We will classify those real quadratic fields K having exactly one noninert prime less than where Δ is the discriminant of K. Moreover, we will list all such K and prove that the list is complete with one possible exceptional value remaining (whose existence would be a counterexample to the Riemann hypothesis).

In this paper we tackle the problem of identifying set-valued mappings that are subgradient set-valued mappings. We show that a set-valued mapping is the proximal subgradient mapping of a lower semicontinuous function bounded below by a quadratic if and only if it satisfies a monotone selection property.

Let λ be a certain measure supported on a curve in R3. We prove that if the curve has nonzero curvature and torsion, then λ * L3/2 ⊂ L2.

Let C(X) be the space of all continuous complex-valued functions defined on the compact Hausdorff space X. We characterize the M-ideals in a uniform algebra A of C(X) in terms of singular measures. For a Banach function algebra B of C(X) we determine the connection between strong hulls for B and its peak sets. We also show that M(X) the space of complex regular Borel measures on X has no M-ideal.

We consider the Liénard's equation with f(x) polynomial. By using the generalized polar coordinates we establish the maximum possible number of small amplitude limit cycles of such equation in terms of the degree of f(x).