Mathematics, Volume 1, Issue 3

Let $M\left(q\right)\text{=}\sum {\text{c(n)q}}^n$ be one of Ramanujan’s mock theta functions. We establish the existence of infinitely many linear congruences of the form: $c(An+B\text{)}\equiv \text{0 (mod}{l}^j\text{)}$ where A is a multiple of l and an auxiliary prime, p. Moreover, we give...

Electromagnetic wave scattering by many parallel to the z−axis, thin, impedance, parallel, infinite cylinders is studied asymptotically as a → 0. Let D_m be the cross-section of the m−th cylinder, a be its radius and ${\text{<mover> x <mo>^</mo> </mover>}}_{\text{m}}{\text{= (x}}_{\text{m1}}{\text{,}}_{}$...

Andrews, Garvan and Liang introduced the spt-crank for vector partitions. We conjecture that for any n the sequence ${\left\{N_S(m,n)\right\}}_m$ is unimodal, where $N_S(m,n)$ is the number of S-partitions of size n with crank m weight by the spt...