Related papers: A problem of Polya

A formula for the irregularity of abelian coverings of the projective plane is established and some applications are presented.

In this paper we improve the estimate for the remainder term in the asymptotic formula concerning the circle problem in an arithmetic progression.

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

The concept of the elegant work introduced by Levai in Ref. [5] is extended for the solutions of the Schrodinger equation with more realistic other potentials used in different disciplines of physics. The connection between the present…

This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.

In this article, we obtain a weighted version of Polya inequality in Cn whose unweighted form was established by V. Zakharyuta in USSR Sbornik, 25 (1975), 350-364.

We prove Simon's conjecture for 3-manifolds.

We prove a local version of the Mazur-Ulam theorem.

In this paper, we present a new argument (see Lemma 3.4) that allows us to simplify the proof of stability of peakons established in Lin and Liu (2009) (Theorem 1.1).

Mathematical proofs are presented concerning the existence of solutions of the Maxwell equations with suitable boundary conditions. In particular it is stated that the well known "delayed potentials" provide effective solutions of the…

In this paper, we will present a new iterative construction for the auxiliary equation of Waring's problem, which seems a little simpler than the one of so called "smooth numbers" in papers [4] and [8], and give same upper bounds of G(k) as…

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

A new construction, with more visible canonical features, of a qKdV equation in a q-Virasoro context is exhibited.

This paper presents a proof of Gallai's Theorem, adapted from A. Soifer's presentation in The Mathematical Coloring Book of E. Witt's 1952 proof of Gallai's Theorem.

In this paper, we first present combinatorial proofs of a kind of expansions of the Eulerian polynomials of types A and B, and then we introduce Stirling permutations of the second kind. In particular, we count Stirling permutations of the…

An equivalent but useful version on the Homological Nerve Theorem is proved.

This paper concerns a nonlinear elliptic equation involving a critical Sobolev growth and a lower-order term. Under a Lions's condition, we prove the existence of at least one positive solution. Our approach consists in constructing a…

We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is complete with respect to polynomial interpretations. The proof…

We verify a conjecture of Lutwak, Yang, Zhang about the equality case in the Orlicz-Petty projection inequality, and provide an essentially optimal stability version.

In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.