Let C : Y 2 = anX + · · · + a0 be a hyperelliptic curve with the ai rational integers, n ≥ 5, and the polynomial on the right irreducible. Let J be its Jacobian. We give a completely explicit upper bound for the integral points on the model C, provided we know at least one rational point on C and a Mordell–Weil basis for J(Q). We also explain a powerful refinement of the Mordell–Weil sieve whic...

The application of the Wilson-Sommerfeld quantum conditions to a conditionally periodic system with orthogonal coordinates involves the evaluation of an integral of the type J = f(q) dq. (1) The integral is to be extended over a.complete cycle of values of q, which oscillates between two roots of f(q). The sign of the radical is to be the same as that of dq, so that if a and b denote the roots ...

For analytic functions f(z) and g(z) which satisfy the subordination f(z) ≺ g(z), J. E. Littlewood (Proc. London Math. Soc., 23 (1925), 481–519) has shown some interesting results for integral means of f(z) and g(z). The object of the present paper is to derive some applications of integral means by J.E. Littlewood and show interesting examples for our theorems. We also generalize the results o...

The self-force and effective mass of a moving dislocation in a generally accelerating motion are explicitly obtained on the basis of a surface-independent dynamic J-integral. Logarithmic singularities due to non-zero acceleration result in divergent integrals in the dynamic J-integral, which are treated by smearing out the dislocation core (ramp-core) and by regularizing in the sense of distrib...

In the present note a general integral inequality is proved in the direction that was initiated by Q. A. Ngô et al [Note on an integral inequality, J. Inequal. Pure and Appl. Math., 7(4) (2006), Art.120].