Write $$\mathrm {ord}_p(\cdot )$$ for the multiplicative order in $${\mathbb {F}}_p^{\times }$$ . Recently, Matthew Just and second author investigated problem of classifying pairs $$\alpha , \beta \in {\mathbb {Q}}^{\times }\setminus \{\pm 1\}$$ which {ord}_p(\alpha ) > \mathrm {ord}_p(\beta holds infinitely many primes p. They called such order-dominant. We describe an easily-checkable suffic...

An analytical version of the discrete ordinates method is used to solve a class of boundaryvalue problems based on a linear Boltzmann equation relevant to the transport of neutral hydrogen atoms in a hydrogen plasma. In addition to a complete development of the discrete ordinates method for the considered application, the computational algorithm is implemented to yield very accurate results for...

in this paper, we investigate some problems which can be reduced to the goursat problem for afourth order equation. some results and theorems are given concerning the existence and uniqence for thesolution of the suggested problem.