besides two theorems, the paper also contains several conjectures together with rel...